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Complex economic growth

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Complex economic growth

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Content INFORMATION T O USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margin*, and improper alignment can adversely affect reproduction. In the unlikely, event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g^ maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the bade of die book. Photographs inchided in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x T black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. A Bell & Howell Information Company 300 Norm Zeeb Road. Ann Arbor, M l 48106*1346 USA 313/761*4700 000:521-0600 CO M PLEX ECO NO M IC G R O W TH by L aw rence C lark P o w ell A Dissertation Presented to the FACULTY OF TH E GRADUATE SCHOOL UNIVERSITY O F SOUTHERN CALIFORNIA In Partial Fulinilmcnt of the Requirements for the Degree DOCTOR OF PHILOSOPHY in Economics December 1994 Copyright 1994 Lawrence Clark Powell OKI Num ber: 9 6 0 1 0 4 7 UMI Microform 9601047 Copyright 1995, by UMI Company. All rights reserved. This microform edition is protected against unauthorised copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, NX 48103 UNIVERSITY OF SOUTHERN CALIFORNIA T U B G R A D U A T E S C H O O L U N IV E R S IT Y P A R K L O S A N G E L E S , C A L IF O R N IA 9 0 0 0 7 This dissertation, written by under the direction of h.1s Dissertation Committee, and approved by all its members, has been presented to and accepted by The Graduate School in partial fulfillment of re- quirements for die degree of DOCTOR OF PHILOSOPHY Dean of Graduate Studiei DISSERTATION COMMITTEE Otairperton Lawrence Clark Powell Dr. Richard Day C O M P L E X E C O N O M IC G R O W T H H is to ric a lly economic growth paths hava not follow ed the balanced growth tra je c to ry c h a ra c te ris tic of the N eoclassical modal. This study examines th e way in which in s titu tio n s , c a p ita l accum ulation, population and technological change in te r a c t to produce complex growth p a tte rn s . In P a rt I a regim e-based growth model andoganisas population, economic output and c a p ita l to analyse growth in th e an cien t p a s t. Increasing population d en sity can p r e c ip ita te a c r i s i s fo r a so ciety when i t s dominant economic stra te g y f a l t e r s from overuse. O ccasionally, the adoption of a new economic stra te g y c a lls for a re o rg a n isa tio n of in s titu tio n s , and the demand fo r d iffe re n t forms of c a p ita l makes a su ccessfu l tra n s itio n p rb b le sia tlc a l. Several such changes are examined culm inating w ith an a n a ly sis of conditions leading to a c ity s ta te . P a rt XI examines tech n o lg ical development in an in d u stry competing tec h n o lo g ically through c o st reduction w ith in a modern c a p ita lis tic economy. The la c o iv a tlb ility of technological com petition and equilibrium becomes apparent w ithin the context of a model endogenising c a p ita l, tech n o lo g ical growth and p r o f its . Technological growth i s viewed as a phenomenon developing from conscious e ff o r ts (such as R fcD ) by firm s who must improve production methods to sta y com petitive, but those e f f o r ts rep re se n t a gamble to i t s m ostly risk -a v e rse backers. The outcome of technological com petition i s u n certain , consequently from a macro p ersp ectiv e conditions of over and under supply crop up re g u la rly . When p r o fita b le periods occur, firm s are encouraged to increase th e ir gambling on S tK D and tech n o lo g ical progress a c c e le ra te s . The feedback a ffe c ts o f the th re e v a ria b le s on each o th e r are discussed and modeled. Contents 1 IN T R O D U C T IO N 1 1 Capturing the Complexity of Growth in the Ancient Past 9 2 T H E N EO C LA SSIC A L M O D E L A N D M A L T IIU S 10 3 T H E S T R U C T U R E O P T H E M O D E L 22 3.1 The Choice of Regim es................................................................................ 22 3.2 Population Density and the R egim e.......................................................... 31 3.3 The Demographic Function ...................................................................... 35 3.4 Switching R e g im es...................................................................................... 39 4 T H E M O D EL 44 5 T H E H U N T E R -G A T H E R E R R E G IM E 54 6 T H E G R E A T A G R IC U L T U R A L R E V O L U T IO N O R T H E F IR S T P O P U L A T IO N CR ISIS? 69 7 T H E V ILLA G E A G R A R IA N R E G IM E S 89 . 8 T H E C IT Y STA TE 119 8.1 Computer History One ............................................ 128 8.2 Computer History T w o ............................................................................... 136 9 SU M M A R Y A N D CO N C LU SIO N S 141 II Technological Change W ithin a C apitalist Econom y 145 10 TECHNOLOGICAL GROWTH: ITS SCOPE AND M EASURE 146 10.1 In tro d u ctio n ....................................................................................................... 146 10.2 Measuring Technological G r o w t h ................................................................ 147 10.3 The Effect of Technology on Economic In s titu tio n s ............................................................................................................ 151 11 CAUSES OP TECHNOLOGICAL GROWTH 155 11.1 Theories of Technological G ro w th ................................................................ 155 11.2 Patterns of Technological G ro w th ................................................................ 160 11.3 R&D, Education and Technological Growth ........................... 163 11.4 Increasing Returns and R&D ...................................................................... 168 11.5 Market Structure and In n o v a tio n ................................................................ 171 11.6 Government and Technological G ro w th ...................................................... 174 11.7 Demand, Risk and Technological G ro w th .................................................. 175 12 ANALYZING THE EFFECT OF TECHNOLOGICAL DEVELOPMENT ON AN INDUSTRY 180 12.1 General remarks on the Chapter's m odels.................................................. 180 12.2 The Benefits to a Firm of a Technological Breakthrough ..................... 184 12.3 The Riskiness of Benefits from R&D ......................................................... 191 12.4 A Model of R&D as a Function of P ro fits.................................................. 193 12.5 Profits and Market E n try ................................................................................ 196 13 A PROFIT DRIVEN MODEL OF TECHNOLOGICAL DEVELOPMENT 206 13.1 Piece-wise Linear Difference Equation A pproxim ations..................................................................................................... 212 14 A MODEL WITH CAPITAL, PROFITS AND TECHNOLOGICAL CHANGE 222 15 SUMMARY AND CONCLUSIONS 251 List of Figures 2.1 Discontinuity arising from the isoquant m a p ........................................... 16 2.2 A Discontinuous Tangcncy L in e .................................................................. 17 3.1 The Birth Rate F un ctio n............................................................................... 37 3.2 The Death Rate Function ....................................... 38 4.1 The Managerial FYmction............................................................................... 49 4.2 The Isoquants for Capital and L a b o r ........................................................ 50 4.3 Birth and Death R a te s ................................................................................. 51 5.1 The Managerial Function.............................................................................. 60 5.2 The Growth Rate of H untcr-G alhercrs.................. 64 5.3 Hunter*Gatherers Reach a Steady S ta te .................................................... 66 5.4 A Group Fluctuates Between Huntcr-Gatherer and Horticulture . . . 67 6.1 An Isoquant Analysis of the Transition from Hunting-Gathering to A g ric u ltu re ................... 77 6.2 Isoquants for a group in the Australian Desert......................................... 79 6.3 The Managerial Functions and the Transition between Hunter-Gathering and A griculture......................... 81 6.4 A Smooth Transition between Hunting-Gathering and Agriculture . . S3 6.5 Switching between the Hunter-Gathcrer and Agrarian Regimes . . .. 85 6.6 A non-succcssful and a successful switch(from hunter-gatherer to agri culture) ................ 86 6.7 An Odd Transition from Huntcr-Gatherer to A g ricu ltu re.................... 88 7.1 The Extensive Agriculture Administrative F u n c tio n .............................. 96 7.2 The Birth and Death Functions in the Agrarian Regimes . . . . . . . 99 7.3 The Social Capital F u n c tio n ........................................................................ 108 7.4 The Effect of the Random Variable on a J u m p ....................................... I l l 7.5 Horticulturalists Revert to a Hunter-Gatherer S t a t e .............................. 113 7.6 Hunter-Gatherer to Intensive A griculture................................................. 115 7.7 A Closer Look at the Transition from Hunter-Gatherer to Horticulture 116 V 7.8 Horticulture to the Verge of City S t a t e ................................................... 117 7.9 The Transition from Horticulture to Chiefdom in the previous figure . 118 8.1 The Agricultural Support Zone for a City S t a t e .............................. 124 8.2 The Eficct of the Administrative Function on the Possibility of Tran* sition to City State.................... 127 8.3 History One—Population, Income and C a p ita l................................. 129 8.4 History One—The Capital-Labor Ratio and Per Capita Income . . . 130 8.5 History One—The First 3800 Y e a rs............................ 132 8.6 The Capital-Labor ratio for the first 3800 y e a r s .............................. 133 8.7 The Capital-Labor Ratio during T ran sitio n s.................................... 134 8.8 History One—The Last 1200 Y e a r s ......................................................... 135 8.9 History Two—Population .......................................................................... 138 8.10 History Two—Income ................................................................................ 139 8.11 A Successful Jump to City S ta le ........................................................... 140 12.1 Linearizing the Demand C urve......................................... 186 12.2 Percent Change in Profits Due to Changes in P ro d u c tiv ity .......... 188 12.3 The Effect of b on P ro fita b ility ........................................................... 191 12.4 The Graph of t = ln ( 0 .4 x ) /ln x .............................................................203 12.5 Three Graphs of Equation (21) for DiflcrcnL Values of p ................... 205 13.1 The Phase Portrait of Profits U(t + 1) = / / ( n ( t ) ) .............................207 13.2 A Simple Piece-wise Linear Approximation of //(n (t)) . . . . . . . . 212 13.3 7/2(n) and H3(H) ...................................................................................... 213 13.4 An Invariant Distribution ..............................................................................214 13.5 Allowing for Positive Profits with / f ( n ) .....................................................215 13.6 An Industry that Eventually Becomes E x tin c t................................... 216 13.7 Another Possible Form for //( n ) Characterized by Convergence to a Two Period c y c le .............................................................................................. 217 13.8 tf(n ) Characterized by a Two Regime Recovery P e rio d ....................218 13.9 An Example of a Phase Equation that Converges to a Two Period Cycle219 13.10The Phase Diagram and Trajectory of a Two Regime Recovery F\mction221 14.1 The Piece-wise Linear Productivity Growth and Entry Functions . . . 229 14.2 A Trajectory when Elasticity is Less than O n e ....................................231 14.3 With g, > c3 Profits Rise without B o u n d ............................................. 233 14.4 Long Recovery Periods Result with a Two Phase R egim e.................... 235 14.5 Instability Results from R&D. The Model Quickly Converges when we Assume no Technological Development Occurs when Economic Profits are Z e ro .............................................................................................................. 236 v i 14.6 The Industry Averages Positive Economic Profits Leading Us to Con clude the Divergence between c4 and c3 must be g r e a t e r .........................239 14.7 A Wider Divergence Between c4 and c3 Causes Profits to Have a Greater V ariation............................................. 240 14.8 A Realistic Trajectory. Profits Average about Zero while Recovery Periods arc L o n g ................................................................................................ 241 14.9 A Two-Phase Response Creates a 15-Fold Increase in O utput per Worker over a 150 Year P e rio d ...................................................................................... 243 14.10A More Volatile Reaction to Economic Profits Results in Lower Overall Productivity G ro w th ..........................................................................................244 H .llT h erc Appears to Be an Optimal Value for C ( in order to achieve Max imum Productivity G r o w th .............................................................................245 M.12Sensitive Dependence on Initial Conditions Introduces the Possibility of a Chaotic tra je c to ry ...................................................................................... 247 14.13The Phase Diagram of a One-Dimensional Condensation of the Model 248 14.14Thc Phase Portrait of the One-Dimensional Condensation . . . . . . 250 1 Chapter 1 INTRO DUCTIO N This study arose out of an attem pt to create an economic growth model that describes the progression of economic activity that humans have historically experienced dating from prehistoric limes. A starling point for such an endeavor is the economist’ s benchmark model, the Neoclassical growth model. The Neoclassical model provides valuable clues to the possible expansion of even a very primitive economy when population density and institutional structure assume a neutral role and when technological change proceeds at a slow pace. It, however, usually produces a smoothly evolving unbounded tra jectory that converges to a "steady state” that reduces the dynamics of the process to never ending proportional iucrcascs in the endogenous variables, a phenomena not reflected by historical records nor prehistorical inferences. First, it cither ignores technological development, almost surely the most signif icant factor in the recent (in a historical sense) surge in economic well-being, or it assigns it a subsidiary role of autonomous occurence. In those cases where it allows technological change to develop endogenously, it generally treats it as a separate in dustry that evolves out of an increasing stock of knowledge—the latter a dubious concept at best; an attem pt to measure knowledge seems particularly fraught with 2 peril. Second, it similarly cither ignores population growth or assumes that it grows autonomously. Nevertheless, many economists going back at least to Malthus have discerned a definite relationship between population and economic well-being. The relationship seems more subtle than Malthus proposed, but his central thesis that limits on resources and a growing population within a static institutional structure can cause crises seems confirmed frequently enough historically to warrant serious consideration. Third, the neoclassical model tacitly assumes that the institutions and social infrastructure of the economy resemble that of a 20th century western economy. Thus it treats the institution of private property then prevailing as if it were god-given rather than a slowly developing system of rights and responsibilities that even today continues to evolve; it freezes the motivations, hopes and fears of its agents in an image of that period; and it assumes the role of government is to strictly promote the economic well-being of its citizens, ignoring the many cases where a ruling class adopts an agenda of its own. Not surprisingly, the Neoclassical model fails to capture the turbulent history of economic growth which, of course, is a dynamic process. Until recently, most of the thrust of analytical effort on the model seemed directed toward developing the model's long-run implications over a period of time th at obscured its short-term relevance. The major theoretical concern with its formulation was liar rod’s conclusion that the optimal growth path was dynamically unstable. Theorists expended a great deal of effort to show that the model would robustly converge to a "steady state" of proportional increases, thus effectively removing the dynamics from it. Economists concerned with practical means of stimulating economies to grow, such 3 as development economists, have either abandoned the model as a tool or modified it to fit existing conditions that clearly should not occur within a Neoclassical economy. As Herrick remarks, ’ ’...most of the assumptions about competitive forces and cm* ployer’s behavior arc indeed open to question.”1 The collapse of the Russian economy into competing fiefdoms established by ganglords who sell protection to even the most mundane of street vendors gives evidence of the need for even the most capitalistic economics to evolve institutional customs and protections against unvarnished profit maximizing behavior. Thus, in order to realistically address historical growth we must supplement the neoclassical model to take account of some of these factors, Recently, many economists have done this, addressing important issues in growth such as technological change, the contribution of foreign trade, institutional stucture, etc. Several of these efforts have yielded significant insights, but many carry with them a vestige of allegiance to perhaps the neoclassical model's most unrealistic assumption—the belief that the model should move the economy along an equilibrium path. Why this belief should persist is difficult to undcrsland-thcrc certainly is no empirical basis for it. One notable break from this tradition comes from R. Day who with a few other economists pioneered the use of non-linear difference equations to explain seemingly random behavior. In one intriguing effort, he created a long-run economic growth model that assumed that historically population density placed certain restrictions on the kinds of technology and economic and social institutions that could arise.3 Within certain population limits, a socio-economic regime might flourish, but as population 1B. Herrick and C. Kindleberger, 1083, Economic Development, p. 39. Also P. Yotopoulos and J. Nugent, 1976, in Economics of Development: Empirical Im>estigations mention inequality of income and persistence of unemployment as disparities between the Neoclassical model and development experience. 3R. Day, 1987 "Economic growth in the Long Run", for this model or R. Day and J. Walter, 1987, for a general theory behind non-linear modelling combined with a regime structure. 4 i * . increased as a result of relative economic prosperity, diminishing returns to the regime would impose Malthusian sorts of limits. At a critical juncture, disruptive forces could create the impetus for a successful jump to a new socio-economic infrastructure more suitable to a larger population, or set off a catastrophic decline in population, plummeting the group to a size where it could again successfully rc-cmploy some past strategy. The success of this simple model in recreating historical trajectories encouraged me to try to extend it by adding the variable of capital. I originally saw my task as one of: 1. Examining more closely the types of socio-economic regimes that one should include in such a model. While the designation of economic stages is ultimately arbitrary, the evidence suggests that one can associate certain forms of social orga nization with generic forms of economic activity and production, at least within the constraints imposed by natural resources. 2. Incorporating capital as an endogenous variable into the workings of cadi regime. This program seemed to work satisfactorily up until the fourth regime—the city state. Until recent times, it seems that the strain that population imposes on a socio-economic regime is the most destabilizing factor in the growth process. For instance, Boscrup and Cohen argue persuasively that population increase rather than agricultural discovery may have been the impetus behind the transition from hunting- gathering to agricultural societies.3 Similarly, one can argue that the collapse of the Roman Empire stemmed from the coordination problems its population of over 150 million caused rather than from any internal decay. Capital, it appears, played a role in establishing the speed with which growth took 3E. Boserup, 19G5, Condition* of Agricultural Growth, and M. Cohen, 1977,TAe Food Crisit in Prehistory, 5 place within an economic regime, but was not destabilizing in itself—an over abun* dance of it might cause inefficiencies, but not a catastrophe. The capital demands of a new regime might prevent a group from making a successful transition to a more complex society, and the specialization that a larger group facilitates, might make possible the development of new kinds of capital that ultimately enable new kinds of social organizations to emerge. For instance the development of war technology en- abled empires to arise from city stales, while the transition from intensive agriculture to the city state may have depended as heavily on the build*up of capital in the form of irrigation systems as the increase in population. Technological change progressed at a slow enough rate that one could capture its essence through a switch of regimes. Support for this position comes from Maddtson whose hierarchy of economic epochs describes the two epochs prior to capitalism as having technical progress "present but imperceptible"4 Nevertheless, the more capital intensive a regime became, the more misgivings I had about ignoring the role of technological change. As I began to explore the causes and consequences of technological change, 1 became more convinced that not only was 1 glossing over an important agent of growth, but also a major cause of instability. As medical science drastically reduced the number of deaths from infectious disease in the last century, I came around to the view that technological development became the major vehicle for inslabilty in the growth process. It did not seem feasible any longer to handle it through regime changes, since the strength of capitalistic institutions, appears to be its ability to promote technological change. Kuznets in an exercise where he defines economic stages according to epochal innovations, characterizes the modern period (which coincides with western capitalism) by its extended application 4A. Maddison, 1982, Phases of Capitalist Development, See the table on p. 5. 6 of science to problems of economic production.* Schumpeter, loo, believed innovation to be a defining pillar of capitalism. Consequently I began to look for ways in which to cndogcnizc technological change within a dynamic model. Schumpeter provided a great deal of inspiration with his observation that the search for monopoly profits drives businesses to innovate. In assessing the degree to which a firm can benefit from innovation I found that modest increases in productivity can have enormously profitable consequences, especially if one considers the increase in market share that often results. The neoclassical model with its stress on steady states clouds these kinds of observations. Humans arc quite adept at learning from past experience. When methods of organization and production occur in a timeless environment of little diange, the assumptions of the neoclassical model of rational expectations or some other form of omniscience can have a surprising degree of explanatory power. Ironically, the growth trajectories of the neoclassical model seem most suited to the 50,000 to 100,000 year period that modern humans were huntcr-galhcrcrs. Technological development changes the picture. Agents actively try to disrupt any equilibrium that may exist, and past experiences only partially illluminatc the future. Predictions about people’s reactions to new products, the success of integrating a new technique into production and the commercial payoff accruing to a research team are educated guesses at best. Naturally, agents make errors. Technological development, studies show, docs not occur simply by chance; rather it occurs as a result of human efforts directed specifically towards some goal, not, however, in a manner that enables us to predict its scope and direction. On average, R&D returns fairly constant returns to effort, but with a high variance. This, of 8S. Kucnets, 196(M/orfem Economic Growth.See chapter 1. 7 course, does not mean that one can simply decide to do R&D and progress will result. R&D expenditures by firms represent costs, and one can be sure that those firms choose to finance a research efiort because they have reason to expect success. The predictability of returns to a single firm varies even more greatly for another reason. Often success depends not only on your efforts, but also those of your com* petitors. In order for a new technique to work you may have to combine it with several advances that others have made. The experiments of your competitors pro* vide a laboratory that you can learn from, provided you have done enough R&D to understand their work. Consequently, capitalism with its institutionalization of innovation introduces an "uncertainty principle" about the direction and form that technological development will take. Just like the position of an electron, we can assign a probability distribution as to the overall amount of productivity growth that will occur, but we cannot be certain just where in that space technological development will be. This implies that if within an industry, R&D takes place routinely (as it docs in industries that compete technologically), then individual firms cannot expand their capital and output in the precise ways that equilibrium models require. If R&D and profits arc positively related as I theorize, one finds that technological growth occurs in spurts, followed by periods of relative stagnation. The second part of this thesis is an effort to capture the dynamics that technolog ical development brings to an industry and its effect on the growth of the industry and its productivity. I assume that an industry competes technologically through cost reduction and that firms expand or enter the industry and contract or leave it in response to profits. 1 get patterns of growth that resemble the empirical patterns described above. 8 I chose to assume that firms direct R&D towards cost reduction as opposed to demand creation because one can predict the market reaction by reference to a single demand curve. In reality, as many if not more firms engage in R&D for the purpose of developing new features or new products in order to favorably shift the demand curve. One would think demand creation would be even more destabilizing than cost reduction, but a rule relating a change in demand to R&D would necessarily be highly arbitrary, consequently I avoided this approach. I would hope to relate the instability of technological industries into repercussions for the economy as a whole. Although one can create contrived situations in which instabilities in one industry just balance those in another and yield a smooth path for the economy, one feels intuitively that this would rarely be the case. But any efforts to show this await the future. Part I Capturing the C om plexity of Growth in the Ancient Past 9 10 Chapter 2 THE NEOCLASSICAL MODEL A N D MALTHUS A newcomer to the field of growth theory might naivety assume that an economic growth model would generate time trajectories of economic data that at least faintly resemble reality. A quick review of the literature will convince him otherwise. Stan dard growth models, when fed initial conditions and allowed to ramble along without disturbance, usually describe an economy characterized by unbounded growth, zero growth or an eternal cycle of boom and bust. As economic historians and development economists discovered long ago, growth theorists sought to identify and analyze forces that characterize economic growth in western economies of the recent past. A set of stylized facts emerged that growth theorists tried to explain1 while relegating the historically critical variables of popula tion and technology to an exogenous role, and essentially ignoring the socio-economic structure other than to assume perfect markets exist. The bench mark model of this program of attack, the neoclassical model, achieved 1 Generally the set or stylised facts growth theorists "needed to explain are: 1. increasing capital to labor and output to labor ratios, 2. approximately equal shares of capital and labor, 3. fairly constant returns to capital, 4, a constant capital-output ratio and 5. an approximately constant saving rate. 11 great success in elucidating the stylized facts—its only notable failure was its inabil ity to account for technological change-but economic historians and development economists found it curiously lacking as evidenced by H arriets earlier quote, and by North who remarks, "from the viewpoint of the economic historian, this neoclassical formulation appears to beg all of the interesting questions.”3 North feels economic historians must explain for a given period the instituitional structure of an economy and its changes. By institutional structure North "includes the political and economic institutions, technology, demography and ideology of a society.”3 Development economists share these concerns and the two groups together have tried to broaden the field by formulating and attempting to quantify such concepts as structural change, growth stages, degree of urbanism, scctoralism, political organi zation, and even (horror of horrors to some economists) borrowing ideas like culture 4 from other disciplines. While their work has greatly contributed to the discipline by expanding the economist’s tool kit, some within the profession have reacted with alarm, believ ing that no worthy economist would work with such concepts. Who knows whether such thinking which, incidentally, clearly violates Samuelson’s reversal of the "Mar shall rule”,4 might not rekindle the field of Political Economy which would leave it open again to incursions by Marxists, political theorists and other unsavory sorts of similar ilk. While we can sympathize with these concerns, harder to understand is the pro* 3D.North, 1081, Structure in fconomic History, p.5. *Ibid„ p.3. 4P,Samuelson in Foundations of Economic Analysis,, p.G, says "..I haw come to feel that Mar shall's dictum that ’it seems doubtful whether any one spends his lime well in reading lengthy translations of economic doctrines into mathematics that have not been made by himself', should be exactly reversed. 12 Cession's reaction to Harrod's (1939) revelation that the growth process itself might cause dynamic instability. The prospect of an economy th at achieved an equilibrium growth rate only by skating along a "knife's edge’ ’ apparently unhinged economists to such an extent th at they rose up to dem onstrate th at this was not the case. Solow (1958) and Swan (1956) replaced Ilarrod's fixed proportions production function with one allowing for factor substitution and got a dynamically stable economy, while the Cambridge economists introduced a savings rate th at diangcd over tim e as the distri bution of income varied and achieved the same result. While these eminent scholars only claimed to dem onstrate the possibility of robust stability which, indeed, ac corded with the long-term behavior of western economics over the last two centuries, the mainstream somehow twisted this into a silent declaration of the universality of stability, fusing these ideas with traditional theory to produce the crown jewel of growth models, the neo-classical growth model of which Unrrick remarks, "The tendency towards equilibrium cannot be overemphasized."5 The profession's preoc cupation with equilibrium culminated in attem pts to deny th at even the short-run business cycle might indicate some disequilibrium process lurking in the economy. But the historical record paints a far different picture. The considerable economic growth th at occurcd over the last 10,000 years took place at a remarkably uneven rate. W hether studying population, income or capital, one observes a jum ble of short periods of rapid growth, epochs with a general trend of slowly increasing output punctuated by considerable fluctuation, long periods of stagnation, and catastrophic decline. In light of this, economists need to actively seek sources of disequilibrium rather than try to deny its existence; for developmental economists and economic historians this need seems especially compelling, which may explain their indifference sIIarrick and Kindleberger 1087,op. cif.m p,5Q, 13 to the neoclassical model. Nevertheless, the neoclassical model is a powerful tool, one that can provide great insight if used properly. In order to do this we need to understand w hat assumptions cause the model to fail. Perhaps the gravest errors come from the unstated premise th at markets function perfectly. North explains why this fails to hold, "...the model assumes an incentive structure th at will allow individuals to capture the returns to society of investment. ...Perfectly specified and costlessly enforced property rights (th at is zero transaction costs) arc necessary (for this) to hold. Such conditions have never been obtained.” He points out that ”As a result, disincentives for saving (especially security of property rights) have kept rates of savings and capital formation low and retarded technolog ical development.” In addition, inefficient political and economic structures (make) competing ideologies a cultural issue in understanding economic history” because the market distinguishes between good and bad actions imperfectly, hence they disappear slowly.® The neoclassical model obscures the necessity for a social group to develop a com munally accepted system of behavior and ethics governing economic relations. A community evolves institutions for resolving disputes in a way that protects commu nity interests. The importance of these mechanisms has recently come to light in Russia's struggle to change to a market economy. FVom a profit maximizing stand point it makes perfect sense to assassinate a competitor who can underprice you, a solution resorted to by business rivals in Moscow with such frequency th a t most feel it is nearly impossible to do business successfully without the protection of a ganglord—but its ubiquitous practice does nothing for the common weal. 6North, op.cit,, pp, 5, 7. 14 Recognizing the importance of these collective factors which we will group under the rubric of ”socio-economic infrastructure*7, several economists and historians have taken to defining periods or stages of development going back a t least to Marx who provoked Rostow to respond in kind nearly a century later.8 The esthetic pleasure the reader derives from the portrayal of a social group pro* grossing through some fore-ordained sequence of stages to fulfill its destiny brought initial acclaim to Rostow’s efforts. Unfortunately, a closer examination of his theory somewhat tainted the whole stagc*hypothcsis enterprise because his sequence did not conform with historical nor contemporary experiences. The take-off stage particu larly seemed to be cither missing or poorly defined, and his choice of stages seemed inappropriate if one extended the analysis to countries beyond the ones he studied. Nevertheless, Rostow’ s effort focused attention on the discontinuity of growth process. Critics of the stage approach validly poinL to the frequent use of stages to describe rather than explain, and decry the tendency to create sharp demarcations which blur the importance of many causal factors. The picture of a social group moving inexorably upward contradicts historical observation. Two examples among many to the contrary include the oscillation between hunting-gathering and agriculture th at characterizes many surviving ’’primitive” societies, and the collapse of the Roman Empire into small warring kingdoms. Nevertheless, few doubt th at the structure of a society heavily influences its eco nomic productivity and limits its expansion—how else can we make sense of the recent upheavals in Eastern Europe; consequently the stage approach still appeals to many scholars. Rostow perhaps relied too much on economic measures of performance to 7R. Eberts 1966, " Estimating the Contribution of Urban Public Infrastructure to Regional Growth” , and R. Looney and P. Ftederickson 1981, "The Re of Infrastructive Investment in Mexico" are two recent eflorts, dW, Rostow, 1960,5fayes o f Economic Growth. define his stages. North (1981) characterized an economic organization according to its formation of property rights and ideology in a manner that promoted the wealth- maximizing objectives of the state. Kuznets and Maddison also discuss economic epochs which we will explore later. Two other premises of the neoclassical model that historically fail to hold are the assumptions of constant returns to scale except for an autonomous outward shift of the production function due to technological change, and a continuous production possibilities curve. Rooted in these premises is the belief th at modern capitalism with its incentives for technological advance can escape the inevitability of limits. Assum ing that knowledge is clastic, technological development will overcome diminishing returns and shatter the Malthusian view. Recent developments in environmental modeling, however, cast doubt on this. To sec the problems th at develop without these assumptions consider the tra ditional formulation of the Solow-Swan neo-classical model. To prove the existence and stability of a steady state path wc write the basic differential equation in its per capita form as 0 < f> (k) = s f ( k ) / k - 6 (2.1) where a is the savings rate, f(k) — F(K/L, 1) is the output per worker as a func tion of capital intensity per worker, k is capital per worker, and 6 is the depreciation rate. Letting n be the growth of the labor force we show that < i> (k ) = n, not only has a solution, but that the market clearing prices of labor and capital force us to move to this solution. W ithout constant returns to scale, however, f(k) is not well defined preventing 9 Among many treatments of this one could see R, Ramanathan, Introduction to the Theory of Economic Growth, Springer-Verlag, 1982, p. 32-50. 16 Figure 2.1: Discontinuity arising from the iso q u a n t m a p processes disrupt the.continuous suP.ti* tut ion betueen capital and labor. 360 -160 -20i 0.00 0.00 the m athem atical exercise. More im portantly, the savings rate s if it responds to returns on capital will change dram atically in response to developments in per capita o u tp u t as diminishing returns set in. For example, we might imagine th a t the isoquant m ap in figure 2.1 represents food production possibilities for a social group with a limited territory. T he numbers on each isoquant represent the output. Suppose we m easure capital and labor in term s of hours of work. T he isoquant m ap reflects two m ethods of production, say horticulture through burning forest land and planting which involves a less capital intensive means of production (here we take capital to be the field preparation), and a more capital intensive form of agriculture th a t requires the digging of an irrigation channel before the method becomes viable. The latter becomes more productive only 17 Figure 2.2: A Discontinuous Tangeiicv f.ine S. 00 flGUBE Th$ points ot tangency botueon the lsoousnts snd the proauction constraint line is oiscont muoue. > 0.00 0.00 e.oo for output greater than 350. Since we m easure capital and labor in term s of hours expended, the production constraint line is C + L — Cc where Cc represents the com m unity’s total num ber of available hours for work. If we look a t the locus of points of tangcncy of the production constraint lines with the isoquants we get a line as in Figure 2.2 where the break represents the output where the more capitat intensive m ethod supplants the other-pcrhaps the line is discontinuous a t this point. T he isoquants for the labor intensive form of production clearly indicate th at diminishing returns are setting in as the comm unity overuses its resources. Theory tells us that as the group population grows so th at its production constraint line in figure 2b shifts to P P \ it should dig the channel and shift to the new m ethod 18 of production. But the transition is more complex because we really must use a production constraint line th at reflects the relative costs of capital and labor, that is an isocost line. The capital intensive method requires a jum p in capital of at least Ci — C\ (and probably more since much of the old capital cannot be used for this new method of production) at a tim e when one would think that present consumption becomes more highly valued relative to postponed consumption since per capita output is falling, pushing people closer to subsistence levels. Present consumption may make the difference between life and death for some people. The production constraint line then changes as population increases to aC + L = C0 with a > 1 and increasing as population increases, reflecting the fact that saving is now less desirable. If the slope of the production constraint lines increase so th at they arc greater than the slopes of the lower segments of the isoquants, production will shift to all labor ( possibly representing a reversion to hunting>gathcring which we might think of as consisting entirely of labor). Of course, per capita income will continue to drop, perhaps causing a catastrophic fail in population as Malthus predicted, a t which time the group can resume the old labor intensive method of horticulture. Granted, one can argue that the group could foresee the impending overuse of resources and plan ahead by accumulating capital for the capital intensive process before diminishing returns become too severe, but in order to do this they must overcome several problems. Who is to do the digging? Who gets to farm the irrigated land? How will the crops be distributed? The answers to these questions require a different political, social, and economic structure, and the group may or may not be up to solving them. Thus the M althusian view, so recently dismissed by scholars because it "failed” 19 lo foresee technological change, has critical importance in understanding historical change. North remarks, ” It is only in the modern era th a t science and technology have been welded so that the overcoming of diminishing returns has become a reality”10, which overstates the case since all we really know is th at we have not yet reached the point of technological saturation. He speaks of ”...thc recurrence of Malthusian crises throughout history”, and employs population growth as a m ajor determinant of structural change throughout his model.1 1 The critical problem in regime modeling arises from the uncertainty of the out come when crises occur. While North’s model identifies and describes many of the economic and institutional factors influencing economic history he docs not consider this indctcrminancy except lo note its existence. Day (19S7) recently created a model th at captures the intrinsic uncertainty of his torical processes within such a structural framework. In his model a single variable, population, captures the infrastructural potential which in turn defines the technolog ical possibilities which a socio-economic organization embraces. By choosing different ' parameters for the techno-infrastructure he describes qualitatively accurate histories of complex growth involving periods of steady growth, fluctuation, jum ps to new regimes and Malthusian collapses back to old ones. Incorporating findings from er- godic theory, he and W alter delineate conditions under which economic and social "evolution” take place amidst chaotic trajectories.1 * His choice of population as the variable of change seems appropriate for all but the last 100 years—it appears th at population density may be the single most im portant ,0North 1981 .Structure and Change tn Economic History. p.G. 1 1 He discusses population growth as a possible cause of the shift from hunting-gathering to agri culture and considers it to be "the most fundamental underlying factor in ancient economic history." (p.109). 13Day and Walter 1988, "A Multiple-Phase Theory of Viable Economic Growth". factor in fostering structural change within a social group.1 3 But we also need to consider two other highly important factors—capital and technology. While one would prefer to analyze the effects of both, capital embodies a great deal of technological change. Furthermore, as compared to the present, technological change occurred at a much slower rate, so slow that Maddison indirectly describes the period from 1500 to 1820 as one where "technical progress was present but imperceptible”, and he docs not even mention it as a factor prior to that tiinc.H Consequently, as a next logical step 1 will consider only the additional effects of capital through four stages, assuming that the growth of capital and the parameters of the regime subsume technological advance. One may regard this paper as an extension of Day's model to include capital and to consider change within a "realistic” parameter space. I present an economic growth model where economic, social and institutional factors interact with population growth within a framework of limited resources to generate plausible trajectories for population, capital accumulation and national income over long time periods. We will find that the inclusion of capital enriches the model both within the regime and in analyzing switches between regimes. I define and characterize regimes according to population density, technology, and the socio-economic structure. More densely populated regimes have a greater degree of specialization thereby requiring a more intensive use of capital and a more complex form of social organization. The ability of a society to successfully change regimes depends on its ability to meet new population and capital requirements. l3See, for instance, Doserup (1905) and Cohen (197*1) for an exposition on the role of population in humankind's shift from hunting-gathering to agriculture, Doserup (1960) discusses the role oT population density in making feasible the emergence of the city state. North (1980) in chapter nine discusses the role population had in the break-up of the Roman Empire HMaddison, op. cit. p.5, see table. 21 Specifically I consider episodes of human development leading from the hunter* gatherer stage of existence to the city state. 22 Chapter 3 THE STRUCTURE OF THE MODEL 3.1 T he C hoice o f R egim es I have tried to show that the regime approach has a legitimate basis despite its tar nished reputation. Physicists and chemists frequently use the approach, for instance, in discussing the behavior of a substance as a gas as opposed lo a liquid. One must avoid using regimes for descriptive purposes—instead they should embody fundamen tal underlying differences. In this regard it is of interest lo sec what Kuzncts and Maddison regarded as fundamental differences. Kuzncts suggested differentiating stages according to its "epochal innovation,...a major addition to the stock of human knowledge which provides a potential for sus tained economic growth—an addition so major that its exploitation and utilization absorb the energies of human societies and dominate their growth..." As examples he cited the epoch of merchant capitalism with the epochal innovation of a breakthrough by western Europe to the New World and the Modern period whose epochal innova tion is "the extended application of science to problems of economic production."1 ’S. Kumets, lflG G , Afodcm Ecouotnic Growth, See Chapter 1 for a general discussion. 23 The epochal innovation has such magnitude that it "necessarily involves insti tutional and cultural adjustments—changes in the economic, political and cultural framework essential for proper use of the greatly expanded power of the production structure.” Because he believed that a stage should encompass the realization of the potential of the innovation, Kuzncts felt that a stage theory implied ”a specific succession of those segments so that b cannot appear before a or c before b.” Realizing that no scheme could provide a universal sequence, he stressed the limits of sudi an exercise. "Although during any historical period a given epoch may characterize the economic growth of several human societies in the world, it docs not follow that it characterizes ail human societies."3 Indeed lie devotes much of his life work lo understanding why all human societies do not pass through the same sequence. Maddison did not envision stages as having unalterable sequences. He identifies six economic epochs: 1. Pre-agrarianism, 2. Agrarianism, 3. Ancient Imperialism, reversion to Agrarianism, 4. Advancing Agrarianism, 5. Merchant Capitalism, 6 Cap italism. These epochs, he feels, reflect "in broadly chronological ordcr...thc evolution of production potential" for Europe and its offshoots. He cautions th at "alt countries have not moved in steady succession through all these stages. Some have skipped an eporh; there have been cases of relapse.” 3 Maddison is vague in identifying the basis on which he chooses his stages. For instance, he describes merchant capitalism as the epoch "in which the leading Eu ropean countries exploited their superior technology in navigation, shipbuilding and armaments to develop trade through monopolistic trading companies", but he says the main difference between the capitalist and the merchant capitalist epoch is the 3S. Kuznets, 1973, Population, Capital, and Growth,, W. W, Norton, p. 212 to 219. 3A. Maddison, 1982, Phases of Capitalist Development, Ch. 1 24 "enormous acceleration in the pace of technical progress; which has required a major increase in the rate of fixed capital formation"4 One should note, however, that his choice of epochs reveal major differences in a typical society’s administrative organ!* zation. We should also mention Marx, the first to develop an influential stage approach to economics. While his analysis clearly erred in terms of its predictions, his model did provide a testable explanation for regime switching, and perhaps most importantly he systematically considered the dynamic instability of an economic process. An appropriate choice of regimes depends upon the tools of analysis one intends to employ. In this section I will try to infuse dynamics into the neoclassical model by superimposing on it Malthusian ideas to describe a system’s limits. Factors that constrain the scale of economic activity include political structure, culture and tech nology. In this regard, the Anthropologist’s view of culture gives insight into an appropriate choice of regimes, especially with respect to population density. Many believe that a social group’s culture evolves from simple to complex mostly depending upon the size of the social group,5 which in turn roughly depends upon population density. We can broadly associate early cultural groups with characteristic forms of eco nomic activity. Iluntcr-gathcrcrs or nomadic herders usually form bands, while slash and burn agriculturalists or liort iculturafists operate within a tribe-like structure with its web of clans, clubs and societies. A more sedentary and dense form of agriculture usually cannot exist without closer group cooperation. People need some mechanism to adjudicate disputes involving claims to fertile land which becomes increasingly *Maddison, 1962, op.cit,, p. 13 and 15. *Sec L. White, 1950, The Evolution of Culture, or E. Service,1975, Origins o f the State and Civilization, for an exposition of the way in which simpler cultures evolve into more complex ones. 25 scarce as density increases. Often more elaborately defined concepts of private prop* crty arise. A chicfdom where an individual has decision-making power over strangers, and where ” noble” clans lead to an increasingly stratified society 6 can accomodate these more complex arrangements. But a city state requires a cultural complexity that transcends the chicfdom. The degree of specialization requires a central authority that can coerce members to routinely produce a large enough surplus to support a much higher fraction of specialists and to finance the huge capital expenditures that arc needed. While in most cases the ruling class employs violence or its threat to establish its superiority,7 it cannot rely only on it to motivate production. Eventually it must foster a willingness among its subjects to actively work within the infra-structure. In the simpler regimes group pressure stemming from kinship relations might provide the necessary justification to keep members from actively or passively disrupting the system (North calls this the free rider problem), but the city state must develop some new form of social validation that is effective with subjects with whom the ruler never interacts. A nearly universal solution to the problem seems to be the development of a religion portraying the ruler as cither a god or an agent of the gods. While the mechanism by which a religion becomes entrenched is not easy to un derstand, when it does become established it lends more structure and stability to a society. Growing out of the religion a body of ideas and behavior become inured in the population. North, who calls this "ideology", points out that it embodies people’s 6E. Sagan, 1985, in A t the Dawn of Tyranny, defines a chief as a "political leader who rules over people with whom he does not come iu contact and over people with whom he has no kinship rela tion." (p.238). He also describes the process of transition form headman to chief to monarchism.(pp. 305-318) 7The emergence of the state through violence is one of the oldest and least challenged theories. See for instance F. Nietische, 1913, Genealogy o f Morals, for an eloquent statement of this age-old theme. 26 ideas about equity and a just distribution of income, and he stresses its economic rote in simplifying every day decision making for individuals. He notes that people alter their ideology only when faced with persistent experiences contrary to its tenets.8 As social complexity increases with population density so does the capital in* tensity, reflecting each cultural group’s form of economic production. Each form of production in turn requires a specific form of technological expertise which a culture must pass on to new members. Huntcr-gathcrcrs, for instance, have few capital demands in the modern sense but require an extensive knowledge of the properties of plants and the actions of animals within their area. Capital requirements arc limited to the production of weapons, containers for transporting food, digging sticks, temporary living quarters along with various household items used for preparing food, etc. Huntcr-gathcrcrs can produce these items relatively quickly and most have a limited life—short enough to lead me to assume in the model that they employ strictly labor in production. Slash and burn agriculturalists jointly "invest” in field clearance and usually invest individually in domestic animals for fertilization and to reduce grass coverings of fallow lands which arc much more difficult to clear than forest. They must, of course, develop expertise in agricultural methods. Intensive agriculturalists must preserve the fertility of their land and since they often plant more than a single crop per year, must worry about irrigation during the dry season. They invest in a more permanent kind of field clearance and often engage in extensive though local irrigation projects. They must maintain large herds of animals for fertilizer and for pulling plows which intensive planting usually requires.8 aSee North 1981,op.cif,, especially Chapter 5 on "Ideology and the FVee Rider Problem." 9Doserup 1965, op.ci/, discusses the difference between slash and burn agriculture and the use of plows. 27 Since they abandon their fields less readily they tend to settle in relatively permanent villages which often entails the construction of some defensive fortifications. The city state requires investment as described above in rural regions but with more extensive irrigation networks. Of the six regions where urban centers apparently developed independently (Mesopotamia, Egypt, the Indus valley, the Huang Ho plain in China, the valley of Mexico and Peru), four of them (the first four) occurred in river valleys with highly developed systems of irrigation and in another, the valley of Mexico, local tribes constructed artificial "floating gardens" called chinampas which proved to be highly productive in terms of land input. In the sixth, it appears that the first city states developed along more than 50 smaller river valleys that cross the coastal desert in Peru. Recent excavations in the Casma valley indicate that irrigation may have formed the basis for cities emerging as long as 3,800 years ago.1 0 Other capital projects of paramount importance to the leaders of a city state include the construction of roads and other means for transportation, temples and palaces, city walls and other defensive fortifications. Since violence potential underlay the power of the state we should regard expenditures on a standing army and the accompanying tools of war as capital also. The way in which capital and the social structure interact makes the inclusion of capital as an endogenous variable more compelling. As the regimes increase in complexity the degree of inequality and stratification also increase, a development to which capital and technology contribute significantly. Flannery suggests that as agricultural technology developed and capital accumulated, it would be used on ever* smaller acreage. Eventually very small areas would feed a large per cent of the ,0See M. Coe, et. al., 1086, Atlas of Ancient America, p. 185-105 for a general review of the various cultures in the area in prehistoric times. See S. Pozorski, June 1991 "Early Andean Cities", Scientific American,, p. 66 to 72 for information on the Casma valley. 28 population. "The most important consequence of the inverse ratio is th at it set the stage for social stratification.” as owner of the most productive land would become more powerful.11 Technology will often alter a society’s choice of regime. Agriculture became an in* creasingly viable option through time as crops became more domesticated and plant ing and irrigation techniques improved. Improvements in transport technology in cluding boats, roads and wheeled vehicles affected the likelihood that an area using intensive agriculture would become a city state.1 3 North observed that the size of the political-economic unit increased enormously from Hammurabi to the Persian Empire of the fifth century B.C., a development he attributed to improvements in military technology.1 3 The city state by creating a small army of spcciatiBls gave birth to a technological revolution in many areas. Sonic of the more obvious needs for technology included hydraulic engineering, architecture and transportation. Pcrhnps the art of war, how ever, was most important. Carnciro writes ”lhc forging of village into chicfdoms and of chicfdoms into kingdoms occurs only through coercion, especially by conquest warfare.”1 4 Aside from its role in the creation of the city state, North believes that military technology primarily determined the optimal size of political units in the ancient world.1 5 If we move chronogically from the emergence of the first city states to the Roman n K.Flannery, 1971, "Origins and Ecological Effects of Early Domestication in Iran and the Near East", p,77. See also K.Witlfogel, 1971, Developmental Aspects of Hydraulic Societies." for the role of irrigation in the structure of the earliest states. ,3See Doserup, 1980,Population and Technological Change, Chapter 0, especially Tfcble 6.1, p.68, for a discussion of the relation between the sise of the city, population density, and transportation technology. ,3North, 1981, op. cit. Chapter 8. u Carneiro, 1972, "From Autonomous villages to the State, a Numerical Estimation,” p,65. ,9See North 1981, op. cit,Chapter 8. 29 Empire we see a tendency toward larger investments by the state, especially in terms of defense and military expenditures, but also in regard to systems and means of transportation and communication. In Mcsoamcrica a t the lime of Cortes* arrival, the Aztecs could send messages 300 miles a day through a relay system they had established. As the size of the state increases and with it the level of complexity as new occupational groups arise, more specialization occurs in existing professions, and class divisions widen, the median isms for decision making and distribution become more involved and require the efforts of a larger fraction of the population. W ith greater social stratification, the elite exert their power through the state. In doing so, the state must divert labor and capital lo activities th at enforce group compliance with its demands. One can interpret sudi capital projects as temples and palaces as an effort to create a dcific reverence for the elite among its subjects, and the expansion of the m ilitary as an attem pt to scare the hell out of them. Although this "work” docs not produce the goods wc associate with consumption, it nevertheless represented a part of adm inistrative technology that a more complex society had to have in order to function smoothly. In addition to administrative functions required by the slate, private producers m ust expend more cfTort in coordination or distribution because of the increased specialization of the labor force. Clearly when a social group becomes more complex a smaller proportion of its work force and capital goes toward directly producing the goods we might wish to associate with income. We can usefully divide economic activity into two sectors, one involved in direct production of "consumption goods” and the other as creating conditions so that direct production can realizesits potential, 30 Ester Boscrup discusses the latter activity which she calls "administrative technology" at great length from prehistoric times to the near present.1 0 Richard Day has modified the typical Neoclassical model by specifically considering the division of the work force between the two sectors as social complexity increases.1 7 Much of the economic success of a regime depends on the kinds of property rights it creates, but the interests of the political elite may not coincide with the economic success of the regime. North, who uses the application of neoclassical theory to a view of the state as the provider of protection and justice for revenue, argues th at "efficient property rights" may increase economic output yet yield lower tax revenues to the state because of higher transactions costs (c. g. monitoring production, measuring production, and collecting taxes) than a system with a more inefficient set of properly rights.1 8 A successful regime must weigh two factors in this respect. If the economic system is too inefficient it will run the risk of internal dissent, but in the process of stimulating economic success it may inadvertently create rivals for political power. We can broadly associate characteristic forms of property rights with the regimes we have specified. Huntcr-galhcrcrs possess communal rights to the band's territory. This, incidentally, may have the effect of causing the group to ovcrutilizc resources if population is not kept in check. Slash and burn agriculturalists similarly pracLicc group access to plots of land, although once a family chooses a plot it may use it without interference until it abandons it.1 0 Since private ownership of land docs not exist, members make little ICE. Doserup,1981,Po/w/efton onrf Technological Change, ,TR. Day, 1987, "Economic Growth in the Very Long Run" iaNorth, 1981, op,cit, Chapter 4. Property rights are efficient in North's sense to the degree in which they equate private returns witli social returns.Property rights that stimulate individuals to seek technological change or to create capital that furthers the common good would be examples of efficient property rights. 1SE, Doserup, 1965, op, cit,, p. 79-80. 31 f c A effort to preserve the land’s fertility. Intensive agriculturalists usually adopt a system of private ownership of land ex* cept for communal plots which they use to graze livestock. In the city state, property rights become more elaborate and private property may take many forms. Some times the stale owns most of the factors of production, but often individuals can own land, capital and people. The coincidence of efficient property rights with economic production must enter the calculus of the group administration technology function. The overlapping of the forms of cultural complexity with property rights, tech nology and predominant mode of economic production leads us to choose for our model the regimes of: (1) hunting-gathering, (2) horticulture or slash and burn agri- culture, (3) intensive agriculture, and (4) the city state. To develop stages beyond the city state one can profit by North’ s suggestion to consider property rights and the incentives that arise out of them, but one must also accomodate technological diangc. One could quite possibly inject the intermediate stage of a complex society. I do not do this because the transition between intensive agriculture and a complex society occurred regularly, while the transition between intensive agriculture and the city state was a rare event. 3.2 P op u la tio n D en sity and th e R egim e In the model we will determine the regime by reference to a group’s total population. Since we limit activities to a fixed geographical region we may speak alternately of population or population density. We assume that groups choose the form of political organization that maximizes their per capita income given their population; either a band, tribe, duefdom or city state. 32 The problem of cooperating and interacting with strangers and the capital and technological requirements of an economic strategy constrain a group to one of our forms of social structure. As population increases to a threshhold value a society strains its existing organizational form. Lowering economic standards create diss- satisfaction and members may seek to change the status quo in a search for a new economic strategy. Thus each structure has a viability interval, a level of population density in which it can operate effectively; but outside of this interval the system fails to solve basic problems—the system breaks down and incomes fall. Huntcr-gathcrcrs need a relatively large land area over which to roam so that they do not exhaust the region’s biological resources. In prehistoric times when a band grew too large, groups could splinter ofT and colonize new territories. In this way humans grew slowly in number and expanded in geographical area until around 10,000 to 12,000 years ago when they occupied most of the prime hunting and gathering areas in the world. The frontiers vanished except for the most inhospitable areas sudi as the polar or desert regions. With relatively peaceful colonization now precluded, as the number of bands increased, each would find its territory shrinking and therefore its population density increasing which reduced per capita output, requiring a form of economic production that used land more intcnscly-namely agriculture. Boserup (1965) writes extensively about the relationship historically observed be tween land use and population density and originally theorized that agriculture arose because of increasing population density, reversing the traditionally held view that the discovery of agriculture led to a leap in population . Cohen (1977) adopts, expands and defends her thesis and examines the archaeological record for the emergence of agriculture in the Mideast, Middle America and South America. We discuss this at length in Chapter six. 33 The first agrarians did not need to invest much effort in land preparation. Prepar- ing a plot by burning off an area of forest or bush and perhaps felling large trees with an axe, they would simply plant around obstacles such as large boulders without bothering to remove them. After the land lost its fertility in perhaps two to four years, they would simply move on to another area. If they allowed the land to lie fallow for at least 15 to 20 years, the forest would reclaim the land. W ith its fertility restored, they could repeat the whole cycle. As population density increased, the fallow period had to eventually decrease. If forest or bush had failed to reclaim the land, a grass covering would remain. Burning grass docs not remove it as its roots remain intact. Consequently agrarians must plow the field. Additionally, the shorter fallow period might require manuring to restore its diminished fertility. Typically a member of a tribe has a right to cultivate any unused plot of land within the tribal territory, and retains th at right while it lies fallow. If the fallow period passes and th at person does not return to it, other tribal members can then plant it. When land is abundant, tribal members have no incentive to retain a par* ticular plot of land, but as population increases, good plots may become relatively scarce. In the past, occasionally a two-tiered society would develop as some tribes resorted to warfare, capturing slaves who were then forced to work the land. Their descendants might not be pressed into slavery, but they did not become tribal mem* bers either, hence they did not inherit the right to cultivate land within the tribe's territory. These people often had to assume a kind of tenant status. Another form of duality that often resulted in servitude arose when a nomadic tribe entered the territory. Sometimes they traded animal products and manuring of fallow lands for vegetable foods. Other times they would conquer the cultivators and 34 establish themselves as a nobility. The point of this is that a tribal structure with a headman ruling by virtue of his eminence could settle disputes in a slash and burn type of agriculture, but a chief with the power to compel actions by strangers was often necessary to establish order as population density imposed more intensive forms of agricultural use.30 A city stale requires an even larger population because the system requires that agrarians support a sizeable minority of the population with its agricultural surplus. As previously noted, nearly all the city states th at arose independently did so in regions where there were extensive irrigation projects. Since irrigation apparently greatly increased yields per hectare,3 1 these regions were probably characterized by a relatively high population density among a group of people who were likely to be homogeneous because of geographical proximity. Agrarians would not give up the surplus willingly. If an elite arose or a nobility already existed, a city state might seem tolerable to a people who undoubtedly faced more raids by outside tribes who were also experiencing crowding from a general increase in population, because of the protection it afforded.33 They might then "agree" to trade the surplus for protection. But as in all trade-ofTs, the villagers under the aegis of the city state had reason to try to avoid taxes, either in the form of agricultural output or through labor conscription when given the opportunity.33 Consequently, the task of enforcement on the part of the ruling elite would eventually become more difficult as the size of the *°I have borrowed shamelessly from Chapter 0 of Boserup's Conditions of Agricultural Growth in the last five paragraphs. , l See R. Adams, 1060, The Evolution o f Urban Soeie/y; Early Mesopotamia and Prehistoric Mexico, for comparisons. 3>Carneiro, 1970, in "A Theory of the Origin of the State", discusses the influence of war technology on the development of the state ^Instances of local revolts against states abound 35 state grew. Again we see that population may impose a limit on the maximum size of a regime. When the size of a group places it on the threshhold of two forms of organiza tion, each has several sources of disequilibrium. One cannot easily predict which organizational form will prevail. 3.3 T he D em ographic Function The demographic function relates birth and death rates to per capita consumption within a regime. Ideally we would prefer to link our birth and death rates of females based on economic conditions to some form of cohort analysis, possibly calculating the appropriate Gompcrtz equation to fill in missing information. Practically, the exercise of estimating cohorts for primitive people living over 5,000 years ago might do much to sway the notion that economists have no sense of humor but little else; consequently we will content ourselves by simply assuming that birth rates positively relate to consumption while mortality rates negatively depend upon it within the framework of a socio-economic regime. Easterlin3 4 points out that at different times limitations on the supply of children as opposed to the demand for children may determine actual birth rates. The supply and demand for children depend heavily on social customs that may arise as a survival reaction to the life-style of a group. For instance, modern hunter-gatherers seem to have developed physical and social conditions that prevent closely spaced together births which would constitute a serious disadvantage to a mother whose economic strategy consists of walking long distances to gather foods and who must carry infants and young children on these trips. 31R. Easterlin, 1975, "An Economic Framework for Fertility Analysis*1 in Studies in Family Plan ning, p, 54-63. 36 W ithin the context of the group’s economic strategy it seems appropriate to as* sociate fertility with income for the period the model covers for several reasons. First, it appears th at individual demand is a less relevant factor for the model’s period. The fertility ’ ’revolution” taking place today is ”a shift from a situation in which fertility is controlled through various social and biological mechanisms to one of limitation of family size by the conscious dcdisions of individual households.’3 5 Second, inasmuch as ”a positive association between fertility and socio-economic class at a given time has been observed in pre-modern times,”20 we might expect that when national income increases, a sizeable fraction of the population may move up socio-cconomically. Third, agrarian societies, cxpecially in pre-modern times, were subject to wide fluctuations in income due to crop failure. Distribution mechanisms in these countries were poorly developed which often led to famine-like conditions for a substantial segment of the population; this certainly must have correlated strongly with lower birth rates and higher death rates. Fourth, many customs from the past regarding permissible marriages seem di rected to increasing the probability the family could economically support children. When income fell, fewer marriages often resulted from such mechanisms as, for in stance an inability to raise a dowry. W ith these ideas in mind we relate birthj and death rates to per-capita income in the following ways: 1. Until per capita consumption reaches a certain low level (The Easterlin thresh- hold), virtually no births will occur; upon reaching th at level births rise relatively sharply until they level ofT at a still relatively low level of income, asymptotically ap- 35R, Easterlin and E. Crimniins, 1085, The Fertility Revolution: A Supply and Demand Analysis. a6R. Easterlin, 1975, "An Economic Framework for Fertility Analysis." Figure 3.1: The Birth Rate Function flo U O tJ 2 ‘ T h * oi0£sui£« linear aosro»matior> ot tn« s i r t n r a ta Junction, o.o: ■ proaching some maximum level. We, in fact, will approxim ate this relationship with a function composed of three line segments whose generic shape is shown in figure 3.1. 2. M ortality rates are very high at low levels of consum ption, but decline sharply as consumption increases, levelling ofF to approach asym ptotically some minimum at a relatively low level of income. Again we approxim ate it with a piece-wise linear function such as in figure 3.2. We suppose th at economic preferences shape the natality function except at very low levels of income while high m ortality rates depend primarily on a group’s inability to provide basic nutritional requirements. Because births depend upon economic choices, the kind of economic strategy th at characterizes each regime may yield widely differing rates of response and asym ptotic limits for th e sam e level of income in two different regimes. M any observations th at m ight appear to contradict the hypothesis that population Figure 3.2: The Death Rate Function a<£ ’ . flfiUSt 3 o ie c o u iii ]«"•»: •03fe«jMit<wt ot tne aeeiti rate tunci ion. 0.12 . ®*r, r f e i 0.00 tends to increase with income arc reconciled when we consider the different economic and sociological factors affecting the choice of having children. For instance, many studies of western economics in the 19th and 20th centuries showed that lower income families have higher fertility rates than higher income families. However, when one corrects the data for the families urban and rural experiences, one usually docs find that income and family size arc positively related. Agrarians find th at children can perform a useful economic function in addition to any utility th at procreation brings. This economic utility disappears in an urban setting, especially when authorities enforce child labor laws. Parents m ust bear the * * cost of providing a much higher degree of training in addition to the costs of physically sustaining a child with no economic benefits to offset it. Naturally urban dwellers tend to choose to have less children than rural parents.27 More pertinent to our model, hunter-gatherers, due to their nomadic life-style find 37See Colin Clark. 1977-2nd edition. Population Growth and Land Use. especially the chapter on "The Sociology of Reproduction" for a discussion of many studies on this issue. 39 the cost of having two small children nearly unbearable; consequently the natality rate for hunter-gatherers is much lower than for agrarians. While physical factors may account for part of the difference, it appears that most of it comes as a result of an economic choice made by parents. 3.4 Sw itching R egim es In studying the chronology of social groups, the rich diversity of experience and the frequency of cataclysmic change strikes the observer. Although most of the world’ s cultural groups have passed through or achieved a form of economic organization comparable lo the industrial revolution, the paths they have followed to reach that stage differ greatly. Few, if any, progressed in orderly fashion from hunting-gathering to village agriculture to a city state, through feudalism and so on. Anthropologists know of many instances where a group fluctuated between hunting-gathering and agriculture for several centuries. Empires rise and fall in such diverse places and times as the Assyrians of the second millcnium BC, the Homans in the first millcnium AD, and the Mayans in the second millcnium AD. Cultures such as that on Easter Island create lasting monuments and then disappear leaving behind a people who have no idea of their significance. Yet in some parts of the world such as the Amazon jungle and the Arctic polar region people cling to a lifestyle that may predate the dawn of history. To complete the model we must consider the cause and nature of regime switch ing. A necessary condition for a regime switch is an increase in population density. Each regime embodies a distinct form of political organization, and institutional and technological rigidity. If a switch occurs, it implies dissatisfaction on the part of some influential sub-group of the population. 40 Well within its viability interval, the regime works smoothly, at least for a segment of the population that can impose its will on the others. The system achieves a sort of dynamic status quo where peoples expectations and realizations at least roughly balance. But while the system is dynamic its structural rigidity imposes limits on its smooth functioning. As population density approaches these limits it operates less efficiently because of diminishing returns to some factor. By the construct of the model I have in mind diminishing returns occurring to one or more of the following factors: (l)Thc political-sociological infrastructure summed up as administrative technol ogy. We sketch the outline of how this occurs in the various regimes. In the hunting-gathering regime we consider the decision-making mechanisms of not just a single band, but of a landscape dotted with them. FYom this perspective the diffusion of authority characterizing the band works well when disgruntled individuals or groups can simply go off in different directions. But when population density increases to the point where bands come in frequent contact with one another, this safety valve ceases to exist. Ambushes and raids increase more than proportionally since no individual has the power to adjudicate disputes. Within a tribal society a group can evolve rules and procedures for the smooth functioning of agricultural systems with non-intensivc land use. A leader’s power depends on his prestige, not upon absolute authority.28 lie can successfully coordinate communal activities such as Held clearance or small irrigation projects when he knows the individuals. But when increasing population demands more ambitious projects that require greater man-power his effectiveness diminishes as the free rider problem emerges. 38See Netting 1072, "Sacred Power and Centralisation" for an account of the use and development of political authority in several agrarian societies characterised by sparse population density. 41 Systems of intensive agriculture have a chieftain who has the authority to coordi- natc larger group efforts and to distribute goods within a circumscribed area. But a hierarchy among such leaders must emerge before some group gains the authority to support the warriors and craftsmen that a city state demands. (2) Natural resources. Every regime is limited by natural resources of one kind or another according to its technology. Thus the prevalence of edible wild plants and game limited hunler-gathcrcrs, while the amount of arable land and access to water limited slash and burn agriculturalists. City states could only emerge in regions where with the use of capital, land-intensive agriculture could develop in a small enough region so that rulers could transport the surplus with relative case. (3) Capital. As capital-deepening proceeds, technological development can post pone the point at which diminishing returns set in. Each regime's infra-structure embodies a capability for creating knowledge and capital. One that encourages cap ital creation and technological advance can increase its viability interval, but, if as North believes, in the past an enormous gap between the private and social returns to inventions and innovation existed due to the form of property rights rulers permitted, the economy will reach this point sooner or later.3 9 In addition a regime's property rights may impose limits on the absolute amount of capital formation because of insufficient incentives for investment.30 When diminishing returns set in, the decline in per capita income creates dissat isfaction and some people begin to look for alternative solutions. In an egalitarian society such as hunting-gathering, the decision to seek change may arise through group consensus while in a highly stratified society the change may come from a disaffected but powerful minority. As per capita income falls, when a ruler tries to "N orth, op.cit, p.lG, "N orth, ibid. 42 redefine properly rights in an ciTort to maintain the standard of living to which he and his most powerful supporters arc accustomed, it may cause the revolt of others who perceive this action to be unfair.3 1 A desire for change and a switch of political leaders docs not guarantee a successful transition. The new leaders have bounded rationality and the new system they try to impose may or may not succeed. One would expect them to make many mistakes, and unless they hit upon a successful combination, a tumultous period would ensue. The resulting chaos could rip apart the social fabric, resulting in many deaths and/or migrations and reducing population to a level where the last regime or even a previous one became viable. In order for a successful transition to a higher regime to occur, the society must adopt a political structure that can coordinate increasing economic complexity. It must forge an ideology that at least eventually enlists more than just sullen obedience among members. It must initially increase investment far beyond the accustomed amount in order to put in place the new capital infra-structure and then maintain higher per capita levels of investment. But even this may not suffice. All socio-economic systems evolve institutions to cope with the uncertainty and variability of life. Regimes in their incipient stage arc particularly vulnerable to misfortune. Agriculturalists commonly hold emergency stores of grain to tide them over during bad years. The first agriculturalists would have little, if any, provision for this. A series of bad years for a group just beginning an agricultural system could have catastrophic consequences, sending the society tumbling back into the previous regime.3 3 3 1 North,/Wrf. p.116. 33 In this case the group would probably think they had made a mistake in switching to agriculture and revert instead to food gathering-but the overuse of the environment would have catastrophic consequences. 43 T he scope of investment th at a new regime m ust put in place also stretches re sources to the limit at the beginning. An incipient city state th a t depleted its agricul tural labor force to form labor gangs to construct irrigation projects, build temples and city walls, dig canals and lay out roads had little protection against crop failure. If th a t were to occur one can imagine subjects cither revolting against or deserting the city state since the alternative, starvation, could be no worse than what transpired out of those activities. Increasing population pressure will create the conditions for a change in regimes to occur, but whether a change takes place depends upon a num ber of individually unpredictable factors-thc adm inistrative skills of the new regime's elite, the regions natural resources, the resistance put up by the old regime and luck among others. The mechanism of change in this model then, is a population th a t increases within the viability intervals of the regime as long as income is sufficiently high. When a society approaches its upper population limit the possibility of a change occurs. Many factors lobby against a successful change so its probability is often small. If a successful change docs not occur, falling income due to diminishing returns causes population to decrease, sometimes gradually, sometimes catastrophically. In either case the process will repeat which insures th at the probability of an eventual change is a virtual certainty as long as the probability of change is positive.33 " W e can apply the analysis, however, to model a narrower geographic area in which a regime has a positive probability of entering a trapping set where the possibility of escape is aero. If it were not for the random element this model would be actually deterministic although we would continue to speak of probabilities to indicate the dependence upon initial conditions. 44 C hapter 4 TH E M ODEL We assume the existence of four regimes, huntcr-gathcrcrs, slash and burn horticultur- alists, intensive agriculturalists and the city slate, enfcli viable over some bounded pop ulation interval [A'e, A'«]. Essentially four behavioral relations describe each regime: (1) a production function, (2) a demographic function, (3) a capital accumulation function and (4) a savings and utility function. We separately analyze the contributions of two sectors to overall production. The production sector directly produces the goods and services th at make up private consumption. We use a typical neoclassical function Yp = F( A', L) where K and L represent capital and labor respectively, F( A', L) is homogeneous of degree one, and Fki Fl > 0 lim Fk = 0 f— o o lim Fl = 0 (— o o In all but the huntcr-gathcrcr regime we use the Cobb-Douglas production function YP = A K aLl~a (4.1) 45 with A and a parameters depending on the regime. In the huntcr-gatherer regime we assume the only input is labor, so Yp ** AL. However, these equations represent potential output rather than actual output in a manner 1 wilt explain. The administrative technology sector, represented by G(.Y, Km) where X is group population and l\m is infrastructure capital, embodies the cfliciency of the regime with respect to total population and infrastructure capital. The administrative sector promotes cfliciency by: 1. Socializing members to ensure they work towards a common goal and have the capability of making meaningful contributions. Today schools and universities, the police and the justice system perform many of these functions. The more complex a society becomes, the more strangers must interact and cooperate, increasing the need for this task. In huntcr-gatherer societies children accompany adults through practically all as pects of their lives, making their socialization and education follow as a m atter of course. This and the fact th at everyone knows everyone else precludes the need for other constraints. In contrast, the recent cold war thawing revealed that in East Ger many nearly 20 percent of the population participated to some degree in the secret police force, indicating how much effort an inefficient state may have to devote to policing alone. 2. Promoting, regulating and coordinating economic activities. The major benefit a large population bestows is the opportunity to specialize as Adam Smith pointed out over 200 years ago. The amount of specialization dictates the scope of these activities. 3. creating the infrastructural capital needed for major economic activities. This may include roads, airports, communication networks, acqueducts, irrigation chan- 46 ncls, etc. 4. alleviating diseconomies from overuse of resources. The administrative technology function, (7(-Y, Km) takes on values between zero and one, the number indicating the degree to which the administrative sector al lows the production sector to realize its potential. The aggregate group production function is Y = G(XJ<m)F(I<tL) (4.2) When G = 1 it implies that the regime's population and infrastructure capital permit the production sector to realize its entire potential, while G = 0.6, for example, indicates that coordination or overuse problems only allow the system to reach 60 percent of its productive potential. A regime usually undergoes a sharp transition between operating more or less effectively and operating inefficiently. Proceeding through more complex regimes one experiences a scries of quantum leaps in specialization; the fraction of the group involved in coordinating these activities increases. The group cannot phase in the administrative activities; when one of them is missing the whole system collapses. Inasmuch as the productive sector must support the administrative structure through its surplus, group population must reach a minimum level before the regime becomes feasible. Once the group reaches a minimal size and its infrastructure is in place, it can grow by phasing in expansions until the whole system becomes loo unwieldy for any one central authority to control it, or until resource limitations prevent further expansion. When the regime reaches the upper limit, overuse or administrative chaos cause a precipitous drop in eficiency due to a breakdown in the social contract. No longer 47 4. guaranteed the usual rewards since no person or group can enforce the accustomed system of distribution, members will not perform their customary tasks. Day, considering only labor, captured this idea through two specific mechanisms. First, he envisioned a single group that required a labor input of M for sustaining the infrastructure, but that would fall apart when the group size reached N. When group size G was such that M < G < N, the labor not involved in managerial activity, G — M , would work in a production sector. Using a power production function he set group income Y y f k(G - M p (N - G ) \ M < G < N \ 0 , t otherwise. K } where k is an arbitrary constant. He then assumed that as population increased other groups would form through fission, shedding and diffusion when spreading the population over one additional group would result in higher per capital income for all groups. The ”absorbing capacity1 * of the environment, however, imposed an upper limit on the maximum number of groups that could form under a specific regime. Thus for n groups total population is A — nG and if n is the maximum population the environment can absorb, the aggregate production function for all groups is F(A) = [ "k max “ M ^ N ~ - 'V 0 )** M < G < J1 (4 4) \ 0, otherwise. * 1 where the maximum is taken for n belonging to (1,2,3,..., if < A/W). In all but the last regime of this model, the absorbing capacity permitted a large number of groups to form. His assumption on splitting assured that the population of the individual groups would hover near the optimal G in the equation in terms of average product except for the first few groups. Consequently, diseconomies to the regime arise almost entirely from the factor (1 - 48 The two factors (A/n — M)0( 1 —a/tl)s are roughly analagous to the function G in my formulation. In attempting to match estimates of human population growth given by Dcevcy (1960), Day used values of S of 2,4,6 and 8 in four regimes which results in simple switches between regimes with no regression to previous regimes, because the value of the second factor becomes small well withing the viability interval (c. g. if A 0.511 and S — 6 then the factor is 1/64). Day's approach allows him to micromodcl the production of a single hunting band but focuses attention on environmental rather than infrastructural elements as the cause of regime breakdown. I prefer to reverse the focus of attention. I prescribe the function G(X, Km) where Km is the optimal amount of infrastructural capital relative to regime population X to behave as figure 4a shows, interpreting G to represent the institutional and environmental effect on production for a population encompassing many groups in which the predominant form of activity is of a specific kind, For purposes of clarity we can assume the groups live in a large bounded geographical area from which there is minimal migration (Australia for example). Since I intend to macro-model an entire region, the reader should not interpret a regime’ s name such as "intensive agriculture" to mean there are no huntcr*gatherers. Rather the name refers to the dominant form of economic activity. Even today hunter*, gatherers such as the !I<ung San of the Kalahari Desert flourish in regions inimicable to usual forms of work. As population increases, the function G reflects the overall efTect of increasing average group size on a single unit employing the dominant means of production, and the impact of total population on the environment. Rather than assuming that groups maintain an optimal level of population by diffusing to form new groups as !!) Figure 1.1: The M anagerial Function c 0.2 20 P o p u la tio n (in 1000a) Ait l l l u a t r a t l v a o aaap la a t 0 (K.K ) t a r a raoliaa w ith a v i a b i l i t y in c a r v a l a t (.0 0 0 t e 20.000 population increases, I describe, a fairly constant num ber of groups who increase in size more or less proportionally. I will describe the assum ptions behind the specification of G for each regime. The reader should note, however, th a t if G has the shape as shown in figure 4.1, it implies th a t the aggregate production function for a regime with viability interval [A'e,A 'u] has isoquants as shown in figure 4.2. In some test runs I will include a random factor 7?(l) to mimic th e effect of the w eather in year t on a society th a t relies heavily oil agriculture. In this case the aggregate production function is K (0 = R(t)G(X(i), I\m(t))F(K, L) (4.5) where the tim e argum ent t which can be attached to all variables is suppressed. T he am ount of labor each regime can bring to the productive sector will differ depending on the am ount of effort needed for adm inistration and on custom s. There* fore we will specify a param eter / denoting the fraction of potential labor going to the productive sector. Thus .10 Figure 1.2: The Isoquants for Capital aiul Labor 0.00 5.00 L(t) = LX(t) (4.6) The demographic function links birth and death rates to per capita income. W hile many factors affect birth and death rates, param eter values specific to a regime model social customs th a t arise as a result of the form of economic activity the group prac tices as, for example, the different birth rates experienced by village agrarians who may regard children as a future labor supply, and hunter-gatherers who emphasize procreative benefits. W ithin a specific socio-economic infrastructure it appears th a t a relationship exists between income or actual consumption and both birth and death rates. One can argue th a t in general a family will not choose to have children until they earn some minimum subsistence level* which we call the Easterlin threshhold. Once they reach th at level l Gasterlin (1073) discusses income's effect on a couple's decision to have children, while Schofield 51 Figure 1.3: Birth and Death Hates c. I f c b « C . P ir C»p. C ent. 10 T y p lctl B irth end o tt th r t t t t t i ■ (u n ctio n o f p a r e tp i ta conouaption. lb th ib n u p l t a i t » p p to « iM t* ly i . l l the propensity to have children increases rapidly up to a point after which it appears that furtlier increases in income have no positive effect and perhaps even a slightly negative effect. Death rales on the other hand rise greatly when income falls close to or below the subsistence level. A proverb from medieval Europe remarks that "the best prevention for m alaria is a full pot" indicating the greater susceptibility of people to disease during times of famine. 2 After some fairly low level of income, however, further increases have a very limited efTect on the death rate within the regime. Different regimes have different param eters due to the varying kinds of resources they can bring to bear on health problems. Figure 4.3 shows the ideal birth rate 6(c) and death rate d(c) versus per capita consumption th at we will model. Here e represents the Easterlin threshhold. In practice we will approxim ate those curves with the piecewise linear forms shown in figures 3.1 and 3.2. If we exclude the possibility of migration, given any set of equal time intervals indexed by t, we find the group’s population according to (1989), discusses its effects oil nuptiality 2 Braudel, 1981, op. cit, p, 81. 52 X(t + 1) = (1 + 6(c) - d(c))X(l) (4.7) In all our runs t will be one year except in the huntcr-gatherer regime where it is five years. We use a traditional capital accumulation function: K{t + 1) = (1 - 6)K(l) + Y(t) - C(l) (4.8) where Y, h \ and C arc capital, income and consumption respectively and S is depre ciation. Capital must be divided between the administrative and productive sector. Paralleling the assumption that a group must reach a minimum population for a regime to exist, so too must it have a minimum level of infrastructure capital. For instance, in order for a group to practice intensive agriculture it must dig an entire irrigation channel, not just half of it. Then as population increases the infrastructure requires a certain amount of additional capital in proportion to increases in popula tion. In its most general form we assume the optimal amount of infrastructure capital Km is K m = K mo+g(X - X e) (4.9) where g has domain [A'e, A'u] , </(•) > 0 on this interval, and /\„lo is the minimal amount of infrastructure capital. Usually g is just a linear transform A{X — A'e). I will assume that the elite manage to extract the optimal amount of capital, and so the productive sector appropriates the surplus K(t) — A'n,(0. To conclude the model we assume that all subjects of the regime maximize the same utility function u(c,s) th at describes their preferences between per capital con sumption and per capita (private) saving. Thus we have X{t) is anticipated private per capita savings a t time I, and, of course, c(f) = . The group's consumption then is r - m - r«) - c(fl - A *m (O V. u i n ^ (0 — vc(Or Y(f) Jrsm ax} (4*11) We choose to depict capital accumulating through individual decisions as opposed to having it respond to the rate of return on capital because the concept of maxi* mizing profits probably alludes to incentives characteristic of today’s society rather than those of hunlcr-gathcrcrs or agrarians. In the city stale it appears th at usually the elite imposed savings decisions on subjects and their reasons for savings would generally not involve maximizing efficiency. The earlier regimes probably describe as closely as any a period when Say’s dictum "Supply creates its own demand" actually applied. In the next chapters we consider several histories to dem onstrate the conditions under which the city state emerged . We assume the feasibility of four regimcs- hunter-gathcrers, slash and burn agriculturalists, intensive agriculturalists, and the city state, using these names to describe the predominant economic activity but not implying exclusive adherence to it. We assume we have an isolated region, perhaps an island, of 100,000 square miles (hence we ignore migration) with natural conditions amenable to the survival of these four regimes unless otherwise indicated. This means, for instance, that regions with fertile soil and water resources exist to make agriculture possible, and th at there is a river valley large enough to support a city state and provide transportation, given the creation of the necessary capital. 54 C hapter 5 TH E H U N T E R -G A T H E R E R R EG IM E In this chapter we will sketch the history of a hnnter-gatherer regime. Wc assume the only input is labor, giving the regime a particularly simple sLrucLurc which enables us to illustrate more clearly many of the themes th at recur through modeling with non-linear difference equations. In addition wc can focus 011 the kinds of assumptions wc make in constructing the overall model. Archaeological evidence indicates th at huntcr-gathcrcrs made tremendous techno logical advances during a period that lasted about 10,000 to 15,000 years preceding the advent of agrarianism. During that span we sec for the first time evidence of the exploitation of water-based resources, more varied stone tools, the invention of the bow and arrow, the use of dogs to hunt with, more advanced tem porary villages in terms of building materials, the development of grinders for food processing, etc.1 We will assume th at our huntcr-gathcrcrs have adopted any such technological achieve ments relevant to their environment. Our model begins at approximately 11,000 BP, although depending on geographical area we could move the tim e ahead by several thousand years. * Washburn and Lancaster, 1968, "The Evolution of Hunting", p.294. 55 Both hunting-gathering and nomadic herding can succeed as economic strategies in a sparsely populated area, but we wilt assume that the latter is not viable given local resources. Also, to avoid complications due to migration let us suppose that our population lives in a large isolated arca-we might imagine th at a large rem ote island contains our world of hunting-gathering tribes, and please don’t ask how they got there. Simplifications aside, wc want to develop realistic param eters so we arbitrarily assume th at this island contains 100,000 square miles and develop further values based on this. When faced with calculating the carrying capacity of the land under a huntcr- gatherer technology, the prevailing emotion among anthropologists is one of despair.3 Since typically, huntcr-gathcrcrs select favored foods first, and only gravitate to less favored foods as necessity dictates, scientists face great difficulties in establishing maximum density levels. However, wc face a simpler task. Undoubtedly the actual figures vary considerably from area to area, and for our model wc only need to es tablish consistent parameters within any physical constraints th at might exist. To do this wc look at existent data. Radcliflc- Brown gave estimates of the population density of Aborigines in several areas in Australia in 1930 which varied from one person per 7.8 square miles to one person per 38 square miles.3 Lee observed thcl the IKung San of the Kalahari desert gathered in base camps located near watcrholcs in groups of about 20 people and rarely exploited resources outside a six mile radius of the camps; travel time becomes a significant constraint outside of that area. This would give a figure of one person per 5 or 6 square miles.4 Both observers note that the regions could easily support ’ Lee and Devore, 1066, Discussions in Man the Hunter, p.94. 3Yengoyan, 1968, "Demological and Ecological Influences in Aboriginal Australian Marriage Sections" 4 Lee, 1068,"W hat Hunters Do for a Living", p.3I, 56 more people. Leakey, in observing the IKung San, estimated that each person needed about one square mile of land although he did not indicate how he arrived at this figure.5 Lacking any other guidance let us use this estimate for our the upper bound of our model. Having specified that our island contains 100,000 square miles, we will place an upper limit on population for this regime of 100,000 people. To assure a large enough breeding population, wc should have a binding lower limit of 500 people which is approximately the size of a band, but this represents a relatively small value so wc will just assume the viability interval of our regime ranges from zero to 100,000.° The working population of huntcr-gathcrcrs depends on the tasks involved. Usu ally adult men do hunting and adult women gather and prepare food, but exceptions to the rule exist. Children rarely perform significant economic duties. Although some groups cast out the aged,7 it appears that most did not adopt this practice. Lee ob served that the IKung San expect only married people to regularly provide food, that women generally enter the work force at 15 while men do so around 20, and that adults "retire” at G O and arc provided for. Since he estimated that about 60 per cent of the population contributed to food supplies 8 wc will use this figure for /, (the fraction of the population that belongs to the work force). Deciding what to classify as capital is difficult even in the best of circumstanccs-in the current context it is even more difficult to answer. Within a huntcr-gatherer so ciety one can plausibly argue that capital should include (1) manufactured weapons such as bows, arrows and knives since they increase hunting productivity, (2) dig “Leakey, 1078, People of the Lake,, p.110. “Some anthropologists regard 500 members as a "magic" number for a tribe. Although the constancy of this number is in doubt, it seems to be a good approximation of an average. See Spooner,Population Growth: Anthropological Implications.,p . 245 or Leakey 1978, op. cit. p .lll for a discussion, 7Coon, 1948,Heading* in General Anthropology,, p55. 8Lee, 1968, op, cit, p,36. 57 ging sticks, pottery, baskets, or other carrying utensils since they increase gathering productivity, (3) pottery, grinding stones and other cooking tools since they promote cooking efficiency, (4) transportation devices such as boats or sleds, and (5) huts, long houses and other living structures in seasonal villages. One might also regard the training of hunting dogs as a capital investm ent-huntcrs in Africa, Australia, and the Americas all domesticated and used dogs for hunting purposes. The potential efficiency that dogs bring to hunters is illustrated by Lee who reports th at a IKung Bushman with a trained pack of hunting dogs brought in 75 per cent of the m eat at one camp, while six other hunters without dogs combined to bring in only 25 per cent.0 However, in each case mentioned above except for boat construction and possibly dog training, the time spent in creating the goods docs not seem cxpecially long, and the life of capital is also relatively short. Hence, for first regime wc will assume the technology uses no capital. The production function for the conglomeration of hunting-gathering tribes then becomes Y = G(X)L (5.1) where G(A') is the "managerial" function. Its shape embodies the notion of dimin ishing returns as tribes begin to overuse their resources, and the (lack of) governing authority between the various tribes. A sparsely populated territory allows all tribes to exploit their region with a minimum of intergroup confrontation. For instance, the Iiazda, hunter-gathercrs in East Africa, made no effort to prevent an agrarian tribe, the Isanzu, from returning to the bush to exploit natural resources during times of famine early in this century, but the famine did not afTect the Iiazda who had multiple °Washburn and Lancaster, 19GB, "The Evolution of Hunting.", p.294-295. 58 resources to exploit and who were not in danger of overusing their territory.1 0 As density increases, however, tribal conflicts inevitably arise. In the past frequent border skirmishes and occasional raids probably occurred regularly, and at some point most tribal members must have felt constrained to conduct economic activities within a circumscribed territory, especially if they could not migrate from the area. In this way tribal boundaries emerged and the process of territorial overexploitation leading to diminishing returns began. Customarily, huntcr-gathcrcrs allow everyone within their tribe to hunt and gather as they wish, and no mechanisms exist for preserving favored foods. Increasing pop ulation density first impacts them by requiring members to walk further to gather favored foods, or to use inferior ones that grow nearer. This in itself would imply a decline in average product, but initially they probably fell as great an impact from intertribal violence and a consequent higher incidence of death. We need to consider closely the ramifications of this crowding. Lacking recent examples of warfare between huntcr-gathcrcrs stemming from increasing population density, we can only speculate on the way in which they historically reacted. Given the behavior of present day tribes though, it seems reasonable to suppose that some tribes would react aggressively while others passively. Initially, those that acted aggressively might gain territory at the expense of more passive tribes which would allow them to grow in numbers. Eventually such a tribes’s population would increase to the point where a split would occur since the social infra-structure associated with hunter-gatherers limits tribal size in both numbers and physical extension. If this process were to continue, eventually the area would be populated exclusively by aggressive tribes who would then either have to eliminate all members of another wWood, 1968, "An Introduction to llasda Ecology", p. 54. 59 tribe or learn to coexist with them. Culturally, hunter-gathercrs lack the social hierarchy necessary to sustain anything resembling a tribal army with the capability of systematically eliminating another group. To do this they would need to produce a food surplus that could support a professional warrior class. While their economic productivity makes this possible, no one has the authority to compel members to contribute to such an endeavor. The advent of community supported armies docs not secin to occur until a society’s culture readies a level of complexity associated with village agrarianism.1 1 Given the improbability of this, wc could expect that many if not most groups facing population pressure learned to coexist with their neighbors. This is not to say that intci-lribal conflicts did not occur—an abundance of evi dence suggests that a major cause of death in prehistoric cultures came from social violence.1 3 But intcr-tribal violence rarely went beyond the level of skirmishes or raids that left cadi tribe intact as a functioning unit. If, in fact, tribes respected general ized boundaries, and if they no longer could resolve increasing population problems through migration, then they had to more fully exploit their territory which inevitably led to a state where diminishing returns set in. In many cases one would expect pop ulation to increase to a level that compelled members to search for an alternative solution such as agriculture if the environment permitted. In other cases tribal vio lence and poorer health due to lower incomes might lead to a steady state of the sort that Malthus proposed. In some probably rare cases environmental constraints may u Boserup, 1005, makes the point that a low density tribe may liara that state perpetuated by losing members to more populous tribes who engage in slave raids to acquire workers for their less desirable jobs. She mentions the Bemba warrior who proudly proclaimed that "they did not know how to hoe for their only trade was war." (p.G7) See also Lathrup's (1008) description of hunter* gatherers in the upper riverine valleys of the Amazon basin who avoided the more easily exploitable flood plain environment because of their fear of the agrarian tribes who lived there who captured them, sacrificing some, enslaving others and even eating some. l , Dunn, 1908, "Epidemological Factors: Health and Diseas in Hunter-Gatherers” , p. 225. (in Figure 5 .1: The Managerial Function o.t t.i i.s 40 < 0 M ovei t i n M M n t u l Function SIX) i l t i a * 0.1 * ta» a o a rla l Function* 0 |n ) fo r v alu o i of a o f 0.0! 0.1 , and 0.3 have led to a state where members reacted so violently that a catastrophic drop in population occurred. These observations lead us to formulate a managerial function as shown in figure 5a where the efficiency of the regime remains relatively high over an interval (of population) encompassing most of the viability interval of its regime, but dropping drastically as population approaches the upper limit. A function th at has this general form is C(.V) = (l + 1§ ) » ( , - I£ j ) ' (5.2) 0 < X < 100, with .V given in thousands, 0 < a < 1 and the closer a is to zero the steeper the final descent becomes. (See figure 5.1 for examples using different values of a, The value of a is instrumental in recreating some of the scenarios we have described above.) To complete the model we m ust specify birth and death rates for our popula tion based on per capita consumption. Given the controversy surrounding the 1990 61 estimates of the United States* population, one can imagine the difficulties associ- atcd with estimating prehistoric population-and to read into these, estimates of both fertility and mortality, seems fraught with peril. Traditionally prehistoric demographers must estimate population by formulating a credible ratio of the number of people per some object, count the number of such objects in some locality, estimate the number of objects in a larger area, and project that ratio over the larger area they wish to estimate. Turner and Lofgrcn illustrated the use of the technique when they estimated the population trends of a branch of the Anasazi Indians in the southwestern United States by "calculating the ratio of the volume capacity of serving bowls and cooking jars used at the household level."1 3 While one should regard the actual figures derived from these exercises with skepti cism, the information yielded about relative increases and decreases over time may be quite accurate. One must keep in mind the implication of compounded growth rates over long periods of time. The reader may use a calculator to verify for himself that a one per cent growth rate, quite small by today’s standards, over 1000 years translates into a 20,959-fold increase! A growth rate of 0.1 per cent will cause a 2.7 fold increase, while a growth rate of 0.3 per cent results in nearly a 20 fold increase. Using estimates for relative changes in population wc can plausibly conjecture that during any reasonably long period (say 100 years) and with any reasonably large population (such as our island), average growth rates would not have varied by more than 0.3 per cent under normal circumstances. However given the fragmentary state of our knowledge of those times, we will not try to press our luck by estimating the birth and death rates that yield such values. So in the huntcr-gatherer regime we will only relate net population ,3Willigau and Lynch, 1982, Sources and Methods of Historical Demography., p,41. 62 growth to per capita consumption. We will note, however, for future reference that we should model hunter-gathercrs as having lower birth and death rates and more stable rates of growth than agrarian groups. Huntcr-gathcrcrs have lower death rates because: 1. A lower population density makes them less susceptible to contagious diseases. 2. Their more balanced diet makes them relatively more healthy. 3. The multiple food sources that they possess makes them more immune to famines.1 4 Hunter-gathercrs have lower birth rates because: 1. They do not derive economic benefits from having children—in almost all cases chil dren do not perform significant economic duties. In fact, they represent an economic burden to all such societies except those that do not have to engage in frequent trav eling due to fortuitous local circumstances.1 6 Lee points out that for the IKung San women, life’s major burden is carrying their children under the age of four. Women, who do all the gathering which accounts for well over half the food production, must carry young children on these excursions. He estimates that a woman carries her child a distance of 4,900 miles during the first four years of its life.1 6 Having two children under the age of four represents such a considerable burden that the people have a saying that * * a woman who gives birth to one oflf-spring after another has a permanent backache.” Not surprisingly, women usually manage to space their live births at least four years apart. This contrasts with agrarian societies who M See Dunn, 1068, "Epidcmilogical Factors: Health and Disease in Huuter-gatherers," for a general discussion of the health of huntcr-galhcrers. Also see Lee and Devore, Discussions in Man the Hunter.. p,337, and Woodburn, 1968, "An Introduction to Hazda Ecology," for assess ments of the health of the IKung San and the Iiazda 18The Northwest Coast Indians of North America are an example of hunter-gatherers who estab lished permanent settlements due to the richness of marine natural resources in their area. See Fferb, 1978, Man’s Rise to Civilisation., p. 140-162 for an account. wLee, 1978, "Sedentary Life among the IKung San." 63 b can use children to watch livestock and perform a host of other chores.1 7 2. Physiological factors brought on by the hunter-gatherers life style also seem to affect fertility. Evidence indicates that the amount of walking typically undergone by IKung women restricts menstruation rates. In addition, lacking milk producing animals, women often breast feed their children up to the age of four which also seems to retard the menstruation cycle.1 8 We should comment on the feasibility of the relationship wc have constructed between per capita income and population growth in the case of hunter-gathcrers. As mentioned above the difference between an 0.1 per cent growth rate and an 0.3 per cent growth rate can be quite considerable, even over a period of 100 years (a tribe > of 500 becomes 553 at the former rate and 675 at the latter). It seems doubtful that a tribe would sense any difference between the two rates over the short run. A study of the growth rates of several tribes would probably reveal a distribution of growth ratcs-some positive, some negative but averaging a low positive number. The figure in our model represents such an average. Certainly other important factors affect population, but none seem to have the global impact that per capita consumption does. Recalling that wc define income in a way that reflects leisure time, some reasons to believe a positive relationship between it and population growth arc: 1. The greater distance that women need to travel in order to gather edible plants when income falls which increases the cost of having children under four. 2. A decrease in fertility that occurs with malnutrition. Although hunter-gatherers suffer from malnutrition far less than agricultural peoples, nevertheless under extreme population pressure this may be a factor. I7Lee and Devore in Man the Hunter. l8Lee and IDevore," Problems in the Study of Ilunter-Gatherers” , p .ll, and Lee, 1978, op, cit, p.340. Figure 5.2: The Growth Hate of Iluntor-Gatherers 61 l . C < l . t : C> £ 0.6 0.91 C . » ' Tb* growth rot* of buntor gatboror* as a function o f par capita iacoaa. The growth ia fo r a fiwa poor period 3. The delay in reaching puberty of children when the diet becomes restricted. Even if no malnutrition takes place, studies show that obese children reach puberty earlier than lean children.1 9 4. We associate increasing population density with a lower per capita income. When population beccunes more dense more deaths from intertribal skirmishes occur. While we would not expect any tribe to eliminate another one, this could represent a major cause of death. The graph of the demographic function wc will use is shown in figure 5.2. We specify birth and death rates for periods of five years. The rationale for its shape comes from the belief that at extreme levels of deprivation (c below 0.3) the death rate increases sharply. However this rarely occurs with hunter-gatherers. Usually birth rates will increase modestly but positively with ease in gathering food up to a maximum birth rate of one per cent over 5 years. For the fraction of the work force engaged in labor we will use / = 0.6 based on Lee’s estimate that about 60 percent of the IKung San’s population is actively l9Katz. 1978, "Biological Factors in Population Control”, p. 357. 65 engaged in hunting and foraging.30 Having established our parameters and the structure of the huntcr-gatherer regime, let’s observe a few histories before wc link it up with the next regime. First we will consider the case where a Malthusian steady state develops. In this case wc might imagine a region comparatively lacking in exploitable resources so that diminishing returns set in more quickly than in a more generously endowed area. Tribal groups would have to extend their exploitable areas which would involve a great deal of travelling; thus strong economic reasons for limiting the number of children exist. One would guess that many hunting-gathering societies that survived into this century may well have lived in this sort of state. The IKung San who survive in the seemingly inhospitable Kalahari desert and some Aborigine tribes in the greater deserts of Australia may well belong to this group. Lee in writing about the IKung San notes that during birth the women take charge of the process and tell the men of the outcome afterwards. In many cases one senses that the men doubted the women's account that a birth was stillborn, but nevertheless accepted it.3 1 Given the economic burden that children impose on IKung San women we can believe that they would have reason to practice birth control in this way, but it is significant that they also have the opportunity to do so. By dioosing a value of a wc can depict this history. In figure 5.3 we show the trajectories for income and population of a hunter-gathercr population that initially numbers 5000. Note that it takes them nearly 2000 years to readi the steady state of about 86,000. This value, lying below the carrying capacity of 100,000, in our curreut interpretation re sults from cultural constraints arising from economic limitations rather than physical 30Lee observed that adults over 00 (about 10 percent of the population) and unmarried children (girls under 15 and boys under 20 or 25) did not work. 3 1 Lee,1968, op. cit. f> fi Figure 5.3: Huntcr-Gathercrs Rcadi a Steady State 4 f t . f r * C l Population 80 40 20 ■ Y e a r s 500 1000 1500 2000 2500 constraints. Anthropologists who have sought an explanation for the fact that this century’ s hunter-gathercrs seem to have readied a state of equilibrium well below the carrying capacity of the land22, while historically at least, some hunlcr-gntlicrcrs evidently did not would do well to examine the case of harvesting in the two cases. Note also that over time per capita income seems to drop at least by the year 500 (to see this consider the relative heights of the two curves in figure 5.3) although population continues to increase for nearly 1500 years. The fact that the population reaches a steady state before reaching the carrying capacity of the environment indicates that perhaps these people experienced relatively few intertribal conflicts, a fact that seems consistent with many hunter-gatherers we know of in such regions in this century. In another history we consider a relatively lush region for hunting-gathering but unsuitable for agriculture 23 Since tribes can more efficiently exploit resources they eventually become more crowded. Because of the nearer proximity they have to one 33Lee and Devore, 1968,. op. cit. 3aSome highland jungle areas in the Amazon basin or the Yucatan, for instance C u Figure 5.4: A Group Fluctuates Between Hunter-Gatherer and Horticulture v* " 1 ^ teCCs) :oo+ A 60" 60- -YmWMVfWf 500 1000 1500 2000 2500 3‘ another increased population growth leads to more intertribal violence. In this see* nario, growth occurs until it reaches some critical number at which time catastrophe occurs (either due to overexploitation or more likely widespread tribal violence). With jumping to a higher regime precluded, this process endlessly repeats itself. In figure 5.4 we recreate the population and income of such a history. Note that the catastro phe in population is always precipitated by a drastic fall in income. In this case we used a value of 0.05 for a. A possible explanation for the state of equilibrium that most of this century’s huntcr-gathcrers seem to have reached lies in comparing these two cases. This century’ s hunter-gathcrers, of course, represent an abnormal sample of the class of hunting-gathering societies throughout history by virtue of having successfully adapted culturally to this state. Past such groups may have inadvertently had higher birth rates that continually pushed them into a situation where they either clashed or adapted to a new regime. In fact, it is unlikely that the cycle of growth and collapse depicted by the last scenario occurs endlessly. One history in which we have considerable interest occurs when a hunter-gatherer regime "adapts” to increasing population density by adopting agriculture.' In the next chapter we discuss the motivation and barriers to such a switch and then model it under different assumptions. 69 Chapter 6 THE GREAT AGRICULTURAL REVO LUTIO N OR THE FIR ST PO PULA TIO N CRISIS? In our choice of endogenous variables we have tacitly accepted the Boscrup-Cohen thesis. In brief it contends that humans adopted agriculture in response to increasing population pressure, a development that required a more land-intensive economic ' strategy. Anthropologists had traditionally conceived of agriculture as a technological break through that subsequently spread throughout the Old World via colonization, con quest or imitation. Henri Frankfort (1957) expressed this view writing: It is clear then that the diffusion of agriculture consisted not merely in spreading the knowledge of cmmer and barley but in a simultaneous dif fusion of the odd and complex harvesting tool, first used as far as we know by the Natufians. Radiating from the near East, the new knowledge spread in widening circles reaching the shores of the Baltic and the North Sea about 2500 BC.1 1 Ilenri Frankfort, 1951, The Birth o f Civilisation in the Near East,, p. 31. 70 A later school of thought attributed its rise to some outside shock th at upset the usual foraging patterns. Flannnery, for instance, focused attention on the economic choice agriculture presented to Stone Age peoples and outlined how a more favorable mutation of maize might lead to the adoption of agriculture.2 In these analyses, archaeologists attem pted to explain the "stylized fact” that agriculture and a (relative) population explosion occurcd simultaneously in geological time; both assumed the former "advance" led to the latter. Underlying the analyses was a Malthusian view of population growth within a given technology. Boscrup’s hypothesis reverses the direction of causality. She holds th at humans understood agricultural technology well before they adopted it; they chose not to use it because liunting-galhcring was a more efficient economic system until overcrowding began to exhaust foragcablc resources. Cohen theorized that luinter-gathcrer clans could alleviate overcrowding by the simple expedient of sending surplus population ofT to colonize the frontier until about 10,000 years ago when most of the easily exploitable areas became occupied. After that it was inevitable that humans would cither limit population through custom or warfare, or adopt a more land-intensive economic strategy. Two relevant observations in the last 30 years tend to support their view. More intensive field studies have revealed that huntcr-gathercrs do not lead the "nasty, brutish lives" so often attributed to them. Lee and Devore (1968) in a definitive study of the IKung San hunter-gatherers of the arid Kalahari Desert of South Africa found that they obtained well-balanced, healthful diets with a work week of about 12 to 19 hours for a labor force composed of only 60% of their total population (see the previous chapter). Approximately 10% of 3K. V. Flannery, 1968, "Archaeological Systems Theory and Early Mesoamerica" in Meggers, ed., Anthropological Archaeology in the Americaa, p. 67-86. 71 its population was over G O , comparing favorably with primitive agricultural peoples. Studies of other foragers, including the Hazda in East Africa and the Bambuti pygmys of the Congo, affirm the pattern of balanced diet and good health with a short work week.3 lluntcr-gathcrcrs also seem to resist epidemics and famines far more readily than agriculturalists. Their peripatetic life-style enables them to avoid the sanitation problems and the invasion by pests that agrarians must endure, and their need to live in smaller groups makes transmission of disease less likely. The fact that their diet conics from a multitude of sources means that the temporal scarcity of one is an inconvenience, not the disaster it is for agrarians when, say their wheat crop fails. A review of our knowledge of huntcr-gathcrcrs of this century indicates that all understood basic agricultural principles. Some groups such as the Indians of the Great Basin encouraged the growth of their more important food crops by damming and diverting streams in allegiance to some primitive form of irrigation. Of course, this docs not prove that the Imntcr-galhcrcrs of the prc-historic past also were capable of using these techniques; perhaps twentieth century foragers learned about them in passing from neighboring agrarians, but this seems particularly unlikely given their stunning accomplishments in other areas. As Clark remarks about the Australian Aborigines, "study by modern ethologists has shown that they possess a remarkably complete knowledge of their environment.'1 Or consider the following description a Cnhuilla Indian in the 1920s gave to a researcher interested in preserving that disappearing culture: The old men used to study the stars very carefully and in this way could 3See Woodburne, 1968, for a study of the Hazda. The Harvard Research Group has conducted several recent studies in the Congo. See Reader, 1968, for a general description of these studies. ^Grahame Clark and Stuart Piggott, 1965, Prehistoric Societies, 72 tell when each season began. They would meet in the ceremonial house and argue about the lime certain stars would appear, and would often gamble about it. This was a very important matter, for upon the ap pearance of certain stars depended the season of the crops. After several nights of careful watching, when a certain star finally appeared, the old men would rush out, cry and shout, and often dance. In the spring their gaiety was especially pronounced, for.., they could now find certain plants ' in the mountains. They never went to the mountains until they saw a cer tain star, for they know they would not find food there previously.5 It is difficult to believe that people able to connect events in their ecological zone to events in the sky with such precision would be unable to deduce the principles of basic agriculture, especially when their lives depended upon it and when they must have devoted a great deal of lime to observing and experimenting with their environment. Some scholars have criticized Boscrup’ s view on the basis that most hunter- gatherers that have been studied, stabilized their population well below the carrying capacity of the environment, therefore why shouldn't we expect prehistoric groups to do the same; or paradoxically, given the imperceptibly low growth rates it would take to populate the world over a period of 10,000 years, overcrowding should have taken place far sooner that the theory purports it to have occurred. The first view seems particularly untenable. Its proponents point to the mecha nisms in hunter-gathcrcr culture that lower the birth rate that we alluded to in the previous chapter. For instance, Susman (1972) estimates that women in the Pleis tocene would have been fertile for about 1 G years (from age 16 until death). Given 6Timot|iy Ferris, 1088, Coming of Age in the Milky IFoy. p. 21. 73 a spacing of four or more years between births lie calculated a woman would have about four live births in her lifetime. Using an estimate of a 50 percent rate of infant mortality, he concluded that a zero or perhaps a very slightly positive growth rate might result. The argument falters for two reasons. First, it is undeniable that the rate was positive from perhaps 100,000 BP to 10,000 BP or else hominids would not have fanned out of Africa to populate almost all the rest of the world. Second, the figures are, of course, estimates. Any estimate, in order to have any credibility, would have to show an approximate growth rate of zero percent. Suppose a generation lasts 20 years; then in 10,000 years there arc 500 generations. If we alter Sussman’ s figures by assuming that of females born alive only 49.9 percent die before reaching child bearing age instead of 50 percent, the average female reaching child* bearing age will bear 2.004 females instead of just two, and population will nearly triple (a 2.7 fold increase) over this period. The zero percent growth rate may reinforce one’s confidence in the approximate accuracy of the intermediate figures (used to arrive at zero), but there is no relevance in reversing the direction of implication. The second position requires more careful examination. As our calculations have shown, a growth rate of only 0.1 percent per year over 10,000 years causes an increase of 21,917-fold. This suggests that indeed cither cultural or environmental influences must have reared their heads to prevent such drastic increases. We do know, however, a small increase occurred. In the previous chapter we have given an economic explanation of why a slowdown might occur as population density increases; an economic inclination to reduce the number of births builds as the utility of a child decreases. This can explain the apparent wide-spread practice of birth control via abortion or infanticide during the 74 Pleistocencc. 0 When frontiers arc available, surplus population simply moves into the unexploitcd territory. However, unexploitcd territories only exist on the boundaries of human occupation. For a circle, as the radius increases, circumference increases proportionally, but area increases with the square of the radius. If we liken area to population and circumference to frontiers, we sec that as population increases, the fraction of total population that has a frontier available decreases. Those groups without a frontier will begin to experience slower growth rates—some that continue to grow might try to expand outward slightly at the expense of their neighbors thus setting off a chain reaction that nudges the radius of human occupation outward somewhat—but the net result is a much slower growth rate for the vast majority of humanity. The groups on the frontier, however, can continue to grow, their size unchecked by economic constraints. The apparently rapid rate at which the Americas became populated after its invasion in contrast to a slower rale for Europe, Asia and Africa at the same time tends to support this view. The presence of bottlenecks for expansion such as the East Indian Archipelago or the Bering Strait would only reinforce this trend. When all habitable areas finally become filled, overall population growth would slow to a snail's pace. If all groups fell to zero population growth we would have achieved a steady state of hunter-gatlierers. But we know that this did not occur, and why should it since each group has its own tastes and cultural practices. Suppose, for instance, one group out of 20,000 (all with the same population) has a propensity to grow at say 0.5 percent per annum. In 1,000 years they would increase 14G.5 fold meaning that flDirdsell, 1968, estimates that anywhere from 15 to 50 percent of all live births were eliminated by systematic infanticide during the Pleistocene. 75 they would now comprise 0.7 percent of the world’s population (up from 0.005 percent 1,000 years earlier.) If this trend continued for another 1,000 years they would now constitute over 50 percent of humankind. I am not suggesting this as a likely scenario in its spccifics-thc point is that if any groups have a propensity to grow, it should ultimately increase population over all since a group with a negative birth rate would soon be replaced by several that had at least a zero percent rate. Thus a median ism exists that would tend to increase population (albeit much more slowly) even as crowding occurs and per capita incomes fall. Suppose now that population does increase to the point where from a rational reckoning of costs and benefits, we would expect a huntcr-gathcrcr group to adopt agriculture. The transition is more problematic than the neoclassical model would have us believe. FVom a non-cconomic perspective a transition requires a change in group organi* zation and values. As hunlcr-gathcrcrs they adopted a basically democratic form of existence where cadi family provided for itself except, perhaps, when men brought back meat from the hunt, and some form of ritual "gift-giving" evolved that dictated its distribution. As agrarians, however, they require cooperation over a m udi wider sphere. They must burn and clear fields and perhaps plant them together; they must • ■ decide how to divide the fruits of their labor. Some form of leadership must emerge to guarantee that this occurs smoothly. As huntcr^gathcrers, when bickering threatened to become disruptive, disputants simply joined different bands the next season. As agrarians this expedient may be less desirable because ownership rights over tribal territories may become involved. Again, leadership must emerge. Finally, as hunter- gatherers they worked for immediate rewards; as agrarians they had to learn to work 76 for deferred gratification. Even if the group overcomes these problems, economic barriers may exist. To illustrate this consider the following hypothetical transition. In this analysis we will tend to identify capital with deferred consumption and labor with immediate con sumption, so suppose that hunting-gathering consists entirely of labor and yields an immediate product, while agriculture uses the capital inputs of field preparation, the digging of an irrigation channel and the labor inputs of seeding and harvesting. Let us for the time being measure capital and tabor simply by the number of hours spent in the activity. The hunlcr-gathcrcr isoquants will simply be vertical lines as in figure 6.1a, where the numbers refer to output. Note that the disproportionality of the numbers indicates that diminishing returns set in to hunting-gathering as the group begins to overuse its territory. The isoquants for agricultural production will appear as in figure G.lb where C0 represents the minimum input from capital necessary for any agriculture production to lake place (e.g. completing the irrigation channel). Once the channel is completed, the irrigated land will need additional fixed inputs of capital and labor for preparing, planting and harvesting. The numbers on the isoquants also represent production. Superimpose the two isoquant maps on cadi other and draw the family of budget lines in the first quadrant L + C — K 0 where K 0 is the number of working hours the group has available to allot between capital and labor (recall both arc measure in hours). Now eliminate the less efficient isoquants (for example, in figure 6.1c we would eliminate the agricultural isoquant of 100 since by devoting all of the hours to labor in a hunting-gathering mode we could receive an output of 260 as compared to the agricultural output of 100.) The map we get would look something like figure 6.Id. In that figure we see that with budget line CC* the group would continue as hunter-gatherers, but that 11 Figure 6.1: Au Isoquant Analysis of t he Transition from Hunting*Gaihering to Agri* culture n « . risuct o .’ ‘ * p - v r — 5.00 C A P r ' i JTni ' " rteooE' w 1 ‘ T H E IS O O imhT S roo H U N T 1 m 6*6#Tm £ B 1 1 < 0 T H E lS O O U A H T S T O O A fiQ ieU L T uSE ' ID S 200 2S0 280 ■ • 100 1 • ■ . ■ c . ------------------- o . " • - - - * ■ * * , . • • 1 a oo --- 1 1 1 1 1 1 • • " 1 • • j . 0 .0 3 ia b o b S . 0 0 0.00 5 .0 0 THE POOBLEIl fir TOM SlTtON 3 3 0 too 1 1 * 8 0 # - LfiB O : 78 agriculture becomes more efficient in terms of group effort at the 350 level (see the constraint line B B n); but wc really should not use a "budget constraint” based on the number of hours to pick a method—rather the budget constraint should reflect the relative costs of capital and labor. Since capital in this example produces mostly deferred consumption, labor should have a greater value. As diminishing returns set in the group’s per capita incomes fall, perhaps moving down to subsistence levels. Consequently, it will value deferred consumption even less than before and the budget constraint line becomes flatter. In figure 6.Id the line flattens to B'B so the group chooses to engage in hunting-gathering, producing an output of 330 when by shifting to agriculture they could produce 350. If this trend of increasing population causing a greater valuation of immediate consumption continues until incomes fall below subsistence levels, a famine or epi demic might occur, causing population to drop drastically, subsequently allowing the group to resume its former luintcr-gatlicrcr existence. Alternatively, the group might try to take over another band's territory, precipitating a scries of skirmishes that also result in a large drop in population. In economic terms the neoclassical model fails because production does not vary continuously. In the previous chapter (figure 5.4), wc modeled just such a time path. The production isoquants for the first time path wc developed in that chapter (figure 5.3 presumably taking place in the Australian desert) might appear as in figure 6.2. In this diagram the number of hours needed to invest in capital, (70, in order to begin agriculture is beyond the number the maximum population sustainable through hunting-gathering can supply. The group, recognizing this consciously or unconsciously, adopts practices that stabilize population below the carrying capacity of the land. Figure G.2: Isoquants for a group in the Australian Desert. 5.00 Capt **- ] I 1 I I I I " I I 1 I " I I I I 1 " T " ' I I I I I T * % fi 8u»e **2 ial . . . . I s o q u a n t s l o r h u n t i n g - g a t h e r i n g a n d a g r i c u l t u r e i n t n e a u s t r a l t d e s e r t . t a n 10 ( a g r ) * ‘Vqp 150 175 180 175 0.00 0.00 I - J - L. \ \ h u n t i n g a n d >. \ q a t h ( r i n g I _ l _ l _ \ I i - J . . . \ \ . _ i , i - i - J _ J L o L a b o r i- J 5.00 80 We know th at most humans ultimately did switch to agriculture. How might this switch have occurred? Two possible scenarios come to mind. In the first, the group, cognizant of the technology of agriculture, starts to phase it in as per capita income from hunting-gathering falls due to overcrowding. Perhaps at first they stim ulate next years * s wild crop of a particularly favored food by deliberately planting a few seeds in addition to harvesting it. The group has some highly regarded people who can move easily into the role of a headsman who can persuade them to lake common action and impose on them a consensus on how they ought to divide the work and distribute the product. T he transition is smooth in spite of the fact th at per capita income has fallen. FVom our point of view, at the time that the administrative function for hunting-gathering, Ghg, begins to fall, the administrative function for slash and burn agriculture, Gta, is fairly close to perfect efficiency. (Sec figure 6.3a). The administrative functions do not give total product, but for the sake of exposition we suppose they arc proportional.) Once the group adopts agriculture and becomes more sedentary, population growth will accelerate, resulting in a perm anent shift to agriculture. Day models this kind of transition between Hunting and Collecting and Village Agriculture in " Economic Development in the Long Run". In the second scenario, a successful transition is problematic because no one in the group has the stature to organize communal action. FVom our point of view, (See fig ure 6.3b) the administrative functions for the two regimes intersect at a relatively low level, implying th at at the time of transition neither system is especially effective; con sequently a catastrophic decline might occur returning the group to hunter-gatherer status, or if population can inch upward to a point where adm inistration becomes more efficient, a successful switch might take place. The inclusion of capital adds complexity to the jum ps. A further difficulty in 81 Figure G ..‘l: The Managerial Functions and the Transition between H unter-G athering and A grirulture 1.50 HGURE a At the.point of transition T the agricultural technology function tor agriculture is relatively, high. (Compare uith figure 56) Population (in 100.000s 0.00 0.00 2.00 1.50 » I t or T H E sa Population (in 100.000s 0.00 0.00 82 transition is the fact th at much of the group’s effort m ust go towards creating the minimum amount of infra-structure or production capital. After becoming established the group need only replace depreciated capital, but at the beginning it m ust create all of it. To the degree to which this takes away from present consumption, population may fall, once again making feasible a new huntcr-gathcrcr regime. Agrarians typically hold a surplus of foodstufls to protect against crop failure. A group adopting agriculture might postpone or take several years building up a surplus, leaving them particularly vulnerable during the first years of transition. Below wc show several computer histories th at illustrate the barriers to transition. In the first, (sec figures 6.4a and 6.4b) the group as huntcr-gathcrers grows a t first quickly and then more slowly until it readies the thrcshhold of the two regimes. The transition takes place smoothly although agriculture docs not restore the group’s former level of per capita income. To sec this observe in figure 6.4b th at when the transition occurs (sec the jum p in capital), income falls. Income in the agricultural regime includes capital, so per capita consumption is even less than the diagrams imply. Once the transition is made the sedentary life-style perm its population to grow more rapidly and it accelerates in the new regime. In both regimes, however, zero population growth is associated with the same pcr-capita consumption (0.45). This history used the adm inistrative function for agriculture th at is shown in figure 6.3a. Compare that history with the portrayal in the previous chapter (figures 5.4) where a successful transition never occurs. The administrative tedmology function in this history is similar to the one portrayed in figure 6.3b. Let us examine the role of capital. In the model wc assume that capital, /f, produced a t time t is used for production in time t + 1. We have assumed hunter- 83 Figtm. (i.-l. A Smootli Transition between Hunting-Gnllieriiig and A griculture H U M T IH B - C U L a. ccj Population regime transition point 0.00 0.00 H00 FIGURE b 8E :T U E E §,1 h85i! HG-SIHiiiSyHO A H D opulation u o Income HO (Income if less in sgriculturei 0 .0 0 ^ - 260.00 84 *• la gatherers use no capital, hence a t the time of the first jum p into agriculture K — 0 and therefore Y becomes zero, meaning no successful jum p will ever take place. We remedy this by assuming hunter-gatherers have developed a minimal am ount of capital which they must supplement during the first period as agriculturalists in order to reach the optimum. (This accounts for the fact th a t in the history depicted in 6.4 capital is not zero before the jum p.) One might picture this capital as the first steps a foraging people take to adopt agriculture, such as the spreading of wild seeds of favored foods, or perhaps the rudimentary attem pts al irrigation engaged in by the Great Basin Indians alluded to earlier. At any rate by choosing different levels of hunting-gathering capital that agricul turalists have to build on, wc can sec the role capital may play in the transition. The next computer histories portray a group that should adopt agriculture when popu lation reaches aproximatcly 82,000. The optimal amount of capital a t this point is approximately 6,400 of which one-third depreciates each year. Wc do several runs giving them transitional amounts of capital K0 ranging from 2,900 to 4,000. (Initial population is 7,000 in all cases). W ith K 0 — 4000 the transition takes place without a hitch (see figure 6.6b). For A'0 taking on values between 2,950 and 4,000, a successful transition takes place usually after a scries of jumps and reversions. See figures 6.5a and 6.5b where the transition takes hold after nine reversions. Dropping K 0 to 2,900, however, (shown in figure 6.6a) yields a trajectory that apparently oscillates between hunting-gathering and agriculture forever. In this case the oscillation lasts at least 2,400 years, although we cannot be certain it will continue, as an examination of the numbers indicates it is not periodic. It may, however, converge to a periodic cycle. Adding mystery to this is the behavior of another run in which the switch was So Figure G.o: Switcliiug between the Huntcr-G atiicrcr and Agrarian Regimes 4 00| n i T r r r n i 'i n ) i n < ri*tt i i i i i i j i u ‘ i i i n i'i 111 n it irrr Population, , fe *.4^5 rtflliftf* J3 _ i Incc Cj d i (in > O C 3 , c : C > 2 \ o o pe and i4oos> HG regime FIG UO E <2 The initial increase in capital that a neu regime reguires m au be the critical lector in the success of the iump, hi ter a series of switches agriculture becomes established. ftgric regime S u it c h i PopuJ'SUon Income 0.00 0.00 1600 i-n . . I* i , 11" 11 i 111 i i 111771 V E ftR l i i i i | t " i r i "i1 f t FIG U R E b nqae and „ . ir’ l4u0s) Switching between H G and agr. Population Income Capital 0.00 1580 sc Figure 6.G: A noii*successful and a successful s\vttcli(from hunlcr-gatlicrer to agricul* lure) 1 O O p-T T Poptfiation, Jng r . and i i " i" v S C > 0.00 aooos> n d T T I • I I IT". ■ . I k -.0 2 3 o The critical role of initial capital accumulation. compare uith —1. Here s “ a successful transnion does not occur iS 6 o V “ ' years. / / / / Population / - — m s Incow Income • I 1 I I ! _! — !_!_ 0.00 Capital i n i p a m 1 1 1 1 '.and ’ ' T ;cAa'a U . 4 00| 11111111 V|~mT| n n | ii n 11111 p i ti j 111111 n i j n 11 riGunc b V ’01 The.critical role of initial , . capital accumulation. The transition P orn. Jat ion, * m e and MGs) Incc CapiH (in l o o l o O 0.00 ta£es place uitFjout a reversion/ (compare uith >1 and -3) 0.00 Population / Income Capita 87 made prior to the point that agriculture was superior. In figures 6.7a and 6.7b with h'o = 2500 a transition successfully took place after about 600 years of oscillation. As I tested K 0 by increasing from 2,500 to 3,000 at intervals of 100, successful switches eventually occurred with generally fewer reversions. With most values tested below 2,500 no successful switch occurred. Strangely, however, with A'„ = 2000 a switch occurred after just a few reversions. This, however, should not be too surprising since the model is nondincar and the transition point may be chaotic-hence we have sensitive dependence on initial conditions. Table 1 in the appendix sums up the parameters and equations used in the com* putcr histories. In the next chapter wc discuss the selection of parameters in slash and burn agriculture and in the next regime, intensive agriculture. Figure 6,7: An Odd Transition from Huntor*Gnthcrer to A griniltun 1 *0 Popt — Inc Capi (in - 1 ' i vrrnTrprrrr rrm- iTi ri i r i ri 'i'i‘ n Ui!~ n o u o e V -0 ! 5 ™oo.-/H £ r0ft" 3lr,0V o F02 a « ll] S ^ '" ,,M"'9 • hijnt ing-gathoring rogimo population--> / I cutiching b9»U99n rogiwoc agr njutfura M -O / / y incomo capi tal tat ion. FIGURE wo.and fid) HO Population cmtching D 9 t U 9 9 n rogimoc lncoM9 capi 89 Chapter 7 THE VILLAGE A G R A R IA N REGIM ES In rough correspondence with both the concept of evolving cultural complexity, and Boscrup’s categorization of agricultural land use wc will distinguish between two regimes in modeling the village agrarian stage. Wc call them the extensive agriculture or slash and burn regime and the intensive agriculture regime. Boserup divides agricultural land use into five systems1. Wc will group her first and most of her second system (forest fallow and extensive bush fallow) into the ex tensive agricultural regime, while including what she terms bush fallow with domestic animals, short fallow and to a very limited extent, annual cropping, into the intensive agricultural regime. Her fifth system, multicropping, and most of her fourth system, annual cropping, characterize regimes that have reached some degree of urbanization, at least in the ancient world. Wc intend the split in the village agrarian stage we have proposed to also reflect fundamental differences in the institutional arrangements that accompany cadi form of land use. Cultivators using extensive agricultural systems generally clear a field by felling large trees with an ax and burning off the vegetation. Adopting the system in order to boserup 1065,op. cit., p.15. 90 reduce the amount of time spent in field clearance, they leave tree stumps, roots and rocks on the land and plant around them, which precludes the use of draft animats and plows. Hence they plant with a digging stick without engaging in further soil preparation which results in less dense plantings. Burning fertilizes the soil for the immediate growing season, but it docs not replenish it with continued use, so the land must lay fallow for long periods of timc-usually 20 to 25 years under forest fallow and six to ten years under bush fallow after only one to three years of use. Conventionally known as slash and burn agriculture, this yields lower returns per input of land.3 Typically growers plant less than ten per cent of the arable land a t any one time, and due to the long fallow periods they move their settlements frequently. Since they do not need plows or draft animals, cultivators using these systems have fewer capital requirements than they would using intensive agricultural methods. The latter system reduces the fallow period. Inasmuch as the bush or forest has not had time to reclaim the land, grass remains. Growers must then clear grass land which is done most efficiently by using a plow drawn by draft animals if available due to grass* extensive root system. Fertilization becomes a significant problem since the land has had less time to recover. Often intensive agricultural methods will require growers to irrigate the fields for at least some part of the year. Heavily irrigated fields require frequent weeding, transplanting and regular upkeep of irrigation facilities. These activities consume far more time than did the previous systems of land use— hence we observe diminishing returns to labor although per acre production increases,3 The two distinct production methods coupled with different population densities create basic differences in the institutional framework of the two regimes. For in* stance, in the intensive agricultural regime, a chief must possess the authority to Chapter 3 aSee the table hi Doserup 1981, on p.45. 91 coordinate such economic activities as construction of irrigation facilities that will benefit alt members. Perhaps the most important difference, however, is the transition to private prop* crty. In the extensive agricultural regime all members of a tribe retain a general right to cultivate any plot of land within the tribal territory that is not currently in use. Thus tribal ownership of land exists but private ownership docs not. Non tribal members living witin the territory may also receive temporary cultivation rights but they do not retain general rights over time. As land use intensifies, however, families begin to acquire cultivation rights over specific tracts of land within the tribal area. This tends to lead to private ownership of land.'1 It is at the stage of intensive agriculture that a feudal landlord class may establish itself. In Europe the reasons for the emergence of this group remain shrouded by the past, but in Africa we know that in recent centuries nomadic pastoral tribes would frequently conquer settled tribes and begin to levy taxes on them, nevertheless leaving intact the existent tribal structure. Despite describing the conquerors as landlords, most observers regard them as a form of local government rather than as rent-collecting land owners since previously established practices including cultivation rights remain in efTcct. Both landlord and cultivator have mutual obligations in the social structure that emerges. For the former it might include the maintenance of • * roads, protection from outsiders, etc.; for the latter it includes paying tribute and offering labor services.5 It is not easy for a nobility to emerge among long fallow agriculturalists since they have a relatively small stake invested in any one piece of land. Any would-be conqueror might triumph only to see his subjects fade away into the forest, later Chapter 9 5Boserup, 1965, op, ciU, p,82*83. 92 reestablishing themselves away from his influence. Thus a pre-requisite for a feudal system appears to be an increase in population density to a t least an intensive land use stage. We will characterize the extensive agricultural regime in our model as follows: 1. T he fraction of the population engaged in coordinating and managing activities (as opposed to producing consumer or capital goods) increases slightly from the hunter* gatherer regime. Both groups organize along tribal lines where a leader plays at most an advisory role and whose power is based on his prestige.0 Nevertheless, higher population density creates more situations th at tnay need arbitration, and some economic activities m ust be coordinated. 2. Per capita output tends to be slightly less than th a t for huntcr-galhcrcrs. P art of this output consists of capital which docs not enter consumption. In addition, more people enter the labor force (children and older people now assume significant duties), and they work longer hours—thus, labor productivity decreases. If we were to m easure leisure as a consumption good, per capita income would fall. This is consistent with the idea th a t people chose agriculture only when the returns from hunting-gathering fell due to overcrowding. 3. Capital requirements increase directly with population. We specifically consider plot clearance, irrigation projects, village construction (both perm anent and tern* porary), and the care and feeding of domestic animals to be investment activities. C apital formation is small in comparison to more populous regimes which use capital to oflset diminishing returns to labor. Although the observation th at in long fallow regimes tribal members tend to work together to clear forest land and to irrigate might cSee for instance Netting, 1972, "Sacred Power and Centralisation", for an account of the use and development of political authority in several agrarian African societies characterised by sparse population. 93 tem pt us to regard capital formation as social in nature, we will make no distinction between private and social capital. Hence the administrative technology function in this regime depends only on population. 4. Birth and death rates under both agricultural regimes arc more sensitive to con sumption than those of huntcr-gathercrs. W ith a limited need to travel, the economic and physiological constraints on the birth rate diminish as we have indicated above. Lee’s study shows th at IKung San women in groups that begin to adopt agriculture experience a decrease in the interval between births.7 Higher and more variable death rates appear because of an increased likelihood of famine and epidemic. The former occurs because agrarians rely on ju st one or two crops which make them more vulnerable when one or both fail, while population density and the fact th at semi-permanent settlements allow pests to congregate, makes the latter more common. Additionally, huntcr-gathercrs enjoy better general health because of their more varied diets.8 We will model the second regime as follows. The interval of viability is [0, 400,000]. Even a group of minimum density can choose to use slash and burn agriculture if they wish. They usually will not opt for this due to its low labor productivity in comparison with hunting-gathering, but the possibility exists, hence the lower limit is zero. We arrive at the upper limit as follows. We assume that 15 per cent of the land is arable9. Under bush fallow, Boscrup estimates the frequency of cropping to range from ten per cent to forty per cent. She seems to associate the latter figure with the TLee, 1072, "Population Growth and the Beginnings of Sedentary Life among the Kung Bushmen.” 8Woodburne, 1072, remarks that pediatricians from Makere Colege who examined Haxda children pronounced them to be one of the best-nourished groups they had seen in jE ast Africa’,p. 244. 9Boserup, 1081, classifies 130 countries according to their arability. Tiie median figure lies be tween 10 per ceut and 20 per cent, p. 27. 94 more intensive land use system of bush fallow that uses domestic animals and the plow. If cultivators leave the land fallow for a relatively long time (say ten years) then the bush cover will have lime to kill off the grass that first grows when the land is left fallow. To clear a grass-covered field one must usually resort to using a plow since burning docs not eliminate grassy roots, but in order to use a plow cultivators must now remove all tree stumps, rocks and other obstacles. The extra labor is so great that tribes invariably dioosc to clear forest or bush land over grass land when they have a choice. When population density increases to the point where the fallow period is too short to eliminate the grass, tribes will often dioosc to increase the number of consecutive years they plant a plot to keep out the grass, but they can only do so if they find other means to regenerate the fertility of the soil. In such a situation the use of draft animals becomes most efficient. The animals can perform much of the most arduous toil, and they also contribute greatly to fertilizing the fields. In Mcsoamcrica the unavailability of draft animals undoubtedly retarded the development of intensive agricultural methods. If the society uses draft animals they need to set aside fairly extensive lands for grazing which reduces the amount available for cultivation. Many of the resulting coordination problems call for the same kind of social integration that we typically see in sodeties that use short fallow and annual cropping systems even though the population density has not yet readied this level. We will assume this is the situation here. A top figure of 400,000 corresponds to a density level of ten people per square kilometer of arable land whidi is well within the range that Boserup proposes for bush fallow agriculture. We will associate the upper range of bush fallow agriculture (10 people/k m 2 to 1G people/km7) with the intensive bush fallow that uses the plow and draft animals. Again we will measure capital according to the number of hours 95 spent in its creation. No, we do not want to resurrect the Labor Theory of Value, but since neither entrepreneurs not markets yet exist, and since the tribe largely works together to create capital we can reasonably assume that people measure the cost of goods in terms of the time spent in its production. Measuring capital in this way we will represent the production function as V = R{t)G{X)AK0'xL0» (7.1) We dioosc the values of 0.1 and 0.9 to represent the fact that at maximum effi- cicncy cultivators will spend About one-tenth of their time clearing their fields and irrigating. We further assume that they allocate their time rationally bcLwecn these two activities. Specifically each person has a utility function ti(£) = log w(l) + log r'(<) (7.2) where w is the return to labor and r ' is the expected return to capital in the next period. If we equate to And r' with the marginal productivities of capital and labor respectively and assume that people measure next year’s capital requirements against this year’s labor force, a few calculations show they will choose between consumption and savings in such a way as to increase (or decrease) consumption to the point where L(t)/K(t -f 1) is in the ratio of nine to one. We assume that all capital is private in the sense we have described, i.e. there is no minimum level of social capital needed. G(X) has the form G(-Y> = ( J q ) ‘< 2 - 2So>‘ (T.3) 1)6 Figure 7.1: The Extensive Agriculture Administrative Function 1.50 notrnc Thi id H in itirativ tf technology (unction (or the e<tensive iq r ic u I.OC 0.00 V V e choose the exponent b to be less than a which skews the curve to the right. (Sec figure 7.1). This has the cflcct of creating a more abrupt transition between the extensive and intensive agricultural regimes than between the hunting-gathering and extensive agricultural regimes. We believe that intensive agriculture requires a more fundamental reorganization of the social structure than docs the jum p from hunting- gathering to extensive agriculture. The latter involves only a decision by individual members to use previously known techniques (agriculture) while the former requires group cooperation. We also introduce a random variable, 7?(f), to explore the interplay between stochastic elements and those elements th at appear to be stochastic but in fact are deterministic,10 T he use of R{t) seems to reflect a truly random factor that had great ^TYuthfully, the difference between these might just depend on how omniscient we assume we are. 97 impact on tlic lives of agricultural peoples—the weather. As mentioned above, huntcr*gathcrcrs depend far less on the weather because they rely on a wide variety of foods. Fbr agrarians of the past, however, famines cropped up with alarming regularity. While it is difficult to come by hard numbers for agrarians of the period we wish to model, local statistics for European agrarian communities invariably show recurrent crises due to crop failures. Because so many peasants lived so close to subsistence levels, famines had a devastating impact on a large percentage of the population, a pattern one would think would only intensify in earlier times. One gains a measure of the devastation by observing birth and death rates for medieval villages. Consider the following chart from Braudel 1 1 on the number of births and deaths in the Flemish town of Eoklo during the 17th and 18th centuries. Usually births exceed deaths by a small but significant margin, but inevitably, times occur when the death rate increases substantially, eroding most of the past gains and resulting in only a small net increase in population. While many would attribute periods of high mortality to epidemics, in fact, the latter were usually closely related to the former. The Plague has justifiably received much attention, but it was one of many diseases that periodically devastated the countryside, and as often as not a famine established the conditions that permitted an epidemic to rage unchecked. Braudel writes, nOne bad harvest was just about bearable; if there were two, prices went mad and famine set in. Famine was never an isolated event. Sooner or later it opened the door to epidemics. 1 2 By having a random variable afiect the level of output which in turn affects birth 11F. Braude), 1977, The Structures o f Everyday Life., Harper and How, |t, 72. C. Cipolla, 1980, Before the industrial Revolution: European Society and Economy, J000-1700. has similar charts showing the same pattern. "Jbid., p. 78 98 and death ralcst we capture a sense of the variability of these rates within a regime rather than just at the point of transition between regimes. The use of the random variable docs nothing to change the overall trend of output, income and capital within a regime. As we explain later, it might have some bearing on the transition between regimes. H(t) is a random variable that captures the impact of weather conditions on agricultural production. It takes on values between 1.2 (indicating a bumper crop) and 0.7 with an expected value of one. The numbers indicate the ratio of output in year t compared to the output in an "average'’ weather year. We show its distribution in the appendix. The choice of values comes from an estimate of the frequency of famines calculated from information given in Wriglcy’s (19S9) discussion of crop yields. (In the last chapter when we modeled the transition between hunting-gathering and agriculture we did not include R(i) so as not to cloud the issue.) The fraction of population engaged in production increases to 0.7. While huntcr- gathercrs have little economic use for children, village agrarians can use them for a variety of jobs, such as herding. The fraction of people actually working is greater than this since some adults now perform administrative tasks. We show the birth and death rates as functions of per capita consumption in Figure 7.2. Note that the death rate drops steeply for values of c between zero and 0.3. In our model 0.3 represents a thrcshhold value where severe repercussions from malnutrition affect a large percent of the population. When c is between 0.3 and 0.6 the death rate falls but at a much lower rate than before. In this interval economic well-being will have an effect on a smaller fraction of the population (the sick, the young and the old) but will not mortally afTect most people. When per capita consumption rises above 0.6 the death rate levels off at 40 deaths per 1000 per !)!) Figure 7.2: The Birth ami Death Functions in the Agrarian Itegimes 0.0(5 0.70 annum . At these levels of income people generally eat well and any. further increases may lift their utility hut will not alTcct mortality. A death rate of * 1 0 per 1000 corresponds to an average life expectancy upon birth of 25 which agrees with some estim ates of primitive agricultural societies.1 3 Recent studies suggest th a t only the very old and the very young were likely to die during times of m oderate food scarcity uncoupled with epidemical disease. However, when a famine of great proportion hit. everyone was a t risk. Braudel (1975) describes how throughout medieval Europe, towns had to protect themselves from "positive armies of the poor" during periods of famine which occurred frequently. This, of course, does not directly apply to our regime since there are as yet no towns, but it does indicate the severity of famines. It appears th a t m any famines were limited to a For instance in Guatemala. Mexico and Brasil in 1000 before most modern medical technology reached those countries, the expectation of life at birth was 23.0, 25.3, and 29.3 years respectively. small geographical region. Garnsey (1988) concludes th at food shortages occurred regularly in the Graeco- Roman world while famines, which he defines as food crises resulting in a dram atic rise in the m ortality rate, were relatively rare. But in the setting lie describes, the existence of a state and an urban center gave peasants recourse to other solutions to mitigate the effects of crop failure. The state learned of the necessity to stockpile a surplus in public granaries in order to reduce the likelihood of a peasant revolt. FVcqucntly during periods of crises wc have reports of small land holders demanding to work for the large land owners. O ur long fallow agriculturalists, surrounded by more or less independent tribes, v lacked such options since traveling outside their boundaries risked violent death. High mortality rates result not just from violent death or starvation but also from the increased susceptibility of malnourished people to succumb to disease. Recently, Galloway found a positive association between changes in wheat prices and death rates from endemic diseases (typhus, smallpox, and fevcr).H It seems likely th at a tribe th at experienced crop failure would consider raiding other more prosperous tribes—we do know of many primitive agrarian tribes with a history of sporadic warfare against their neighbors.1 * Thus wc have ample reason to associate crop failures with a high mortality rate. T he natality function postulates th at a t particularly low levels of income people will choose to have no children, that birth rates respond positively to income at intermediate levels, but th at higher incomes do not further increase them. The first HGalloway,1985,"Annual Variations in Death by Age, Deaths by Cause, Prices and Weather in Loudon, 1670-1830", pp.487-503, ,6The battles among the Iroquois that lasted until they formed the League of Five Nations is just one of a myriad of examples of warfare between agrarian tribes. See Farb, 1D78, Man’ s Rite to Civilization.t for others. 101 linear segment captures the Eastcrlin hypothesis that couples require a minimum subsistence level before having children .1 0 Income also affects birthrates by advancing or retarding the age at which marriage typically occurs, especially when a suitor must give a dowry to the family of the prospective bride, a custom th at might have evolved at this stage. The second segment depicts a positive relationship between birth rates and income. Lindcrt (1983) among others slates th at fertility responds endogenously to economic growth. After people achieve a certain level of income, however, birth rates seem not to rise. Most studies, in fact, indicate a decline as people "substitute’ 1 other consumption goods for children.1 7 However, this assumes the existence of alternative forms of consumption normally associated with urban environments, a condition not met at this stage so wc will not incorporate such a feature. While many writers believe that other factors eclipse the demographic relation* ships wc have described above, wc would argue along with Day (1986) th at they have a significant effect at low incomes. Furthermore, we believe wc have controlled for many of the structural influences on birth and death rates by restating the relationship within different socio-economic frameworks. The intensive agricultural regime encompasses, as wc have indicated, Boserup's bush fallow with domestic animals, short fallow and in certain cases her annual crop ping systems of land use. In all three systems domestic animals and the plow play a large role because of the need to till fields covered with grass. Fertilization also in* creases in importance due to more frequent land use. Domestic animals are invaluable in this regard, but if fallow land becomes scarce, cultivators will have to discontinue their practice of having them forage and begin to provide fodder as one of the crop ,6Easterlin, (1973),"Relative Economic Status and the American Fertility Swing". 17See Easterlin and Crimmins (1985) for a summary of this argument. 102 rotations. Irrigation plays a much larger role, and if used frequently it requires ex* tensive weeding and sometimes transplanting of crops which further diminishes labor productivity in agriculture. 1 8 On the other hand some degree of specialization be gins to appear in producing non-agricultural goods. The sedentary lifestyle is more conducive to acquiring more durable goods. These production factors constrain a group to a more highly integrated system of social cohesion. A need for some kind of land tenure system approaching that of private property arises along with more reliable methods of resolving disputes. As population continues to increase, conflicts over land use arise. The tribe must make provision for the foraging needs of domestic animals which usually results in designating areas for common fields, and enough of a political structure to guide communal irrigation projects must emerge. When the population of several tribes in an area increases, tribal battles will likely erupt and provision for the common defense becomes another organizing need. Carnciro includes warfare along with agriculture, population density', and environment as the four key factors in Die process leading to statehood. He writes "the forging of village into cliicfdoms and of chicfdoms into kingdoms occurs only through coercion, especially by conquest warfare.*11 0 We can only speculate on the way in which a more integrated social infra-structure developed in prehistoric times, but we have clues from present day observations. Nash describes the social structure of the Sianc, a tribe in New Guinea who ap peared to have readied a stage of bush fallow agriculture. They lived in villages whose members belonged to the same patrilineal clan. Within the clan some social differ entiation existed among men although nominally all were brothers. While peaceful ,8Boserup, 1005, op, rif.,p. 30. ,9Carnelro, 1072, "From Autonomous Villages to the Slate, A Numerical Estimation," p.65. 103 relations might exist between coterminous clans a state of warfare prevailed against all others in spite of the fact that all belonged to the same tribe. One can imagine that with the impetus of further population growth, one clan might gain dominance over others and form a chicfdom where tribal economic plans could be formulated and carried out.3 0 An interesting account of how this transformation can lake place comes from Sagan who describes the transition from headman to chief in his description of the I3ugandan Kingdom of East Africa. The power of chiefs seems to grow naturally from the aristocratic lineages of primitive society, the heads of these noble lineages usually becoming the clan and village headmen. Most chieftainships seem to have begun their political life in this way, and then, by an undocumented historical process, some of these leaders manage to establish a rule over a clan or village in which their kinsmen do not reside. The chief continues as leader of his own clan or village, still more or less as headman, but over the stranger clan he is now a chief. His clan, then, becomes the royal clan of the chieftainship; the successor to his oilicc as clan headman also succeeds to the whole chieftainship. Succession to the chieftainship is determined by the rules that govern the kin group from which the chief comes.3 1 However, a transformation similar to the one we have just described is by no means assured. Lacking a victor, prolonged warfare might result in many violent deaths and a relapse of the group into extensive agriculture or even into hunting-gathering. MNash, 1966,Primitive and Peasant Economic Systems., Chapter 3. a,Sagan, 1985 At the Dawn of Tyrany., p, 265. 104 We will choose a viability interval of 390,000 to 2,500,000 for the intensive agri cultural regime. Wc choose the lower figure because wc want to mesh the previous regime with this one, but this requires some comment. Boscrup associates a density of 16 to 64 people per square kilometer for present day countries using short fallow agriculture at low technology levels.32 Later in discussing agricultural development in Mcsopolomia she cites an estimate of Sanders and Price indicating that Sumcria in the third millcnium B. C. had a density of about 20 people per square kilometer which she says corresponds well with her classification system. Smith and Young however, in their model of the emergence of civilization in Mcsopo lomia indicate the use of short fallow agriculture by at least 5000 B. C. Between this time and the time of which Boscrup speaks, population doubled several times. By the end of the third millcnium Sumcria had readied the stage of urbanism for at least 1500 years. This indicates that short fallow agriculture came into use well before population densities readied 16 per square kilometer. However, one cannot determine how much arable land Boscrup included in the region over which she made her calcu lation. Furthermore, while she discusses adjustments she made for the percentage of arable land in the data she uses in her book Population and Tcdinological Change, it is not dear whidi diarts the adjustments apply to. I believe that we can resolve any discrepancies that arise by a proper consideration of the arable land available. One must consider that primitive techniques, and plants less suitable for agriculture would reduce the productivity of groups in prehistoric societies and result in overcrowding sooner than would occur today. Our figure of 390,000 corresponds to a density of 10 people per kni2 over the region of arable land. Along with Boscrup we assume that annual cropping will begin at a n Boserup, 1980, p. 23. See Tfeble 3.7. 105 density of 64 people per km2, and wc will associate this density with the first stages of urbanism. Our figure of 2,500,000 represents this density on arable land. In the intensive agricultural regime the social infrastructure readies a level of complexity where wc distinguish between social and private capital. A successful transition will require a society to have in place a certain amount of the former. In order for the regime to function smoothly as population increases, the group will have to add to its social capital and it must begin to siphon off labor from primary produc tion to perforin unifying duties. Social stratification begins to take place, increasing sharply as population density increases. An elite begins to take control of the decision making and adjudicating roles of the kinship groups. Craftsmen and specialists ap pear. Some people spend most if not all of their working time in redistributing goods, organizing groups, resolving disputes, inculcating others in tribal traditions, impart ing knowledge, and performing religious functions. Defensive requirements result in the creation of a group that ultimately becomes a warrior class. In the middle and later stages of this regime sonic villages become large enough to merit the term town. Many large villages and towns require extensive defensive fortifications. Leaders construct religious temples and other symbols of magisterial power. The precursors of kingly forms of political power appear. Specifically we will consider communal village structures sudi as temples, storage houses, fortifications, roads if any, and common irrigation works to be social capital. Private capital includes many of the same sorts of things taken to a higher degree (especially irrigation) as in the previous regime, but also includes one important new element—livestock and draft animals and their maintenance in its widest sense. It is true that not all peoples utilizing intensive agricultural systems had draft animals; most notable in pre-Columbian America one impediment to the development 106 of intensive agriculture was the lack of any draft animals. Nevertheless, in much of the world, they became especially valuable with the advent of intensive agriculture for essentially two reasons. First, since the fallow period decreases, agrarians replant the land before forest or bush reclaims the land, hence grass (which relics on unblocked sun in order to thrive) remains and the field must be plowed. With all soils, but especially with clay type soils, plowing is far easier with the use of draft animals. Second, the shorter fallow period reduces the time for natural vegetation to regen- crate the fertility of the soil, consequently other means of fertilization must be used. Animal manure has historically been the chief source of fertilizer. To maintain draft animals, the group, of course, must feed them, cither by set ting aside pasture land or by feeding them part of the harvest. While the former method requires less labor, people may have to resort to the latter when grazing land becomes scarce. Boscrup describes how a grazing shortage in Europe led to a change from short fallow cultivation to annual cropping with fodder plants—especially legu minous crops—forming a part of the rotation.33 She feels that net output per unit of labor must have fallen with the new system. Paralleling the controversy about whether the adaption of agriculture led to a population increase or vice-versa, a sim ilar question arose over whether or not the adaption of this system of cultivation led to another population increase. However, evidence suggesting that agrarians in the Roman empire employed crop rotation with leguminous plants has led economic historians to revise their view and look at population increase as the causal factor.3 4 An alternative system often seen in the past in Asia to producing fodder for draft animals when population density increases is to intensify the planting of the best land 33 E. Boeerup, 1965, Conditiont of Agricultural Growth., p. 37. 94/hid., p. 38. 107 and turn over the worst to pasture land. This system often requires quite elaborate methods of irrigation so that capital requirements still increase dramatically. The fraction of population engaged in the production function remains at 0.7 but these people now work more hours. In addition to private production the elite may levy "labor” taxes on the populace to create some of the infrastructure capital, and increasing social complexity requires more workers to spend their time in the unifying activities wc have described. A priesthood may no^ begin to acquire considerable power. While some may feel that their activities contributed little to the common good, undoubtedly the cohesive force they provided to bind the group together played a critical role, and the well*documented astronomical observations that many priests made certainly contributed to agricultural output. To take these factors into account wc represent production as V = R(t)G(Xf Km)AK02L°8 (7.4) R(t) is a random variable similar to the one in the previous regime. However, disasters will occur with more frequency reflecting the greater role that war plays in the lives of the inhabitants and their greater reliance on juBt a few crops. G(A', A'm) has the form * • Cl Y fi \ (^ ” 350.„.2500 — A' .fr . . G(A, Am) - ( - ^ 0 7 5 —) ( — Q 7 5 ) M It will have the general form of the administrative technology function for slash and burn agriculture when K m takes on its appropriate values. We justify its shape by observing that if a group successfully reorganizes itself as described above, at the beginning the regime will be quite productive. As popu* lation increases, however, diminishing returns to agriculture set in due to the more 10S Figure 7.3: The Social Capital Function 100.00 riO tJB E "1*'? o c u l C ap ital in th«, n u n i i v o A g ric u ltu ra l 'aqitie. 0.00 PQPULrtNOM 2500.00 0.00 frequent use of the land. This will be olTsct for awhile by greater production from craftsmen and specialists. However, when population becomes very large relative to its infrastructure, the need swells for large scale projects, especially in irrigation, but undertakings of this size require another m ajor reorganization of the society which encompasses a much greater degree of social differentiation. A'm(.Y) has the form shown in figure 7.3. It indicates that the group needs some minimum amount of social investment A'mo in order to get started and that this am ount increases with population. At some point (in this case when population reaches 1,800,000 people) the amount of social capital per capita increases. We can interpret this to be the stage where small towns spring up and the need for fortifi cation, roads, and transportation vehicles accelerates; we might associate it with a complex society. The exponent of capital in the third regime is greater than in the second, reflecting 109 its increasing importance in private production. Private capital includes the care and training of plow animals, irrigation projects and land preparation which now takes more effort. As towns develop, it might also include major agricultural projects such as the planting of groves and vineyards that large landowners might undertake. The birth rate, death rate and utility functions remain the same as in the extensive agricultural regime. In the transition between the agricultural regimes, three factors come into play. The first requirement is a sufficiently large population to permit a switch from a tribal structure to a chicfdom. The latter form of political organization assures that rulers have the authority to direct the mushrooming activities of specialists that emerge as labor becomes more diversified. Such authority may require the creation of a noble class and the maintenance of a warrior class to enforce their status. The administrative function G(A', A'm) models this effect. The second requirement !b for another jum p in capital. Not only do wc assume that the group must now create social capital, but the capital used in private production increases. Wc reflect this requirement by an increase in the exponent for capital in the Cobb-Douglas component of the production function. The third factor is the effect of the random variable on production. In fact, we could omit the use of this variable in the model since wc principally wanted to explore deterministic contributions to seemingly stochastic behavior. If we limited the investigation in this manner we certainly would not intend to assert that linear modeling can explain all white noise. We take the position that seemingly random fluctuations have both deterministic and stochastic elements, and we would like to shed light on the degree to which non linear equations can explain this variablility. Nevertheless, we will include it because the effect of the weather on agricultural n o production would seem to be the major area in which events outside the purview of human action have a profound impact. In spite of the fact that our model represents an average of human activity over a wide geographical area so that often local famines here would be offset by bumper crops there, the weather on a large geographic scale still varies substantially. It introduces the possibility that the positive probability of a bumper crop at a point of transition between two regimes could be the determining factor in whether a successful switcli takes place. For instance, consider the two administrative technology functions under the two regimes in figures 7.4a and 7.4b. In figure 7.4a at the point of transition neither regime may be able to support an increase in population. The only way for a successful jump to occur is for population to increase from say P, in extensive agriculture ot P, in intensive agriculture. If the maximal increase near P, tinder usual circumstances is too small to reach Pj, a successful jump could not occur. But if provision is made for such an increase when the group enjoys a bumper crop, then as long as population resumes growing after an unsuccessful jump, it is inevitable that a successful jump will eventually occur. This could correspond to the possibility that a temporary increase in population due to exceedingly favorable conditions created the surplus tabor that a new regime required in order to produce the additional social and private capital. By admitting the possibility of this transition we are not committing ourselves to it. Perhaps the relative efficiency of the regime is as in figure 7.4b, in which case the eventual transition does not depend on such an element. Now let us consider some possible histories. Our first history describes a region where agriculture is possible but not very Figure 7.1: The Effect of the Random Variable on a Jum p FIGURE G(X, The transition (row extensive to intensive agriculture. Without a bumper crop a jump in population (ram P to P is not possible, s i Mini lem papt 10 int V at ion drou in tnstve agr. 0. D O J i t_L—L 2.00 PO PU LA TIQ M c in 100.000s) 6.00 1.50 Q(X, l.ot 00 ct groi of t—i—i—i —|—I —i—i —i —|—i —i—i —I —|—i —i —i—r FIG URE The transi lion, does not depend upon a bumper crop. regimes ujll at the point •ansition. 0.00 2.00 POPUlflriQH < in (00.000s) ®-00 112 productive. When wc first observe the region it is populated by approximately 120,000 long-fallow agriculturalists. A change (possibly a shift to a drier climate as seems to have occurred in North Africa) makes the land even less productive and over the next 200 years population drops to about 90,000 (see figures 7.5a, 7.5b and 7.5c). For the next 1200 years the group fluctuates between hunting-gathering and long fallow agriculture. The great variability in income is indicative of the extensive agricultural regime. Figure 7.5c gives a closer look a t the income trajectory. The relatively stable segments (for instance from approximately 1290 to 1310) indicate periods where the group practices hunting-gathering. People subsist successfully as huntcr-gathercrs, but the population increase invariably forces them to return to using agriculture. The reason the group cannot sustain itself in this mode comes from the inordinately high death rate during times of famine while population docs not increase suflicicntly during times of plenty, although these outnumber the poor years. A second underlying cause of the failure of the group to make a successful transi tion is the need of the group to produce capital. In fact, at this level of population average gross income for the group is higher in the intensive agriculture regime, but since they must expend some of their effort in creating capital goods, average net income is less. Such a situation may well have prevailed in the far northern and southern regions of the Americas where some Indians practiced rudimentary forms of agriculture along with hunting-gathering. The second ease concerns a group that progresses from hunting-gathering to the sporadic use of intensive agricultural systems. (See figures 7.6 and 7.7). They remain as hunter-gatherers for about 1650 years, fluctuate between hunting-gathering and long fallow agriculture for about 600 years, and finally successfully make the transition Figure 7.5: Itorticulluralists Revert to a Huntcr-Gatherer Slate f-ipulatun 1 no- 105 100 90' 200 400 C O O •00 1000 1400 1200 I n e e n * V » » O O f c ) •0 I n c o m t % 1CS0 1100 1150 1200 1250 1300 1350 1400 **»r 114 a t which time they grow rapidly until they reach the stage of intensive agriculture which they recurrently enter and leave. Note the rapid acceleration in population growth when the transition to long fallow agriculture is successfully made (beginning with the year 2300. Figure 7.7 gives a close-up view of the transition.) As population increases to near the 400 level, the rate of population growth halts as they are unable to successfully reorganize into the economic infrastructure needed for the intensive agricultural regime. Several brief forays into this regime occur after approximately the year 2850 (the sudden jumps in capital give evidence of this). If wc were to continue this run the group might eventually succeed in making the next jump. The primary barrier is the channeling of production into capital which takes away from consumption. Despite this, the group made one run into the next regime around the year 3100 only to be undone by a series of bad crops. In our next history wc take the same group but rather than have them rationally divide their time between consumption and capital creation so as to minimize the labor input, wc allow them to "adapt” to poor years by devoting more time to current consumption at the cost of more work later on. W ith this specification the group successfully makes the transition to intensive agriculture after about 150 years. Figure 7.8 shows the trajectories of capital, income and population for the entire 1500 year period which takes them to the verge of civilization. Figure 7.9 gives a close-up of the transition from extensive agriculture to intensive agriculture. In the next chapter we discuss the final stage of the jump to the city state. Figure 7.G: Huntcr^Gatherer to Intensive Agriculltin 4 0 C 1300 1300 3000 2500 1000 P o pulation 1000 ;i46 id 6 i i i i i iofio 10c Ineoiea ,1 230 200 m ISO m 100 J f 30 —— u - 3& o 1000 1300 2000 2300 J0001 40 30 2 0 1 0 tu r C a p ita l 360 1000 1500 2000 2500 JQQ0***C lu a ta f ^ a tf e a r a r s v ltk a s I n i t i a l population o f t , 000 baccaa n atan aiv a v illa g a q n t l i M and t b u flu c tu a te batvaan •ita n a tv a and la te a a iv a a g ric u ltu re tin Figure 7.7: A Closer Look at the Transition from Hunter-Gathcrcr to Horticulture Population ■00 1»00 3000 3100 3300 3300 Incoaw ifaar Tkt two t U p u i t k c n abow a eloao-up o f th o tr a n a ltlo n fro * b u n to r-o ath o rar to u t i u k n a p r le u ltu r a lla ta fro a fi«oro Population 3400 3000 Incon* 3«00 •Poor 3500 3t00 -Poor A co n tin u a tio n o f th o t r o j . c t o r t o . f r o . Figure T.S: Horticulture to the Verge of City Slut* P o p u l a t i o n 2000 1500 500 Y e a r 200 400 600 800 100012001400 I n c o m e 2000 1500 1000 500 Y e a r 200 400 600 800 100012001400 - 500 400 300 200 100 ■ Y e a r 200 400 600 800 100012001400 rX G O R E n .,8 Population, incoae and capital trajectories fron long fallow agriculture to the tbreshhold of tbe city atate 1)8 Figure 7.9: T he Transition from H orticulture to Chiefdom in the previous figure Population 420i 400 390 50 100 150 Income 20 50 100 150 2F(?e a r 119 Chapter 8 THE CITY STATE The final episode of the odyssey from huntcr-gnthcrcr to the city state embodies many of the elements we have already seen. The choice of the name "city state” evokes the first images of civilization as well it should, since civilization derives from the Latin word for city, civilas. Archaeological evidence, historical observation and common sense indicate that city states evolved out of complex societies; the constancy of this relationship might have led us to include the complex society as an intermediate stage between village agriculture and the city state. A complex society frequently develops an intricate form of political organization, a professional military society, and a fairly specialized labor force. The essential differences between it and the city state involve the degree of specialization of the labor force, often the existence of some form of written communication, monumental architecture, the extent of its transportation network and probably most significant, the size of the urban center. This last requirement renders our hyupothesis that the transition to city state depends upon population density as self-fulfilling, although as we will see, the size of the urban center depends on the achievement of many of the other conditions. Disagreement about the definition of civilization makes the division between a 120 complex society and a city state somewhat subjective. Nevertheless, there is no doubt that most complex societies did not and probably could not evolve independently into a city state. In modeling "the emergence” of the city state, we place emphasis on the first manifestations of the phenomena—those that did not occur through the borrowing of ideas or technology developed by existing city stales. The division of labor induced by the first city states caused a technological revolution, especially in transportation, allowing later societies to become more easily urbanized than previously. The essential condition for a city state to emerge was the ability of the state to create an agricultural surplus to feed residents of the city. Two factors within a local area critically afTcct the likelihood of this occurring: (1) the population density, and (2) the efficiency of the transportation system that the stale can create. Early attem pts at explaining urbanization in the Middle East focused on the fertility and productivity of the soil in the river valleys of the Nile and Mesopotamia, areas where the first two civilizations appear to have risen independently. Boscrup shows how these explanations " miss the crucial point.”1 Europe north of the Alps, had superior tools and more fertile soil than in Mcsoainorica, yet the latter produced urban centers independently over 1,000 years earlier than the former. It is not even clear that Egypt and Mesopotamia had more productive agricultural systems in terms of hours of work as many long-fallow agricultural systems when one takes into consideration the effort spent in creating and maintaining irrigations) systems. We need to understand why population became dense in those areas in the first place. Throughout our analysis of the first three regimes, we have noted th at the desire for people to maximize their "income” in the broad sense (taking into account l E. Boserup, 1981, Population and Technological Chaugc,, p. 65. leisure tim e), motivated them to attem pt to equalize population density within the constraints of environmental conditions by moving to less populous areas so they could resume using more labor-efficient systems of food procurement. Netting observed that pastoralists and long-fallow agriculturalists in Nigeria preferred to move to less populous areas rather than change their customary methods as population increased rapidly in this century.2 The fertility of the river valleys made it possible for population density to increase, but it did not provide the motivation to do so. The primary advantage th at induced agrarians to adopt a capital intensive method of irrigation so they could remain in a river valley m ust have been the protection it afforded them from increasingly hostile neighbors. Carnciro reasoned that conflict between two groups should rise as they create more villages in the space lying between them.3 As population pressure for the entire region builds, the cost of moving from a densely populated area increases but the benefit of doing so decreases. Eventually, population density over the entire region might reach some critical point where a local area suitable for the emergence of a city state begins to grow relatively faster than the surrounding areas. A suitable local area will not consist of an abundance of land th at is equally desirable. Europe, north of the Alps, had quite fertile land and abundant rainfall; consequently population density tended to equalize over a wide area since one piece of land was not preferable to another. A group living there whose population grew could adopt intensive agricultural throughout its territory, perhaps expanding outwards concentrically a t the expense of its neighbors, without ever achieving the density in any one area th at perm itted an urban center to rise. aRobert McC Netting, I960, //iff Farmers of Nigeria. aR. Carneiro, 1970, "A Theory of the Origin of the State ” , Science, 122 In contrast, in Egypt and Mesopotamia, while the land was extremely fertile be* cause of silt deposits left by the flooding rivers, the aridity of the climate meant that the irrigability of the land was a crucial factor in its productivity. Oates observes that in Mesopotamia, the variability in land values due to irrigation must have produced analogous inequalities in hereditary wealth, thereby adding to the inequalities inhcr- cnt in a complex society and encouraging the emergence of a class based society.4 She notes th at in historic periods it appears that property was the basic factor in determining the Mesopotamian social structure. The second critical factor affecting the emergence of the city state is the trans portation infrastructure the state can create to supply a candidate city. To sec its importance we must examine how dense a region must become in order to support a city state. The agricultural surplus a group amasses must support not only people in the city but also those sustaining the irrigational system and other rural infrastructure. It appears likely th at productivity per worker was not greater than th at of many long fallow agrarians, perhaps substantially less given the amount of additional weeding that irrigation requires. Davis suggests th at at probable productivity levels, only one-tenth of agricultural output could supply the city.5 This implies that rural areas near enough to supply an urban center had to have ten times the population of the center. At the time that the first cities began to appear in the near East, the principal means of transport were porters, pack animals, river craft and animal-drawn carts. The latter, more cflicient than porters and pack animals, nevertheless had a limited 4J. Oates, 1081, "The Emergence of Cities in the Near East." in Cambridge Encyclopedia of Archaeology. 0Kingsley Davis, 1955, "The Origin and Growth of Urbanisaitou in the World.", American Jour nal o f Sociology. 123 range because harnessing techniques and wagon technology was in a rudimentary state. Finley indicates that even in classical Greece and Rome when technology had improved immensely, peasants transported their crops no more than eight kilometers while large farmers needed to locate within 15 kilometers of their market if they expected to turn a profit.0 River transport was by far the most efficient means of transport which probably accounts for the fact that all the independently developing civilizations did so in areas where water transport was possible via large rivers or lakes. As cities grew in size they typically invested a great deal of cflort in building canals, a highly desirable alternative for shipping given the vagaries of river flow; but the amount of work involved in digging a canal'precluded this strategy from being used by smaller groups. In Table 8.1 we estimate the maximum size of an urban center supportable by a group of which 90 percent work in agriculture, under varying levels of population density and maximum transportation distance. One notes that the technology of the time limited the size of the first cities. One can hardly imagine many could have exceeded 10,000 inhabitants. To give perspective for the density levels, the approximate density of Japan, India and China in 1990 was 326, 254, and 115 inhabitants per square kilometer respectively. TABLE 8.1 MAXIMUM SIZES FOR URBAN CENTERS Transportation Distance (km) Densi 32 ty (inh 64 ab. per 128 sq. km.) 256 5.0 7.5 10.0 15.0 250 565 1000 2260 500 1130 2000 4520 1000 2260 4000 9040 2000 4520 8000 18080 Sanders and Price discuss the characteristics of from 20 to 30 city states in Sumeria *M. Finley, 1973, The ytncienf Economy, Figure S.l: The Agricultural Support, Zone for a City S ta te \--------------3LO k m --------------J T VJ «r b J e b a h c & " r C c n *V 0. t— Pk l V L1 V * in the third inilleniutn DC. On average their total population (including agrarians) numbered 17,000.' If Davis’ figure is correct it implies th a t they had a maximum city size of no more than 1,700. These city states drew their agricultural surplus on average from about 100 k m 2 of irrigated land which implies a density of about 170 people per k m 3 within their territories. If we envision the irrigated land as lying within a rectangular strip of land bisected by a river and extending say two kilometers on either side of the river, then the length of the strip would be 25 km. If an urban center were located at the m idpoint of the strip, shipping along the river would have reached only about 12.5 km in the cither direction. To get an idea of the largest urban centers possible let us allow farm ers to transport their crops 5 km by land to the rivers edge, and then 20 km by b oat or barge to the urban center (see figure S .l). This perm its 400 k m 7 of agricultural land to supply it. Even with a density of 200 people per k m 7 the maximum urban center would number only 8,000. Once a city state becomes established, the construction of canals would increase the area th at could supply the center. This coupled with technological improvements in transportation and irrigation m ade possible the consolidation of several smaller urban centers. Archaeological and historical evidence of the tim e indicates th at if r W. Sanders and D. Price. 1068, Mcsoam erica: The Evolution o f a Civilisation. 125 one city state defeated a neighbor, they would often slaughter or enslave its urban in* habitants and link its distributive network to their own, depopulating the vanquished center to enable their own to grow. By the last millcnia BC, the existence of civilizations th at an empire could force to pay tribute, and the development of transportation on sea-going vessels made feasible the support of cities of over 100,000 inhabitants. It is no accident that ancient Rome, the largest city of its time, had developed a highly sophisticated technology in harbor construction, and built roads of such scope and quality th at they still inspire awe today. M ortality rates after the emergence of city states must have increased substan tially. The lack of hygiene and crowded living conditions would make a city a relatively unhealthy place to live. Lacking d ata from earlier times, wc can infer trends from urban centers during the last millcnia. Cipolla remarks that ”thc general impression is that the cities of pre-industrial Europe had a negative demographic balance and they survived only because of a continual inflow of people form the countryside.8 This seems only logical since problems with disposal of sewage and the likelihood of epidemics could only have increased with population density. Apparently the prevalence of warfare increased substantially with the city state. Boscrup writes, "Because the ancient urbanized economics relied upon slave labor, tribute and labor services obtained through war and conquest, they seem nearly always to have been at war... Wars between different urban centers as well as attacks on the urban centers by nomads and other tribal populations, often ended in sacking towns and cities. Residents were slaughtered and the economic chaos th at followed further raised mortality.”9 *C. Cipolla, I960, Before the Industrial Revolution., p. 164. ®E. Boserup, 1981, Population and Technological Change., p. 83. 126 To model this regime it seems clear th at we must increase the importance of capital, both for private production and for the administrative infrastructure. This implies that population density must reach a critical thrcshhold before the group can generate a sufficient surplus to support the division of labor and the work force needed to create and maintain the capital. We should make mortality and natality rates more sensitive to per capita consump* tion since higher incomes for the community probably translate into better diets for both the poor and for slaves who became commonplace. The asymptotic mortality rate as per capita consumption increases should be higher than under intensive agri- culture because of the greater incidence of warfare and the increased likelihood of epidemics. As we have remarked, most complex societies did not become city states until technological developments pioneered by the first stales eased the necessity for a dense population. The barriers complex societies faced were: (1) an inability for the society to increase its population density to a point where a transition could occur, and (2) an increased mortality rate a t the time of the attem pted transition because of the fall in per capita consumption that occurred when an elite "taxed” the populace through forced labor in order to create the necessary capita] infrastructure. In the former ease we would model it simply by having the administrative technology function fail to overlap that of the village agrarian regime as shown in figure 8.2a where clearly no jum p can take place. This must have been the most common reason for the failure to jump. We will see an instance of the latter in the computer histories below. We now portray two computer histories that encompass the entire scope of our work. In both histories to follow, we model the city state with the equations shown in 127 Figure 8.2: The Effect of the Adm inistrative Function on the Possibility of Transition to City State. i.so fltX .K iO 0.00 p-TT^-p-rrvyT-i-n-j-: i-.T-p-. . : , riGusc Q The io n im ctra iiv o (on en on e,lor the e n g t u i e end intensive agriculture ere too separates to allou a transition. 6 ii intensive agriculture cs_ c it y state 0,00 l.SOj . i i . j . i i i | . . i i ‘G c x .k h) riuucc b The administrative (unctions (or intensive agriculture ana tne c it y sta te overlap eating a transition possible. aoricuiture a CO c ity state 0.00 )c> H o p u isiio n < loWfl'u&S ' oe.OQ 128 Table 2 in the appendix. Note that the param eters for the adm inistrative technology function CrfA',/vm) allow it to overlap with the intensive agriculture's function (see figure 8.2b), so a transition can occur. 8.1 C om p u ter H isto ry O ne Computer history one simulates the 5,000 year history of a population th at originally numbers 7,000 huntcr-gatherers who move to the verge of a city state before collapsing. Figure 8.3 shows the trajectories of population, (gross) income, and capital for the entire period. Table 8.2 gives the approximate population intervals of dominance for each regime. One can (barely) discern an acceleration in population growth after each regime becomes established in figure 8.3. The obtuscncss of the income and capital trajecto- rics after the year 2,000 is due to the random variable factor which may cause yearly deviations of 20 percent or more. TABLE 8.2 APPROXIMATE VIABILITY INTERVALS FOR EACH DOMAIN "Regime Population Interval (1000s) Hunting and Gathering 0 to 90 Horticulture 90 to 380 Intensive Agriculture 380 to 2450 City State 2450 to 6400 In figure 8.4 wc see the capital labor ratio from which one can infer the regime. Prior to the year 1600, the group remained in the hunting-gathering regime, conse quently the capital-labor ration is zero. From about 1600 to 2600 the group switches between hunting-gathering and slash and burn agriculture. The variability of agricul tural production (from the random variable) and the drop in per capita consumption resulting from the need to apportion part of income to investment causes population to drop so th at hunting-gathering beocmes feasible again. Figure S.3: History One—Population. Income ntul Capital BISTORT O e. Tht S. 000 y«tr h isto ry o f tb s group i s atusaad up in th s s s th r ss graphs. An i n i t i a l population o f 5.000 l l v s as huntar-gathsrsr* u n til 1000, sw itch rapsatsdly batwaan hunting-gatharing and slash and burn agrieu ltu ra batwaan 1600 and 2600, f in a lly s a ttlln g in to tha la tta r a fta r 2600, awlteh batwaan i t and in tan siva agrieu ltu ra for 100 yaars bafora adopting i t u n t il 4700. At th is tin a an unauecaasful jump in to tha c it y atata causas a eo lla p sa which sands than pluonating back to tha huntar-gatharar ragina. 2000 1S00 1000 500 1000 2006 3666 4666 £6'tfFar Ineons 2000 1500 1000 500 1000 2000 3000 4000 fia r Capital 500 400 300 200 100 Year 130 Figure S.l: History One—The Capital*Labor Ratio and Per Capita Income filSTOK t Ocit*. , 'CONTINUED) Tha n p l u l * l i b u r a tio aignala tha 'group’a ragima. Par ca p ita lneoaa la i n i t i a l l y high Cor huntar-gatharara but f a lla aa danaity lncraaaaa. Tha aueeatding raglaaa ganarally o ffa r incraaalng (but mora varlab la) incoma u n til tha ultim ata collapaa. Capital-Laoor Ratio 2S00 ta Incoma 0 . 3 1 0 0 0 2 0 0 0 3 0 0 0 < 0 0 0 5 0 o 2 fM r 131 One can see the fluctuation in the capital-labor ratio between 0.1 and lower values during this period. Probably without the random value function, the transition to slash and burn agriculture would have taken hold sooner. Given the initial condition of a population of 7,000 the trajectory is completely determined up until the first jump into agriculture. (Whether this is similar to the true trajectory is not possible to say since the computer rounds o(T numbers and we may well have sensitive dependence on initial conditions for the jump.) Note that per capita income begins to fall after the year 800 because of overuse of hunting-gathering resources. By the time we reach the first agriculture regime, per capita income is generally lower than in the heyday of the hunting-gathering rcgimcj. In figure 8.5 wc get a belter picture of the first 3800 years. Population levels off in about the year 3400 as the group readies the limits of slash and burn agriculture. In looking at the jumps in the capital-labor ratio in figure 8.6 and figure 8.7 or the jumps in capital in figure 8.5, one sees the switching back and forth between the two agrarian regimes. Again the increase in capital the third regime requires causes temproary reversions. In figure 8.8 the last 1200 years arc shown. As population approadics the limits of the intensive agricultural regime the three trajectories deccclcratc. The first jump into the city state demands sudi a large increase in capital that per capita income falls to the point where a disaster occurs, dropping population down to a level where hunting-gathering returns. In some ways this resembles the Spanish conquistadores1 early attem pts to create European type states out of complex societies on Hispaniola. Enslaving the native population to build what seemed to them to be necessary infra-structure, they depop ulated the island of its native inhabitants. TVue, the major cause of depopulation was 132 Figure S .-V . History One—TIj c ' First 3801) W ars Tha group a o v a a fro * / bunting*< j*tbarin< j t o i n t a n a iv a a g r i e u l t u r a € 00 ' 5 0 0 ' 4 0 0 3 0 0 ' 3 0 0 ' 100 3 0 0 0 3 0 0 0 1000 5 0 0 ' 4 0 0 ' 3 0 0 ' 200 100 3 0 0 0 3 0 0 0 1000 120 100 20 3 5 0 0 3 0 0 0 Figntc S.G: The Cnpilnl-Lahor ratio for the first 3S00 years BISTORT C K<. -T S t CAFXTM.-LXbOR RATXO Tbu f te u p u t i l i t y ( t u t t l M w hieb a l a l a l i M t o t a l la b o r t o r a g iv an o u tp u t and tb a C obb-D ouglai p ro d u e tio a f u n c tio n eau aaa tb a c a p i t a l - la b o r r a t i o t o r a a a in n e a r ly e o n a ta n t w ith in a a e h r t g i a t , hanea junpa i n i t a w alua o f tu n a ig n a l n g i a t a w ite h e a . In t b a to p d ia g ra n 3 .0 i a a a a o e ia ta d u i t b h u n te r - g a th e r a r a . 0 .1 1 u i t b a la a b and b u rn a g r i e u lt u r a and 0 .3 0 u i t b in t e n ti o n a g r i e u l t u r a . Tba group a t t a i n t in t a t a a d i a t e v a lu a a d u rin g tu a a a o f t r a n a i t i o n whan c a p i t a l fr o * a b ig b a r r a g ib a d a p r a e ia ta a w ith o u t b e in g r a p la e a d . Tba b o tte a iia g r a * abowa tb a b e g in n in g a d o p tio n o f a la a b a n d b u rn a g r i e u l t u r a . Capital-Labor Ratio 2000 3500 C a p it ^ lt ^ a b o r R a tio 0.1' 0 .0 5 1600 134 Figure S.7: The Capital-Labor Ratio during Transitions BISTORT C CAPITAL-LABOR RATIO (C 0M T1M U SD ) A fter about 3250 tho group p rim arily amploye alaah and burn a g r i eu ltu ra |to p diagram ). W e d ap let tba t r a n iit lo n Cron alaab and burn a j t ie a lt u t a to in te n s iv e ag rieu ltu ra in tb a bottom diagram. Capital-t^abor Ratio 0.05' 2200 2400 Capital-Labor Ratio 0.2 0.25 0.2 0.15 o.: 0.05 2500 2700 •Vaai ■ZITOttrO*><...TItS CAPITAL-LABOR RATIO (C O M T X M B E O ) Tba tr a n s itio n to io ta n a iv a a g rieu ltu ra ia n et com plete u n t il a fta i T 450 (top diagram ). Tba nodal provides Cor an in crea se la a o e la l - a p lt a l uban p opu lation roaeboa 1500 accounting fo r tba upward 4 1 1 f t around 4400 la tba b ottoa diagram. Tba *cataatropba* eccurt ; n t bafora 4C00. C apital-L abor Ratio 0.2 0.25 0.2 0.15 o.; 0.05 2 2 5 0 37o? 5335 T s< f5 * r 78 135 Figure 8.8: Ili.slory One— The Last 1200 Years New in tb a U t a u i v * t f t l e u l t t i n L 1 U 4 1 th a group’* p o p u la tio n In eraaaaa r a p id ly u n t i l ju a t b a ta ta 4 i 0 t . A t o i t e t t a tb a e i t y • t a t a ta g ta * and* in d la a a ta r . 2000 1300 1 0 0 > 0 0 4200 4400 4600 4600 “ 3ooS**r 2000 1300 1000 4200 4400 4 6 0 ^ 4 6 0 ^ T o5?, * C 500 400 300 4200 4400 465 o 4600 iOoX*** Capital-Laoor ratio 0 .3 3 ’ 4600 4200 o 136 disease, but epidemics typically take hold after periods of famine when the general health of people is low. 8 .2 C o m p u ter H isto ry T w o In this history we model a succcsful transition from huntcr-gatherer to city state over a 6100 year period. We have, however, made one change from the previous model. At the point where the group is ready to make the transition between intensive agriculture and the city state we "allow" the ruling elite the discretion to phase in the increase in capital. Essentially we allow the regime to add to its private capital only when per capita consumption reaches a level high enough to prevent population from decreasing. In doing so the economy will operate for a time with a sub-optimal capital-labor ratio. The regime still has no protection against fluctuations due to the random variable factor. The population intervals of dominance for each regime are the same as in the last computer history (sec table 8.2). In figure 8.9 the population trajectory is broken into three segments. The trajec tory for the first three regimes resembles th at of computer history one except th at the transition to intensive agriculture takes longer. In about year 5200 the group makes the first jum p to city state. In figure 8.10 we give the trajectory for averaged income (so-called because we have averaged income over ten year running periods to smooth out the variability arising from the random variable). Although the group usually stays in the city state regime after 5200, it cannot add to its capital sufficiently so th at per capita consumption permits it to grow until about the year 5800. One can see the trajectory of population after 5850 and income after 5900 in the bottom dia grams of figure 8.10. After 5950 the city state regime takes off and population climbs relatively rapidly. 137 Compare this with a partial history shown in figure 8.11. In this run we eliminate the ruling elites discretion in creating capital but we create a greater overlap of the two administrative technological functions so th at the economy of the third regime is healthier at the time the group switches to the fourth regime. This enables it to better withstand the shock of a quantum jump in capital. We pick up the history when the intensive agriculture regime has a population of about 2.45 million. In figure 8.11, the capital-labor ratio again reveals a switch to the city slate when it jumps to slightly above 0.5. in about the year 75 a disastrous year (stemming from the random variable) plunges the group back into intensive agriculture, but after about 100 years its population climbs and it makes a successful transition. Figure S.9: History Two—Population Population 3 00W 2000J 2000 4000 1000 2000 3000 20004 500 1000} Y e a r 4500 5000 5500 Population 3200} 3000} 6000 1:19 Figure S. 10: History Two—Income A v e r a a e d I n c o m e 2500 2000 1500 1000 2000 <000 e a r l I n c o m e 200 100 Y e a r 2000 3000 1000 * A v e r a g e d I n c o m e 1750 1000 500 5000 5500 Y e a r A v e r a g e d I n c o m e MO Figure 8.11: A Successful Jump lo City Slate m u M F tt or » t t m i i m j i w to m c m tr x r t Pepuljtien Avar*f*a IneoM iceo JOC Clpltil r«r e*p cem t«»r 400 t i l t c*p- i »d n tio 12 141 C hapter 9 SU M M A R Y A N D C O N CLUSIO N S The institutional structure of an economic system has a profound effect on its effi ciency, but the cITcct is extremely difficult to model. The method of using non-linear equations within a regime framework is one way to mathematically embody the po tential and limitations of institutional infrastructure based on specific considerations. Furthermore the non-linear aspect of the model captures many aspects of growth that economists have often attributed to random elements, but may, in fact, result from feedback elements inherent in the growth process. In this case we have considered structural possibilities and limitations imposed by population density when supplemented by capital. The inclusion of capital as a vari able influencing and influenced by the socioeconomic infrastructure can capture many aspects th at hindered or promoted change, but that population under-represented. The two together give a more realistic picture of long-run economic growth th a t the * * pure neoclassical model cannot emulate. We have chosen to portray the model as describing a large area where the tran sition to a regime occurs from a gradual build-up of population pressure thorughout the territory, creating forces th at cause a crescendo to occur in a critical local region. 142 However, we can use the model to effectively model local phcnomcna-indecd, we have suggested interpretations of certain runs th at are essentially local in nature. Those who object that we know of many instances where development did not take place in the way described here, can create a model to effect those local condi tions. For instance, the Indians of the Northwest Coast formed chicfdoms in spite of the fact that they essentially were huntcr-gathcrers. They could do this because they lived in a region rich in collectible resources; consequently they could achieve pop ulation densities th at perm itted a chicfdoin without having to resort to agriculture as an economic strategy. Nevertheless, to fully harvest the natural bounty as their population increased, they had to create capital (e.g. boats, wooden long houses) and cooperate economically (e.g. diverting streams to catch salmon during their yearly runs) in ways that only their population density allowed. The failure to include nomadic pastoralists constitutes a significant omission. Still, we can model pasloralism as an economic strategy in its pure state. The tendency of many pastoralists to become warriors, conquer agrarians and establish themselves as a nobility did not occur in a vacuum; it awaited the development of village agrarian societies in the way we have described here. Prior to that they could not effectively enforce such a strategy because their subjects would simply move from the area. We embody this activity in our current model when the pastoralists become part of the agrarian community. A more interesting drawback of the model in its current form is its omission of migration as a mechanism for changing population density. It seems analytically possible to divide a territory into local areas, create separate adm inistrative functions to describe each area, and link population changes with migration between the local areas taking place in accordance with specified rules, but we leave this for future 143 work. A second weakness is the model's failure to account for technological change. To the point where we have carried the model it appears not to be a serious omission; but beginning with the city state it becomes more critical. We have indicated how technological change in transportation made the creation of new city states far easier later in time. To this we should mention the development of military technology which eventually made the creation of empires possible. In addition, technological change in goods with fewer global ramifications began to occur more rapidly in the city state, undoubtedly accelerating because labor became more specialized. In the first three regimes the most critical area of technological development we have ignored is the domestication of plants. One example among many is the devel opment of maize in the Americas. The size of an car of corn changed from perhaps one inch long in 5700 BC to nearly its present size around 2000 years ago.1 Besides technological development a further problem wit h extending the existing model through the city slate regime concerns the assumption wc made that groups had economic incentives to try to equalize population pressure. Earlier regimes, other things equal, offered a way of procuring food involving less work. With the city state wc have a substantial amount of non-agricultural production, consequently per capita income may begin to rise. Even if it does not, it certainly rises for the elite who now have greater power. Consequently the motive to equalize population pressure diminishes. The ruling elite now has an incentive to eliminate medium and small size urban centers so as to permit the growth of a larger city which increases their income. Instead of a tendency to equalize population pressure we may have a tendency to exaggerate its differences. •Warwick Bray, 1980, "Early Agriculture in the Americas,” in Cambridge Encyclopedia o f Archaeology, 144 Finally, it appears that the acceleration of technological change beginning with the ' city state regime makes the transmission of technology through imitation or learning a significant factor. In all regimes prior to it the lion’s share of economic production depended upon techniques that were either well-known or relatively easily assimilated. The failure to adopt a technique generally resulted from choice rather than ignorance. W ith the city state this is not longer the case. In Part II wc begin to analyze the causes and cfTccLs of technological change within a modern context. Part II Technological Change W ithin a C apitalist Econom y 146 Chapter 10 TECHNOLOGICAL GROWTH: ITS SCOPE A N D M EASURE 10.1 Introduction Technological innovation is the engine of economic growth with the greatest impact upon human experience, yet it remains growth's most elusive agent in terms of its cause, its measure and even its effect. No one doubts the central role it plays in growth theory, but attem pts to define it, to measure it and to explain it inevitably generate controversy and confusion. We can easily see the pervasive role technology has played in shaping our lives and institutions over a short period of 100 years, or over a longer period of 10,000 years. One hundred years ago a 500 mile journey was a major undertaking—indeed only a small fraction of humankind strayed that far from their birthplace within their lifetime, yet now many travel that far every week; out-of-town communication took place by letter or on special occasions by telegraph; at night a minority enjoyed the luxury of home lighting with oil lamps, and no one had heard of such home entertainments as television and radio. Most people relied on their own physical strength or that of animals to satisfy energy requirements in the conduct of their daily 147 lives. Ten thousand years ago most humans depended on their skills at gathering wild plants and hunting animals for survival. Despite such obvious upheavals and improvements in human well-being, the attem pt to measure the contribution from technological change saddles us with innumerable riddles and questions. All of our undoubtedly imperfect measures indicate that the unprecedented changes taking place in material well-being since 1820 stem largely from an enormous increase in labor productivity. Angus Maddison (1982) estimates that for 16 Western Euro pean type economics, labor productivity increased twenty-fold on the average from 1820 to 1980, a fact that defies belief when one considers the evident talents and drive of people of that era. They had, after all, discovered many of the scientific princi ples in the hard sciences that even today only a few specialists understand; used that knowledge to build powerful machines, harnessing energy in a way that freed industry from its dependence on animal power; conceived of the major areas of mathematical inquiry; created literary, musical and artistic masterpieces that shaped the landscape for further exploration; discovered and colonized continents while developing world wide empires; formulated the basic principles of economic organization; and outlined and implemented the ideas of statehood that still govern our lives. 10.2 M easuring T echnological G row th Three sources for the remarkable increase in labor productivity come readily to mind: (1) capital deepening, (2) a more highly trained labor force, and (3) technological development. The first of these, the most important in the popular view, seemingly accounts for only a fraction of the increase by standard measures, although a minor controversy flares over exactly how one should allocate growth among those three fac tors, Maddison, for instance, shows that from 1820 to 1978, gross non-residential fixed 148 * j. capital per person employed increased a little over five fold in the United Kingdom (from ($3,922 to $20,931 in 1970 purchasing power).1 Wc cannot precisely compare this figure with his previously quoted one of a twenty-fold increase since the latter encompasses other nations, but wc do get a sense of the magnitude of productiv ity growth as compared to capital deepening. Kuzncts describes the usual means of assessing productivity growth and attributes an even larger share to technology.3 If labor inputs are measured in hours with allowances for age and sex composition of the labor force; if net stock of reproducible capital is used to gauge capital inputs; and if labor and capital arc weighted by the rough proportions of labor and capital shares in total factor income, factor in puts can be estimated. The results for a number of developed countries over long growth periods arc clear: the combined factor inputs account for a small fraction of per capita product, leaving a large unaccounted-for residual. This residual, well over three-quarters of the growth in pcr-capita product, is presumably due largely to underlying technological inovations, which permit larger outputs with unchanged amounts of labor and repro ducible capital. Solow who pioneered the approach that Kuzncts describes, attributed 7/8ths of the increase in output per man-hour to technological change and only 1 /8th to the increase in capital.3 Nevertheless, economists differ widely in their estimates of the contribution of technological change. ‘A. Maddison, 1982,PAases of Capitalist Development. See Table 3.5 on p. 59. 3S. Kusnets, 1979, Growth, Population and Income Distribution, p. 76. 3Robert Solow, August, 1957, "Technical Change and the Aggregate Production Function." Re view of Economics and Statistics, p. 312-320. 149 Denison, for instance in a study of nine countries from 1950 to 1962 found an over* all average growth rate in gross domestic product of 4.29% per year. He explained 2.66% through total factor productivity (which is nearly equivalent to technological change) while 0.87% came from growth in capital inputs (labor accounted for 0.76% J/1 Maddison using the same data but a different methodology found a growth rate of 4.39% of which increases in capital explained 2.14%, nearty three times Dennisons figure.5 Kendrick also attributes more to capital and less to technological develop* mcnt. A major source of the disagreement between Kendrick and Denison revolves around whether to use gross domestic product or net national income as the ap propriate measure of productivity. Denison (1993) reasons that net national income better measures welfare and docs not increase from a shift in composition from a lightly taxed industry to a heavily taxed one. Kendrick (1993) endorses the use of gross capital stocks since capital goods tend to have the same output producing ca pacity over their lifetimes. Estimates of depreciation greatly overstate any decline in productive capability, he believes. Maddison ti adds that gross capital better cap tures the contribution of capital to growth because it compensates for the fact that a later vintage of capital has a higher marginal productivity than an earlier model with the same production cost. He also points out that Denison’s method which gives no weight to government-owned capital overlooks the contribution of investments in roads, schools and other public infrastructure. Denison, far from repentant, responds that the gross capital approach ’ ’divorces cause from efTect.” Wanting to identify the contribution of capital with savings, he notes that ’ ’Fulton could build a steamboat 4E, Dennison and J. Poullier, 1967, Why Growth Rates Differ,, Brookings Institute, B A. Maddison, 1962, op, cil,, p.24. «A. Maddison, 1982, op.cit,, p. 24. 150 having a higher marginat product than boats that had equal production costs but were propelled by sails, oars, or poles because he and others invented the steamboat, not because his boat required more postponing of consumption. In fact, he feels that his method overstates the rote of capital because it ignores technological change that takes place within the capital goods sector.7 In passing wc should note that D. Jorgenson and Z. Grilidics using a different approach from Denison and Kendricks, concluded "that there had been almost no postwar increases in American productivity1 1 and that factor inputs could account for all the increase. While their paper raises interesting issues in measurement, my conception of technological change and simple observation makes such a result seem preposterous and I will ignore it. Bliss sums up the reason for the disparities re marking, 1 1 When economists agree on the theory of capital they will shortly reach agreement on everything else.1 1 8 If one tries to measure the cfTcd of technological development in more than a growth accounting tradition, many problems and ambiguities arise. How can one measure the value of new products? Many of the goods wc now occupy our lives with (automobiles, airplanes, television, movies, computers, hula hoops) did not exist 100 years ago, and as Kuzncts (1979) points out, one cannot simply measure the difference in cost when a new technology replaces an older one. For instance, the re placement of candles by electric illumination greatly reduced its cost, but by changing the structure of economic life, it created additional benefits by freeing us from our dependence on nature for light, and additional costs by making us more vulnerable to 7These views can be found in E. Denison, 1003, "The Growth Accounting Tradition and Prox imate Sources of Growth", in J. Kendrick, 1093, "How Much Does Caplia! Explain", both in ed. A Szirma et, ah, 1093, Explaining Economic Growth; Essays in Honor of Angus Maddison., North Holland Publishing Co„ and in A. Maddison, 1982, op. cit., p. 23-25. s Bliss, 1067, Capital Theory and the Distribution of Income., North Holland Publishing Co. p.vii 151 breakdowns arising from over reliance on a single source. New technology inevitably closes alternative paths. Those wishing to use steam-driven automobiles undoubt* cdty suffer from the retardation of that technology that occurred when gas*powered internal combustion engines gained superiority over it. New technology alters our most basic institutions and ways of life and creates costs and benefits th at no one foresees. The industrial revolution accelerated the pace of urbanization, making possible further technological breakthroughs—speciality shops, mass transit systems, etc.—but it also created new costs—slums, smog, concentrated pollution, etc. Much new technology arises only to solve problems that a previous technology created. An especially perplexing question is how to value the increase in leisure tim e th at increased productivity brings. One's answer is bound to have a profound impact on any measure one adopts. Truly, to disentangle the ramifications of technology adequately would require us to answer the age-old question of the meaning of human existence and form weights in accordance with our answers. 10.3 T h e E ffect o f T ech n ology 0 1 1 E con om ic In stitu tio n s Technological development has the capacity to fundamentally alter institutions, ways of thinking, modes of organization—indeed the very structure of life. Throughout most of human existence technological development, while persistent and with pro found long-range effects, took place a t a slow enough pace th at we could effectively ignore it in our growth model leading to the city state, accounting for its contribution in discrete quanta th at marked the change of a regime. Because of its slow pace, we could just as well have distinguished between regimes according to the way they embodied m ajor technological innovations rather than using the form of social or 152 ganization it entailed. Thus agriculture would characterize the primary agriculture regime, irrigation the intensive agriculture regime, military and defense technology the city slate, and so forth. Kuzncts advocated this approach asserting that if one uses the concept of economic epochs to categorize human history, then "the epoch must be seen as the realization of the potentialities involved in the single complex identified as the epochal innova* lion.” However, on his list he distinguished the last epoch, the modern period which began less than 200 years ago, by its embodiment of innovation itself, that is by ”the extended application of science to problems of economic production.”0 Maddison divides Europe's economic experiences over the last 2000 years into five economic epochs: Ancient Imperialism, a reversion to the Agrarianism that prevailed before ancient imperialism (500-1500), Advancing Agrarianism (1500*1700), Merchant Capitalism (1700-1820), and Capitalism (1820-present). Only during the last epoch docs he feel th at technological progress played a major role. He describes technical progress under capitalism as "tangible and perceived as compared (with technical progress in the two previous regimes) where it was present but imperceptible.” He adds that little innovation occurred during the agricultural regime because of its risk—an idea familiar to many development economists in the 1960s who used it to explain the reluctance peasants showed in employing newly developed genetic strains of staple crops despite demonstrations of its qualities in local town plazas. The idea of the coupling of innovation and risk and the way thal one's wealth fundamentally afreets their willingness to assume risk is one 1 will return to later.1 0 The pace of technological growth accelerated greatly during the last 170 or so 9S, Kuinets, 1966, Modern Economic Growth. The quotes are from p.4 and p.D respectively, but more generally see his section in Chapter 1 on economic epochs and epochal innovations. 10A. Maddison, 1982, op. cit. See the table on p.7. 153 » ■ * years, a period we might call Industrial Capitalism, as both direct observation and the more technical studies wc have cited attest, and wc can no longer ignore it. Schumpeter (1050, p. 110) makes this point emphatically writing, ”It is therefore quite wrong to say...that capitalist enterprise was one, and technological progress a second distinct factor in the observed development of output; they were essentially one and the same thing or, as wc may put it, the former was the propelling force of the latter.” Schumpeter felt th at the efficiency of the capitalist system, so highly acclaimed by most economists, if it ever existed, was now only a myth. The success of the capitalist system stems from the way in which it harnesses the talents of individuals and encourages them to innovate through the lure of economic profits. He emphasized the evolutionary capability of capitalism, that it ”is by nature a form or method of economic change and not only never is but never can be stationary.” He christened this process of innovation ”Creative Destruction.” 1 1 Maddison makes a similar point. ”A major driving force of modern economics is the strong propensity to risk capital on new techniques th at hold promise of improved profits in strong contrast to the defensive wariness of the pre-capitalist approach to technology.”1 2 These remarks indicate that a growth model of a capitalistic system must come to grips with the influence of technological change. It is the first system to institu tionalize the process of innovation. With this in mind, Schumpeter, despairing of the economics profession’s aproach to growth, remarked, ”...in dealing with capitalism we are dealing with an evolutionary process—yet that fragmentary analysis which yields the bulk of our propositions about the functions of modern capitalism persistently 1 1 Schumpeter, 1050, Capitalism, Socialism and Democracy., p. 82. 13Maddtson, 1982, op. cit,, p. 56. 154 ignores it.”1 3 Our goal is clear. If we want to explain modern economic growth within a capital* istic setting wc must create a model that cndogcnizcs technological change. In what follows wc will make further efforts to understand how it works. wSd»umpeter, 1050, op, cit„ p.82. 155 C hapter 11 CAU SES OF TECH NO LO G ICAL G R O W TH 11.1 T h eo ries o f T ech n ological G row th The first theories on the process of technological evolution regarded it as a heroic activity th at progressed randomly in accordance with the vagaries of human creativity. Marx was among the first to note the evolutionary path that technology followed. In an attem pt to synthesize these ideas William Ogburn hypothesized th at while geniuses created tcdinical progress, a certain percentage of the population had the ability to engage in inventive activity. By nurturing these traits a society could speed up technological development, while the subsequent accumulation of inventions would stim ulate further innovation as the number of elements available for combination grew. S. Gilfillan dc-emphasizcd the role of the inventor. Using ship building as an example, he theorized th at inventions progressed along a continuum with little or no role played by the inventor.1 A more sophisticated approach recognized the impact th at institutions have on the level of innovative activity. Schumpeter stressed th at the very essence of capitalism is lBasalls, 1088, The Evolution o f Technology,, p. 21-23. 156 its presumption th a t Arms pursue innovation. Kuzncts in characterizing the modem epoch by its use of science in production, remarked th at the "application of science via technology would not have taken place without changes in its social institutions."3 He noted the feedback effect th at technology has on the growth of science, further stim ulating economic growth. North, in a more abstract approach noted th at institutions embody the incentive structure of society. It follows that one can relate the am ount of innovative activity to the degree to which incentives reinforce th at search.3 Schumpeter first analyzed the destabilizing influence th at innovation has on the economy and hinted at a feedback effect th at has profoundly influenced many of the "new growth” theorists.4 In spite of Schumpeter's early insights, until the 1960s most growth economists regarded technological progress as an im portant but unexplainable phenomena. Con* tem porary growth models incorporated technological change as an exogenous factor— one occurring regularly but autonomously (sec, for instance, the classic 1956 Solow* Swan models). In the 1960s after considerable evidence accumulated pointing to the dom inant influence of technological diangc on growth, some economists tried to develop models that cndogcuizcd technological change. The most famous of these articles included: 1. Arrow's (1962) "Learning by Doing" which essentially embodied the concept of the learning curve. Arrow assumed that technical change came from the experience th at producers accumulated. He used cumulative gross investment as the index of th at experience. 3S. Kusnets, 1966. op. cit., p. 12. 3D. North, 1993, "The Ultimate Sources of Economic Growth" in ed. A. Srirma, Erplaining Economic Growth, 4J, Schumpeter, 1934, The Theory o f Economic Development., English edition. 157 2. Uzawa (1965) and Phelps (1966) two sector models that divided the economy into a consumer goods producing sector and one producing technological change. An equilibrium in this model depends on the assumption- of decreasing returns to the technology sector. 3. Conlisk’ s (1969) model which postulated that technical progress depends on na- tional income. An inspiration for his approach, perhaps, came from Schmookler’s (1966) view that demand determined the direction of innovation. His model has the merit of producing faster growth with a higher savings rate, a quality the models above generally lacked but which seems to agree with the empirical evidence. The early models assumed technical progress to be Harrod-neutral which, they believed, implied it was labor-augmenting, since the omission of this assumption precludes a balanccd-growlh path.5 Economists could give no reason necessitating Ilarrod-nculral growth; moreover, intuitively it seemed that most inventions were labor-saving.0 Much of the literature, therefore, focused on the question of embod iment of technology. This question will not concern this paper, however, since the major area where embodied and disembodied technological change models differ is on convergence to a steady state. I believe that technological progress implies that a steady state outcome is highly unlikely for a capitalist economy as I will attempt to show later. The literature on embodiment does bring out one important facet of technological change (and indirectly indicates another problem in measuring it); it only has meaning with respect to a set of factor prices and these determine the direction in which technical change takes place. Technical change under one set of factor prices may be ‘See Ramanathan, 1982, op. cit., p. 83 for a proof of this result. ‘ Intuition, however, could be wrong. We do know of many capital saving inventions such as the wireless. 158 economically unfeasible under another. Salter (1966), who has studied this problem in depth, illustrated the concept noting that before 1915 oil-fired locomotives were technically feasible but not worth developing due to the relative prices of oil mid coal at the time.7 The embodiment question generated a scries of models th at appointed capital as the carrier of new technology. Johansen (1959) first argued th at only new ma chines embody new technology, hence the age of a machine reflects its efficiency. This launched the vintage capital models which visualized the production function as a summation of individual production functions indexed by the age of capital it employed. Typical of this approach is Solow(1960). lie let A'„(0 represent the capital sur viving a t tim e t that was put into service at tim e v, L v(t) the labor needed to work the capital, and B evv the index of technological progress in machines produced at tim e t> . Then total output by machines manufactured at tim e v during time t is given by Qv(t) = B cvvL v(t)*K v(l)l~* and total output Q by Q = fLw Qv(t)dv. While this approach docs not explain why technological progress originally takes place, it does describe a way in which new technology radiates through an economy. Salter strongly supported this idea and gave evidence that much of the change in year to year pro ductivity occurs as entrepreneurs adopt the latest technology only after their existing capital stock depreciates. This does not mean that these entrepreneurs operate in efficiently; rather it indicates that they take into their calculations when estim ating future profits th at a period of time will exist when they will produce a t a higher cost than some of their rivals. Schumpeter observes th at "capital investment would not take place if entrepreneurs did not know th at exceptional favorable situations 7A similar situation may have developed with respect to electric automobiles. Several major automobile corporations have now offered models for sale. 159 arc likely to arise which if exploited by price, quality and quantity manipulation will produce profits adequate to tide over exceptionally unfavorable situations.”8 Salter collected d ata empirically supporting the idea that one observes a wide range of pro* ductivity within an industry (Sec Table 11*1). TABLE 11.1 Gross Tons of Pig Iron (Reproduced from Salter) Year Best Practice Plants Industry Average 1911 0.313 0.140 1917 0.326 0.150 1919 0.328 0.140 1921 0.428 0.178 1923 0.462 0.213 1925 0.512 0.285 1926 0.573 0.296 Maddison gives further evidence in a more modern context of the disparity.0 In Table 11.2 (from Maddison) the ratio of most efficient to average productivity has an arithm etic average of 1.G2 while most cflicient to least cflicicnl has an arithm etic average of 3.66. He writes that, ” these in ter plant variations arc due mainly (but not exclusively) to use in different plants of different vintages of capital embodying technical knowledge of successive periods.” He believes technological progress is most closely related to the rate of best practice productivity increase, although lie appar ently docs not equate the two because learning by doing will still take place in older plants. aJ, Schumpeter, 1950, Capitalism, Socialism and Democracy, p. 90. "Maddison, 1982, op. cit. p. 104, Table 5.8. Here he uses U. S,Bureau of Labor statistics whch divides the plants into quartiles, T am.c 5.5 P r o d u c tiv ity S p re a d s W ith in U S In du stries, 1 9 6 7 (Q u a rlilc s) 160 Kalin o f productivity Kalin o f productivity in 'most efficient' in ’m m t efficien t * to averape to 'least efficient* Hydraulic cctnctii 1.71 2.97 Wall furnace* and Heel mill* l.4 | 2.% Slccl pipe and tube* 1.58 2.89 Aircraft 1.28 ' 4.54 Aircraft engine* and engine part* 1.58 4.05 O lhcr aircraft equipment 1.65 3.57 C otton weaving 1.50 2.40 W omen’* hoitcry, except *ock* 1.60 2.80 Knit fabric 2.20 4,90 Tufted carpel* 1.90 5.20 Sawmill* 1.70 4.10 Tyret 1.40 3.20 Aluminium rolling and drawing 1.50 4.00 Source: DLS, Technotepieat C h a w and Manpower trends in 4>* Induiinn, Uullciin 1817. W aOttngion, 1974, and Tcchnotoplcal Chanteand Munpntvrr Tnrnrii in th e Induttrm, Ilulldiu I85A, W attim fioti. 1975. 11.2 P a tte r n s o f T echnological G row th The pattern by which new technology develops is unclear. Some theorists believe that in an industry technological growth describes a logistic curve (similar to the models of epidemic diffusion of disease), with slow development initially, rapid acceleration and finally a leveling off to a horizontal asymptote. The reasons given for this fall along two story lines: In the most prominent scenario (due to Soete (1993) demand for the good plays the leading role. Soon after the introduction of a new product, consumers purchase it only when their income exceeds a certain level; over time this level falls as con sumers im itate others, or as information about the product becomes more widely disseminated. Finally the rate of sales falls as the market becomes saturated, Given the ubiquity of technological development in the last century one doubts th at a slowdown results because oppportunities for further development run out, The 161 wave of diffusion of new technology transcends the harriers of industry. The assembly line that Ford used to revolutionize the automobile industry was composed of several elements from the evolving American manufacturing tradition of mass production. Ford did employ a highly efficient team of engineers who constantly devised specialized machine tools, and he used numerous time and motion studies to reduce assembly time, all witlun an atmosphere receptive to innovation. ” Company policy was to scrap machines as soon as they could be replaced by improved types.” 1 0 Similarly innovations in the computer chip industry today set ofT waves of technological growth that ripple through most of the American economy. I believe as Socle docs that demand plays a role in technological growth, but not in the way he has described. Demand reflects among other things the relative prices of substitutes or near substitutes for the product. As technological develop* mcnt takes place a good begins to compete effectively with, even replace some of its substitutes. This creates more profit opportunities within the industry and stimu lates futhcr technological change. However, the substitutes may themselves undergo technological diangc with a similar effect on its substitutes including the good in question. Thus demand becomes an index of current success within a price and prod uct rivalry whose future contours cannot be readily discerned. In those instances when substitutes reclaim technological superiority, demand may fall off, or in some instances saturation may occur as Soetc asserts, but I believe the emphasis should fall on the way in which demand affects the profit potential within an industry rather than on the pattern which emerges from this dynamic process. Many economists stress the general continuity of technical change, arguing that huge breakthroughs rarely occur and when they do the subsequent accumulation of ,0Flink, 1990, in ed. Purcell Technology in America. 162 small gains can still swamp tlic cflcct of the original breakthrough, Salter points to the cotton textile industry where improvements in detail but not in basic methods allowed a potential increase of labor productivity of 50 per cent between 1910 and 1936 after an initial major breakthrough in 1910. The types of changes lie observed included larger spinning bobbins, improved design, chain drives and greater speeds. The introduction of new mechanical methods for producing electric light bulbs gives an even more dram atic example of continuity. A method introduced in 1925 significantly departed from the old way, but in the following six years, improvements in detail caused a five-fold increase in output per m an-hour.'1 Perhaps the more rapid pace of innovation today renders the logistical curve unim portant even if it is correct in its pure form. Kuzncts (1979) divided the cycle of major innovations into three phases which he called Initial Application, Diffusion and Slow down. He believed the first phase lasted twenty years while the second lasted even longer than that. In a world of rapidly changing technology, the Initial Application phase of a new innovation may occur before the third phase of an old innovation be gins. If so wc would observe a rate of productivity diange summing the productivity growth from the two innovations which would effectively hide the logistic shape. Recently some economists have begun to ascribe some of the residual increase from factor analysis to investments in human capital rather than technological growth. Al though one might regard this as technological development of a sort, one can perhaps see the difference in concept most clearly in Romer's (1990) ” Endogenous Technical Change.” He first notes that most economic goods are both -rivalrous and excludable. To Romer, rivalrous means that the use.of a good by an individual prevents its use by another, c. g., eating a pic. If an owner can prevent other people's use of a good u Salter, op, cit„ p. 5n, 163 by invoking a patent, lie calls it excludable. Romcr then asserts that technology is a non-rival, only partially excludable good, hence spillovers from technology exist. Human capital skills, however, arc rivalrous and excludable since only an individual possesses the actual knowledge or skill; in order for another person to acquire the same skill, he or she must also undergo training. It seems plausible th at increases in human capital partially explain some of the residual formerly attributed to technological growth, but it seems highly unlikely that it accounts for nearly all of it as Jorgenson and Grilichcs (1967) and Lucas (1988) seem to propose. I do not choose to debate the point at length, however, and will limit myself to a few remarks in the next section. For the purposes of the models I will simply include any increases coming from human capital under the banner of technological growth. 11.3 R & D , E d u cation and T echnological G row th The belief that the search for profits will induce technological change requires a mech anism for generating new ideas. Most economists use Research and Development (R&D) to fulfill this role in their models or in their attem pts to empirically measure the phenomena. Expenditures on R&D undoubtedly represent the best index that we have for the resources an economy devotes to innovation, but one cannot overlook its shortcomings. Certainly much of a firm’s innovative activity takes place in a context that does not enter formally into a R&D account. The failure to include Learning by Doing is perhaps the most egregious omission. In addition, problems arise when we must decide how to treat R&D performed outside the specific industry, for instance by individual inventors or university researchers. In a listing of the most important 164 inventions from 1900 to 1957 Jewkes found that independent researchers generated 49 of the 61 inventions. Any list of the 61 most important inventions will lead to a spirited debate, but it docs indicate that a great deal of inventive activity occurs outside the industry. Nevertheless, this omission probably docs not present a serious problem. We must differentiate between technological development and technological feasibility on the one hand and technological development and scientific advance on the other. It appears that our theoretical knowledge surpasses our technical capabilities to a considerable degree. Most R&D involves searching for, understanding and applying knowledge that already exists to new situations. In order to do this one must have a % certain amount of technical capability just to understand current work. Engaging in R&D is an excellent method of acquiring this capability. Cohen and Lcvinthal (1989) developed a model recognizing two benefits that result from a firm's investment in R&D; it generates new knowledge and it enhances the firm's ability to exploit and assimilate existing information. They dispute the position of many economists that the amount of spillover in R&D within an industry decreases the resources it devotes to it since the temporary benefits it bestows do not endure as long. On the contrary, they note that the more spillover within an industry the greater the incentive firms have to develop their capacity to use this knowledge. Consequently they conclude that the higher the price elasticity of demand or the less concentrated the industry, the more likely R&D will increase with spillovers. Romer (1990) used the theme of the co*dependence of human capital and tech* nology in one of his models of technological progress. In this mode) the amount of new knowledge generated depends on the amount of human capita) in the research sector. In turn the research sector uses new knowledge to produce designs for new 165 capital goods. The output sector uses capital goods, human capital and labor to produce final output. An interesting tradc-olT emerges when an increase in human capital devoted to research increases the rate of production of designs which tends to increase final output, but the resulting decrease in human capital in the final goods sector tends to decrease it. It does appear that an economy can accelerate its rate of productivity growth by increasing the training its workers receive. Two reasons for this conic to mind imme diately. If technological growth takes place largely by small but steady improvements in processes, machines and organization, then everyone involved in the production process S b a potential contributor to progress. The educational level of the labor force afTcctB its ability to study and discover improvements in machines and processes, and perhaps just as important, to communicate its ideas. Some technological breakthroughs depend on having enough technicians who can successfully use the new tools. Technicians in short supply command high salaries thereby making certain applications economically unfeasible. As the supply increases and relative salaries fall new methods become cost efficient. One suspects that part of the recent rapid expansion in the use of computers conics from an improvement in the computer skills of the work force. Several empirical studies show that the educat ion an economy supplies its citizens is a large factor in its per capita income growth. When one separates countries by income, one finds that from 1960 to 1985 primary and secondary education has the greatest explanatory power in low and lower middle income countries, while university enrollment is most significant among upper income and industrial market economies. Among all countries primary education had the greatest importance in the early part of the post war period, while secondary education became most important af- 166 ler that. Strangely enough the importance of university education among advanced economies seems to have decreased over tim e.1 2 Several writers have suggested that universities have lately produced workers in non-productive occupations such as lawyers by way of explanation. Historically, the United States, who Maddison says became the world’s technolog ical leader around 1890 taking over from the United Kingdom, probably led the world in the percent of its population with a primary education implying it may have had the highest literacy rate. This would seem to contribute significantly to the nation’s ability to apply mass production techniques to such a large part of its cconorpy. Because of the feedback effect of per capita income on education (i.e. higher income people consume more education), it is difficult to decipher the precise influence that education has on productivity growth. Perhaps a symbiotic relationship exists between the two. A more educated work force can better develop new methods of production, but new methods of production become economically feasible with a more educated work force. The efforts of some economists to attribute the increase solely to increases in human capital, I believe distorts the idea of technological growth. The lion’s share of technological growth appears to take place in small increments as Salter's examples indicate. Even some instances of radical breakthroughs may be more gradual than they seem. W hitney’s invention of the cotton gin borrowed from both the charka of India, a device th at used wooden cylinders to separate seed from fiber, and from cotton gins in use in some places in the West Indies for Sea Island cotton which had easily removeable fibers but a limited growing range,1 3 W att’s invention of the steam engine improved on one developed earlier by Newcomen and * ’See Wolff, 1093, p. 164-165. )3See 0 as alia, 1968, o;». cit, for an interesting summary of this and for his belief in the continuity of innovation. 167 drew on other recent scientific advances. I do not intend to denigrate the efforts of those two nor to minimize the impact of their inventions, but to emphasize that technological progress rarely, if ever, proceeds immediately from fundamentally new discoveries. Instead it arises from the recognition by practitioners that adjustments to current technology can result in profitable opportunities. The important question is whether a nation or a firm can increase its productivity growth by deciding to devote more resources to innovation. The evidence strongly indicates the answer is yes. In addition to a great deal of anecdotal confirmation, one can find a broad concurrence between the growth of institutionalized R&D and increased productivity growth in several western nations. Industrial R&D began with the synthetic dye manufacturers in Germany who es tablished the first industrial labs in the 1870s. Edison established his lab in 1876 and almost immediately produced outstanding results with the inventions of the phono graph, the carbon telephone transmitter and many inventions in electrical lighting systems. General Electric built the first corporate research facility in the United States in 1901 and labs run by Parkc-Davis (1902), Bell (1911) and Eastman Kodak (1913) followed. Within twenty years 526 firms in the United States had research laboratories and by 1983 the number had grown to over ll.OOO.1 4 Using statistics from Maddison’s Phases of Capitalist Development one sees a pattern of association emerging between growth in R&D and productivity growth. Naming his last two economic epochs Merchant Capitalism (1700-1820) and Capi talism (1820-present), Maddison notes that the major difference between the two is the striking increase in productivity growth. He estimates that the average annual increase in gross domestic product per capita during the first period averaged 0.2%, _____ 168 increased to 1.0% from 1820 to 1870 for Denmark, Prance and the United Kingdom (the only countries for which lie gives figures), and jumped further to 1.4% from 1870 to 1913 for 16 western European type economics while GDP per man-hour increased to 1.6% (this is an arithm etic average for the nations involved).1 * P art of the initial increase from (1820-1873) came from a pronounced increase in investment during which time, one would think, a great deal of R&D took place although it had not yet become institutionalized. FVoin 1913 to 1950, a period of rapid expansion in industrial research laboratories, (Purcell says that in 1917 375 such labs existed in the United States and this increased to over 1600 in 1931)10, GDP per man-hour increased to an average of 1.8% in spite of the devastating effects of two world wars and a prolonged depression. FVom 1950 to 1973 it skyrocketed to 4.5% per year before decreasing to 2.7% per cent from 1973 to 1979. It is more difficult to assess the effect of government sponsored R&D and pure research. An indication of its importance comes from a study by Everson and Kislev (1973) of 75 maize-growing countries. They concluded th at scientific research in maize contributes greatly to maize productivity and that it had a high payofT. They state further th at ”a major component of research's contribution is through the acceleration of the transfer of knowledge. Little knowledge is borrowed if no indigenous research takes place.” 11.4 In creasin g R etu rn s and R & D Recently many growth theorists, borrowing from international trade economists have become enamored with the idea that R&D may yield increasing returns to scale. Romer (1986) remarks th at the attem pt to use increasing returns to explain long-run 1 & Maddison, 1982 ,op, cit, l6PureeII, "An introduction", in Technology in America,, ed. Purcell, MIT Press, p,5 169 «. i. growth goes back at least to Adam Smith's pin factory, and points out that Marshall introduced internal and external economics to elaborate this concept. However, these initial attem pts foundered on the presumed rationale th at increasing returns result from specialization and division of labor. Knight successfully attacked this approach leading Romcr to remark, "It is now clear that these changes in the organization of product cannot be rigorously treated as technological externalities. Formally, in creased specialization opens new markets and introduces new goods. All producers in the industry may benefit from the introduction of these goods, but they are goods, not technological externalities.1 7 For a period of time after this exchange increasing returns became unfashionable. % Surely pari of the reason for its unpopularity stemmed from the intractable mathe matics arising from a search for an optimal solution to a profit maximization problem within a competitive economy of firms with increasing returns, rather than from any inherent defect in the concept. In its revived form its proponents usually hypothesize that an individual firm will experience decreasing returns to R&D from its own research efforts, but because all firms capture externalities from their competitor's research, the industry wilt expe rience increasing returns. Borrowing from international trade theory, an externality commonly mentioned is the effect that an increase in market size has. One can treat the output of R&D as a design of new capital equipment. Once one has the design in hand its repeated use incurs no additional expense, hence, it behaves like a fixed cost which, of course, decreases as market size increases. Another reason why a firm may face decreasing returns while the industry benefits from increasing returns stems from the spillover effect of R&D. An individual firm may ,TItomer, 1980, "Increasing Returns and Long-Run Growth," p. 1005. 170 lack the resources to solve every problem arising out of new technology in time to fully benefit from its market advantage before spillovers in R&D dilute that advantage. As the technology develops, bottlenecks arise that firms did not anticipate, and some problems can only be solved through trial and error which takes time. The industry serves as a kind of lab where firms can learn from each other’s mistakes. The sum total of R&D may give a more complete blueprint of what all firms can eventually do. The main benefit to the firm in the short run comes from gaining an advantage over competitors and developing market power which it can parlay into exploitation for monopoly profits or a larger market share while the advantage lasts. When the knowledge gained through R&D is only partially excludable, the benefits to the firm based on comparative advantage will not last, but those benefits still extend to the industry in its competition with substitute-producing industries. A situation where firms gain an inter-industry but not an intra-industry compar ative advantage arises when several firms make technological cost-cutting advances in different areas, or incorporate different but comparable product improvements. If all firms see their costs reduced by equal amounts none will gain at the other’s expense, but the entire industry will benefit at the expense of other industries by moving fur ther down along the industry demand curve. The inter-industry advantage increases as all the firms in the industry absorb the spillover benefits from their competitors. The concurrence then of increasing returns to the industry to R&D and decreasing returns to the firm seems compatible and seems to salvage the possibility of a com petitive equilibrium. But docs it really ensure a long-run competitive equilibrium? 171 11.5 M arket Structure and Innovation Economists lmvc asked whether certain market structures more easily generate tech* nological growth than others. Following Chamberlin, Cournot and Robinson’s work on monopoly and imperfect competition in the 1920s and 30s, the view developed that firms with market power might use that power not only to restrict output and raise prices (as the models of the time demonstrated), but also to retard technological progress (which the models, lacking dynamics, did not show). Schumpeter, the most eloquent critic of this view clearly differentiated between the static conclusions the models reached regarding efficiency, and the dynamic reality that makes, capitalism such an .effective vehicle for economic growth. ”[T]he firm of the type that is compatible with perfect competition is in many eases inferior in internal, especially technological cflicicncy. If it is, then it wastes opportunities. It may also in its endeavors to improve its methods of production waste capital because it is in a less favorable position to evolve and to judge new possibilities.” 18 Schumpeter believed that a firm’s opportunity to gain some form of market power induced it to invest in new technology. The payofT in those instances when it succeeded compensated for the cases in which it did not. Usually normal profits prevailed, but the successful examples ”provide the baits that lure capital on to untried trails.” 10 Maclaurin (1949) in his study of the radio industry argued that in a truly com petitive industry, research will not take place since success gains only windfall profits. He felt that only through patents do firms earn returns through innovation. Romer (1990) shows that if R&D has increasing returns then an equilibrium cannot occur in a price-taking industry. He therefore modeled an industry full of monopolis- ,flScl)umpeter, 1950, op. p. 100. I9 /6 ir f., p . 9 0 . 172 tically competitive firms in his influential paper. Kuznets (1979) and others indicate that while large-scale firms have the resources to engage in R&D they can delay innovation even when its feasibility is established. Dasalla claimed that Dell labs realized from the beginning the value of patenting all minor variations that it developed, not necessarily to use them but to forestall potential competition or to give them something to trade with other firms that had patented some development it needed. Nevertheless, Schumpeter felt that critics overemphasized the power of large firms to retard technological growth. Observing that since a corporation wants to maxi mize the present net value of its assets and not the value of any individual piece of equipment, it should then adopt a new method of production when it promises to yield a larger future income per unit of corresponding future outlay. Many instances of delay, he asserted, really represent instances of ”cx ante conservation of capital in expectation of further improvement.” Since technological development continually occurs, a firm will not immediately junk its existing capital stock to incorporate every new wrinkle that comes along. Instead it tries to find the proper time to upgrade its capital stock. Schumpeter pointed to the automobile industry as an illustration of the process. The bonanza for the industry peaked about 1916, and although many firms entered after this date, most were eliminated by 1925. The few firms surviving still operated under competitive pressure despite their more protected position because a failure to keep abreast and improve quality would bring in new competitors. He felt that the expansion in quantity and quality of the Rayon industry in the 1920s also illustrated the dynamic power contained in an imperfect industry,20 10Ibid, See p. 00 for liis description of the automobile and rayon industry. 173 While Schumpeter may be correct in his position that a Arm with monopoly powers should continue to innovate, it may also be true that some Arms do slow down the process. Writing in 1950, he did not witness the decline of the United States automobile and steel industries. Had he observed the aftermath he might have felt that the automobile industry's failure to modernize led to its crisis when European and then Japanese competitors Aoodcd the market with higher quality automobiles. After mud) turmoil and considerable revamping, it seems the domestic auto makers will survive, but not without incurring considerable losses during the transition. Much of what we have just said applies equally well to the United States steel industry. It seems that up to a point some degree of market power will increase the tech nological growth potential of an industry. Much of the technological development that has taken place within those industries characterized by small Arms and nearly homogeneous products (such as agriculture), seems to have come from government sponsored research. However, as the automobile and steel industries since the 1960s show, immense market power that requires huge capital investments can slow down tcdinological development when the Arms within the industry feel too protected, and when they act unwisely—at least for a while; but in order for this to occur Arms also have to wield enough political power to shield themselves from their only other cflective source of competition—the foreign sector. One would think that even this power could have its limits without a large domestic market to exploit. Certainly the intransigence of the automobile and steel industries prevented them from expanding as far as they might have in foreign markets, but perhaps the size of the market they did exploit prevented them from worrying unduly about this. 174 11.6 G overn m en t and T echnological G row th So far we have ignored one important source of technological growth—government sponsored R&D. In the United States it has grown to monumental proportions, and has had a profound clfcct in many areas. Agriculture has received ongoing support since the Hatch Act in 1887 which created agricultural stations throughout the United States and led to a continual stream of technological breakthroughs, notably in genetic improvements of various crops. Because of this the United States has enjoyed a substantial competitive advantage in agriculture despite relatively high labor costs. Government support of R&D in the defense industry has had widespread diffu sion effects on other industries. Its support during World War I greatly aided the development and spread of the internal combustion engine in both truck and air plane transport. During World War II, government sponsored work on atomic power, radar communications and electronic controls led to breakthroughs that greatly al tered the landscape of many postwar industries in the United Slates. Recently the United States space program supported R&D that led to major improvements in the computer and industrial robot industry which in turn have spilled over to countless other industries. While government sponsored R&D lacks the cost constraints that private firms face, it seems that the benefits from government sponsored R&D have far exceeded the costs. Government sponsorship of training in skill industries must have played a large role in technological growth. The United States first engineering school was the U. S. Military Academy in 1802. Legislation during the civil war eventually resulted in the founding of an agricultural and mechanical school in each state of the Union.31 While this form of support develops human capital rather than affecting technological 3 1 Carroll W. Purcell ed., 1086, "An Introduction", in Technology j» America,, p. 4. 175 growth directly, the symbiotic relationship between the two indicates it may have had a significant contribution. This relationship is an area of active study at this time. 22 11.7 D em a n d , R isk and T ech n ological G row th Schmooklcr (19GG), who studied innovations in the capital goods industry, concluded th at demand primarily shaped the direction and magnitude of technological change. He describes scientific discovery as "far more a permissive than an active factor in the invention process.” When one branch of science lacks the expertise to tackle a problem, other brandies develop a "functionally equivalent invention. ...[T]he very high correlations oblaincd...bclwccn capital goods invention and investment levels in different industrics...indicatc th at a million dollars spent on one kind of good is likely to induce about as m udi invention as the same sum spent on any other good.” lie pictures an clastic technological frontier th a t one can extend in any direction by simply creating incentives to do so through demand. Schmooklcr’s view seems extreme. Rosonburg (197G) among others points out that in many areas a well-established demand lias failed to provide for a long-lived human need. Maddison (19S2) feels that persistent demand forces partially explain the unprecendcnlcd increase in productivity th at prevailed in western economics from 1950 to 1973 (4.5 percent compared to a 2.4 percent average from 1870 through 1979). During long periods of expansive demand, price fluctuations almost invari ably go upward, reducing borrowing risks. "Instead of worrying about investment risks, entrepreneurs become more aware of the consequences of not investing. " 23 I believe Maddison properly shifts the focus from demand to the profit environment 3,See articles by Romer, 1986 and Lucas, 1988 for models that relate productive growth to human capital. The latter attributes practically all technological growth to increases in human capital. The former believes that it must constitute a significant part of the increase. ^M addison, 1982, op. cit„ p. 99. 176 that entrepreneurs envision. In my view the most glaring omission in economic models that endogenize techno logical innovation is the critical role that risk plays in the process. Several economists have commented on the riskiness involved in capital expenditures in general, but par ticularly in capital embodying new technology. In a similar fashion new methods of production and the introduction of new products carry the promise of large profits but also an extremely high risk of failure. Shell (1967) succinctly remarks, ” the .inventive process is characterized by extreme riskiness.’1 An entrepreneur who introduces a new machine into production or who develops a new product has no relevant historical precedence to guide him in predicting the outcome of his actions, and mathematical, engineering and economic theory inade quately prepare him for the soothsaying role that he must assume if he is to make the sorts of calculations that equilibrium theory calls for. Kuzncts emphasizes how the cumulative effects of a major innovation cause an enormous transformation of economic relations (as for instance in the introduction of electric power or short waves in communications) with widespread unexpected bene fits, but also unanticipated diseconomies. "The significant aspect is that the surprises cannot be viewed as accidents; they arc inherent in the process of technological (and social) innovation in that it contains an element of the unknown,1124 Edison demonstrated the perils in forecasting potential uses when upon inventing the phonograph and thinking of its commercial potential, listed the ability to play music as only its fourth most important function.25 With the benefit of hindsight the utility of many inventions seems obvious, yet examples abound of many seemingly brilliant and viable innovations that received ^Kusnets, 1973, op, cit., p. 175, "Basalla, op, cit., p, M3, 177 substantial financial backing but that miserably flopped. For instance: 1. In the 1840s in Great Britain many felt that the atmospheric train line represented the wave of the future. They spent large sums in developing the technology but ultimately they built only 30 miles of line as certain technological shortcomings were never overcome. 2 . Industry and government spent billions of dollars on trying to develop a nuclear powered rocket and airplane and $ 1 0 0 million was spent on developing a nuclear merchant ship. 3. Attempts to commercially adopt a rotary internal combustion engine (the Wonkcl) failed in the 1970s. 4. The highly touted combined planc-automohite of the 1930s never took ofT . 5. Engineers could never solve all the technical problems in alternative automotive power plants using modified steam and electric power in the 1970s. I could cite countless other less dramatic examples that nevertheless devastated their promoters. An excellent illustration of the uncertainty of the direction in which new technology leads comes from the early competition between gas, steam and elec tricity as the source of power for automotive engines. In the early 1900s no one could foresee the ultimate outcome of this battle. All forms of power had strengths and weaknesses.50 Gas-powered engines had the longest range (about 70 miles), but the engines were noisy and required a sophisticated system of transmission of rotary to linear power. This necessitated the parallel development of gear shifts and transmissions. Because of the heat the engine generated, promoters also needed to develop an elaborate lubricating and cooling system. These needs made early models unreliable compared 54Most of the facts of the following account come from Dasalla 178 to steam and electric cars. Steam power did not have quite the cflicicncy of gasoline engines and starting them created problems since one needed to wait for the water to heat into steam (which took about 30 minutes in early versions and was ultimately reduced to a few minutes). However, it had fewer moving parts and thus required less precise engineering. Its ability to deliver maximum power with fewer RPMs meant that it needed only a rudimentary clutch, gear shift or transmission. However, it only had a range of about 30 miles before it needed more water. Electric cars were easy to start, nearly noiseless and required the fewest moving parts. Unhappily, they generated the least power and consequently had the most limited range, Nevertheless, in large cities where companies could make deliveries within a limited geographical area, electric trucks competed effectively into the 1920s. Gas apparently did not win out as a result of a rational study evaluating the rcl- ativc merits of the three; rather, it seems that entrepreneurs associated with steam power (the most prominent being the Stanley Brothers) ”lacked the ambition and managerial skills needed to produce cars in quantity and distribute them across the nation. Nor were they quick to incorporate existing technical improvements that would have made their vehicles more attractive. " 37 In 1914 the Stanley factory pro duced 650 cars a year while Ford manufactured that many in a day. Many historians also attribute the triumph of gas to its suitability to rural areas where range was important and where one could exploit the region's gas and oil deposits. Clearly the outcome of the battle had a dramatic effect on the participants in terms of material rewards and also on the infrastructure or the nation. Because of the uncertainty involved, one should realize that failure is not just ,TQasalla, op. cit. 179 reserved for those who sec less clearly or who make miscalculations. Rational par* ticipants must incorporate failure as a likely outcome in their ventures and plan accordingly. As Schumpeter observes, this explains ”how it is possible for so large a section of the capitalist world to work for nothing: in the midst of the prosperous twenties just about half of the business corporations in the United States were run at a loss, at zero profits, or at profits which, if they had been forsccn, would have been inadequate to call forth the effort and expenditure involved.” 28 Our goal from here is to develop some models that capture the process of techno logical innovation as a circumstance that occurs as a result of the intentional actions of agents, but within an environment of great risk. MSchumpeter, op. cit., p. 90. I. 180 Chapter 12 ANALYZING THE EFFECT OF TECHNOLOGICAL DEVELOPM ENT ON A N INDUSTRY 12.1 G eneral rem arks on th e C h ap ter’s m odels In the models that follow I will assume that technological development occurs as the result of intentional actions on the part of producers, and that the dollar amount of expenditure on R&D represents the intensity of those actions. Furthermore, I will assume that expenditures on R&D do promote technological growth in a fairly continuous fashion from the industry point of view, but probabilistically from the firm's vantage point. I will usually assume that a firm has a general but imprecise understanding of the probability distribution of results from R&D. I picture R&D as a more inclusive phenomena than the one that national accounts measure. Any employee who reduces his or her production activity in order to study a production process, develop a new product or improve a machine engages in R&D in my mind, although his salary for that period may not fall under such an account. Few economists doubt the effectiveness of R&D in promoting productivity growth. 181 Several studies show a strongly positive association between R&D and productivity. In addition to the agricultural study by Everson and Kislcv previously cited, Grilichcs (1964) and Mansfield (1969) oflcr further evidence. A question as to the eficicncy of R&D in increasing productivity does exist. However, many economists now charac terize R&D as having increasing returns to scale, a position I discuss below. Several recent studies stress the role th at the accumulation of human capital plays in increasing productivity (c.g. King and Rcbolo (19S7), Lucas (1988)), even on occasion denying the existence of technological growth. These papers prefer to use an increase in human capital to explain the residual in factor accounting; previously most economists believed th at technological change accounted for the residual. While their approach seems to me to lead to conclusions that seem unrealistic, it is unimportant for my purposes how we account for the shift in productive capacity as long as wc admit that it exists. If wc do, I will call the increase technological growth. One im portant lesson wc can derive from the human capital models concerns the positive relationship between the benefits from R&D and the amount of human capital. I prefer Roincr's (1990) approach to the problem. In his model, increases in human capital lead to an increase in the output of blueprints for machines that embody technological growth. This implies th at human capital can create gains in productivity that prevail even if it is subsequently removed. The more extreme approach of denying any technological improvement outside of increases in human capital would lead one to conclude th at if we were to remove from the economy the labor force engaged in R&D, production would fall to pre-industrial levels. One can imagine in such a circumstance that growth would cease, but one can hardly conceive of per capita output descending to 1750 levels. I will sidestep the human capital issue, however, and simply assume that if a certain level of human capital is required for 182 productivity growth, then the institutions provide it. I will often assume that investment by a firm in knowledge has decreasing returns to the firm but increasing returns for the industry. Roiner (1990A) sums up the case for increasing returns to knowledge. If production consists of rival inputs R, and non-rival inputs K, (for a definition of these inputs see the previous chapter) and wc make the usual assumption of homogeneous returns to rival inputs, then F (tR ,K ) — iF (R ,K ). But since F(tR, tK ) > F (tR ,K ) we must have increasing returns. In non*mathematical terms wc say that knowledge gives us a blueprint for production with whatever rival inputs wc dioosc to include. Once we have the blueprint wc can continue to use it in building as many factories as wc wish with only proportionate increases in cost. If wc increase our efforts in creating blue prints we should come up with better ones that wc again can replicate as often as wc wish (within resource limits, of course.) Wc can regard R&D as producing partially excludable inputs since a firm can patent the blueprints it produces—but not fully excludable since other firms can mimic most successful innovations to some degree without infringing on the patent. In addition, they can learn from other firms* failures. If an individual firm attem pts to increase R&D without bound, bottlenecks and other problems should arise in whidi they have no opportunity to benefit from the experiences of their rivals. But even if we were to assume increasing returns for the individual firm instead of just the industry, unlimited expansion of R&D would not necessarily take place for a rational firm, because the riskiness of the benefits from the expenditure would increase as the firm proceeded further into the unknown even as the expected value of its R&D increased. W ith risk averters, a firm should reach a point where the diminishing marginal utility of the expected benefits from R&D falls below its cost. 183 It would seem that risk aversion must characterize practically all firms over some interval; the rational firm’s goal is not to maximize its expected revenue for every period, but to maximize revenue over some unspecified period extending into the future. When a firm pursues this latter goat its survivability becomes a factor, and it will have a trade-ofT between its expected profits and its probability of survival. The rare firm whose competitive zeal remains unimpressed by the above considerations would find great difficulties in convincing their capital lenders to share its ardor. I make the critical assumption that a firm gambles with most of its R&D ex* penditure. While innovations and their assimilation and development may bear a reasonably consistent relationship with R&D spending for the industry, the returns to a single firm are less predictable if for no other reason than the Law of Large Numbers. In fact, wc have other reasons to expect this which I have detailed in the previous chapter. When a breakthrough occurs that advantageously positions a firm with respect to its rivals, it can gain substantial benefits—economic profits for a reasonable length of time, or perhaps more important for its long-run prospects, an increase in its market share. On the other hand the firm may find that existing factor prices or bottlenecks that prove to be unsolvable render their efforts unuseable. Given the riskiness of R&D one might ask whether most firms would not find it better to leave breakthroughs in R&D to a few firms in the industry and to institute only small programs that attem pt to imperfectly imitate the successful innovations that occur. In some industries with little apparent opportunities for technological progress, or for firms within an industry with inelastic demand and substantial bar riers to entry this might occur, but in most industries where firms compete even minimally on a technological basis, this would not likely be a viable strategy. The model below attempts to show that even small breakthroughs in productivity can pay enormously profitable dividends to a firm. The firms left behind may not suffer disastrous consequences over the very short-run, but if they leave the gains of successful firms unanswered, the negative consequences can quickly build into a disaster. 12.2 T he B enefits to a Firm o f a T echnological B reakthrough I will assume that an industry consists of n firms each with a Cobb-Douglas production function q = (aI<)°Ll-° (12.1) where q is the firm's output, K and L the amount of capital and labor input respec tively, a is an index of gains in productivity a firm makes from its R&D operations and 0 < o < 1. This specification assumes that technological change is botli Ilarrod neutral and Hicks neutral since the elasticity of substitut ion is one. While I have written the equation in a form indicating that technological development is capital augmenting, by rewriting the index of technological change as n '“° or a we can re gard it as labor augmenting or neutral. Letting tv and r represent the cost of labor and capital respectively, routine calculations give the cost-ininizing capital and labor needed to product q units of output of 185 where B = and the minimum cost of producing q is . rB a~x + w B a cq = 9 ~a (12.4) with c s= rB a“x + w Ba I assume that the industry is monopolistically competitive and that each firm attem pts to defend its market share. To illustrate the influence of productivity growth on profits wc will assume a = 1 for n — k firms and wc wilt consider values of a > 1 for k technologically advanced firms. The k firms with superior productivity become price leaders in the industry and they maximize profits by assuming (correctly) that all the, other firms in the industry will try to defend their market share and mimic their price and output decision. The industry demand curve giving price P as a function of industry demand Q is P = D(Q) = D{ng) (12.5) so price leaders maximize the profit function II = D(nq)q - £ q (12.6) To make further progress wc need to make some assumptions about the demand function. Suppose we linearize it around some known point (P0,Qo). Then we have * P = P0 — m(nQ — Qo) = P0 — mnq where — m is the slope of our linearization and * Po = Po + ™Q0 is simply the vertical axis intercept of the tangent line to the demand .curve at {P0 y Q0) (see figure 1 2 .1 ). The profit maximizing output and price for the most productive firms is 186 Figure 12.1: Linearizing the Demand Curve (12.7) and their profit is _ (A « a - c)a “ 4 mna7° (12.S) Since we want to use this model to study the effect that technological growth has on a firm’ s profits expressed as a percentage of normal profits, wc will abandon the traditional concept of a normal profit and use instead and index of money profits. Therefore we may speak of an industry where firms continually earn profits over the long-run, but such profits may represent zero or negative normal profits. Suppose that initially all firms had the same level of technological expertise with a — 1. Then « * the ratio of increase in profits for the technologically advanced firms is M U n. (12.9) iP o -c )* As an (hopefully realistic) example let w ~ r s= 1 and o = 0.5 implying that c = 2 and B = 1 . Let P0 = 2.2, m = 0.001 and n — 20. (n will affect total profits but it will have no effect on (9) which why we use the ratio of normal profits.) Using 187 different values for a in (9), the function A n „ /n a — /( a ) is shown in figure 12.2 and Table 1 2 .1 with lit representing the profits of the technologically retarded firms. TABLE 12.1 Percent Change in Profits a % Prod. Inc na Us % inc. % dec 1 0 .0 0 0.5 0.500 0 .0 0 .0 1 .0 2 1 .0 0 0.6034 0.494 20.7 1 .2 1.04 1.98 0.7131 0.484 42.6 3.2 1.08 3.92 0.9487 0.427 89.7 14.6 1.16 7.70 1.4710 0.240 194.2 52.0 1.25 11.80 2.1130 -0.062 322.6 1 0 1 .2 In this example the values of a fall well within the range of productivity change observed in the marketplace. When a increases from 1 to 1 .0 2 this represents a productivity increase of approximately 1% while the highest value of a in the table represents a productivity increase of less than 1 2 % (sec the second column of Table 1 2 .1 ). Kendrick (1993) whose Total Factor Productivity (TFP) residual understates the amount of technological change in the way I have conceived of it in this paper esti mates an average T FP residual for 18 countries of 1.80% per year from 1960 to 1990 (although it is only 0.69% in the United States). His figures for Japan and Italy over this period arc 3.43% and 3.05% respectively. One should keep in mind that his estimates encompass the whole economy. If wc considered different sectors of the economy we would find, in general, higher rates in agriculture and industry and lower ones in services. Maddison (1990, p. 117) calculates the average annual growth of output per person in FVance, Germany, Japan, Netherlands, UK and the USA for the period 1950 to 1973 for the sectors of agriculture, industry and services as 5.8%, 5.2% and 2 .6 % respectively. While we can attribute some of this difference to better opportunities for capital deepening in the first two sectors, we cannot account for all of it in this way. 1 S S Figure 12.2: Percent Change in ProfiW )tic to Changes in Productivity 1 ” < * - s“ C C L V - A ' ■ < ' v- c W o 15$ «et-'-Uj C — <k V t r £ C*« *~CL V * * £ V ^ - C . V U C - w . * ^ e k < L 0 “ C i ^ £ t , r w o Upon considering individual industries wc encounter even higher rates. Recall that Salter estimated that the light bulb industry experienced a five fold increase in output per man-hour over a period of six years after 1925 by introducing technology that improved only in details and not by revolutionalizing the process. When one considers intra-industry variations in productivity, even a value for a of 1.25 is quite ordinary. A close examination of (9) reveals that the difference of Pa — c heavily influences the magnitude of the percentage changes shown in Table 12.1 (although not the relative magnitude of change) since this determines the absolute amount of profits during the benchmark year. However, the choice of P0 = 2.2 and c = 2 in the example above yields profits of 0.5 compared to a factor income of 10, that is profits represent 5% of factor income generated by the industry which does not seem far 189 out of line. Using P0 — 3 profits would amount to 62.5 on a factor income of 50 or 125% which does seem unrealistic. Even in this instance a = 1.08 corresponds to a productivity increase of 3.92% and would increase profits by 15.7%. It appears inescapable to conclude th at the kind of technological change typically observed in this century provided opportunities for firms and industries to gain substantial advantages in their competition with rivals, and it therefore became incumbent for copctitiors to respond in kind (by doing R&D) in order to remain in the game. In examining the fall in profits for the firms that lag technologically, the conse quences of falling behind for a single period do not seem fatal. For instance, when a = 1.04 which corresponds to a productivity increase of 1.98%, profits drop by only 3.2%. This occurs because the firms defend their market position and lose only because they must accept a smaller profit margin on a larger volume. But if the differences accumulate then these firms indeed have dim prospects. For instance, if during four years productivity grows by say 1.98 % per year for the technologically advanced firms, then the cumulative effect will cause a drop of over 50 % for the conservative firms. If the demand curve for the industry shifts to the left because of technological improvements in rival industries, they face even more dire consequences. Note th at our assumption that firms defend their market position implies th at if all the firms in the industry have identical productivity gains, then all will have the same increase in profits. A possible objection to this example might arise from the assumption I have made of linearizing the demand curve around the known point (P — ot Qa), Let us consider the effect in percentage in profits by considering a demand curve of the form P = P — o — tnnq1 1 (12.10) I will not consider (as in the previous example P — Po-^n^nq as it becomes m athematically intractable. Using the latter specification would change the absolute amounts somewhat but we would get the same qualitative results, tn this case we get A n a n„ (Paa - c)H* (P - c ( 12.11) Using the same specifications as in the previous example and setting a = 1.04, by varying b wc get the results shown in figure 12.3 and Table 1 2 ,2 . TABLE 12.2 The Effect of b on Prof tabilily A ll/ll 6 0.248 4 0.207 3 0.305 2 0.426 1 0.403 0.875 0.703 0.5 0.917 0.375 1.429 0.25 Wc sec immediately that as b increases the benefit from technological change de creases. Upon reflection wc might expect this result since the elasticity of demand at the point (PoiQo) is Ed — P/bmQ implying th at elasticity decreases with b. The higher elasticity is, the greater the market responds to a cut in price th at technological change makes possible, hence our assertion th at in industries with inelastic demand and barriers to entry the incentive to increase productivity with R&D decreases. Our computer models will show that if the long run demand curve is inelastic and compe tition leads firms to lower prices (i. e. they do not collude) then technological change will lower their long run profits unless they can force out some of their competition. Observe th at if 6 > 2, demaud rapidly becomes highly inelastic; it seems probable th at for most industries the value of b would hover around one. 191 Figure 12.1 ]: The Effect of li on Profitability t v* pv"oC’ ‘*‘ V ^ ^ \ A S (e p ^ - o b ^ O - * v • w o ^ . C - ' ^ c d s .. C - ^ - 5 - ^ ^ T p t L . P 't e£~ C vt-\V*< v < $ S , C--3 ^ 2 - ^ 12.3 T h e R isk in ess o f B en efits from R & D Different kinds of R&D projects clearly have different levels of risk attached to them; for instance, R&D aimed at adapting elements of successful innovations by other firms has a more sure return than that spent on developments in untried directions. We can conceptually split R&D into the two components described by Cohen and Lcvinthal l . A firm engages in R&D in order to: (1) gain new knowledge and thus gain a competitive edge over its rivals, and (2 ) exploit and assimilate existing information within the industry. The former quest will have a relatively high expected value but a relatively low probability of success, whereas the latter should yield limited but more certain gains as the firm navigates in previously chartered waters. Inasmuch as a perennial concern for a firm is survival, one would think th at the ratio between the two types of R&D must fall as profits fall. Development economists have intensively studied the problem of adapting existing lCohen and Levintlml, 1980, "TI10 Two Faces of R&D," 192 technology. A theory current in the last half century holds that the growth rates between developed and developing countries must eventually converge since it seems easier to copy technology than to create it. 3 Maddison believes this explains how Western Europe and Japan could close the per»capita output gap so rapidly with the technologically more advanced United States after World War II. He cautions that ”onc should not exaggerate the case of this process. (Imitating nations) have had to adapt known technology to their particular needs in terms of product mix, factor prices, resource endowments, labour relations, consumer tastes, cxporl ambitions, size of plant, etc. All of this requires ’improvement engineering1 , technical and managerial skills, and an ability to remain familiar wilh a range of technical practice that is constantly changing in the lead countries.113 Imitation between rivals within the same nation poses many of these problems and the additional challenge of attempting to duplicate advances without infringing on patent rights. Because of these difficulties, in many industries it may pay firms to engage in some 1 1 cutting edge1 1 R&D since it seems obvious that a firm in a position to search for new innovations is also in a better position to adapt existing technology. In some technologically competing industries the ability to evaluate, adapt and assimilate is perhaps more essential to the survival of the firm in lean times than is the ability to forge breakthroughs. However, one would think that once a firm reached a position of financial security it would more willingly devote resources to R&D of a more speculative nature but with the potential for a high payoff In general, one would expect a firm to increase its R&D more than proportionally as its profits rise, but cut them back and concentrate on survival when its profits fall. We saw last year ^Nevertheless in recent times many economists have adopted the view that the convergence theory holds only for nations belonging to the same 'cluster’. The 'clusters' are generally differentiated by by economic structure, economic institutions and economic wealth. aA. Maddison, 1880, op. cif„ p. 108. 193 that both IBM anti Apple substantially cut their R&D budgets as their profits dove.4 But we do not have to rely on anecdotal evidence to believe this. Utility theory in economics leads us to the same conclusion if we acknowledge the gambling nature behind R&D as the next model shows. 12.4 A M odel o f R & D as a F unction o f P rofits We will assume that the more R&D a firm performs, the greater is its potential cost reduction in the next time period which may therefore increase its profits. Let t be the dollar amount allocated to R&D and c(t) be the cost reduction which occurs with probability 7 . We assume the amount of cost reduction increases at a decreasing rate of t so we have d(t) > 0 and c"(l) < 0 . W ithout technological change the firm produces x units of output at cost c. If it devotes t dollars to R&D it will have a per unit cost of c — c(i) with probability 7 c with probability 1 — 7 and its expected profits Ew become E ,r = (1 — 7 )[(p - c)x - 1 ] + 7 ((p - c + c(t) ) 3 - 1] = (p - c)x - t + qxc(t) ( 1 2 .1 2 ) The Pratt-Arrow measure of (absolute) risk aversion is /?*(!') = —Un(Y )/U ,(Y) where [/(.) is a utility function of wealth Y. The hypothesis of Decreasing Abso lute Risk Aversion asserts that an individual’s willingness to accept small gambles increases with wealth. Arrow points out that if absolute risk aversion increased with wealth, people would decrease the number of risky assets they held as their wealth increased, a phenomena that seems to conflict with our everyday experience.5 4See James Flanigan’ s article in the Los Angeles Times "Where there is no Research, Companies Perish", July 25, 1993. SK. Arrow, 1984, Collected Papers o f Kenneth J, Arrow,, Belknap Press, p. 153. 194 I propose to apply this hypothesis to a firm where the rate of return to equity replaces wealth as the argument. I believe one can justify this substitution because: ( 1) a Arm, like an individual is more reluctant to gamble when its survival is in question, but will defend incursions on its currcnl position and may gamble to improve its current position when its prospects for survival seem intact, trails which seem to underlie the hypothesis when it is applied to a person’s wealth. After all, people whose success is linked with the firm make the decision as to which gambles to accept. (2 ) A firm unlike an individual is under compulsion to earn at least a normal return even when it has huge assets. A wealthy individual docs not need to earn the same interest as a poor one in order to maintain a comfortable position. A firm, however, exists solely to make profits on the assets it possesses, and when the rate or return falls, threats of bankruptcy or takeover by outsiders arise regardless of its size. A large firm must use its greater assets to extend itself further in the marketplace. Therefore its income acts as an indicator of its willingness to lake short term risks, just as wealth serves this function for a person. If we accept the adapted version of Arrow's hypothesis of Decreasing Absolute Risk Aversion we have: P roposition. As (1) the probability of a cost reduction breakthrough increases, or (2) as a firm's anticipated profits independent from R&D increase, so will the amount of resources devoted to R&D. Proof: Let U(U) be an Arrow utility function. The firm's expected utility from profitB resulting from investment in R&D of t is £?[t/(n(0)] = < jU [n - 1 + *c(0] + (i - q)u\n - /] (12.13) where fl is the profits earned without engaging in R&D. Note first that if the expected 195 < • f c value of qxc(t) — I is non positive a risk averter will do no research so either t = 0 or qxc(i) > t on the relevant range. In the latter case we maximize (1 ). We see that 0 = implies that xc'fo = i + * ~ ^__^'(n — i) . . x c w 1+ , u'(n-( + xc(())- 1 ' A solution exists because c”(/) < 0 implies that d(l) is a decreasing function in t, while as t increases the right hand side of (14) increases since qxc(t) > t implies that xc(f) > t (since 0 < q < 1, hence as t increases £/'(n — t) increases (t/n < 0 ) while C/'(II — t + xc(t)) decreases. By examining equation (14), assertion 1 is immediately obvious. If q increases the right hand side decreases which implies that d(t) decreases and so I must increase. To see assertion 2 first note that decreasing absolute risk aversion implies that for h > 0 + (12.15) { / ' ( < + h) £ / ' ( . ) or U”{s + h )U \s) > £/"(s)£/'(s + h) (12.16) Let R = U\ n - t)/U'{n - 1 + *c(0). Then dR u ' { n - t + x c ( t ) ) u ' ' ( n - t ) - u ,( n - t ) u n( n - t + xc(i)) < m w {n - / + xc(0)a ( } Letting s = II - t and h — xc(f) in (16) we see from (17) that jjjf < 0. In examining equation (14) we see that if II increases then the right hand side decreases which means that d(t) decreases implying that t increases. So we now have theoretical reasons to believe that the amount of expenditure on R&D depends on profits. We can interpret a great deal of empirical evidence as 196 supporting this thesis. Several economists have remarked on the way in which innovations respond to mar* kct demand. Schmooklcr flatly argues th at "the very high correlations oblained...between capital goods invention and investment levels in different industries ...indicate that a million dollars spent on one kind of good is likely to induce about as much as the same sum spent 011 any other good. " 0 Uttcrback (1990) says th at from 60% to 80% of the innovations in a large number of fields have occurred in response to market demands and needs. Romcr states that "larger markets induce more research and faster growth.” 7 I would suggest th at it is not market demand per sc, but profits that do the inducing. When market demand increases it creates initially a potentially profitable environ ment for the industry's firms, and one observes a strong correlation between increases in demand and profits. This accords with Maddison's observation that innovation increases its pace during periods of "high and stable” demand—times when many firms have higher than usual profits th at they earn with lower than normal risks. 12.5 P ro fits and M arket E n try I now want to consider the question of why a firm chooses to enter or leave a particular industry, and how the industry adjusts to this fact. In beginning microeconomics we learn th at the presence of economic profits in an industry signals new firms to enter it, their entry taking place in orderly fashion until profits disappear. We learn that the existence of economic losses requires the least efficient firms to take a good look at themselves in the mirror before unceremoniously slinking out the back door, always in order of degree of inefficiency. The invisible 0Schmookler, 1966, op, cit. 7P. Flomer, 1990, op, cit,, p. s73. 197 hand creates a state of zero economic profits and the economic world resumes its beatific demeanor until the next disturbance occurs. Many economists, while proud of the latent lessons carried in the parable, recog nize that such a view oversimplifies, and they alert their more advanced students to the possibilities of a cobweb convergence model, a four period cyclic model or even a diverging cobweb model, although the latter, they admit* would not occur with ratio nal agents who .have knowledge of the structure of supply and demand and therefore can see more than one period ahead—I mean, how often can you react rcflcxivcly and get it in the neck before you begin to exert a little caution? The economics profession proceeds as if it believes that in the first ease the system converges rapidly enough th at one can effectively ignore the adjustm ent process—the nonconvcrgcncc ease presents an academically interesting problem with little real significance in the economic world. I feel th at even if we could hold outside influences constant we have little reason, theoretically or empirically to expect such an orderly transition. Let us first examine the question of entry from a theoretical point of view. Theoretically a firm enters an industry solely with the hope of making profits, but such a venture carries with it a gamble, so a firm chooses to enter based on its assessment of the expected utility of profits, the degree of risk, and the likelihood th at it can compete with existing firms. In Knightian terms unccrtaintly surrounds its choice; it must predict the reactions of existing firms and other unknown potential entrants.; it m ust forecast future demand and the prospects for major developments in substitutes for its product. In a technically sophisticated industry it must assess its ability to routinely innovate relative to other firms. In most cases it must commit itself to a course of action th at will entail substantial losses before it gains significant 198 feedback on the success of its actions. It seems unlikely under the circumstances th at a potential firm can construct a probability distribution that realistically describes its chances. On this basis alone we might expect th at the number of firms that enter an industry in response to some market disturbance would differ from the number the industry can carry. Frank Knight's suggestion that the overall sum of economic profits is negative8 indicates that such a phenomenon may have even established the long-term presence that gives it the stature of tradition. Even if a firm could formulate a true probability distribution, we have no reason to expect that the number of new firms would match the number the industry can tolerate. Suppose that all k potential entrants, omniscient in the present time, know that a market development creates opportunities for q new firms. They know that each prospective firm has wealth u»,, that the present expected value of profits for successful entry is II, and the present expected loss from unsuccessful entry is L. Furthermore they know cadi other's expected utility functions Ui and so they calculate for i belonging to ( 1, 2 ,3, ...,£) + n ) + (1 - l)Ui(uti - L) > Ui(wi) (12.18) for cadi positive integral value of n up to k. The largest n that satisfies n of the equations in (0.18) will be the number of firms that enter the industry. Nothing in this relationship leads us to believe that n should equal q. We can certainly imagine ourselves, for instance, entering an industry knowing we had only a 50% chance of success under the right circumstances. W hat constitutes the right circumstances? From (0.18) we see th at besides the 8F, Knight, 1927, p.8. 199 probability of success qfn% such circumstances include the size of expected profits, the potential losses, the degree of risk aversion and present wealth position. One might expect that the most recent industry profits would act as an indicator of the first two factors, market structure might characterize the last, while the third would depend on the industry. It suggests that we might develop a relationship between entry and industry profits. Clearly we have no theoretical reason to expect that negative economic profits will cause just enough firms* to exit and thus restore a slate of zero economic profits, nor do we have reason to believe that positive economic profits will draw just the right number of firms to eliminate those profits. Forming a relationship between profits and entry based on empirical evidence presents problems because in reality we do not want to just look at the entry of new firms but at the addition to supply. This can come from new firms or from current firms that expand their operations. If wc measure excess supply we do not really know the degree to which wc have excluded previous accomodations to market conditions. The stock market gives us an example of how groups of individuals react to the anticipation of economic profits or losses. The Efficient Market Hypothesis, which in its strong form essentially asserts that a company's current stock market price rationally reflects all information available to investors and that new price behavior results only from new information0, received a serious blow when Shiller (1981) re vealed that neither new information nor subsequent dividend changes could account for price volatility in the stock market.10 The behavior of the stock market might lead us to believe that some level of economic profits might trigger firms to overreact 8See G. Farms et. al., 1969, "The Adjustment of Stock Market Prices to New Information,” International Economic Review„ p.1-21, for a discussion of this process l0Shiller, 1981, "Do Stock Prices Move Too Much to Re Justified by Subsequent Changes in Dividends?" 200 on the question of entry. In the case of economic losses, an examination of our own likely reaction might lead us to expect that many linns would tolerate limited losses for a while; their pres* cnce in the industry represents a considerable investment th at they cannot instantly liquidate—an investment not just in assets but also in life experiences. Rather than a continuous relationship between alternative sources of income, a sizeable gap may exist between what they expect to earn in this industry and their next best alterna tive. They would likely exit only when subsequent happenings confirm the bleakness of their future prospects, or bankruptcy forces them out. One would not expect a rapid convergence to equilibrium. Cohen and Cycrt in a discussion of the bituminous coal industry from 1910 to 1957 state that observers view it as a "sick industry...unable to attain a long-run competitive equilibrium when demand dcclincs...bccausc exit is difficult whcras entry is relatively casy.n Similarly they suggest that the cotton textile industry, described as ”a closer approximation to perfect competition than any other manufacturing industry in the United States" had "chronic excess capacity from 1924 through at least 1936.” 1 1 These observations give us confidence in postulating that a lag might exist between negative profits and exit from an industry. Returning to equation (O.IS) in order to sec what kind of relationship between expected profits and firm entry we can deduce, wc see our first order of business is choosing a class of utility functions. I have chosen a utility function for wealth x of the form U(x) = where 0 < a < 1 and which has some unspecified upper bound. The following considerations motivate this choice: 1. The St. Petersburg paradox12 requires an individual to have a bounded predomi- “ Cohen and Cyert, 1965, The Theory of the Finn., p.154-159. “ The St, Petersburg paradox consists of a person tossing a fair coin n t imes unt il a head appears 201 nantly risk-averting utility function. (This docs not prevent her from having intervals characterized by risk-loving.) 2. Risk aversion for small gambles should decrease with wealth. The Arrow-Platt measure of (absolute) risk aversion /2* = ^ U v > (x)/U> (x) in this case is a/x which certainly decreases with wealth. 3. Arrow shows that another measure, Relative Risk Aversion, Rr = — xUn(x)f(/,(x) should ultimately increase with wealth, probably spending most of its time around one. He demonstrates that the upper boundedness of the utility function implies that Rr must tend to a limit greater than or equal to one as wealth becomes infinitely large. On the other hand its lower bound implies that Rr must approach a limit less than or equal to one as wealth approaches zero. He concludes that "if for simplicity, wc wish to assume a constant relative risk aversion, then the appropriate value is one. ...[T]his implies that the utility of wealth equals its logarithm", appropriately bounded at both ends.1 3 This utility function has a constant value, Rr = a which is necessarily less than one. The log function is inappropriate in this instance because it prevents calculations with zero wealth which has different implications for a firm than an individual. This should not create serious diflicultics because we can choose a close to one. In fact, since Rr increases with wealth, and in what follows one possible outcome is zero wealth, we could regard our choice of a near to but less than one as an approximation of a utility function that approaches and exceeds one as wealth becomes very large. I assume th at all potential entrants envision the same probability of success p, at which time she receives 2n dollars, The expected value of this is 2n(l/2 )n) = oo. Hence if she worries only about the expected value of money she should be willing to pay any price to play. Observation and self-6tudy indicate that she does not. 13K. Arrow, 1984, "The Theory of Risk Aversion", from Individual Choice under Certainly and Uncertainty, Belknop Press., p. 154. See his appendix, p.164, for a proof of these assertions, 202 that if successful they expect the same increase in wealth of x — c (with x > c), that if unsuccessful they will lose their investment and the opportunity to engage in their next best prospect c, and that if they engage in their next best prospect they will surely have a wealth of c. Only the degree of absolute risk aversion differentiates the prospective entrants. They therefore will enter the industry if they have a sufficiently smalt a satisfying ' ■ ( r b ’ i + ( 1 -', ) (rb°"*) > rb""- ( 1 2 - 1 9 > A few calculations show this occurs when a < ijj The assumption of constant relative risk aversion implies th at a firm will worry only about p and the ratios px and x to c, so let us assume c = 1 and that x is sealed accordingly. Then we must have “ < T ^ <««■> for a firm to enter. To go further wc must make an assumption about the distribution of a. With no other information wc might just as well assume it has a normal distribution (what else would you propose?) with mean ft and variance ct2, If wc let y(ar) equal the fraction of potential entrants who enter the market given the ratio of profits contingent upon successful entry x to profits without entry 1, then y(;r) = P(a < ln(;«)/lna?) = J exp dw (12.21) where P(a < I) is the probability that a is less than t. The shape of y (j) now depends on p, the probability of success. Considering only 203 Figure 12.4: T he Graph of I = ln (0 .1 x )/In x • i -T - 2 P(a < t) we would find that a increases at an increasing rate with respect to t up until i equals the mean of < i, which probably encompasses the relevant range for a; rarely, if ever, should profits explode to a point th at induces over half of all potential entrants to enter. But t docs not grow uniformly with x. The exact form of the relationship depends on p, but for all p between zero and one, t increases at a decreasing rate (with respect to x). We can see this by considering the function t — ln (p x )/ln x , where, dt — In p _ . , n = > s,ncc x > l m d P < cPx — In p = ( 12.22) (12.23) A typical graph is shown in figure 12.4. The two functions counterbalance each other, so we cannot say for sure whether j/(x) is concave or convex above y = 0. I give three cases for different values of p in figure 12.5. As p approaches one, the relationship between a and x appproaches a compressed version of a ’s cumulative density function. Of the three cases shown, p = 0.8 seems most likely to occur since it requires profits only on the order on one to two times other opportunities, while 204 p — 0.1 implied a ratio of 50 to 1. My analysis of the effects of a assumes that unsuccessful firms fall to zero wealth in order to reduce the complexity of the relationship. However, the worst*case wealth would also have a distribution function, most likely a kind of skewed normal curve. If wc accept the decreasing relative risk aversion hypothesis, wc would expect a greater tendency to enter among the wealthier firms. These two factors together might lead us tentatively believe that over the relevant range, y{x) is a concave upward function. 205 Figure 12.5: Three Graphs of Equation (21) for Different Values of p o . i \ - V s | . U L J p = 5 - O - S 206 Chapter 13 A PRO FIT DRIVEN MODEL OF TECHNOLOGICAL DEVELOPM ENT Let us use the two relationships wc developed in the last chapter to create a simple profit driven model of technological development. In this setting one can see moBt clearly the forces that I believe prevent a stable solution. If firms within an industry compete partially or wholly through R&D directed at cost reduction or product im provement, one can expect that the traditional picture of a stable equilibrium with firms earning normal profits in between disturbances and a convergent adjustment process during disturbances will not hold unless industry parameters sevcrly limit entry to the industry. In the model I will link technological growth and entry into the industry to mea surable disturbances in the firm's profit environment. I essentially propose that in the industries I have described, the difference equation IT(i + 1) = i/(II(t)), where 11(f) represents economic profits during time I, will typically have the shape shown in figure 13.1. Note that we have one equilibrium point at A = (p,p). The dynamics of the system depend on //'(/>). It is well known that if |//'(p )| > 1 then p is an 207 Figure 13.1: The Phase Portrait of Profits fl(* + 1) = #(11(0) rrc tr-^ ’ ) rrt^ ) 208 unstable equilibrium, but if J//'(/i)| < 1 on some open interval containing p, then all trajectories reaching the interval will converge to p. In defense of the shape for II that I have proposed, consider the following points. 1. If firms compete wholly or partially through R&D they will conduct it during times when they cam normal profits. A slate where all firms earn normal profits then cannot-be an equilibrium since the cumulative effect of ongoing R&D will lead to technological growth that either reduces per unit costs or shifts demand curves upward so that in the near future the industry's firms earn economic profits. 2. If economic profits make firms more willing to "gamble'' and they increase R&D more than proportionally, technological development will accelerate, creating even more opportunities for profits. 3. The crescendo of increased profits will lead other firms to enter the industry which tends to reduce profits. The interplay of the two forces, entry and technological growth, leaves two possible outcomes. In the first ease the two cancel cadi other smoothly. This corresponds to a value of IV at point A of absolute value Icsb than one. In this ease the amount of R&D creates opportunities for increased profits, but their realization is just counterbalanced by the entry of new firms. Hence all firms including new entrants make positive economic profits for the foreseeable future. Since we do not seem to observe this empirically, and since on reflection wc must wonder why other outsiders would not eventually take advantage of the opportunity of earning sudi profits, wc conclude that this occurs rarely, if ever. Certainly no disciple of rational expectations could fee] comfortable with this kind of equilibrium. If it does occur, it would seem that barriers to entry must exist and we really see existing firms expanding their operations. If size is the barrier wc would expect to have an oligopoly rather than monopolistic competition; if the barrier exists because only 209 a limited number of people possess the technological expertise needed to innovate, then over the long run the demand for their services should increase to a level that eliminates profits. In the second ease the two do not smoothly counterbalance. A typical trajectory might unfold as follows: FVoin a state of zero economic profits the industry's R&D expenditures create technological change that permits economic profits; this in turn leads to more R&D, technological change and profits until such a time that the entry of new firms overwhelms the market and reduces the level of profits. It seems probable that the reduction would fall to at least zero profits on occasion—if not, a history of fluctuating bill positive economic profits would signal enough potential entrants so as to eliminate them. After the fall in profits slows down entry, the process will qualitatively repeat itself, but one cannot predict the period of expansion nor the amount of falNofT in profits. Another plausible trajectory falling under this case follows a high-order cycle— long enough that participants could not determine for certain whether or not they perceived the cycle. In this ease, 7/'(/i) < — 1 implying the existence of chaotic trajectories. Theoretically a low order cycle could occur, although with a probability of zero in the mathematical sense. If it actually occurred, participants would learn its structure and their changed behavior would destroy the pcrmanance of 77. 4. We have observed that the curve 77(x) does not intersect the origin because R&D expenditures occur even when firms make zero economic profits—the firms compete technologically. Similarly the intersection of the curve with the 45 degree line below zero must create an unstable equilibrium because the failure to do so would imply that the industry could easily reach an equilibrium where firms earn negative profits; clearly we want to rule this out since it violates well established economic theory and 210 empirical observation. The unstable equilibrium has a probability of zero occurring; if troublemakers compel us to give meaning to its occurence wc might again interpret it as a case where the permanency of / / breaks down since now participants have knowledge of at least this one point of the curve and they act on that knowledge. 5. We depict a closed system in figure 13.1. However, with a minor change we can introduce the possibility (indeed over time the inevitability) of the extinction of the industry. If wc alter the shape of / / slightly so that I{(q) falls below b (the intersection of H with the 45 degree line) and extend / / so that it lies below the 45 degree line for n < 6, then with probability one the Sisyphean adventure wc have described will come to an end. Instead, eventually a catastrophic fall in profits will induce firms to cease R&D, while technology proceeds in industries producting substitute goods, allowing them to take over the market, thus shifting our industry’s demand curve downward dooming it to extinction. Wc therefore get a picture of an industry that docs not converge to equilibrium in the most likely scenario. Theoretically, it would seem the most likely choice for H{Yl(t)) is a function that yields cither chaotic paths or cyclic paths of a very high or der in most situations. Wc could understand the qualitative properties of the process but we would fail to pin down its details no matter how many periods we observed. We have deduced this simply by showing the incompatibility of an equilibrium point with zero profits and the instability of the only other equilibrium points. While we have focused only on profits within a single industry in this analysis we should not lose sight of what path an economy made up of many such industries takes. If all other things remain the same, technological change in these industries continually takes place, although at different rates, resulting in the development of new products, and/or improvements or lower costs in the existing ones. 211 * . * . To consider the ease of lower costs, each industry increases production since alt firms now produce at a lower cost and move down on the demand curve. This means th a t the industries contain more firms or th at the average rate of production per firm increases. In this more dynamic setting all things do not remain the same. Each industry produces goods th at, broadly speaking, substitute for one another, hence the demand curves for the industries change. Technological change docs increase the economy’s buying power in the form of increased income for the expanding industries, thus tending to shift demand curves upward in the long run, but does it always shift them upward regularly? One would think th a t on occasion the sum of factor income indirectly represented by the industry curves would fall. Surely the sum would not always grow at an even rate. Also, intuitively one would anticipate th at chaotic "cycles” within key industries might lead to resonances of chaotic ”cyclcs”within the economy as a whole, m udi as the clumping of m atter in the primordial universe eventually led to the formation of stars. Could this be the m ajor source of an economy's so-called cyclic behavior? Wc deal strictly in conjecture since one can produce combinations of industry interaction th at lead to almost any result. Nevertheless, it should cast some doubt on economists who insist on the existence of an equilibrium path for the economy th at would gently undulate except in iis response to unanticipated shocks. Rather than random shocks, the real reason for its unpredictable nature may be more profound. If theory leads us to conclude th a t the most dynamic industries behave chaotically, can we expect the economy which is the sum m ation of these processes to behave differently? Possibly so, but I have my doubts. 212 Figure 13.2: A Simple Piece-wise Linear Approximation of //(lift)) 13.1 P iece-w ise L inear D ifference E quation A p p ro x im a tio n s While wc have outlined the qualitative effects of profits on technological development and entry, we clearly do not know enough to confidently assign functional forms for these relationships. Nevertheless, the exercise of doing so illuminates possible scenar ios, and no harm is done if wc keep in mind the tcnuousncss of our assumptions. To illustrate the difference equation we discussed in the previous section, and to under stand its basic properties wc will first analyze three of the simplest approximations of this relationship, piece-wise linear forms consisting of two line segments. The first form we will consider is shown in figure 13.2. The system has two fixed points, neither of which seems supportable by economic theory; however, both are unstable and the probability of either occurring from a randomly chosen starting point is zero. Furthermore, the system has no stable periodic points as one can see by considering the graph of / / (2\ etc., (see figure 13.3) although it has unstable 213 Figure 13.3: / / 3(I1) and / / 3(n) 4 cycles of order 2n for all natural numbers re. These graphs simply squeeze in copies of / / in the same interval, hence the slopes of the lines become steeper. The intersection of any of these graphs with the 45 degree line (which represents the periodic points) must also be less than -I.1 Thus with a probability of one the system will pursue a chaotic path. In such eases one may ask if the system has an invariant distribution, that is a function that serves as a ’’density function” for trajectories drawn from randomly selected initial values. In this case the invariant distribution is simply the uniform density function over (x,c) which wc can show quite easily. To do so we will translate the system on (x,c) to the unit interval [0,1]. Note that if the first line has slope m, the second line’s slope is m /(l — rei). Letting D(x) be the density function, invariance implies that D(x) — D(f/~l(x)) and / D[x)dx = 1. From figure 13.4 this means that for a small interval dar, D(x)dx = 0(y)dy + D(s)ds where x = Jf(y) = //(c ). Thus the density function must satisfy lSee Day and Pianagiani, 1091, "Statistical Dynamics and Economics", J. of Economic Behavior and Organisation., p. 37*64, for a review of the properties governing stable and unstable cycles. 214 Figure 13.4: An Invariant Distribution DW - T ^ i L + D(= > Substituting into this D(x) - 1 wc have i = i + 1 = 1 . (13.1) (13.2) m m /(m — 1) By uniqueness, this must be the solution. So profits in the industry appear randomly distributed over the interval [:r,c] with a mean profit of (x -f c)/2. By examining figure 13.2 one sees that this would imply that firms earn positive economics on the average which conflicts with the Knightian assertion that average profits arc negative, and also with the reasonable belief that an industry that averaged positive economic profits over a long period should attract more firms thereby eliminating positive profits. One remedy for this state of afTairs simply involves a shifting of the interval (x,c) to the left so th at jx| > c. If we feel that an industry must earn positive profits before new firms swamp the industry, the peak of the graph would skew to the right (as in 215 Figure 13.5: Allowing for Positive Profits with //(II) figure 13.5); having (he peak on the left would seem inconsistent with the concept of economic profits. Another remedy would have us introduce the idea of extinction to the industry (see figure 13.6). Note that if industry profits fall below x, the industry enters a downward trajectory approaching — oo. We would simply interpret this to mean that because profits arc so low, R&D falls to such low levels that competing industries through product improvement or cost reductions via technological change so outdistance this industry th at it becomes extinct. This could describe the electric or steam automobile industry at the turn of the century. From figure 13.6 one sees that when profits fall in the interval (o, 6), in the next period they become greater than d thereby causing profits to fall below x in the fol lowing period, eventually leading to extinction. Almost all trajectories will ultimately fall into (a, A ) so the industry becomes extinct with probability one. Nevertheless an uncountable number of trajectories will never fall into extinction and the points of the interval that remain active form a Cantor set {see the appendix for a proof of this). Suppose p is the probability that a randomly chosen point belongs to (a, b). If Il£ is average profits before extinction, then the industry will earn average profits of 216 Figure 13.G: An Industry that Eventually Becomes Extinct —'TT L i >; (1 — jjJIIe + px over the life of the industry which may or may not be negative. In general we can say little about IT#. In figure 13.7 I consider another possibility for an industry. In this case extinction will not occur since profits never fall below A , and when it falls as low as A enough firms leave the industry so the profits begin to move upward subsequently due to technological growth. In general, one cannot characterize the invariant distribution that random trajectories define. However, we can characterize them under certain broad conditions and under some very specific ones. Again we will translate the equation to the unit intcral and represent / / by //(X) = { °x + l (13.3) where a, A > 0 and a -f b > 1, 217 Figure 13.7: Another Possible Form for / / ( n ) Characterized by Convergence to a Two Period cycle ITLlJ) If the absolute value of the product of the two slopes is less than one (i. c. a3/ ( a + 6 —1) < 1), then the system will converge towards a two period cycle (see figure 13.9 for an example) encompassing a relatively high (probably positive) and relatively low ( probably negative) value. One doubts th at such a cycle would occur since it seems to require easy entry and easy exit coupled with rapid technological change-two conditions th at would seem to work against rather than complement each other. If a > 1 we can characterize the density function in the special case th a t / / (n*(0) = 1 for any positive integer n. In this ease the density function is a step function. Huang (1989) proves this for the ease where the » reiterations occur on the first piece-wise segment of / /. In fact the density function will consist of piece-wise flat segments no m atter how often the system oscillates between the two segments before attaining the value one (see the appendix for a proof.) Aside from this case, however, we can say little about the density function. Qualti- 218 Figure 13.S: //(II) Characterized- by a Two Regime Recovery Period tativcly we know th at a period of increasing profits will ultim ately culm inate with a fall in profits, although a sequence resembling a two-period cycle might preclude the fall. If we knew the underlying equations we could give a maximum number of increases before a fall occurs, but wc could not otherwise guarantee when the fall would occur. T he piece-wise approximation to the form I believe to be most likely (sec figure 13.S) has much the same qualitative behavior as the case we have ju st analyzed; the basic difference between the two concerns the recovery period which in the latter case consists of two phases, one gradual and the other accelerated before a collapse again occurs. One, of course, could in principle create as many phases as one wishes to characterize the upward phase simply by inserting more line segments. If the equation has the form of figure 13.S, and //^ ( O ) = 1 the density function wilt again be piece-wise linear with a higher density on the flatter segments since more iterations occur on those segments before progressing on to other ones. 219 Figure 13.9: An Example of a Phase Equation that Converges to a Two Period Cycle 1 ,00 Li i I'ip T T T ) M' r 11 i m 11 n n n j i n i ) i riT jT r r c 1 1 1 1 i i I i 11111 1 1 1 1 n i i 1 i t i 11 i i i ; l-i 0.00=LU J b u 1.00 t t i 1.00 220 Figure 13.10a depicts an example of the phase diagram of the profit trajectory for a fifty year period starting with initial profits of zero. Figure 13.10b gives both the profit trajectory and the average profit trajectory. Note th at profits tend to have fairly long periods of ascent, often but not always followed by a sharp drop. Average profits hover close enough to zero to raise doubts in the mind of any would-be entrants th at this volatile industry may nevertheless have positive average profits. Figure 13.10: The Phase Diagram and Trajectory of a Two Regime Recovery Function 1.00 figure The phase < of grouts 50 gear per - 1.00 1.00 -1.00 1.00 Pro/its irof i ei ftqgre i3 ,*cb , The trajectories of pro and average profits for a period. , . 1.00 50.00 222 C hapter 14 A M ODEL W IT H C APITAL, PR O FIT S A N D TECH NO LO G ICAL C H A N G E % I will now consider an outline of a higher dimensional growth model in which capital and technological change serve as state variables. Doth will affect profits which in turn influences investment and R&D, thereby leading to further technological change. The added dimensionality allows more flexibility in assigning causal relationships and enables one to construct a more realistic model th at generates more complex and uncertain orbital paths, and suggests relationships and constraints th at might otherwise escape notice. The model assumes the following causal relationships prevail. It is the promise of future profits th at stimulates R&D and induces technological change. Current profits, the most significant indicator of future profits, provides the means for financing what essentially amounts to a gamble and increases a firm’s willingness to embrace risk-an argum ent I have made elsewhere in the paper. This leads to an equation of the form r ( < + i ) = G (n (0 ) (14.1) 223 where Tis the rate of technological change, n is industry profits, and G '(II) > 0. One might wish to write G(Tl(Hc(t))) in equation (1) in order to emphasize the role that R&D plays in the analysis, but for the sake of simplicity I assume that the form of G takes into account any such transitive relationship. Trundling along the path of conventional economic theory, I assume th at the level of economic profits induces changes in supply. In the previous model I used the number of firms in the industry as a proxy for supply; now I allow the industry’s capital stock to assume this role. This more accurately reflects the fact that changes in supply result from both entry and exit from the industry, and expansion or contraction of operations by existing firms. Investment in the current period (which I assume firms use in the subsequent pe riod) depends upon current profits and indirectly on the rale of technological change. The first factor is conventional—indeed it is the essential mechanism by which a capitalistic system responds to social desires. The second, while not controversial, perhaps deserves some remarks. As noted above, industries generally exhibit a range of techniques encompassing various degrees of efficiency. A firm th at decides to in vest in a technologically advancing industry must plan on operating at a technological disadvantage at a later time because it knows it cannot abandon its current capital every tim e a new development comes along. Certain in the knowledge that today’s new technology will become obsolete a t some tim e in the future, it strives to time its investment in such a way that maximizes high returns during the initial phase of its use, and minimizes its relative inefficiency during later periods when other firms with more recent investment have a technological advantage, One notes th at in theory, the durability of capital figures only loosely in the firm’s decision to replace it, and its original cost plays no part since it is water over the 224 dam . Thus the firm needs only to ponder whether investment wilt improve its current operations sufficiently to compensate for its cost. Of course, if old equipment functions inadequately, then its durability comes into play, but in a technologically advancing industry, obsolcscncc rather than durability seems to be the key depreciation factor. In this ease capital consumption allowances really represent an estim ate of the time th at will elapse before technological advance makes capital obsolete. These remarks lead to the equation A'(< + 1) = (1 - 6)K(i) + /(H (0 , T(t)) (14.2) where / , symbolizing investment has no sign restriction, but its two first partial derivatives arc positive. In this formulation (1 — 6) represents the fraction of current capital th a t can remain functional in the next period. However, the am ount of de preciation attributable to obsolcscncc because of technological change is captured in the function /( .,.) . Finally profits in period I depend upon industry supply (whose proxy variable is I\(t) ) and on the rate of technological change. Thus the equation 11(0 = P(T(t),K{t)) (14.3) completes the system. Some economists embody technological change in new capital. To the degree to which this formulation is correct, an air of ambiguity surrounds the form th at this last equation should take. On the one hand an increase in capital alone would indicate an increase in supply thereby tending to decrease profits. On the other hand new capital embodies the latest technology which therefore increases productivity and tends to increase profits. 225 Support for the latter position comes from the previously cited studies by Salter (1966) and Maddison (1982) that show the wide disparity between the best practice and the industry average in productivity. Salter embellishes this picture in his study of specific techniques used in the United States blast furnace industry from 1911 to 1926, and in the United States cigar manufacturing industry in 1936, showing that one can attribute much of the disparity in intcrplant productivity to temporal differences in the adoption of the latest technology. He found th at 30% of the blast furnace industry in 1926 had not adopLcd the two techniques of mechanical charging and casting which made their debut in 1905. He also examined the cigar industry's tabor requirement for producing a thousand five cent cigars under four methods of production still in use (in 1936). The least efficient method, hand made, required nearly three times as ,many man-hours (33.38 hours to 11.94 hours) as the most efficicnt-usc of a two operator machine.1 Nevertheless, one cannot tic productivity increases to capital alone. The above example illustrates disparities in labor productivity which is greater than the dis parity in productivity per sc. In addition, manufacturing processes do not involve indivisible melhods of production. Entrepreneurs can and do modernize certain facets of production while maintaining segments of older techniques, hence modernization takes place in discrete chunks. Salter again illustrates the process in an excellent study of the uneven rate at which improvement took place over a gamut of separate production steps in the United States cotton textile industry from 1910 to 1936. Looking at Table 14.1 one sees th at increases in output per man-hour ranged from only 11.8% in the cloth room to 150% in spooling and warping.3 l Y V , Salter, 1900, op. cil., p, 48-49. 3Ibid., p . 83-83. 226 TABLE 14.1 Percentage Increases in Best-Practice O utput Per Man-Hour by Processing Departments of the Cotton Textile Industry, U. S., 1910-1936 Departm ent % Inc. in ______________________________ Output/M an-H r. Carding 85.1 Spinning 32.2 Spooling and Warping 150.0 Slashing and Drawing 50.0 Weaving 48.4 Cloth Room 11.8 A great deal of technological change takes place through the reorganization and streamlining of the overall production process that changes as the firm modernizes a segment of it—Arrow’s ’’Learning by Doing” must have this process in mind—and the gains arc physically independent from the installation of new capital. The additional fact th at in many instances the introduction of new capital actually decreases capital expenditures (the wireless radio is the classical example), justifies our specification of technological change independently from investment. To put these ideas together more concretely, assume industry profits depend upon the difference between selling price and production cost multiplied by the output sold and that the industry demand curve has constant elasticity e. The demand curve then can be written as ■ (»r (14.4) with P representing market price and Q market supply. Further assume th at produc ers initially face a per unit cost of C0 which stems from a Cobb-Douglas production function f. 227 Q(l) = T f O / ^ r ^ t O 1 " 0 (14.5) where K and L represent capital and labor and T Is an index of technological progress w ith T(0) = 1 . If for simplicity we assume th a t the capital-labor ratio remains a constant m ade equal to one by our m ethod of measuring capital and labor, and th at factor prices arc stable, we can represent average cost at tim e t by Then industry profits arc n w - [ ( & ) * - $ f ] 9,0 (14'6) v / p l / e y l - l / e \ = r m \ K m — c °) (14* 7) since Q{t) = T{t)K(t). I will assume th a t the industry competes technologically, hence when firms earn normal economic profits some technological development will take place. T he index of technological change then is + + (14.8) where C?(0) is some small positive constant equal to the increase in productivity that would occur during periods of normal profits and G'(I1) > 0. T he equations (5), (10) and (11) constitute the model. The key to the behavior of the model revolves around the relationship between the functions I and G, th a t ib th e effect of profits on investment in capital and on technological progress. Let’s put P0 — C0 — 1 in equation (7) and assume th a t K{ 0) = 1, T(0) = 1, and 11(0) — 0. For analytical clarity we will consider the piece-wise linear functions for 228 T(t) and K(t) below. T(i + 1) = T(l) + | J,n (,) { { $ * £ (14.9) with P\ < 0. K (t+ l) = K(t) + c»n(t) + (c2 - c ,) P a n ( 0 < p 2 c^nfo pt < n (0 < p3 (i4.io) . c3n (i) + (c2 - c3)p 3 n(f) > p3 with c3,ci > c2 and P2 < 0 < P3 (sec figure 14.1). The specification for T guarantees that some R&D and thus technological growth occurs until profits fall to P\ < 0, while the formulation for I\ insures that net investment is zero when the industry earns normal profits, and that P2 and P3 arc thrcshhold levels of profitability that usher in an accelerated reaction to the current state. A little bit of experimentation quickly suggests the following constraints on pa rameter values for the model. LEMMA 1: If the industry elasticity c < 1 (in equation (5)) the system models an industry characterized by: i. eternally negative profits that approach a steady state. ii. capital that decreases steadily and is nearly inversely proportional to a frac tional power of the technology index which steadily increases. To see this note that one can write the profit function as n(t + i ) - / r (14.11) If profits converge to zero then A'^e = T~^~e^e, but since T(t + 1) > T(t) when profits are zero then K in the next period must fall which implies that profits must 229 Figure 14.1: The Piece-wise Linear Productivity Growth and Entry Functions K(ttl) * K(i) t r<Pr<i>), K(i> > I t.O t 0.10 b 1.1 0 H u l l « H i) » q(Pr(l>>, T(l> > I 0,10 0.10 230 have been negative. On the other hand if jT(f+l) = T(i) then profits are negative and hence capital in the next period will fall. If profits stabilize at some small negative level p ,T = A'1 / ' + p/A '(|- e)/e. Economists should intuitively expect this result. A technological development that reduces a firm's cost and allows it to charge a lower price may benefit the firm initially because it can capture a larger market share, but if it cannot maintain its advantage over time and other firms regain their market share, its profits will ultimately decrease since total revenue for the industry will have decreased while its output must have increased. It seems unlikely that this outcome could often repeat itself—more likely the firms with a technological edge would use their leverage to gain a decisive advantage and permanently increase their market share at the expense of laggards. Perhaps it is this combination of inelastic demand and opportunities for technological change that give birth to an oligopolistic industry. The surviving firms might then concentrate on technological development aimed at product improvement or differentiation in order to shift their demand curve outward. Several economists have suggested that oligopolistic firms characteristically compete in this fashion.3 In an industry with inelastic demand and a dearth of opportunities for productivity growth such as the buggy whip industry, one might expect to see little investment in R&D with most productivity gains that do occur arising from external sources. At any rate it seems that the assumption made here that R&D aimed at cost reduction takes place when firms earn normal economic profits is inappropriate for an industry with inelastic demand. Figure 14.2 shows a typical trajectory under this assumption when elasticity is less than one. Lemma 2: If demand has elasticity greater than two and c* > cs, the industry will 9See Tor instance Cyert and Colien, 10G5, op, cit. 231 Kigtnc 11,2: A Trajectory when Elasticity is Less than One 2.00 T H E TR A JEC TO R Y IJITH ELASTICITY = 0.5 PP00UCTIUITV CAPITAL PROFITS -0.10 150.00 0.00 eventually earn positive profits that increase without bound. To sec this again consider formulation (0.14) of the profit function. If profits arc negative then K falls until > K l/e or T e~x > I\, Let 6 be the productivity increase that occurs when profits arc zero. In the next period {T + s + ^ny5 - 1 > k + c3 n (1 4 .1 2 ) since c > 1. Hence profits will continue to increase thereafter. Observation: When 1 < e < 2 the system either produces positive profits without bound or converges to a positive value unless outrageous combinations of e,and c3 < c* are allowed. If we were to specify c .» > c3 we would imply that economic profits stimulate productivity growth at a faster rate than they do entry to the market, even when 232 economic profits reach astronomical heights. This, of course, is empirical nonsense and we will exclude these cases from future consideration. Figures 14.3a and b give trajectories of such cases. I have not discussed the issue of whether entry to the industry can occur in such a way as to just ofTset any profits that productivity growth would have allowed without expansion. While one cannot rule out the mathematical possibility of such an outcome, it hardly seems likely that such a path typifies the kind of industry examined here. It would have to skate along a knife's edge of a path far more undulating than the one that Ilarrod described over 40 years ago. It would require the omniscient capability of firms to not only predict the ulti mate productive benefits from their own efforts at R&D, but also the increase in productivity resulting from their adaption of technology produced by competitors. Furthermore, they would have to predict the reactions of any potential competitors, including those who currently have not joined the industry. Even if they could successfully do this, as section 5 in chapter 12 argues, we have no reason top expect potential competitors to abort their entry to the industry simply because they have a positive probability of failing. The model hypothesizes the existence of a multi-phase response to positive profits; it specifically embodies two responses although the addition of more phases would not endanger any of its conclusions. The first phase consists of a mild under reaction when profits are positive but small. The second consists of a more violent reaction when profits become larger, sometimes resulting in an over-reaction. Why should we expect this? First, we seem to observe it empirically. Shiller's characterization of the stock market as excessively volatile is an instance of this. The boom and bust cycle of real 233 Figure M.3: W ith c4 > C 3 Profits Rise without Round 3*O O i 1 ir i]n 1i m i i]'n TfjTn'i p 'i i i | i h i 11 n 1 j 111» ( —Productivi ty (—Capital ci > c3 rocuj}s in positive profile I orover. ci - 1,2, c3 * I elasticity = 1.5 Profits - 0.20 0.00 100. 10.00 Profits rise uithouy bund uhen "fcrri.Wi rfar.’ i ) Product ivi ty—> (—Capital Prof its—> - 0.20 0.00 234 estate prices in California, Texas and Tokyo arc other well-known examples. The Day* Gu model’s success in mimicking excessive volatility in the slock market by assuming a two-agent response lends credence to the representation adopted here.4 Second, the decision to establish a new firm or to expand existing operations is a greater commitment than, for instance, buying a stock. One must plan for such a move and consequently predict further into the future; the costs of miscalculating are greater. Humans—indeed all mammals—have developed through evolution the trait of seeking a "comfort zone" before plunging into new situations; some of this must carry over to the decisions of at least some firms which, after all, arc made by humans. If so an initial under*reaction seems highly likely. Nevertheless, when one observes others making large profits by performing tasks that one contemplated doing and, in fact, feels perfectly capable of doing, the pressure to enter increases. Such a "herding" instinct, an instance of Keynes' "animal spirits", need only exist among a minority of potential participants in order to kick off the reaction described here. The model proposes a three regime approach when both positive and negative profits occur because it seems that the same forces that cause a differentiated response to positive profits should also cause a differentiated response to negative profits. Firms, having committed time and resources to an endeavor and already possessing a degree of expertise in the industry that they may lack in other pursuits, might prefer to stick things out for awhile when conditions become adverse. Sudi a belief is not irrational; most firms will, in fact, survive. Nevertheless, the essential behavior of the model docs not depend upon the third regime. Its exclusion would simply result in longer periods of slowly increasing profits following declines in the industry. (See 4It, Day, W. Huang and M. Gu, 1990, "Fundamentals, Hubbles and Excess Volatility” , Work in progress, University of Southern California, 235 Figure 14.1 : Long Recovery Periods Result with n Two Phase Regime f * 1 ^ -0 O Si t T"» 200. figure 14.4 and compare with figures 14.7 through 14.11). The relevant feature characterizing the orbital paths of this model arise from the interplay between the constants c, and C 3 which linearly relate increases in produc tivity and investment respectively to profit levels beyond certain threshhold values. But before we discuss the relative values of c4 and 0 3, let us first aflirm that it is indeed productivity growth that creates the model's instability. If we assume that no productivity growth occurs when firm's earn zero economic profits, the model quickly converges globally to a steady state of zero profits, no productivity growth and no net investment after some initial adjustment. Figure 14.5 shows the orbital path when initial profits arc 0 . 1 0 , a relatively large amount compared to profits in subsequent experiments. One observes that productivity immediately increases, stimulated by positive profits. The high level of profits causes an over-reaction leading to economic 236 Figure 14.5: Instability Results from R&D. The Model Quickly Converges when we Assume no Technological Development Occurs when Economic Profits arc Zero 1 [ • product im tv CAPITAL 3 > ^ PROFITS - 0 . onU .1 t i I i l-i i I t i i i 1.1 . . . I . . . .i I . . . t f . . . . I losses in the next period. Subsequently supply gradually decreases causing profits to converge to zero, while no technological growth occurs after the first period. Naturally, if initial profits were zero, the model would have remained in this steady state. I feel this point is critical. With widely divergent values for c* and cj (but with C 4 < C 3 ), the model converges to a steady state of zero profits, zero productivity growth, and no net investment simply by changing it so as to eliminate productivity growth when economic profits are zero. In most runs I specify productivity growth of 0.01 and 0.005 when economic profits are zero, but far smaller values than this would create either instability or a kind of steady state with positive profits. Many equilibrium theorists were perhaps originally attracted to the idea of equi librium because they noticed that even violent reactions to an unstable state usually 237 led to a stable equilibrium that included zero economic profits. But in this model zero economic profits is not stable precisely because firms compete technologically and productivity growth occurs when profits arc zero. Empirical observation and thco* rctical musing lead me to believe that the latter case is more typical. The amount of productivity growth can be very small, far smaller than the amount of productivity growth modern economies typically average, in order to create instability. The as* sumption that productivity increases occur during periods of zero profits seems far more plausible than the alternative. Do we really believe that technological develop ment occurs only as a result of random forces creating brief instabilities that quickly abate? Or do we believe that the process of competition typically involves deliberate efforts on the part of entrepreneurs to improve their means of production? In admitting a multi-phase reaction to profits and permitting a small amount of productivity growth to occur when economic profits arc zero, we must find values of c3 and C 4 that give us realistic orbital paths. In experimenting with different values of C 3 and c* one finds that C 3 must be surprisingly large relative to C 4 in order to avoid orbital paths that converge to a steady state of positive profits. I should note that the thrcshhold profit value P3 , where the industry changes from a mild to a violent reaction, also affects the relative values of c3 and C 4. This occurs because the higher p3 is, the greater profits have a chance to build because of increasing productivity. I have set p3 = 0.04 or 0.06 in most of the test runs. I interpret this figure to represent the percentage return over a normal economic profit that the industry returns on the average for that period. A realistic model should give paths that either yield positive and negative profits that average near zero, or else produce fairly long episodes of negative profits that would scare the pants off some potential competitors, giving them pause for consid- 238 I- cration before deciding to enter the industry; a trajectory of even wildly fluctuating profits will hardly act as a deterrent to potential entrants if average profits are positive over both the short and long run. In the first example C 3 * = 5 while C 4 = 0.7 (see figure 14.6). This trajectory is clearly unrealistic. Capital and productivity increase relatively smoothly while profits seem to converge to a positive level. In reality the profits arc not unchanging. In figure 14.6b, the top trajectory shows that profits fluctuate in possibly a chaotic manner around a level of 0 .6 . Nevertheless, the fact it is positive makes the path highly unlikely. In the next example c3 is raised to 15 (see figure 14.7). The more violent reaction to \ positive profits creates a widely fluctuating profit picture. The first downturn heralds an approximately 30 year period of stagnation with negative profits and minimal productivity gains. Nevertheless, after this phase, although profits fluctuate they rarely become negative. Again the orbital path seems unlikely to occur. The existence of unstable but positive profits (see the more volatile path in figure 14.6b) while perhaps scaring some firms out of the industry would nevertheless ultimately attract enough new firms to eliminate profits. In the next example (figure 14.8) C 3 is 20. This gives the first viable photograph of an industrial path. We gel a picture of an industry characterized by episodes of profitability inducing rapid technological change closely shadowed by increases in investment, followed by longer periods of technological stagnation and below average profits. In order to gain a different interpretation let us arbitrarily call each period a year and imagine that the increase in capital takes place while the number of workers remains constant. Suppose that the exponents in the Cobb-Douglas production func* 239 Figure 14.G: The Industry Averages Positive Economic Profits Leading Us to Con-, elude the Divergence between c.| and C 3 m ust be greater CAPITAL - 0.20 ISO. 0.00 0.50r « 150 x 240 Figure 14.7: A Wider Divergence Between c4 and c3 Causes Profits to Have a Greater Variation PPOQUCJJOITY 150. time: x 241 Figure H.S: A Realistic Trajectory. Profits Average about Zero while Recovery Periods arc Long - 0.20 150. 0.00 242 lion are both 0.5. Noting that productivity nearly quadrupled (increasing from 1 to 3.85) while capital per worker nearly doubled we would get an increase in produc- tivity per man hour of between Five and six over this period. In the United States over the last 150 years, output per worker increased by more than this. However, by increasing c* and /> 3 we can boost the total increase in output per worker over this time period. In figure 14.0 a two phase response gives a syustcm characterized by long recovery periods with nearly a seven-fold productivity increase and nearly a five-fold increase in capital. Under the same assumptions as above this would amount to an increase in output per worker of about 15-fold. Let us note sonic other features of the model. As one might expect, the more volatile the reaction to economic profits, the less profitable the industry will turn out to be. When profitability stimulates technological change, this results in lower productivity growth over time within the industry. In figure 14.10 we compare the productivity indices when c3 is 20 and when it is 25. Because of the long periods of stagnation, the productivity index increases only to about 2.5 in the latter case. More surprisingly, larger values of C| which represents the linear relation between profits and increases in productivity can have a similar effect. In figure 14.11 we compare the productivity indices when cA = 0.9 and O .G . Although productivity increases more rapidly in the former case when profits arc positive, the additional profitability it creates during those periods provoke a greater reaction leading to longer periods of stagnation and an overall lower rate of technological change (about a 3.8-fold increase compared to a five-fold increase). It is difficult, in general, to prove that individual trajectories are chaotic. In a practical sense, this is probably a moot point since the trajectories do appear to be 213 Figure H.9: A Two-Phase Response Creates a 15-Fold Increase lit Output per Worker over a 150 Year Period 6.00 - 0.20 0.00 i --------1 --------1 --------1 --------1 A tuo-phaso eyelet* uith a high increase aroPSeroC IAV ^2y «cc>noM ic profile a ; a ■ °-5 P > ’ _ o = 1.9 Producti v ity--> p H a 0.02 /— ( - - C a p i t a l Prof its 150. 0.20 Profit trajectory in the tyo phase system uttn high productive* ----- during periods of zero czzz___ 0.00 244 Figure 14.10: A More Volatile Reaction to Economic Profits Results in Lower Overall Productivity Growth Product ivhij „ unon Cy* 20— > / Productivi <—uhen c ■ Profits (c » 25) -0.20' 150. 0.00 niilf 245 •Figure 14.11: There Appears to Be an Optimal Value for c* in order to achieve Maximum Productivity Growth 5.00 vity Ull <— Product ivi I uilh ci= 0. 150.00 nflr 246 unpredictable over their duration in a precise sense. We do have two indications that suggest that at least some of the trajectories exhibit chaos First, figure 14.12 indicates that there may be sensitive dependence on initial conditions. We do two runs of the same model with initial profits set to zero and 0.01. The runs begin to diverge significantly after about 40 periods. Another run with initial profits set at 0.001 gave a similar result with divergence delayed perhaps 10 periods. Second, if we try to condense this three dimensional model into a one dimensional counterpart, we get a model with chaotic tendencies. We accomplish the condensation by relating changes in productivity and supply to changes in profits. We assume ri(t + i) = n (o + a n (14.13) where AF1 = 1 + AA' “ 1 + AT* *14' 14) Then we create piece-wise linear functions for the changes in supply and produc tivity in a fashion analogous to the three dimensional model. We have A T as p4 -f m axf-p.i.dp*) (14.15) a r » / c,n n < Pi ...... “ { c2 n + /Me, - c2 ) n > p2 < 14* 16) The difference equation then is n << + , > = n M + T + Z 7? - H T S f ( l 4 a 7 ) 24? Figure 14.12: Sensitive Dependence on Initial Conditions Introduces the Possibility of a Chaotic trajectory 0.20 SENS I HUE DEPENDENCE ON INITIAL CONDITIONS? f " t - 0. 201 - 0.00 150,00 TIME * 248 Figure 14.13: The Phase Diagram of a One-Dimensional Condensation of the Model P r ( i ) pe n sio n s I approxJuYl ion hroo d ia e n c io n a i sgrtsm A one-dli ol iha tl.. undar c o n s i d e r a t i o n 0.15 •0.05 (see figure 14.13). One easily sees that the slope of the function at the positive fixed point is less than -1 indicating instability. Figures 14.14a and 14.14b picture the phase diagram after 50 and 300 iterations; the latter seems to cover most of the domain. In figure 14.14c the orbital path of 30 iterations shows no disccrnablc pattern, nor does the path of 1000 iterations ( not shown). The qualitative behavior of this model does not depend heavily upon the choice of constants other than having C j < c* < cj, and taking care that the system does not have a positive probability of falling to a value below in figure 14.13. Although I can certainly choose values of cj and cj that would give a periodic point of order 3 indicating periodic points of all orders, this would not guarantee that chaotic trajecto* ries have a positive probability of occurring. In a more practical sense, however, when 249 one chooses different initial values, one generally can find no predictable patterns in the profit trajectory; if these trajectories are periodic, they are of high enough order as to be indiscernible to a finite-lived individual. 250 Figure M. 11: The Phase Portrait of the One-Dimensional Condensation Id Prt p o rtra it of p r o f ile in,tbi itonai approximation. Prfttl) ! • p o rtra it a lta r 300 iia ra ti^ n c i i i t I t ProfiiE ir a ia c to ru for 50 urarc I I < . I l l . | , i , -0.01 0.00 5 0 . 251 Chapter 15 SU M M A R Y A N D CONCLUSIONS In P art I I have explored the dynamics of an industry th at competes significantly through technology. 1 have concluded that it will probably not reach an equilibrium state—a chaotic trajectory or a high order periodic cycle is a likely outcome. This results from the facts that (1) investment in R&D represents a gamble characterized by uncertainty as opposed to risk—an outcome far less predictable than even investment in capital, as risky as that can be. (2) Nevertheless, from a macro perspective one can better predict the benefits of R&D. Technological change accumulates a t a rate more or less proportional to expenditures on R&D. Economists have reason to believe th at industry-wide R&D exhibits increasing returns to scale, although the conclusions of this paper do not depend upon this. If it docs, the instability of the industry path increases and the proper forum for understanding the dynamics of it comes from Adaptive Economics, equilibrium analysis being particularly unsuited for the purpose. (3) Technological progress carries the seeds of industrial instability. It guarantees that a state of normal ccouomic profits is not a fixed point. So far I have largely ignored the effect that an unstable industry has on an economy as a whole. Conceivably several chaotic industries could complement each other in 252 such a way th at their peaks and troughs cancel out. Empirically, we have no reason to believe this; the history of economic growth over the last 200 years in the West, a time of unprecedented technological change, has been far from smooth. Other compelling reasons argue against this. Technological breakthroughs do not confine themselves to a single industry. In* stead innovations in one area often seem to lead to similar innovations in others. This occurs for at least two reasons. Technological development in capital goods nearly always afTcct several industries. Consider, for example, the effect of technological development in the computer industry and its effect on productivity in a multitude of other industries. In addition to changing the calculus of minimum cost packages in user industries in a static sense, one should additionally consider the dynamics of the situation. One sees that a different least cost package can lead to new directions for R&D in the new environment. For instance, a firm with high labor costs might likely direct its R&D efforts into those areas. A new invention that reduces its la* bor component might cause the firm to redirect its R&D to an area that now seems more im portant to its new cost framework, thereby leading to breakthroughs in the new area. A freight company before the commercial success of the gas engine would have little incentive to worry about reducing automotive repairs until it adopted that technology. 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Creator Powell, Lawrence Clark (author)

Core Title Complex economic growth

Degree Doctor of Philosophy

Degree Program Economics

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag economics, general,economics, history,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Day, Richard H. (committee chair), Kalaba, Robert E. (committee member), Moore, G. Alexander (committee member), Nugent, Jeffrey B. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c20-578931

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