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Planning For Stability And Self-Reliance: An Evaluation Of Policy Approaches For India

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Planning For Stability And Self-Reliance: An Evaluation Of Policy Approaches For India

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Content PLANNING FOR STABILITY AND SELF-RELIANCE AN EVALUATION OF POLICY APPROACHES FOR INDIA by • Gopal Krishna Kadekodi A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Economics) June 1973 INFORMATION TO USERS This material was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1.The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated with a large round black mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus cause a blurred image. You will find a good image of the page in the adjacent frame. 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete. 4. The majority of users indicate that the textual content is of greatest value, however, a somewhat higher quality reproduction could be made from "photographs" if essential to the understanding of the dissertation. Silver prints of "photographs" may be ordered at additional charge by writing the Order Department, giving the catalog number, title, author and specific pages you wish reproduced. 5. PLEASE NOTE: Some pages may have indistinct print. Filmed a s received. Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 73-31,356 KADEKODI, Gopal Krishna, 1943- PLANNING FOR STABILITY AND SELF-RELIANCE: AN EVALUATION OF POLICY APPROACHES FOR INDIA. University of Southern California, Ph.D., 1973 Economics, general I University Microfilms, A XERO X Company, Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALI FORNIA 9 0 0 0 7 This dissertation, written by GOPAL. .KRISHNA„1^DEK0DI........ under the direction of Dissertation Com mittee, and approved by a ll its members, has been presented to and accepted by The Graduate School, in partial fulfillm ent of requirements of the degree of D O C T O R O F P H IL O S O P H Y Dean Date DISSERTATION COMMITTEE Chairman ACKNOWLEDGEMENTS I would like to acknowledge the assistance of Professors Gerhard Tintner, Michael De Prano, and Richard Bellman who served as members of my dissertation committee The initial encouragement on this topic came from Professors Gerhard Tintner and Jeffrey Nugent. I am greatly indebted to Professor Tintner, my chairman, for his enthusiasm and valuable guidance in my study and research throughout my graduate work. Special thanks are in order for the financial support I received during my research assistantship with him. I am very grateful to Professor Nugent for his inexhaustible efforts in enhancing my understanding of economic theories of develop » ment. I received very pertinent comments on earlier drafts of this manuscript from Professor DePrano. I have greatly benefitted from our long discussions, espe cially relating to chapters IV and V. I am very thankful to him for all the useful suggestions and the patience with which he engineered through several drafts of this ii manuscript. Many of my discussions with Professor Bellman on topics on stability of a dynamic system were useful in structuring the models in my research. I am grateful to him for his enthusiasm in seeing this work completed'. The guidance I received from the members of my committee greatly improved the quality of this disser tation. However, all errors if any, remain mine. I am extremely grateful to the members of the Woodrow Wilson National Fellowship Committee for granting financial and moral support in this research. Acquaintance with my colleague Dr. Elliot Ponchick often led to long discussions on certain questions in research methodology and I have been benefitted by his untiring patience in going through several earlier drafts of my writings. I wish to thank him for his generous friendship. I wish to thank Mr. John Wolken who skillfully read the mathematical draft and made the final typed manuscript readable. Finally, the best I can do in words, for all the help I received from my wife, Savita, in pre paring the bibliography and typing earlier versions of this paper, is to say that her patience and help made it possible to complete this work several months earlier. • • • 1X1 TABLE OF CONTENTS Chapter Page I. INTRODUCTION .............................. 1 The Problem............................. 1 Purpose of the Study..................... 5 Definitions and Concepts ................. 6 Dissertation Organization ............... 7 II. REVIEW OF THE LITERATURE ON AID POLICY AND ESSENTIALS OF MONETARY POLICY .... 9 Introduction .............................. 9 Aid as an Investment Resource........... 10 Approaches to Planning with A i d ........ 13 Performance of A id....................... 19 Emphasis on Domestic Policy ............. 25 Conclusion................................ 31 III. AN INVESTMENT ALLOCATION POLICY WITH FOREIGN A I D .............................. 33 Introduction .............................. 33 Structure of the Model................... 36 Controllability in the Model............. 42 Chapter Page Finite Horizon Planning ................... 47 Analysis of Domestic Saving ............... 75 Analysis of Empirical Results ........... 77 IV. A MONETARY DISEQUILIBRIUM-ADJUSTMENT POLICY MODEL ................................ 85 Introduction ................................ 85 Structure of a Monetary Policy Model .... 88 Stability Properties of the Model .........107 Conclusions................................122 V. AN OPTIMAL MONETARY POLICY PLANNING MODEL FOR SELF-SUFFICIENCY....................... 123 Introduction................................123 Restatement of a Planning Problem .........126 Analysis of Empirical Results for the Indian Economy ............................144 Conclusion.................................. 182 VI. EVALUATION OF THE POLICY MODELS AND SUMMARY CONCLUSIONS........................184 A Comparison of the Two Policy Models . . .184 Scope for Further Study................... 188 Summary.................................... 190 v Chapter Page APPENDICES........................................ 193 A. DESCRIPTION OF THE DATA FROM THE INDIAN ECONOMY, 1970-1971 194 B. DATA DESCRIPTION FOR THE MONETARY POLICY M O D E L .................................... 205 C. INVESTMENT ALLOCATION IN A MONETARY POLICY MODEL ............................ 207 BIBLIOGRAPHY ..................................... 210 Vi LIST OF TABLES Table Page 3.1 Optimal Pattern of Capital Growth . . . 80 3.2 Labor Employment and Labor Froce Growth.................................. 81 3.3 Optimal Patterns of Output and Stipu lated Consumption Growth ....... 82 3.4 Optimal Foreign Trade Components . . . 83 • 5.1 Levels of Investment K, After 30 Years of Planning for Different Values of a and 0 ...............................145 5.2 Levels of Capital Stock and Real Balances after 30 Years of Planning for Different Values of a and 0.......... 147 5.3 Optimal Choice for a for Given n and a .................................148 • • Vll Table 5.4.1 5.4.2 5.5.1 5.5.2 5.6.1 5.6.2 5.7.1 Page Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 3=0.2 ............. 151 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates 3=0.2 ..... 152 Levels of Real Balance Supply, R@al Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 3=0.4 ............ 154 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates 3 = 0 . 4 .............................155 Levels of Real Balance Supply,'Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 3=0*6 ............ 157 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates 3 = 0 . 6 .............................158 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 3=0.8 ............ 160 viii Table Page 5.7.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates 3=0.8 161 5.8.1 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 8=1.0 163 5.8.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates: 6=1.0 164 5.9 The GNP Growth Rates (in percentages) for Combinations of 0 and a .... 173 5.10.1 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation . . . 175 5.10.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth R a t e s ...................... 176 5.11.1 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation . . . 178 5.11.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates ...................... 179 ix Table Page 5.12 Capital Stock and GNP after. 15 Years for Different Values of n...............182 6.1 Comparison of the Estimates with the Two Policy Models After Fifteen Years of Planning.............................185 x LIST OF ILLUSTRATIONS Figure Page 3.1 Optimal Time Path of rt ......................66 3.2 Optimal Time Path of 68 3.3 Optimal Choice of e for Different Choices of t = t ^ .......... 73 5.1 Time path of r3 t ........................... 130 5.2 Time paths of r ........................... 142 2t 5.3 Time path of GNP for Different Values of 8 ............................167 5.4 Optimal Time Paths of Supply and Demand for Real Cash Balances: 8 = 0.2..............168 5.5 Optimal Time Paths of Supply and Demand for Real Cash Balances: 8 = 0.4:..............169 5.6 Optimal Time Paths of Supply and Demand for Real Cash Balances: 8 = 0.6..............170 5.7 Optimal Time Paths of Supply and Demand for Real Cash Balances: 8 = 0.8........... 171 5.8 Optimal Time Paths of Supply and Demand for Real Cash Balances: 8 = 1.0........... 172 xi Figure Page 5.9 Time Paths of GNP with Different Technological Configurations ........... 181 CHAPTER I INTRODUCTION The Problem With the enormous growth of literature on economic development, the present day student of economic develop ment and planning is often forced to think that the problems of development are not unique and neither are the required economic theories to explain the process of econ omic development. As an illustration, consider the surplus labor theory (zero marginal product of agricultural labor), often associated with the names' of Lewis, Fei and Ranis.^ It was questioned by Jorgenson in a neoclassical dual ^A. W. Lewis, "Economic Development with Unlimited Supplies of Labor," The Manchester School, XXII (1954), pp. 139-191. J.C.H. Fei and G. Ranis, Development of the Labor Surplus Economy, Theory and Policy (Homewood, 111.: Richard Irwin, 1^64) . 1 2 2 economy model of development. Sen argued that the theory is debatable without any end, since the issue is one of measuring labor. The marginal productivity of labor employed could be zero but that of man-hours may not. The whole issue of the allocation of resources in the less developed countries has reached a state where both the classical (including the neo-classical) and the Keynesian theories of equilibrium and allocation of resources have been found to be lacking in explaining the rationality of behavior in the agrarian economies. In a recent conference on agriculture and economic develop ment, Daniel Thorner makes the following comments: The subject of this conference according to some of the papers, is peasant and sub sistence economies; according to others, it is peasant and subsistence economics. ... town persons find the peasant irra tional. Among the town persons least quali fied to understand the behavior of the peasantry were the classical economists, particularly Ricardo and his followers. 3 Thus, hypotheses on economic rationality, profit maximization, resource allocation, responses to economic 2 D.W. Jorgenson, "The Development of a Dual Economy," Economic Journal, LXXI (1961), pp. 309-334; A.K. Sen, "Peasants and Dualism with or without Surplus Labor," Journal of Political Economy, LXXIV (1966), pp. 425-450. Daniel Thorner's comment on a paper by Gorgescu- Roegen, "The Institutional Aspects of Peasant Communities: An Analytical View," Subsistence Agriculture and Economic 3 policies, etc., are to be tested taking into consideration various social, political, and institutional factors. A basic problem in economic development is the identification of the real issues. Several writers are of the opinion that on the demand side, it is the lack of incentives to invest due to the small size of the market and a low rate of saving on the supply side, that causes the spiral of economic poverty in the less developed economies.4 The supply of savings as a source of economic development and a critical minimal effort in investment are the real issues of capital formation and economic development. Arthur Lewis writes: The central problem in the theory of economic development is to understand the process by which a community which was pre viously saving and. investing 4 or 5 percent of its national income or less, converts it self into an economy where voluntary saving is running at about 12 to 15 percent of national income or more. This is the cen tral problem because the central fact of economic development is rapid capital accumu lation (including knowledge and skill with capital). 5 Development, ed. by C.R. Wharton (Aldine Publishers, 1969), pp. 61-104'J Georgescu-rRoegen stresses the need for analysis with village as the economic unit instead of firm or individuals. 4 See Ragner Nurkse, Problems of Capital Formation in Underdeveloped Countries and Patterns of Trade and Develop ment (Galaxy Book, Oxford University Press, 1967), Ch. 1. 5 A.W. Lewis, p. 155. See also H. Leibenstein, Many writers emphasize the role of the inflow of foreign capital to the developing economies to break through the low saving and low investment cycle. Aid acts both as a supply of saving and a minimal level of investment to raise the economy's income high enough to put the economy on a full employment growth path. But several economies have faced the problem of a high con sumption of luxury commodities due to the "demonstration g effect" and end up with heavy imports compared to exports. Thus, in addition to breaking the low saving and investment cycle, several economists argue that aid can 7 also be used to solve the balance of payments problem. Several recent studies have shown that aid, instead of enhancing the rate of savings in the receiving countries, O has reduced it. Economic Backwardness and Economic Growth (New York: John Wiley and Sons, 1963) , ch. 6, and P.N. Rosenstein- Rodan, Capital Formation and Economic Development (Cam bridge , Mass.: The MIT Press, 1964). ^The exports of less developed countries, consis ting mainly of agricultural commodities, face a very in elastic demand in the world market. See Paul Zarembka, Toward a Theory of Economic Development (San Francisco: Holden-Day, Inc., 19^2), ch. S. 7 H.B. Chenery and A.M. Strount, "Foreign Assis tance and Economic Development," American Economic Review, LVI (September, 1966), pp. 679-73T: See K.B. Griffin and J.L. Enos, "Foreign Assis tance: Objectives and Consequences," Economic Development and Cultural Change, XVIII (April, 1970), pp. 313-327. 5 The central problem of development is increasing the investment and savings potentials in the economy on a stable growth path. For the Indian economy, the problems of capital formation and stabilizing the growth paths have been the key issues during the last three plans. In recent years, with a foreign aid policy, the growth of the burden of foreign debt has added another dimension to the problems of economic planning in India. The empha sis of planning in India, today, centers on these three issues. In the fourth five year plan, the objectives of planning is summarized as: ...the plan proposes to step up the tempo of activity to the extent compa tible with maintaining stability and progress towards self-reliance. 9 Purpose of the Study This research will examine the implications of planning for self-reliance and full employment upon the domestic saving and investment rates in an optimizing policy model for India. The coneept of self-reliance is treated as a required goal for economic progress.^ A two 9 Government of India, Fourth Five Year Plan 1969- 74 (New Delhi: Government of India Printing Presis) ,T . p. 28. 10Barbara Ward and P.T. Bauer, "Two Views on Aid to Developing Countries," Occasional Paper 9 (London: The Institute of Economic Affairs, 1966) , pp. 35-36. Bauer 6 sector optimal investment policy model with external aid will be employed to study the savings path. As an alternative to the optimal investment policy model, a monetary policy model will be developed and its growth and stability properties will be studied. Applying such a policy model for the problems of planning in India, the estimates of the growth paths and their comparative statics will be evaluated. Finally, a comparative evalua tion of the policy implications of the two models for India will be made and further additional studies will be suggested. Definitions and Concepts In various sections of this dissertation, repeated reference will be made to certain concepts, definitions and terminologies. The word self-reliance will mean no dependency on foreign capital inflow for economic development. Often we will use the concept, equivalently as, self-sufficienay in growth. The policy variables are the choice elements in our study in the same sense as Tinbergen uses in his policy models. They may be either economic variables, writes that foreign aid and its relation to the balance of payment crises undermines the status and prestige of the self-reliance required for material progress. growth rates or ratios of certain economic variables. Often reference will be made to control variables which are the same as policy choice variables. The models will be tested on a comparative static basis, for change in certain parameters. References to such comparative static analysis will be often termed as sensitivity analy sis. The natural rate of growth is the potential full employment growth rate. Dissertation Organization Literature on the approach, use and efficiency of aid in development process differ substantially. Even the empirical experiences reveal a variety of opinions on aid. We review some of the major studies on planning with aid and evaluate the economic policy aspects in Chapter II. We also review in the same chapter the litera ture on growth and stability in a monetary economy and suggest possible approaches to the use of such monetary models to stabilize the saving and investment growth paths In Chapter III, we develop a two sector, two factor model, and analyze the implications of planning for full employ ment and self-sufficiency with a policy to eliminate the dependency on aid. With the data on the Indian economy we show that the domestic saving rate decreases with the termination of aid. 8 Based upon the discussion in Chapter II and in view of the conclusions from Chapter III, we note that it is essential to develop alternative growth models for stability. In Chapter IV, a disequilibrium monetary policy model (with fiscal policy as a special case) is developed along the lines of Tobin and Hadjimichalakis. The stability and growth properties of the model are analyzed. In Chapter V, such a domestic policy model is used for the purpose of planning in India to determine the full employment stable growth paths of income, investment and saving. The rate of supply of nominal money and the rate of the public sector growth are optimally determined. Chapter VI compares the two sector optimal invest ment policy model with aid and the monetary policy model. Certain policy conclusions on planning for self-reliance are drawn and scope for further research suggested. CHAPTER II REVIEW OF THE LITERATURE ON AID POLICY AND ESSENTIALS OF MONETARY POLICY Introduction Several studies have been made to examine the stability of an open economic system. Generally, it has been shown to be more difficult to examine the existence of growth equilibrium in an open economy. This has been discussed by Nikaido and many othersOniki and Uzawa working with a two-country, two-sector, two-factor model,2 have examined the dynamic path of capital accumulation and equilibrium levels of imports and exports of the two countries, under the assumptions of different patterns ■^N. Nikaido, "Balanced Growth in a Multi-sector Model of Income Proportion under Autonomous Expenditure Schemes," Review of Economic Studies, XXXI (January, 1964), pp. 25-42. 2 H. Uzawa and H. Oniki, "Patterns of Trade and Investment in a Dynamic Model of International Trade," Review of Economic Studies, XXXII, No. 89 (Jaunary, 1965), pp. 15-38. 9 10 of specialization. Ryder and Bardhan study (with similar 3 models) the optimal paths of capital accumulation, the former with trade and no aid fchd the latter with aid but no trade. Traditionally many authors have used dis counted intertemporal consumption levels in the objective function and examined the policy implications of such a path. See, for example, Intriligator and Stoleru.4 Aid as an Investment Resource The approaches to planning for an open economy differ from those of a closed economy. In the infinite time (Ramsey type) models, or the finite time horizon models, maximizing the savings rate is equivalent to maximizing the rate of investment growth. In the open aggregated models, the investment resources can be sup plied by domestic saving, excess of imports, or by foreign borrowing. Hence, planning models maximizing 3 Harl E. Ryder, Jr., "Optimal Accumulation and Trade in an Open Economy of Moderate Size," in Essays on the Theory of Optimal Economic Growth, ed. > Karl Shell (Cambridge, Mass.: MIT Press, ld67); P.K. Bardhan, "Opti mal Foreign Borrowing," in Essays on the Theory of Optimal Growth, ed. Karl Shell (Cambridge, Mass.: MIT Press, ‘ T9TT7T7 4 M.D. Intriligator, "Optimal Trade and Aid for a Developing Economy," (paper presented to the Econome tric Society meetings, San Francisco, California, 1967); L. G. Stoleru, "An Optimal Policy for Economic Growth," Econometrica, XXXIII (April, 1965), pp. 321-348.*— 11 the investment path for an open economy have the choice of combining different domestic saving profiles with or without foreign aid. In such models maximizing domes tic savings may not necessarily be equivalent to maxi mizing investment and vice versa. The treatment of aid in such planning models is based upon various economic/ psychological and political considerations. The economic rationale of aid is to supplement the domestic resources of the developing economies in their development planning. Often, low rates of saving and lack of inducement to invest are used as explanations for the low rate of income growth and the vicious circle of poverty in the less developed economies. Understanding the problems of such economies is the same as understanding the social attitudes, 5 institutions and human skills. As Kaldor says, the only way to explain Capitalism is through the changing atti tudes to risk-taking and profit-making. In the absence of risks and uncertainty in the social life of those economies, the low level of savings at individual levels is justifiable. With the vicious circle of poverty in those economies, whether the low level of savings is to 5 N. Kaldor, "Characteristics of Economic Develop ment ," International Congress of Studies of the Problem of Underdeveloped Areas (Milan: October, 1954) . 12 be considered as due to the attitudes, abilities or the lack of incentives is still debatable. In either case, in the spirit of the "critical minimum effort" hypothesis 6 of Leibenstein, foreign aid is treated as a stimulant to raise the income level initially, so that on the equilibrium growth path, the rate of domestic saving will have increased. With the flow of foreign aid, the developing economies can supplement their domestic saving in their effort to increase investment. Secondly, with the aid, those economies may not divert their income resources away from consumption to increase their saving. Hence, foreign aid acts not only as a source of saving but also as an engine to keep domestic consumption from falling. Chenery and Strout consider foreign aid as a 7 separate factor of production. In redent times, from both the doners and receivers' point of view, several political and psychological factors are considered in the determination of the level of aid. The donors of aid may have certain motivations to provide ^EU Leibenstein, Economic Backwardness and Economic Growth (New York: John Wiley and Sons, 1963), pp. 96-lb4. 7 H.B. Chenery and A.M. Strout, "Foreign Assis tance and Economic Development," American Economic Review, LVI (September, 1966), pp. 679. 13 assistance, out of their savings in the form of taxes, to the developing countries. Professor H.B. Chenery states: In the mest general sense, the main ob jective of foreign assistance, as of many other tools of foreign policy, is to produce the kind of political and economic environ ment in the world in which the United States can best pursue its own social goals. 8 Recipients of aid have been led to critically evaluate the performance and worth of the aid. Factors that are considered include: (1) the capital intensiveness of project aids, (2) the need for further intermediate capital goods to maintain such investments calling for imports of tied goods, (3) the burden of debt and the associated balance of payments difficulties. Thus both political and psychological factors are to be considered in the evaluation of aid performance. Approaches to Planning with. Aid In general the following types of models are considered in the development literature on aid. They are presented in brief for comparison and evaluation. Consideration of such a review of pertinent literature 8H.B. Chenery, "Objectives and Criteria < 5 1 3 Foreign Assistance," in The U.S. and the Developing Economies, ed. G. Ranis (New York: Norton, 1964), p. 88. 14 suggests methods for further analysis and study. (1) Using the Ramsey type utility function with a finite time horizon planning, Rahman shows that if suf ficient aid is available and the marginal output-capital ratio is greater than the rate of interest on foreign loan, foreign capital must be employed to the maximum available to supplement the domestic saving as well as 9 consumption. Rahman does not consider the effects on the domestic balance of payments conditions during the plan period. The finite horizon model that he considers leads to a heavy accumulation of leans by the terminal year of the plan. His own numerical exercise for Pakistan shows that,*® the ratio of external debt to the gross national income in twenty years will have increased from 0.054 to 8.1239. The interest payment in the twentieth year will be almost half of the gross national income. The gross national savings to gross domestic product ratio is in fact negative and decreasing during the last Q M.A. Rahman, "The Welfare Economics of Foreign Aid," The Pakistan Development Review (Summer, 1967), pp. 141-1*57. 10 Ibid., pp. 148-49. 15 18 out of 20 years of the plan period. With such a model, the burden of the debt servicing will become so great during the post plan, that it will bring heavy balance of payment difficulties and will weaken the exchange rate. An alternative to his approach is to consider the infinite time horizon model with a discounted utility function. In such a model, even though we expect that the effi cient demand for aid will account for the burden of debt 00 the objective function / U(t)dt itself may not converge. 0 In such a case we will not be able to associate a unique time path of consumption corresponding to the maximizing utility problem. (2) The second type of model treats the availa bility of foreign assistance as limited and the burden of debt is considered exclusively in the welfare func tion. Chenery and MacEwan in their development model for Pakistan^ consider a welfare function with three For details of this problem see S. Chakravarty, "Existence of an Optimum Savings Programme," in Capital Formation and Economic Development, ed. P. N. Rosenstein Rodan (Cambridge, Mass.: MIT Press, 1964) ^H.B. Chenery and A. MacEwan, "Optimal Patterns of Growth and Aid: The Case of Pakistan," in The Theory and Design of Economic Development, ed. E. Thorbecke and I. Adelraan,(Baltimore, Md.: Johns Hopkins Press, 1966), pp. 149-179. 16 components: (a) the discounted sum of consumption prior to the termination of the plan; (b) an indicator of the discounted value of consumption in all years posterior to the plan; and (c) the discounted sum of total capital inflow with a weight -v . v can be interpreted as a measure of social utility of receiving aid. The upshot of their model is a basic solution identifying three phases of the plan period: (a) phase I of maximum investment growth permitted by the absorptive capacity limit, given by the level of skill and other institutional factors; (b) phase II of production with foreign assistance for trade improvement, by increasing exports and holding imports at the minimum level corresponding to the income growth; (c) phase III of balanced growth in which, capital, imports, and exports grow at the same rate as the income, and aid is zero. Chenery and MacEwan in their model, treat the flow of foreign capital as equal to the balance of trade gap.'1 '3 But in a planning period of twenty three years, it is extremely impractical to assume that there is no debt servicing during the plan period. Thus, they under estimate the flow of foreign aid. Secondly, with the income growth, most of the underdeveloped economies go ' 1 '3Ibid. , equation (4), py 157. 17 through tiie phenomencn of "demonstration effect. " The increase in demand for imports has generated serious foreign exchange bottlenecks in several developing coun tries (including India in 1965). In either case the balance of trade deficit becomes very crucial to the planning problem. Thus the way they treated the balance of trade gap distorts the planning problem away from the real development problem. (3) A variant in the optimizing model of Chenery and MacEwan is a consistency model for India by Manne.14 Defining a concept of self reliance, he estimates the time path of aid,^domestic savings, income, and investment. In his model, the concept of self reliance prompts the psychic disutility of receiving aid but the termination of the aid is such that fresh capital inflows just offset the debt servicing during the post plan period. Thus Manny's approach takes into account the balance of pay ments problems during the post plan period. As an implication of reducing aid, he finds that the marginal propensity to save declined from 23 percent to 15 percent. To keep the marginal propensity to save from declining, he finds that aid has to be continued 14 A.S. Manne, "How Much Aid to End Aid?" Economic and Political Weekly (August, 1967). 18 for a longer time. (4) The two problems o£ limited domestic supply of savings and the balance of trade bottleneck that most of the developing economies are facing in recent years, led both the doners and the receivers of aid to consider the aid as an independent factor of production and to examine the performance of aid under certain allocative efficiency criterion.15 Chenery and Strout treat the development problem as maximizing the consumption until the target growth rate of gross national product is reached. They assume in their two gap theory of development that in the initial stages of the plan, the inability of the developing coun tries to raise sufficient domestic savings through a tax policy sets certain limits on their investments. Thus the gap between the domestic investment and saving becomes the binding constraint to the maximization of consumption. They assume that at this stage of the planning, the balance of payments does not become a binding constraint. The aid. is demanded to supplement domestic saving. The 15 Chenery and Strout show with the data for 1957- 62, of the 31 countries they considered, 19 did not show any indication of attaining self-sustaining growth either because they have a low saving rate or because they have serious trade deficit problems or both. See H.B. Chenery and A.M. Strout, pp. 708-09. 19 balance of trade becomes a binding constraint after some years of the plan. Then the amount of aid demanded is equal to the trade gap. The donors of aid, treating the availability of aid as limited, should provide the funds to the developing countries just to match the investment-saving gap in the initial stages and later to match the trade gap. Performance of Aid Prom the policy point of view, the transfer of assistance should be guided by factors in addition to allocative efficiency of aid. Two observations can be made concerning the validity of Chenery and Strout's assumptions. Firstly, they assume that the aid will not build excess capacity or reduce the domestic saving by substituting for it. Second, their assumption of the trade gap not being binding in the first phase of the plan is questionable. In the classical view, the main purpose of foreign assistance is to raise the domestic savings rate. As Chenery and Strout state: ... it is probably more important in this phase to focus on securing increases in production and income, a start must also be made on raising taxes and saving if international financing is to be justified by performance. 16 ^Chenery and Strout, p. 725. 20 The experience of some of the developing coun tries, however, does not show the validity of their assump tion of aid increasing the rate of domestic saving. Griffin and Enos show that as long as the cost of aid, i.e., the rate of interest on foreign loans, is less than the incremental output-capital ratio, it will pay a country to borrow and substitute for the domestic savings. Thus domestic savings and foreign assistance act as sub stitutes.^ An alternative suggestion to the Chenery and Strout treatment of saving dependent upon the levels of 18 domestic income, is to treat saving as a function of both the domestic income and the foreign assistance and to optimize the saving rate. McKinnon lists at least three reasons to explain why the developing countries face a large balance of 17 K.B. Griffin and J.L. Enos, "Foreign Assistance: Objectives and Consequences," Economic Development and Cultural Change, XVIII, No. 3 (April, l£?6), p. 320. With a cross section data for 32 countries during 1962-64, they find a negative correlation between Sd/y and Sf/y where Sd/y is the gross domestic Savings as a percentage of gross national product and Sf/y is the foreign savings as a percentage of gross national product. Similar re sults are found for a group of 13 countries from Asia and the Middle East (with or without Israel). See Ibid., p. 321. 18 Chenery and Strout, pp. 685, equation (5). 21 19 trade gap than an investment-savings gap: (a) the exports of the less developed countries consist of agricultural products and they face an inelastic demand for exports in the world market; (b) the developing coun tries are forced to agree upon certain quotas on their exports of light manufactured goods like textiles to the developed countries; and (c) the highly overvalued currencies maintained by the developing economies lead to serious shortage of foreign exchange. In addition to these reasons, the high consumption due to the "demonstration effect" and the capital inten siveness of the "project aid" lead to increases in im ports by more than the minimum stipulated levels. Chenery and Strout emphasize the required policy as: (a) bringing about the changes in the pro ductive structures needed to prevent fur ther increases in the balance of payments deficit, and (b) channelling an adequate fraction of increased income into.^saving. Although theoretical discussion has tended to stress the second requirement, the first appears to have been more difficult in practice in many countries. 20 Two alternative to this problem of balance of 1 R.I. McKinnon, "Foreign Exchange Constraint in Economic Development and Efficient Aid Allocation: Rejoinder," The Economic Journal, LXXVI (March, 1966), pp. 170-171. 20 Chenery and Strout, p; 726. 22 payment difficulties can be suggested: (a) given the trade restrictions, treat imports as being related to both the levels of income and the inflow of foreign capi tal; (b) treat the aid requirement to the trade gap alone?* One of the problems in the evaluation of the per formance of aid is to measure the productivity of aid. Should we evaluate the performance of aid in terms of what it is supposed to do in the receiving countries? Should we consider the effect of aid on other aspects like distribution of wealth and economic development? Is the short-run analysis a sufficient guideline to allocate the aid resources? Chenery and Bruno define the marginal productivity of aid as the increase in the gross national product in any year due to the increases in aid during the plan period.22 If we consider the purpose of aid as only to supplement the savings and to promote income growth, their 21 See B.I. Cohen, "Foreign Exchange Constraint in Economic Development and Efficient Aid Allocation: Comment," The Economic Journal, LXXVI (March, 1966), p.168. Cohen argues that the two gaps have to be equal and aid doners should emphasize the receiving countries to develop policies to make the necessary equality between the two gaps. 22 H.B. Chenery and M. Bruno, "Development Alterna tives in an Open Economy: The Case of Israel," Economic Journal, LXXII (March, 1962), p. 181. 23 measure is quite justifiable. But as Griffin and Enos point out, so long as aid acts as a substitute to domes tic savings, both the substitution effect on saving and the complementary effect on income will have to be con sidered. Griffin and Enos find no close association between the aid received and the rate of growth of gross.national product.23 It is often argued that the inflow of aid dis torts the allocation of the investment resources in the receiving countries to the advantage of the donor countries. After the two plans of five years each, India faced serious food shortage and a foreign exchange crisis in 24 1964-65. Prices have been increasing at an average rate of 10-15 percent. The foreign exchange shortage was thought to be due to the overvaluation of the Indian currency and India devalued the rupee in 1966. The capital intensiveness and the high technology associated with the "project aid" imposed serious foreign exchange difficulty, distorted pattern of investment, and resulted 23 K.B. Griffin and J.L. Enos, pp. 317-318. 24 Indian foreign exchange reserve decreased in 1964-65 by Rs. 56.2 crores, the maximum decrease since the beginning of the plans in 1950. See Government of India, Economic Survey 1970-71 (New Delhi: Government of India Press, 1971), Table 6.2, p, 134. 24 25 in excess capacity in certain sectors. With the aid available as a gesture of political goodwill, the aid receiving countries may postpone cer tain domestic policy measures to increase the rate of growth. Instead, aid donors should suggest certain tax policies to the receiving countries to increase their domestic saving. Emphasis should be put on changing certain institutional structures that are taken as given. Very recently the Indian government implemented land reforms and certainppolicies to control the monopoly business. Thus, ideally, performance of aid transfer has to be judged on the basis of such distributional effects in addition to its effect on the income and the growth rate. The misallocation of both domestic and foreign investment resources further deteriorates the balance of payments condition and leaves the economy with a heavy burden of debt. Thus, both from donors' and domestic policy makers' point of view, an efficient allocation of investment resources with an objective to reduce the burden of debt should be the guideline in the treatment ^See H.B. Chenery and A.M. Strout, p. 727; see also H.B. Chenery, "Trade, Aid and Economic Development," in International Development, ed. S.H. Robak and L.M. Soloman (New York: Dobbs Perry, 1965), p. 187. 25 of aid. In Chapter III, with a two-sector model, we will consider the problem of efficient allocation of invest ment resources so as to minimize the burden of debt. Then it will be shown that such an optimization mbdel leaves the savings rate decreasing as the aid is being terminated. A simple aid policy without any other domes tic policy to induce higher savings rate is likely to lead to unstable savings path. Thus, increasing the domestic savings rate along with investment growth and stabilizing the savings path, the price level and the exchange rates remain as the crucial planning problems for which certain domestic policies are to be considered in addition to the dependency of aid. Emphasis on Domestic Policy The experience with the inflow of aid as summarized in the previous section and the increasing international competition to receive aid prompts the developing econo mies to search for new approaches to investment planning. The recipients of aid may have to consider alternatives to asking for aid. In addition, certain domestic policies may have to be emphasized. Various hypotheses have been proffered concerning the responses of people in the less developed economies to changes in the tax structure, 26 monetary policy and exchange rates. Rottenberg finds some evidence on the positive responsiveness of the 26 people to government policies. ° One policy often considered in a mixed economic system is to increase the role of the government to' augment the level of investment in the economy through monetary and fiscal actions. The role of money in economic growth has been 27 emphasized by Tobin. Tobin considers a two asset port folio model with capital stock and cash balances. Tobin's money is purely a government debt created through deficit financing. The money is distributed either as transfer payments or as government spending.28 So long 26 See S. Rottenberg, "Incentives in Underdeveloped Economies," American Economic Review, L (May, 1960), pp. 73-83. 27 See J. Tobin, "A Dynamic Aggregative Model," Journal of Political Economy, LXIII (April, 1955), pp. 103-115? J. Tobin, "Money and Economic Growth," Econometrica, XXXIII (October, 1965), pp. 671-684; J. Tobin, "The Neutrality of Money in Growth Models: A Comment," Economica, XXXIV (February, 1967), pp. 69-72; J. Tobin, "Notes oh Optimal Monetary Growth," Journal of Political Economy, LXXVI (July-August, 1968) . 28 Tobin in his 1955 article considers the govern ment deficit only in the form of transfer payments. How ever, such a government debt can be used for the govern ment purchases also. See J. Tobin, "A Dynamic Aggregative Model," pp. 109. 27 as people want to hold some id!6 cash as an alternative to holding other forms of wealth, the total private wealth can be treated as the sum of reproducible productive capital and real cash balances. In a non-monetary economy, at equilibrium, all desired saving is absorbed into in vestment. In a monetary economy, on the other hand, when people choose to hold part of their saving as idle cash balances, at equilibrium, the rate of investment will be different; and in fact, it will be less than that of a non-monetary economy. Thus, Tobin?shows that in a monetary model, the long-run equilibrium capital-labor ratio is lower than that in the non-monetary equilibrium model. This non-neutrality of such "outside" money is based upon two specifications in his model: first, he assumes that changes in the stock of money are only for distribution as transfer payments; second, all the in vestment in the economy is done by the private sector, as the total wealth in the society is owned solely by the private sector. We in our study, consider the case of government owning part of the wealth in the economy and undertaking public sector investment through deficit financing. Johnson criticized Tobin's non-neutrality based upon his assumption of treating saving behavior related 28 only on Income and not on the rate of return on capital.^ As long as money is created as "outside" money having its own interest rate (even zero) and saving does not depend on the interest rate but on the disposable income, an increase in money implies increased private wealth and saving potential. Johnson on the other hand considers the "inside" money. So long as the government has to borrow at a non-zero interest rate, an increased supply of money does not constitute an increase in wealth and saving. So long as the saving potential does not change, money would be neutral on the long-run growth path.” *® In a recent article, Hadjimichalakis generalizes the basic Tobin model to the case of a disequilibrium in the money market with the elasticity of price expec tations other than unity. The equilibrium in the money market as well as in the saving and investment market 29 H.G. Johnson, "Money in a Neo-classical One-sec tor Growth Model," in Essays in Monetary Economics, ed. H.G. Johnson (New York": Allen and Unwin, 1^67), Ch. 4, pp. 161-178. 30 Considerable amounts of literature have come out on this controversy since the first article of Tobin in 1955. See D. Levhari and D. Patinkin, "The Role of Money in a Simple Growth Model," American Economic Review, LVIII (September, 1968), pp. 713-753? M. Sidrauski, "In- flation and Economic Growth," Journal of Political Economy, LXXV (December, 1967) , pp. 75*6-810^ M.G. Hadjimichalakis, "Equilibrium and Disequilibrium Growth with Money - the Tobin Models," The Review of Economic Studies, XXXVIII (October, 1971), pp. 457-4&d. 29 depends upon three factors: (a) the speed with which people recalculate the anticipated price changes when their previous anticipations are not realized? (b) the rate of adjustment of prices when certain disequilibrium in the money market (e.g., excess supply or excess demand for money) are observed? and (c) the substitutability of money for capital. As long as people's propensity to hold money depdnds upon the market rate of interest, money and capital stock are substitutable in their asset preference. In the presence of the speculative demand for money, if people recalculate their anticipated prices instantaneously and the elasticity of expectations with respect to price changes is greater than unity, the price level will be extremely unstable. A small increase in the actual price away from the anticipated price level will cause people to anticipate a larger price change and the market interest rate? and they reduce their cash balances bringing disequilibrium in the money market and thus giving rise to a further increase in prices. Thus, as long as the rate of adjustment of prices (in the money market) and of price anticipations are infinite, Tobin's model is shown to be unstable. Hadjimichalakis argues that Tobin's model is basically unstable as long as the assumptionsof instantaneously clearing markets and 30 price anticipations are always valid. The equilibrium in the model is a saddle point. We show in Chapter IV that, the necessary and sufficient conditions for the stability of the Tobin model is that the speculative demand for money is zero. Then price level and interest rate changes do not affect the real market equilibrium. Money in the form of public debt is not a perfect substitute for capital (as Hadjimichalakis assumes). Money, in such an economy, is non-neutral in economic growth. 31 Hadjimichalakis shows that in the monetary model, the equilibrium capital intensity is less than that in the non-monetary equilibrium model. He states: A We shall be referring to this k as the Solow capital intensity [n= s/(k/f(k))i. It is obvious.... that for m*> 0 (i.e., in order to have money in the economy) we need sf(k*)> nk*(or f(k*)/k* >n/s. It follows .... that k*. < k 32 But his own result for the monetary economy can be written as: (s/(k*/f(k*))> n 3^M.G. Hadjimichalakis, p. 470. 32 Ibid.; k is the capital intensity; f(k) is per capita^ output? m stands for money; * stands for the equilibrium solution; n is the natural rate of growth; and s is the marginal propensity to save. 31 Then, the Tobin model is unstable in the Harrodian sense. I.e., the warranted rate is greater than the natural rate. We show in Chapter IV, that for a proper choice of the 33 government deficit and the share of the government in vestment in the economy's total investment, the Tobin' model can be stabilized. Thus, a domestic policy to stabilize the long run saving and investment paths without inflation can be developed with a proper choice of the rate of nominal money supply and a bhoice of government investment. Such a policy can be used to retire the foreign debt and to attain economic self sufficiency. In Chapter V, we con sider such a policy for India. Conclusion An optimal choice of monetary policy with an associated unique choice of the share of government spending on investment can stabilize the long run savings rate. Then, from a planning point of view, aid becomes only a residual, to match the savings gap away from the long run path during the planning period. Such a 33 Tobin, assuming balanced budget, gives the required deficit in order to make the warranted rate equal to the full employment natural rate. See Tobin, "Money and Economic Growth," p. 678. 32 treatment of aid policy has both growth and stability properties. Chapter V considers the sensitivity of such a monetary policy model for India and examines the sta bility properties. Planners in the developing economies may have to reconsider their dependency on foreign aid and look for alternative domestic policy measures to guarantee a full employment steady savings rate. CHAPTER III AN INVESTMENT ALLOCATION POLICY WITH FOREIGN AID Introduction Foreign aid performs a dual role in the develop ment process: (a) it provides real resources for invest ment; and (b) it reduces the pressure on raising the taxes to finance the plan, as part of the investment is supplied from the foreign countries as capital aid. The plan may not have to bid the resources away from the domestic consumption in the form of increased taxes. Moreover, part of the inflow of aid may be for direct consumption. Thus, the consumption demand in the economy can be kept at least on a stipulated growth path. Foreign trade, on the other hand, promotes the growth of the domestic export industries on the principle of comparative advantage. 33 Oniki and Uzawa, and Srinivasan, among others, have examined the pattern of trade and the long run growth paths with specialization and trade.^ Chenery and Strout, Chenery and MacEwan and others have identi fied two different types of bottlenecks in the economic 2 growth process, namely, investment limited growth and trade limited growth. Their models demonstrate that if proper absorptive capacities are created, with a planned aid program, the long run balanced growth can be reached in three phases. In the first phase of the plan, there is a saving-investment gap and foreign aid matches the gap; in the second phase the foreign exchange constraint dominates and import substitution through aid are stressed and in the final phase, the balanced growth path is reached. The two gaps are the result of misallocation of *H. Uzawa and H. Oniki, "Patterns of Trade and Investment in a Dynamic Model of International Trade," Review of Economic Studies, XXXII,(January, 1965), pp. 15- 38; T.N. Srinivasan, “A Dynamic Model of International Trade," (paper presented to the meetings of the American Econometric Society, Boston, 1963). 2 H.B. Chenery and A.M. Strout, "Foreign Assistance and Economic Development," American Economic Review, LVI (September, 1966), pp. 679-^33; H.B. chenery and A. Mac Ewan, "Optimal Patterns of Growth and Aid: The Case of Pakistan," in The Theory and Design of Economic Develop ment , ed. I. Adelman and E. Thorbecke (Baltimore: Johns Hopkins Press, 1966), pp. 149-180. 35 O investment resources. A very high rate of investment in the consumer goods sector with a high marginal propen sity to consume (mpc), leaves the savings rate very low. Hence, the desired savings (equal to the desired invest ment) may not match the realized savings. If the desired savings is greater than the realized savings (Chenery and Strout's saving-investment gap), the excess invest ment demand cannot be met and hence the production declines through a multiplier process. The process is cumulative as described by Harrod. Moreover, there is a great diver gence between the social and the private marginal produc tivity of investment in the consumer and the capital goods sectors. The private marginal productivity of investment in the consumer goods sector is much higher than the social benefit; whereas they are comparable in the capital goods sector. Hence it is hypothesized that the saving 4 investment gap is a misallocative gap. Such misallocation of the investment resources can be evaluated using a social rate of return criterion. 3See B. Cohen and R. McKinnon, "Foreign Exchange Constraints in Economic Development and Efficient Aid Allocation: Comments and Rejoinder," Economic Journal, LXXVI (March, 1966), pp. 168-171. ^In many developing countries a comparatively large portion of total investment is observed in the consumer goods sector. There is a low risk and a small time lag between the investment and the total expected returns in such an investment. 36 e As suggested by Cohen and McKinnon, the planners in the aid receiving countries should develop policies to equa lize the two gaps. Chenery and Strout, as pointed out in the previous chapter, assume that the two gaps are unequal and they suggest an optimal aid policy to match the larger of the two gaps in each phase of the plan. Alternatively, we assume that the two gaps are equal and develop a plan for an optimum allocation of investment resources to the consumer and capital goods sectors such that both the gaps are minimized simultaneous ly during the plan period. The time phasing and allo cation of investment goods is a real planning problem for the aid receiving countries; whereas, the phasing of the plan as treated by Chenery and Strout, and Chenery g and MacEwan, are in the interest of the aid donors. Structure of the Model Consider a two sector, two factor open economy model along the lines described by Oniki and Uzawa, Srinivasan, Ryder, Bardhan and Stoleru.^ Let us define 5 B. Cohen and R. McKinnon, p.. 169. ®For a critique of their approach, see M.A. Rahman, "The Welfare Economics of Foreign Aid," Pakistan Develop ment Review (Summer, 1967), pp. 141-157. 7 See G.L. Stoleru, "An Optimal Policy for Economic Growth," Econometrica, XXXIII (April, 1965), pp. 321-348. 37 the plan period as the time duration during which, given the technological and behavioral relationships between various variables of the two sector model, certain policy choices will be made in order to optimize a particular goal. We designate the beginning of the plan period at time zero, and make time T the terminal time of the plan. The two homogeneous factors of production we consider are labor and capital stock and we assume that these factors are used with certain allocative efficiency criteria to produce two types of homogeneous goods, namely, consumption and capital goods. We consider a simple Harrod Domar type domestic production function with exports, im ports and foreign investment activities. Supply, of Eactors The supply of labor L^, and capital to the consumer and capital goods sector at any time t can be expressed as: Lt — Llt + L2t (3*1) Kt - Klt + K2t' 0 - 1 T *3*2* where the subscripts 1 and 2 stand for capital and con sumer sectors respectively. KQ and Lq are the initial We follow basically his approach of constructing the two sector model for optimization with a control policy. 38 capital stock and the labor force at time zero. Labor supply is assumed to be exogenously given as: nt L = L e (3.3) t o where n is the rate of population growth. For a surplus labor economy like India equation (3.1) can be treated as an inequality with a surplus labor supply. Production Function Let X, and X94. be the levels of domestic out- lt puts in sectors 1 and 2 respectively, expressed with the assumption of a fixed coefficient production technology, as: xit ■ aiKit ( <3-4> < Production functions X2t = a2K2t ' (3’5) Lit = biKit S <3-6) \ Labor demand func- L2t = ^2K2t tions (3.7) where a is the output-capital ratio in sector i, and b- • JL i is the labor-capital ratio in sector i (i = 1,2). These production functions are in the Domar-Harrodian spirit. X^q and X2Q are given as the initial levels of output rates for the time zero. Domestic Demand Let us define the net imports as imports minus 39 exports. Let M^t and M2t be the levels of net imports of capital and consumer goods sectors respectively. Let the total net imports Mt be related to the components M-^. and as: Mlt " eMt ) ( (3.8) M2t = (l-e)Mt, e > 0 \ where e may either depend on t or may be a constant, e > 0. The components of current consumption and net capital formation are given as: Ct = X2t + M2t <3-9> K - xit+ Mit - >*Kt (3-10) where is the level of total private and government • • • consumption at time t and = K^t + K2t is the g total net investment demand. The total consumption at time t consists of the domestic production of consump tion goods plus the net imports of consumption goods, y is the rate of capital depreciation. The gross invest ment in the economy at any time t is equal to the sum of the domestic production and net imports of capital goods. Net imports include imports financed through 8 The dot above a variable stands for the time rate of change of the variable; in the case of capital, Kt is the rate of investment. foreign aid and gifts. Let the saving behavior be given as: Sf c = sxf c (3.11) where St stands for the desired saving in the economy, given the level of gross domestic product Xt = X^f c + s is the marginal propensity to save, which is assumed to be equal to the average propensity to save. Equilibrium is defined as: K. = S. + M (3.12) t Foreign Exchange Restrictions We assume that the long term foreign borrowing is used to match the current account deficit. Hence the balance of payments restriction will be written as: Mt = At " pNt ~ a2Nt (3.13) where p is the fraction of loan accumulated to be repaid at time t, and a2 is the interest rate on the foreign debt Nt« Supposing that the country receives part of the aid as a gift which is not to be repaid, the net addition of foreign debt at time t is equal to the repayable fraction of the aid received minus the fraction of the existing loans returned. 41 Q where (1-ot^) is the fraction of aid received as a gift. From the equilibrium relation (3.12) and the balance of payments restriction (3.13) we see that the investment and saving gap is equal to the excess of imports or the balance of trade gap on current account.^® The input output ratios in our production func tion are assumed to remain constant. This assumption is not valid in the planning process, particularly when import substitution is to be introduced. In a surplus labor economy one possibility is to develop labor inten sive exports sectors so that part of the pressure on for eign exchange can be reduced by import substitution through increased exports. The capital-labor ratios are also treated as fixed. With data on the Indian economy we will show later that the capital-output ratio in capital goods, 9 The gift and grants are direct transfers of foreign goods to the receiving country, without any ob ligation to repay the debt. ^°McKinnon argues that it is quite common in many of the less developed economies to find a large trade gap rather than an investment-savings gap due to an overvalued domestic currency. In practice aid donors transfer aid to match the trade gap without suggesting the receiving countries to develop domestic policies to increase their internal saving rate. See B. Cohen and R. McKinnon, p. 171. 42 1/a^ is higher than the one in the consumer goods sector, l/a2» (a^ < a2) This would imply that the capital goods sector is capital intensive. Also we have < b2 implying that the capital-labor ratio in the capital goods sector is higher. Controllability in the Model Following Stoleru and Rao,^ we define a new set of variables as transformations of the variables dis cussed above. yt Zlt = (Klte /K10}' Z10 = 1 (3.15) . Z2t = (K2teUt/K10)' Z20 = (K20/K10> (3-16) Then the interpretation of Z1 is as follows: it is the ratio of the actual capital stock in the capital goods sector at time t to the stock which would have existed at time t if there had not been any investment in this sector since the time zero. Similar transformations are defined for other variables for the sake of uniformity. ■^T.V.S.R. Mohan Rao, "Approaches to Economic Policy for Stabilization> ; and Growth," Unpublished Ph.D. Dissertation, University of Southern California, Los Angeles, 1968; G.L. Stoleru, p. 321-325. 43 Pt Z3t = ^Ate /K10> ' Z30=^A0/,K10^ (3.17) yt Z4t = (Nte ^lO*' Z40= (N0/K10) (3.18) yt Z5t = (Cte /K10), Z50 = (C0/K10) (3.19) yt z6t = (Mlfce Aio) f z60= (M10/K10) (3.20) Z7t = *M2te /K10>' Z70 = *M2(/K10* (3.21) The investment decision in a planned economy is based on several criteria. One accepted criterion is the concept of profitability or the expected rate of 12 return. Following the approach used by Stoleru we consider the problem of allocating the investment resources to the two output sectors. The expected rate of return can be used as a criterion to allocate the re sources efficiently. If the expected rate of return from the investment in the capital goods sector is higher than that from the consumer goods sector, it is rational to invest in the capital goods sector. 13 Let us define a control variable uf c as follows: 1? See J. Hirshleifer, "On the Theory of Optimal Investment Decisions," Journal of Political Economy, LXVI (August, 1958), pp. 329-352. 13 In subsequent sections, we will drop the time subscript from the variable. The subscript t will be introduced explicitly wherever necessary for the pur pose of discussion. 44 m gross investment in capital goods sector ■ total investment (3.22) Then, 0 _< u <1. Now the investment decision becomes t ~ the choice of u under the above mentioned criterion From equation (3.22) we write, u = (Kx + yK1)/(K1+K2+pK) (3.22.a) • • • • where K^+K2 = K and K + UK is the total gross invest ment to be denoted as Ig. Then gross investment in consumption and capital sectors can be written as: • • K-^+yK^ = ulg ; K2 + yK2 = If u » 0 at any time t, then the investment in the capital goods sector 1 is zero and the total investment is allocated to the consumer goods sector. If u = 1 at any time t, then the investment takes place only in the capital goods sector. ut will be called an invest ment allocation policy variable. In case 0 < u <1, the investment resources are distributed between the capital and consumption sectors in the ratio of u and (1-u) respectively. Differentiating Z logarithmieally 1 and using equations (3.22.a), (3.10), (3.8), (3.4), (3.13), (3.17) and (3.18) we write, ( V zl) = u*ai +<e/zi) (Z3-(a2+y) )Z41 45 or h = *1Z1 + etz3-<0t2+v,)Z41 } (3.23) Similarly, we derive Z0 = (1-u) { a Z + e[Z ,-(ot,+y)Z ]} (3.24) 2 11 J * 4 Finally, we introduce the concept of controlla bility of an accumulation of loan (burden of debt to foreign countries) . Accumulation of the loan adds to the disutility in the future (post plan, and even during the plan). Hence planners may like to decide about bor rowing as an equilibrium between the productivity of aid in achieving certain goals and the disutility of the loan. Let us define a control variable, v, as: • • v = (A+yA)/ (N+yN) , 0 < v _< 1 (3.25) • Using equation (3.14) we can write A = A(va^-y) (3.25.a) where (vot^-y) is the rate of change of aid. v is the ratio of (gross) aid to (gross) loan added in any year t. If we substitute p = y in equation (3.14) we see that v never exceeds unity. But v can be unbounded below. If v = 1, then using equation (3.14) we have, • • N + yN = a^A = A + yA Hence A = (c^-y) A Then (cx^-y) is the rate of increase of aid. Since > |if^ the implication is that foreign borrowing is increasing at time t. Similarly, if v = 0, then A = -yA; aid is to be decreased at the rate of y. If v = y/a^, then A = 0, implying no change in the level of borrowing. In view of saving-investment gaps, a sudden decrease of aid to zero may lead to an immediate fall in autonomous investment with cumulative under productive effects. Hence we treat v as bounded from below. However, the exact lower bound will be determined on the basis of the productivity of aid, the disutility of loans and aid, and socio-political factors. In this study we treat 0 _< v _< 1. Prom the ‘definitions of Z^ and Z^, using equations (3.25) and (3.14) with p=y (i.e., rate of payment of loan during plan period = y), we derive, Z^ a vaiZ3 (3.26) Z4 = a1Z3 (3.27) ^ai, being the fraction of repayable aid out of total aid is quite large compared to the capital de preciation rate y. Our empirical estimate of a, = 0.913 and we use y = 0.1. 47 Then the differential equations (3.23), (3.24), (3.26) and (3.27) are the basic equations of motion with policy decisions variables uf c and vfc. Finite Horizon Planning Approaches Several approaches are used to study the process of capital accumulation. Again, different goals can be defined in the finite horizon planning models depending upon the problem. The traditional approach is to define a social welfare function and optimize the objective 15 function under the capital path conditions. In contra-distinction to this approach one can develop a stochastic approach where the observed values of the ■^Discounted consumption or a utility function with the constraint on the capital path is a common tech nique. For details see S. Chakravarti, The Logic of Investment Planning (Amsterdam; North Holland Publish ing Company, 1959); S. Chakravarti, "Alternative Pre ference Functions in Problems of Investment Planning on the National Level," in Activity Analysis in the Theory of Growth and Planning, ed. E. Malinvaud and M.V.L, Bacharach (New York: St. Martin's Press, 1967); F.P. Ramsey, "A Mathematical Theory of Savings," Economic Journal, XXXVIII. (December, 1928) , pp. 543-559; S. Chakravarti and R.S. Eckaus, "Choice Elements in Inter temporal Planning," in Capital Formation and Economic Development, ed. Rosenstexn-Rodan (Cambridge, Mass.: MIT Press, 1964); T.N. Srinivasan; J. Tinbergen,-On the Theory of Economic Policy (Amsterdam: North Holland Publishing Company, 1957). 48 systematic performances of the economic variables being subjected to measuremental errors make the model non- deterministic. The stochastic approach allows choice of techniques as in the traditional deterministic approach and in addition, allows for variations both in the econ omic variables and in the parameters of the model. Most of the works done for India are the deter- 17 ministic optimizing plans of the linear programming type. The objective in general is optimizing the discounted consumption. A Modest attempt is made on the stochastic optimization of the capital accumulation path by Rao and Tintner.^ 8 In this study attaining full employment is treated 1 6 See J.K. Sengupta and G. Tintner, "An Approach to a Stochastic Theory of Economic Development and Fluc tuations Problems of Economic Development and Planning," in Essays in Honor of Michael Kalecki (Warsay: 1966) , pp. 373-391; G. Tintner, J.K. Sengupta, and E.J. Thomas, "Application of the Theory of Stochastic Processes to Economic Development," in The Theory and Design of Econ omic Development, ed..I. Adelman and E. Thorbecke (Balti more: Johns Hopkins Press, 1966), pp. 99-110. 17 See T I.W. Eckaus and K.S. Parikh, Planning for Growth (Cambridge, Mass.: MIT Press, 1968); S. Chakravar- ty and L. Lefeber, "An Optimizing Planning Model," The Economic Weekly (February, 1965). A®G. Tintner and T.V.S.R. Mohan Rao, "Investment Allocation, Realtive Price Stability and Stable Growth," Artha Vijnana, X (March, 1968), pp. 1-10. 49 as one of the targets. Following the planning approaches of Tinbergen and Theil,!^ we distinguish a target from an objective. We call a fixed objective, e.g., full employment, as a target. We will choose the values of the control variables in such a way that we reach the fixed target of full employment. For a country like India, due to considerable unemployment, following the full employment capital ray criterion (as used by Rao)20 may require a large sum of external resources to reach the required investment path. Such a dependency on external assistance may result in heavy accumulation of the loans from foreign countries and international agencies. As has been the experience with many countries the external debt of the plan may have several effects during the post plan period (like reduced consumption and disposable income, etc.). Hence it is postulated that an accumulation of loan adds to the social disutility.. Thus, minimizing the disutility is treated as another goal.2! 19 For a brief survey of the two approaches see Bert G. Hickman, ed., Quantitative Planning of Economic Policy (Washington, D.C.: Brookings Institution, 1968); H.B. Chenery and M. Bruno, "Development Alternatives in an Open Economy: The Case of Israel," Economic Journal, LXXII (March, 1962), pp. 79-103. 20 T.V.S.R. Mohan Rao, Approaches to Economic Policy, 196-6. 21 The term goal stands for minimizing or 50 An efficient allocation of investment resources will enable the domestic capital to grow in such a way that the economy can develop an import substitution 22 policy to reduce the investment saving gap over time. However, with the rise of income, there'may be distribu tional effects with a tendency to increase imports. This is particularly the case with countries suffering from "demonstration effects" where the misallocation of invest ment resources leads to heavy dependence upon imports. The growth of the deficit in the balance of payments led India to devalue in 1966. Hence, import substitution, to improve the deficit in the balance of payments, is kept as the third goal. Rao shows that if the investment path is optimized by minimizing the deviation of the path from the highest attainable capital ray, the optimal policy implies allo cating the entire investment resources to the capital goods sector for almost 90 percent of the plan period. This means a heavy imposition on society to waif for maximizing a certain preference function depending upon the problem. 22 Cohen and McKinnon argue that the donors of foreign aid should make suggestions to the receiving countries about efficient allocation of investment resources. See B. Cohen and R. McKinnon, pp. 169-171; and H.B. Chenery and A.M. Strout, pp. 726-728. 51 increased consumption. As has been the experience with the planning in India during the three plans, it is realized that the agricultural sector has been severely neglected and forced to rely on heavy imports of PL 480 food or other foreign aid. Hence, instead of optimizing the capital path, we minimize the time horizon of the plan to attain full employment. It is suspected, as has been the experience with the Indian second five year plan, that the consumer goods sector may not grow when the allocative criterion is used for investment. Hence, during the plan period the consumption may fall below the initial levels. In such a case, two approaches may be specified. First, the consumption path can be constrained not to fall below a certain minimal stipulated path. In this case, the choice of the stipulated rate of growth becomes crucial to the model. Second, maximizing the discounted consump tion can be considered as an additional goal. We consider 23 only the first case in our model. Consider a finite terminal time planning model. Let T be the terminal time of the plan. The full employment target by the time T and during the post ^For the models on India using the second type of approach see Eckaus and Parikh; and Chakravarty and Lefeber. 52 plan period will be written using equations (3.6), (3.7) and (3.3) as: nt b1K; L + b K2 = LQe for t > T 2 which can be written in terms of the transformed variables as: (n+y)t b1Z1 + b2Z2 = (LQ/K10) - e for t > T (3.28) We denote (L /K, .) by H . The balance of payments o 10 o restriction (3.13) can be written in terms of the trans formed variables as: Z6 + Z7 = z3 - (ct2 + y)Z4 (3.13.a) Let m be the minimum stipulated growth rate of con sumption. If m = n, then the per capital consumption remains constant during the plan period. Let m be greater than or equal to n. Then using the definitions (3.19) and (3.21) and the equations (3.9) and (3.4), we write the consumption as: z5 = a2Z2 + ^7 (3.29) Using equations (3.8) and (3.13) and the transformations (3.17) and (3.18), we differentiate equation (3.29) and substituting equations (3.26) and (3.27), we derive the differential equation for Z as: 53 Z5 = a2Z2 + (1“e) Cv-(ot +y) ]a1Z3 (3.30) and with the minimum stipulated growth rate in consump tion of m, we impose the restriction: a Z + (1-e) [v-(a +p).]a1Z_ > (m+y) Z (3.31) 2 2 2 1 J — 5 Balanced Growth If the deficit in the balance of payments is maintained at zero for t ^ T, and the aid is cut to zero during the same period, we can solve for the capital path in the two sectors with the full employment condi tions during the post plan period. Using equations (3.23) and (3.24) with full employment condition (3.28) we solve the paths for Z-^t and Z2t as" (n+y)T e,(t-T) (n+y)t Z = [Z, - 02e ]e + 0 e (3.32) it* 2 (n+y)T 0 (t-T) (n+y)t Z = [Z - 0 e ]ex + 0 e (3.33) 2t 2T 3 J where ©1 = (a1b2/(b2-b1)) > 0 02 =[ (n+y)/(a1b2-(b2-b1) (n+y))H (3.34) 83 = ^a1-(n+y)]/[a1b2-(b2-b1)(n+y) For values of a^, b^, , n and y from the Indian data we can show that 0„ > 0 and 0 >0. 2 3 We can see that the balanced post plan growth path is possible if the terminal values of the two capital paths are: (n+y)T Zlrp = 0 e (3.35) u 2 (n+y) T w - (3.36) The corresponding full employment growth paths of the capital stocks in the two sectors are given as: ^lt m iL—— . . . . . ---. ------------ Lnenl: (3.35.a) a!b2 ~ ( 2 1 *n+p* t > T Kzt " ) -(SW----- V * <3-36’a> Both the capital stocks grow at the same rate as the natural rate n. Planning Objective With full employment as the target and an objective of minimizing the burden of loan at the terminal time of the planf we consider a weighted objective function of the burden of debt and the disutility of unemployment. 55 The weights reflect the relative importance of the two objectives. If achieveing full employment is the only target without any consideration of the burden of loan, then the total weight is associated with the employment gap. On the other hand with all the weight/attacfied^.to.’ the disutility of debt, we can minimize just the loans, if full employment is not a target. From equation (3.27) we see that loans are a monotonically increasing function of aid. If the aid is increased, the burden of loans accumulates faster. If aid is decreased over time, the loans are still accumulating but at a slower rate. Hence minimizing the terminal loan is the same as minimizing the total aid during the plan period. Manne defines self 24 reliance as planning to reduce the terminal aid to zero. Since the long term planning objective is to main tain a full employment dondition, let us consider the deviation of employment from its long term full employ ment path as a stochastic variable, denoted as wt, with the following specifications: (n+y)t b Z. + b = I e + w (3.37) 1 It 2 2t o t But he finds that its implication is a reduced domestic saving rate and a lower growth rate during the post plan period. For details, see A.S. Manne, "How Much Aid to End Aid?" Economic and Political Weekly (August, 1967). 56 2 where E(w ) = 0, and the variance of w. = a . We assume t t that w are intertemporal'lyyindependent. At any time t, w since the full employment is the target, we associate a f i , social disutility index e for having one unit of labor unemployed or an excess supply" of labor. We assume 6 > 0.25 Using a quadratic criteria, the total disutility of expected unemployment during the plan period will be minimized. The total disutility of unemployment during the plan period can be written as: T (n+y)t . / E[b1Z1+b2X2-Jt( ) e e dt Applying the specifications (3.37), we write the un employment as: /T a2e5tdt 0 The target of attaining full employment along with the goal of minimizing the terminal burden of the loans can be written as a weighted function of the two objec tives. Equations (3.35) and (3.36) give:: the terminal conditions for full employment. The accumulated loans -yT at terminal time T can be written as Z. e K. 10 or equivalently as Z4_e'"^T since K is a constant. T 10 For 6 > 0, the disutility is an increasing function of time. .Disutility of unemployment is higher for higher t. 57 We measure the disutility of the burden of the loan by 26 the amount of the loan itself. An Optimizing Model Let us state the optimization of the model as follows: Let the plan period be 0 _< t _< T Minimize -yT ( (n+y)T \ liZ4Te + * b -Z + (n+u) V 1 1 2 l( IT (n+yrj + X b } -Z + ai - (n+y) g._a(n+y)T 2 2 ( 2T aib2"'b2"b1) tn+p) + X /T o2e5tdt (3.38) 3 0 Z., Z , Z f Z are the state variables. X , X , X are 1 2 3 4 1 2 3 non-negative weights. Equations of Motion: Z1 = u{a1Z1 + e[Z3- (a2+y)Z4]} (3.23) Z = (1-u) {a Z +e [Z,-(ou+y) ZJ } (3.24) 2 i i 3 4 4 26 Alternatively, one could associate a monotjoriic function of the total loan as the utility function. 27 We treat the problem as maximizing -J. 58 Z = vo Z (3.26) 3 13 Z = a Z (3.27) 4 13 Choice of Policy Control Variables: 0 <u <1 , 0 v .5 1 Initial Conditions: Z , Z , Z , Z are given. 10 20 30 40 Path Conditions: (n+y)t + f c >2Z2 < I e for t _< T (3.28) Choose e such that l 2^2 * [V“(«2+y)]a1Z >_ (m+y)Z5 (3.31)28 Terminal Condition: (n+y)t b Z + b Z = £ e for t > T 1 1 2 2 0 28 An alternative is to treat equation (3.31) as a constraint on the choice of Z2f s©e G. L. Stoleru, pp. 336 ff. For the problem in his model, to minimize the time for full employment, he arrives at the same switching time from u=l to u=0. This is so because the junction point is shown to correspond to the discontinuity in u and there is only one junction point. Rao and Tintner use stipulated consumption path. 59 The first three terms of the objective function J are functions of the terminal values of the state variables, Z^, an<* z4* They are called scrap value functions. X^, X2> and X3 are constants chosen as weights between the different components of the objective function. We use the same X^ for the terminal labor employment gaps^ in the two sectors, so that the two gaps together mea sure the total unemployment. If X = 0, then minimizing the disutility of the accumulated loans and the total intertemporal disutility of unemployment are considered as the planning objectives, without any weight attached to the terminal full employment target. Similarly, if X^ = 0, the loan is treated as not adding to the social disutility. Let *2t' r3t anc* r t cont;* - nuous functions of time, defined as costate variables. We write the Hamiltonian as: 2 6t H = + r2Z2 + r3Z3 + r Z4 ” ^3° ® (3.39) H can be interpreted as the objective function to minimize the time t subject to the equations of motion (3.23) - (3.27) . 29 We call the deviation from the full employ ment condition as the employment gap. 60 We minimize the objective function J using the Pontryagin principle. Then the necessary conditions for the optimality are the existence of continuous co state and state variables for the following differential equations and the system of equations of motion (3.23)— (3.27) . r = —(r -r )a u - r a (3.40) 1 12 1 2 1 r = 0 (3.41) 2 r =-(r -r )eu - er - va r - a r (3.42) 3 1 2 2 1 3 1 4 r = (r -r )e(a +y)u + r e(a +y) (3.43) 4 1 2 2 2 2 The terminal conditions for the costate variables can be written from the scrap values of the objective function 3° J as: rlT = X b r r = X_b 2 1 2T 2 2 ( (3.44) r = -X e-^T 4T 1 30 The problem is treated as maximizing - J instead of minimizing J. 61 The necessary conditions for the choice of the control variables to maximize the Hamiltonian are written as: u = 1 if r - r >0 1 2 u = 0 if r - r < 0 1 2 0 <u<l if r -r = 0 1 2 v = 1 if r >0 3 v = 0 if r <0 3 0 <v<l if r =0 3 From the definition of the Hamiltonian (and also from the definition of the Return function) we interpret r and r as the expected rate of return from investment 1 2 in sectors 1 and 2 respectively. From equation (3.45), the optimal choice of the policy variable u can be interpreted as: invest all the investment resources in the capital goods sector if the expected rate of return from investing in that sector is higher than that from the consumption sector. Similarly, reverse the invest ment decision if the expected rate of return from invest ing in the consumer goods sector is higher than that from the capital goods sector. If the two rates of return (3.45) (3.46) 62 are equal, allocating the investment resources to the two sectors in any ratio has the same level of efficiency. Prom equation (3.46) we see that at any time t the policy decision to increase aid or to decrease aid depends upon r^. Here r^ is interpreted as the net social marginal utility of aid. r^ takes into account both the productivity of aid and the disutility of aid. If r3 <0, then the social marginal disutility of aid is greater than the utility of aid and hence the policy implication is to reduce aid. If r3 > 0, the marginal utility (analogous to marginal productivity) of aid is greater than the disutility of aid and aid should be increased, r^ is the marginal utility of a loan. If r^ is negative at any time t, then there is a net dis utility in incurring a loan. The terminal values of the costate variables (shadow costs) reflect the duality of the objective function J and the terminal conditions of state varia bles. Since, r1T - r2T = X (b.-b2) < 0, we see from equation (3.44) that the terminal investment policy is one of intensifying investment in the consumption goods industry. This is feasible since the consumer goods sector is labor intensive and hence the full employment gap can be matched by investing in the consumer goods sector with a lower social cost than otherwise. The 63 terminal marginal utility of the loans is negative (r4T < 0). This means that with the accumulation of loans, there is still a disutility of public debt. Solutions of the Processes and the Optimal Choice of Controls From equations (3.41) and (3.44) we solve for r as: r = X b2 for 0 < t < T (3.47) 2t 2 2 " " Let r - r,. * r_ . Then, from equations (3.40) and t it 2t (3.41) we can write: 31 r * = -ra u-aXb<0 (3.48) 1 12 2 r is a decreasing function of t with the terminal value; from equation (3.44) we have, r = X (b -b ) < 0 T 2 12 Hence, r < 0 in an interval t, . _< t. _< T and from (3.45) for r < 0 we have the choice of u * 0 in the time interval t _< t _< T. In this interval the solu tion for rt is obtained by integrating (3.48) and we write: Note that ru > 0. Hence r < 0 for all 0 < t < T. 64 r = X b a (T-t) + (b -b )X <0 (3.49) t 2 2 1 1 2 2 Since r is a decreasing function of t and r < 0 in t t this interval, there is a possibility that t = 0. If 1 t = 0 then, from equation (3.49) putting t = t = 0, we 1 1 have : r = X [b a T + (b -b ) ] (3.49.a) 0 2 2 1 1 2 For the values of b^, b2 and a^ from the Indian data, and the terminal time T, we can show that r would be 0 non-negative. In that case, from equation (3.45) we would have u = 1 which is a contradiction since we have chosen u = 0 in t^ < t < T. Hence, t^ £ 0. From equation (3.49), since r is a decreasing function and is negative t in t^ _5 t _< T, we should have r^ = 0 at some time t = t-^ where t^ is not equal to zero. From equation (3.49) we can solve for T-t^ such that rf c = 0: T - tx = [(b2-bi)/b2a1) (3.50) or t = T - IO^-b^/b^] (3.50.a) For any t > = T - [ ( b ^ b ^ / b ^ ^ , rt is negative. 65 Again, from equation (3.48), since r is a decreasing u function and rt = 0, in an interval tQ <_ t < t^, we should have rt > 0 and from equation (3.45) we have u = 1 in the interval t < t < t . Then the path of r. in 0 " “ 1 * the interval tQ _< t _< t^ is given by integrating the differential equation (3.48) with u = 1 and we have: a. (t-j-t) r = 1 b [e -1] > 0 (3.51) t 2 2 For t = 0, we have from equation (3.51): al^"l r = A b [e - 1] >0 0 2 2 Hence, u = 1 at time t = 0; and t = 0 is included in the interval tQ _< t. _< t^. Since our planning period starts from time t = 0, we set tQ = 0. The optimal choice of u in expression (3.45) can be written using the solution path of rf c as: uf c = 1 for 0 < t _< t^ u = 0 for t _< t < ■ T V (3.45.a) W X 0 < u <1 for t > T “ t ~ The time path of r is illustrated in Figure 3.1. t 66 FIGURE 3.1 Optimal Time Path of rt o r>0 u=l [(b -b.)/b-a ] t T T = terminal time We call the time t^ the "switching time" since it stands for the time when the optimal investment policy switches from investing only in the capital goods sector to investing in the consumer goods sector. The relative expected rate of return, rfc, is ex pressed as the difference between the expected rates of return of investing in the capital goods and consumer goods sectors. The policy decisionsabout the optimal i investment plan are: invest in the capital goods sector J during the period 0 t t^ of the plan and then switch 67 over to investing in the consumption goods sector. The solution for r, is given as follows: From 4 the differential equation (3.43) we have: r = rue(a +p) + X b e(a +y) > 0 (3.43. 4 2 2 2 2 Differentiating (3.43.a) with respect to time we have: r = rue(a +p) < 0 4 2 Hence, r i s an increasing function, increasing at a decreasing rate. From the terminal conditions, (3.44), the terminal value of r^ is negative. In the interval t^ _< t.«T we have u = 0, and hence the path of r^ in this interval is obtained as: -yt r = -X b e (a +y) (T-t) - X e (3.52) 4t 2 2 2 1 We see that r, < 0 in the interval t,, < t < T. In the 4 1 — — interval 0 < t < t^, we have u = 1 and hence from the differential equation (3.43) we have, r =)e(a +y)X2b2 ) a1(t1-t) ' 2 Ml - e j - X2b2e (a2+p) (T-t^) al -pT (3.53) - X e 1 r < 0. 40 | 68 i : is negative in 0 < t ^ t^. The function is illustrated in Figure 3.2 FIGURE 3.2 Optimal Time Path of r4fc - y T -Xe 4t 40 The social marginal utility of loans is always negative but continuously increasing from t = 0 until the terminal time is approached. It remains negative at time t = T. The social marginal utility could in crease (of course in the negative quadrant) for two reasons. Either aid received is decreasing with time or loans are being repaid faster than the rate of increase in aid, or both. In this analysis we assumed that the rate of repayment of loans during the plan period is fixed at y; and the rate of increase of aid is (va^-y) . Since the rate of repayment is treated as 69 fixed at y and the social marginal utility of loans is negative but increasing in the interval 0 _< t _< T, the only possibility is that the aid is decreasing with time. From equation (3.25.a) we know that the decreasing rate of aid is possible if we choose v < y/a-p But since r^ is the marginal utility of aid, a decreasing rate 32 of aid means r^ is negative. In other words, there is a marginal disutility of aid. From the conditions in 32 Let us define the return function, t) as: T 2^t -yT T X(Z ,t) = Max / -Xe [ / a Z dt] -X / a“e dt 3 {u,v}) 1 t 3. 3 3 t ■X b 2 1 (n+u) &ne_____ P _r _^. al 2 ^b2“bi)(n+y) (n+y)T - Z IT ■X b 2 2 al " (nV i e(n+ii)T_ . alb2'(b2'bl)(n+y> 0 2T Then we know from the Hamilton-Jacoby theory, -yT t+h (3 x fo Z,) = -X e J 1 a_dt = r for h > 0 but small 3 3 -yT = -X e ah <0 1 1 Henee, r3 < 0 for all t 70 equation (3.46)r we have for r3 < 0, v = 0. Then the optimal borrowing policy implied is to reduce aid at the rate y. This is consistent since in view of equation (3.27) for the accumulation of loans, the only possi bility of minimizing the total loan at time T is to reduce aid at the maximum possible rate. Thus the planning model will be summarized as a two phase planning with aid being retired continuously at a fixed rate y and an optimal investment paths as given below: Since the optimal choice of v = 0, from the differential equation (3.26) we have Z3t = G for 0 < ■ t _< T; and hence we solve for At, using the trans formation (3.17): Z = Z (3.54) 3t 30 -lit A = A e (3.54.a) t 0 Borrowing is reduced at a uniform rate of y. The accumulation of the loans can be solved from the dif ferential equation (3.27), using the definition (3.18), as: Z = a Z t + Z for 0 < t < T (3.55) 4t 1 30 40 -yt N = N e + a tA (3.55.a) t o I t 71 The level of net imports can be obtained from the balance of paymentsconstraint (3.13), using the solutions (3.54) and (3.55), as: -yt M = A [1 - a (a +y)t) - (a +y)N e (3.56) t t 1 2 2 0 The levels of net imports of capital and consumer goods can be obtained using definition (3.18). The investment paths are obtained by solving Z^ and % 2 th® two phases of the plan period. Phase 1: 0 < t < t^; u = 1, v = 0. From the definition (3.22.a) we have for u = 1, all the investment resources in equation (3.10) are to be alio- I cated to the capital goods sector during the time period 0 _5 t < t^. From the differential equation (3.24) we have, I I Z2 = 0; and hence Z2t = Z20 (3.57) From the definition (3.16) we have the capital path of the consumer goods sector as: K2t = K20e'St (3.58) Capital stock in this sector depreciates at the rate of y. i Let us define : I 72 d. = (l+e)Z - e(a +y)Z 1 30 2 40 and d = -a I(a +y)Z 2 1 2 30 Then we solve for Z^t from (3.23) as: al^* 2 Z = e 1 [1 + (d /a ) + (d /a r] - (d /a )t It 1 1 2 1 2 1 -[(d /a ) + (d /a ) 2] (3.59) II 2 1 and from the definition (3.15) we have the capital path in the capital goods sector: -yt K = K Z e (3.60) It 10 It The consumption path can be obtained using the solutions (3.56) and (3.58) and equation (3.5) as: C = a K + (l-e)M (3.61) t 2 2t t with v *= 0 and using the definition of Z in the defini- 5 tion (3.19), we write the consumption constraint (3.31) as: (m+y)t -(1-e)(a +y)a Z > (m+y)(C /K )e (3.31.a) 2 1 30 0 10 Since e >1 we see from the constraint in (3.31.a) that c and t are positively related and for a chosen value of t we can find a unique minimal value of s for which (3.31.a) holds. The relationship between the minimal choice of e for a given value of t is illus trated in figure 3.3. FIGURE 3.3 Optimal Choice of e for Different Choice of t = t^ c 19 1 10 t I Since the capital stock in the consumption path is continuously decreasing during 0 < t < ^ as in . ‘ (3.58), we choose the minimal value of c for t * t such that equation (3.31.a) holds with an equality where t^ is the ; switching time from the first phase to the second phase 33 of the plan. We denote the chosen value of e by e . > 1 oq JJWe keep the choice of e at its minimal level i so as to satisfy the consumption path at its Then from (3.23) we have z = 0 and hence, 1 -yt Z = Z , K = K Z e (3.62) It lt± It 10 ltx For the choice of e « e in the expression (3.31.a), the consumption path constraint is satisfied at its minimum level34 at time t^, and in phase II, K is increasing 21 and hence we treat the same choice of e in phase II also, and the consumption growth rate is greater than (m+y). .From equations (3.24)<and using (3.57) we write: 2 2 Z = [a Z +d ](t-t.) + (d /2)(t -t.) 2t 1 ltx 1 1 2 1 + Z (3.63) 20 and hence -yt K = K Z e (3.64) 2t 10 2t boundary solution (minimum stipulated growth) at time t . The consumption path can be kept at any level higher than this by another choice of e, but this is equivalent to choosing another m. In other words we have only one degree of freedom. Hence we decided to choose e, for a bhosen m. 34 As shown by Stoleru, at time t = t^, the jump condition is satisfied. After t = t-, , the control variable u(t) can not remain at u = I; otherwise the Zgt path will lie on the boundary, contradicting a unique junction point. See G.L. Stoleru, pp. 336-340. 75 and once again the consumption path is given by expres sion (3.61). The switching time t^ is given in equation (3.50.a). The terminal time T will be chosen such that the full employment level is reached in the minimal amount of time as stated in the Hamiltonian (3.39) . Analysis of Domestic Saving In the macro model that we considered, there are 16 equations in 17 variables.35 So, we determine one of the variables outside the model, namely, the inflow of foreign aid, through an optimal policy choice and then derive the time paths of the remaining 16 variables. The rate of domestic saving can be written, using equations (3.12), (3.8), (3.13), and (3.10) as: S = X - yK - (1-e) [A- (a +y)N] (3.65) 1. 2 So long as the time path of the foreign aid is deter mined outside the model,35 the time path of the accumu lation of loans N, is given from equation (3.14). Then 35The variables are: LI, L2, I*; Ki, K2, K; Xx, X2, X; Mx, M2, M? C, S, A, N, and ft. 36In our case, A = -yA where y is a constant. 76 the level of net imports are determined by the foreign exchange restriction (3.13). Both the levels of net imports and the time path of investment in equation (3.10) together determine the levels of output and X2, and the capital stocks in the two sectors. From equation (3.65) we note that as long as the policy of import substitution is maintained, the domestic saving decreases.3^ Differentiating (3.65) partially with respect to time we have: (3 S/3 t) = (3 S/3 A) (3 A/3 t) = -(1-e) (3 A/3 t)«0 (3.66) As long as the policy choice of aid is to reduce it over time, (3A/3t) <0; and since e>l, we see that the domestic saving is decreasing as the aid is reduced over time.38 3^The growth of exports over the imports makes the total net imports decrease over time. The.choice of e >1 means a higher rate of imports of capital goods at a time when the economy is importing more than its export ing. Such a choice of excess imports of capital goods increases the investment resources in the economy. On the other hand, when the country's exports are greater than imports, for e>l, the net exports of capital goods are greater than the total net exports. 38 Manne shows that the marginal propensity to save decreases as the inflow of aid is reduced to make the terminal aid dqual to zero. • Thus, such a policy of optimal investment and j I self-reliance has adverse effects on the domestic j i i savings. The implications of such a goal may be i i serious during the post-plan period, when the economy | will be left with a low savings potential. The optimal investment policy may become, effectively, a business | ! cycle phenomenon. Investment increases during the plan period due to the inflow of foreign aid and the domestic savings rate decreases. When the aid is reduced to zero, the burden of the aid is still left in terms of debt servicing and the economy's saving will not be suffi cient to maintain the level of investment required to maintain the full employment income growth. j ! We consider in the next two chapters, an analysis j of income and capital growth with emphasis on domestic J policies. Unlike the present analysis, we consider the foreign aid solely as residual, and evaluate the role of domestic monetary and fiscal policies to attain self- sufficiency and stability in growth. Analysis of the Empirical Results i With the estimates <5f e for different t, we i i estimated the time paths of K-^ and K2 using expressions j (3.58) , (3.60), (3.62), and (3.64)?^ Using the condition I 39see Appendix A for the description of the data, j 78 (3.50.a), the minimal terminal time T to reach the full employment level is estimated. Our estimates of the two phase periods are: t^ = 10.16, end of phase I; and T = 12.29., end of phase II. In Tables 3.1 and 3.2 we present the time paths of the estimated capital and employment growth, treating fche plan period as 0 < t < 13. Capital grows at the rate of 6.87 percent in the first year of the plan and decreases to 4.73 percent in the middle of the first phase. With the allocation of all the investment to the capital goods sector, the rate of accumulation of capital increases to 10.46 percent by the end of the first phase. In phase II, the growth rate of capital falls to reach the full employment balanced growth rate of 2.27 percent. Employment also reaches the full em ployment level by the terminal year and continues to grow at the rate of 2.27 percent. The economy with an unemployment of 139.55 in 1970 reaches full employment in thirteen years. With our assumption of fixed capital-output and capital-labor ratios, we see that output also reaches the full employment potential level by the terminal year and grows at the balanced growth rate during the post plan period. The estimates of gross national product 79 are shown in Table 3.3. Table 3.4 shows our estimates of foreign trade components. The economy will have to maintain a net export (i.e., negative M) to reduce the dependency on aid. The inflow of foreign aid desreases from Rs. 424 Srores at the beginning of the plan to Rs. 116 crores by the end of the plan. Such a choice of self reliance implies heavy emphasis on import substitution. This can be seen from the growth of net exports of capital goods to balance the net imports of consumer goods. The burden of the loans is Rs. 1943 crores at the beginning of balanced growth period. That means the debt servicing will still be a problem during the post plan period. With the estimates of output and foreign trade, the estimates of consumption and savings are shown in Table 3.3. The estimates of average propensity to save during the plan period rises from an initial rate of 8.4 percent before the plan to a high of 27.4 percent at the end of the first phase. The stipulated consump tion growth, the optimal choice of investment in the reproductive capital goods sector and hence a higher rate of gross national product growth increase the savings rate during the first phase. But in the second phhse the rate of savings decreases to a low of 5.5 percent which is lower than that at the beginning of the plan. 80 TABLE 3.1 Optimal Pattern of Capital Growth Time t K 1 Capital Stock K2 Total Net Invest ment Growth Rate of Capital 0 21367 17934 39361 - - 1 25784 16281 42065 2704 ' 6.87 2 29698 14732 44430 2365 5.62 3 33295 13330 46627 2197 4.95 4 36771 12062 48833 2296 4.73 5 40319 19014 51232 2400 4.91 6 44152 9875 54029 2795 5.45 7 48507 8935 57442 3415 6.32 8 53652 8085 61737 4295 7.48 9 59902 7316 67218 5480 8.88 10 67628 6620 74247 030 10.46 11 61192 19604 80797 6549 8.82 12 55369 29531 84900 4104 5.08 13 50100 36914 87014 2114 2.49 14 51241 37755 88996 1981 2.27 15 52407 38615 91022 2026 2.27 Notes: All figures are in Rs. Crores (1960-61 prices). Plan period for t = 1, ...f 13 Balanced Growth period: t greater than 13 81 TABLE 3.2 Labor Employment and Labor Force Growth Employment Full Time __________________________________ Employment t L^ L Total Labor 0 63.93 171.97 235.90 375.45 1 77.14 155.60 234.74 384.10 2 88.85 140.79 229.64 329.94 3 99.62 127.40 227.01 401.99 4 110.01 115.27 225.28 411.25 5 120.62 104.30 224.93 420.72 6 132.09 94.38 226.47 430.41 7 145.12 85.40 230.52 440.33 8 160.52 77.27 237.79 450.47 9 179.21 69.92 249.13 469.84 10 202.33 63.26 265.59 471.46 11 183.07 187.36 370.43 482.31 12 165.65 282.23 447.88 493.42 13 149.89 352.79 502.68 504.79 14 153.30 360.82 514.12 514.13 15 156.79 369.04 525.83 525.83 Notes: All figures are in millions (1960-61 prices) Plan Period: t = 1, ... 13 Full Employment Growth Period: t greater than 13 82 TABLE 3.3 Optimal Patterns of Output and Stipulated Consumption Growth Time Output Total Saving S/GNP t X1 x2 = GNP Consumption^ = S % 0 6891 12799 19690 12799 1 8316 11580 19897 12799 2777 13.96 2 9579 10479 20058 12799 2482 12.37 3 10740 9482 20221 12799 2351 11.62 4 11860 8579 20440 12799 2387 11.68 5 13004 7763 20767 12799 2602 12.53 6 14241 7024 21265 12799 3013 14.17 7 15645 6356 22001 12799 3644 16.56 8 17305 5751 23056 12799 4531 19.65 9 19303 5204 24524 12799 5720 23.32 10 21812 4708 26521 12799 7270 27.41 11 19737 13945 33682 18814 6788 20.15 12 17859 21006 38864 26036 4338 11.16 13 16159 26257 42416 31371 2344 5.52 14 16527 26855 43382 32156 2327 5.36 15 16903 27467 44370 32931 2337 5.27 Notess All figures are in Rs. crores. Plan period: t = 1, ..., 13. Balanced Growth Period: t greater than 13. ♦Stipulated consumption during the first phase is held equal to at time zero. 83 TABLE 3.4 Optimal Foreign Trade Components Time Aid Loan Imports M 1 .. M2 Net 0 424.3 2753.5 — — — — — — — -- l 383.9 2851.2 -1405.4 1333.1 -72.3 2 347.4 2905.4 -2771.2 2653.7 -117.5 3 314.3 2923.4 -3879.6 3726.2 -153.4 4 284.4 2911.7 -4771.7 4589.6 -181.5 5 257.3 2875.7 -5481.6 5278.8 -202.8 6 232.9 2820.2 -6643.4 5825.0 -218.4 7 210.7 2749.3 -6485.9 6256.7 -229.2 8 190.6 2666.3 -6836.0 6600.0 -236.0 9 172.5 2574.2 -7100.7 6861.4 -239.4 10 156.1 2475.5 -7358.3 7118.3 -240.0 11 141.2 2372.2 -5107.0 4869.6 -238.3 12 127.8 2266.2 -5265.7 5030.9 -234.8 13 115.6 2158.91 -5343.6 5113.8 -229.8 14 0 1943.0 -345.3* 15 0 1748.7 -310.88* Notes: All figures are in Rs. crores (1960-61 prices). Plan period: t = 1,... 13 Balanced Trade self-sufficiency period: t >13 *These are debt■servicing only. 84 In absence of any technological change, such a savings rate is sustainable on the balanced growth path. On the other hand, a labor saving technological change increases the natural rate of growth. With such a tech nological change, the desired investment on the growth path will be higher; but with the savings rate decreasing during the post plan period, the stability of such a growth process is not guaranteed, unless another aid poli cy or domestic monetary and fiscal policy is formulated. The balance of payments position will also deteriorate. Thus, any investment policy, solely based upon foreign aid, is likely to destabilize the economy's growth path. The planners, alternatively, will have to consider certain domestic policies to stabilize the investment and savings paths. The next chapter considers a monetary policy model for a stable growth. The government, through a monetary-fiscal policy mix can increase the savings potential by increasing the dis posable income in the economy and guide the investment growth through a public sector investment policy. Chapter V presents the results of a monetary model with an opti mal public sector investment policy for India. CHAPTER IV A MONETARY DISEQUILIBRIUM-ADJU STMENT POLICY MODEL Introduction In this chapter the paths of optimal investment and saving are analyzed by looking at the positions of wealth holders in equilibrium. The desire to save depends upon the real rate of return. If wealth holders wish to hold part of their wealth in the form of real cash balances, increases in money in the form of government debt leads to increased saving potential and total real wealth in the economy. Thus a monetary and fiscal policy mix can be used to increase the capital stock as well as the savings potential. As pointed out in the previous chapter, the stability of the savings path is important in guaranteeing balanced growth with a minimum dependence on foreign borrowing. Emphasis should be placed upon domestic policies to ensure increased saving potential to meet the required rate of investment on the full 85 employment growth path. With stability as an objective we develop a mone tary policy model. Unlike the two sector optimal allo cation model considered in the previous chapter, we treat output as a single homogeneous commodity. The accumulation of capital stock is made to depend upon the choice of public sector's share of investment. The growth and stability properties of the economy with money are examined. In Chapter V, such a monetary growth model is applied to the problems of capital accumulation and self-reliance in India. Consider a two asset portfolio model such as Tobin's.'*' Let capital stock and money be the only two types of assets that people desire to hold. The introduc tion of other monetary assets (such as private bonds) woMd make the model more realistic. However, in our analysis we are primarily interested in the implications of in creasing or decreasing the supply of money along with planners' desire to maintain equilibrium by making public investment whenever necessary. Moreover, in a less developed economy where a well developed borrowing and lending market does not exist and people hold a negligible ■*"J. Tobin, "A Dynamic Aggregative Model," Journal of Political Economy, LXIII (April 1955), p. 106. 87 part of their wealth in the form of bonds, a bond market mechanism may not be sufficient to induce higher invest ment. Hence , we consider the simple Tobin model with only "outside" money, created through government deficit financing. Tobin defines portfolio balance by requiring equilibrium in the money market, namely: (M /P) = M (K, r, Y) (4.1) s d where Md(K,r,Y) = the liquidity preference of the individuals (M /P) = the supply of real cash balances S K,= total capital stock r = market rate of interest Y = income P = price level Ms = supply of nominal money. Essentially the equilibrium follows from Tobin's assump tion of price stability and anticipation of zero infla tion. If for some reason the rate of return on capital (i.e., rental rate) exceeds the real yield on money, people will switch from cash balances to real assets. This temporary excess demand for capital eventually reduces the rate of return on capital and the equilibrium is maintained when the two rates become equal. In our analysis we consider the money supply either for transfer payments as "gifts" or to finance government purchases. We investigate the case of a disequilibrium in the money market due to the elasticity of price expectations being greater than unity. Then the instantaneous clearing of the market as implied by equation (4.1) will have to be modified to introduce disequilibrium adjustments. As a corollary to this ana lysis we study some special cases of the equilibrium rate of investment growth in an economy where the antici pated rate of inflation is zero, where money is distri buted only as "gifts," and where money is created only to finance the government purchases (of capital goods). We make an attempt to generalize the basic Tobin model in these cases. Such a general model is tested for its short-run and long-run stability. Structure of a Monetary Policy Model Basic Model with Money and Public Sector Let ot be the fraction of government investment • • out of total investment at any time t. Then a K. is t J t t the rate of public sector investment to be referred to as public sector undertaking. (l-at)Kfc is the private investment or private sector undertaking. If = 0, we have the basic Tobin model with only private ownership 89 of capital and money is created only to distribute as "gifts." We allow ( * t to vary either continuously with time t, or to take only a finite number of values in (0,1). Prom a planning point of view, if plans are formulated as five year projects, with the fraction of public sector investment fairly constant during the plan 2 period, at may take on only discrete values. Let Wt stand for the real private wealth, consisting of private capital stock and real money balances. Treating the private capital stock and the stock of real balances as the summation of the pri vate rate of investment and the changes in real money balances over time, we may write the private wealth as: t Wt = I [l-at]Kf c dt + (Mg/P)t (4.2) »oo Of the total stock of money created by the government, let Mgl be the amount of money distributed so far, in the form of transfer payments through deficit financing 2It is also possible to choose the value of a from the continuous interval (0,1) provided, plans can be formulated and revised on a continuous scale. and M be the amount introduced so far. to finance the sz government investment at the rate of crK*.. From an t u accounting point of view we write: M = M + M :Stock of nominal money (4.3) s si s2 Or in real terms, (M /P) . = (M /P) +(M _/P) ): stock of real s t si t s2 t cash balances (4.4.a) (M /P) =(M /P) + (M ,/P) : flow of real s t si t t cash balances (4.4,b) For any change in the capital stock the government's share of investment expenditure is afcK , which is financed by creating an additional amount of real balances (Ms2/P)t The change in the real balances required to finance the government investment can be written as: (Ms2/P)t = atKt (4’5) We denote by (Ms]./p)t the chance in real balances which is distributed as an additional "gift." Treating transfer payments as negative taxes through deficit financing and using equations (4.4.b) and (4.5), we write the net private disposable income as: 91 Y = F(K,L) + (Mgl/P) ^ t = F (K,L) + (M /P) - a K (4.6) t S t t t where F (K,L) ^ is the homogeneous net output in the economy; and we assume a constant factor proportion production function as: Y = F(K,L) = a K : production function (4.7) t t L = b K : labor demand function (4.8) t t Labor is treated as abundant,,i.e., L. < L- where “ ft a is the net output-capital ratio and b is the labor- capital ratio. Lf is the full employment potential labor force. Let s be the average propensity to save out of the net private disposable income defined in (4.6). The flow equilibrium is obtained by equating the change in wealth and the level of desired saving. Using equations (4.2), (4.6), and (4.7), we derive: • • • • (1-a )K + (M /P) = slaK +(MS/P) -o K ] (4.9) t t s t t t t t or, • • K = saK - (1—s)(M /P) t t s t (4.10) ------i“ (I-s)()------ t In Tobin's equilibrium relationship, wealth holders' desire to hold real cash balances as part of their wealth plays an important role. An increase in the rate of change of real cash balances, given the capital stock, reduces the desired change in the capital stock (i.e., desired investment). Stated in other terms, given the rate of desired investment, an increaseoin the rate of change of real cash balances requires a higher capital stock and vice versa. In this model, the increased rate of money supply is brought about by the government through deficit financing. This dissaving of the government is compensated by an increase in desired private saving as a result of an increased aggregate income. As long as this desired saving is matched by the desired investment, the capital stock continues to grow. Tobin states that the decline of the re&l rate of return on capital brings the portfolio to an equilibrium where the capital stock is larger. Capital deepening in production requires monetary deepening in portfolios. ... Given the yield on money, the stock of money per unit of capital must rise. Provided the government can engineer such an increase, capital deepening can proceed. ... To maintain the fixed relation between the stocks, money and capital must grow at the same rate. 3 3 J. Tobin, "Money and Economic Growth," Econome- trica, XXXIII, No. 4 (October 1965), p. 679. 93 Hadjimichalakis classifies the role of money in capital growth as the second kind of non-neutrality of money where monetary authorities, with a proper choice of the rate of money increase, can affect the equilibrium 4 rate of change in the capital stock. Let 0 be the rate of increase of nominal money, t We then write (M /M_) = 0. . Writing m_ for (M /P) we s s t 5 g derive the differential equation for the supply of real balances as:^ m = m [0 - P/P] (4.11) 5 S Clearly, changes in the real balances depend upon three factors, namely, the level of real money balances, the rate of increase in the stock of nominal money, and the rate of inflation, P/P. Tobin in his equilibrium analysis makes the rate of inflation P/P = 0 as the necessary and sufficient condition for portfolio balance equilibrium. Disequilibrium 4 M.G. Hadjimichalakis, "Equilibrium and Disequili brium Growth with Money — the Tobin Models," The Review of Economic Studies, XXXVIII, No. 116 (October l$7l) , p. T5T.--------- 5 Henceforth the subscript for time will be omitted from the variables unless it is essential to the discus sion. 94 in this two asset model can be introduced if we allow price instability. Following Walras' law, the rate of inflation (or deflation) can be treated as a function of the excess demand for goods or the excess supply of real balances. We also allow for people's recalculations of price expectations based on whether their previous expectations were realized or not. Let us denote the anticipated rate of price inflation by f, which we express as: E (P/P) = i r (4.12) where E stands for anticipation. Once again as in equation (4.1), m stands for real Balance demand. d We write the price adjustment due to any disequilibrium in the money market and the recalculation of expectations of price inflation as: P/P = 3(m-m ) (4.13) s q ir = v ( P /P - it) ( 4 .1 4 ) where 3 and v are positive constants.^ If the demand for real balances adjusts itself instantaneously to the supply of real balances then the price inflation is zero. This is attained when 3 = « . Then the cost of any For greater generality, one may also consider the case when either 3 or v or both depend upon t and vary in some systematic manner. disequilibrium is so high that people adjust their liquid ity demand m^ to mg immediately. 1/0 is the mean time required for the adjustment between supply and demand of real balances to become equal. Tobin's equilibrium model can be specified by letting 0 -► «. Then we have instantaneous equilibrium in the money market as shown in equation (4.1). Equation (4.14) shows an adjustment of price expectations after experiencing an actual inflation of P/P which is different from the expected inflation of <tr. If people's expectations of inflation are realized in stantaneously, then there is no reason for them to re calculate the expectations. So, they continue to assume the inflation to be i r and hence t = 0. From equation (4.14) we can see that the adaptive expectation model we specified has this property, i.e., i r = 0 in the limit, £ for large v, only when P/P = ir. Then we have the situation of perfect (myopic) expectations. However if P/P >ir then i r > 0, i.e., people expect a still higher rate of inflation. Let r be the market rate of interest on nominal balances and let the rental rate on capital be equal 7 to the marginal product of capital .FK(K,L). Then the 7 Partial derivative of F(K.L) with respect to K is denoted by F (K,L). K 96 portfolio balance, in the absence of inflation, requires that r be equal to F (K,L). But, in the presence of K inflation , the real yield on cash balances is - tt; and hence, the market rate of interest on real balances is F (K,L) + ir. Thus the portfolio balance requires: K r + t t = F (K,L) (4.15) K Let us define a demand function for real balances m as: d m , = m (K,r) (4.16) d d The demand for real balances depends upon the level of Q income (and hence on the capital stock) and the market, rate of interest. Again from equation (4.15), since F (K,L) depends upon K, we can write the liquidity pre- ference as: m = m (K,tt) (4.17) d d 9 We also specify: mdk > 0 an(* md7r — 0 (4.17.a) Q In our model, income Y is defined as being equal to aK and hence, K is used instead of Y in (4.16). g We write the partial derivative of m^ with re spect to K as m,. and the partial derivative of m, with respect to tt as mdTr. 97 With the increase of capital stock and hence of income, the transactions demand for real balances in creases. With the increased rate ..of inflation, the real yield on money balances decreases and the demand for real balances also decreases. Special Cases of the Model We treat both a and 9 as the government policy variables. The choice of a depends upon the long run goal of reaching the steady state capital path. For the planners an important policy decision is to select an optimum time profile of to reach the steady state capital path in a minimum time T. The choice of 9f c remains as an additional degree of freedom of choice to bring about the monetary equilibrium by the terminal time T. The generalized Tobin model can be examined for its policy implications under certain specific assump tions. Tobin, treating money as government debt to distribute as transfer payments (as Msi) shows the non neutral effects of money upon growth under the assumption of stable prices. Hahn^ introduced the government • ^®F.H. Hahn, "On Money and Growth," Journal of Money, Credit and Banking, I, No. 2 (May, 1969) , pp. 172-187. 98 investment financed by printing money as well as trans fers (negative of tax), but again, under the assumption of.stable prices. We consider in addition to these several other cases. Case (a) : Money created only as M^, to finance the public sector investment, in an economy with stable prices, i.e., P/P = 0. This is similar to Tobin's treatment but without any transfer payments. In this • • case since m 0 = aK and M = M , any policy choice of s s2 a is equivalent to choosing certain values of 0, the rate of introducing nominal money by printing, to finance the public sector investment of aK.-H Hence, the two policy instruments are not independent. Choice of either a or 0 depends upon the steady state conditions and in turn, its. time path determines Mg2 (see equation 4.11.a). The system can be written as: • • K = saK - (l-s)mS2 ------------------ (4.10.a) 1-a(1-s) = saK 11 * * * XJ-Since Ms/Ms = ms2/ms2 = 0 and mS2 = aKf we can write 0« a(K/M ). In this sense Tobin's monetary policy is equivalent to a fiscal policy. 99 (4.11.a) (4.5.a) (4 .13.a, 4.14.a) Prom equation (4.10.a) we note that the total investment is independent of the government share of total invest ment. If the government decides to increase its share of investment by increasing the supply of real balances, ms2' t^ ie 9ov®rnment investment increases? and the wealth holders increase their cash holdings, substituting for productive capital assets. Thus, the private investment decreases to the same magnitude as the increase in public sector investment, leaving the total investment unchanged. In this case, money is neutral in changing the investment rate and hence the capital growth. Thus, such a monetary model will not have any non-neutral effects on growth. Case (b)t Money created only as Mg2 to finance the public sector investment, where the price expecta tions are other than stable prices. People experience a rate of price change which is different from zero (i.e., disequilibrium in the money market). Putting Mg^ = 0 and Mg = MS2, the corresponding system can be written as: m = 0m s2 s2 ms2 - “K P/P = I T = 0 100 K = sak - <l-s)ms2 _ sak (4.10.b) (l-ct-ll-s)) m s2 (4.5.b) P/P = 3(n»g2 - md) (4.13.b) i r = v [P/P - it] (4.14.b) In this case, the choices of a and 9 depend upon the long run objective of increasing the capital stock and the stability of monetary equilibrium. The time path of a determines Mg2 and that of 0 determines the time path disequilibrium model has a neutral effect on economic growth also. model to a disequilibrium model is examined by Hadjimi chalakis. In his model (which is a generalization of Tobin's model), Hadjimichalakis has MS2 = 0; hence, Mg = Mg^. The simple Tobin model can be derived from this case by assuming P/P = 0. This model can be written of the price levels.*2 However, as in case (a), this Case (c): The generalization of the simple Tobin 12 See equations (4.5.b) and (4.11.b) 101 be letting o = 0 in our formulation, as: • • K = sak - (l-s)m (4.10.c) si m = m „ = m [0 - P/P] (4.11.c) s si s P/P = B(m ,-m,) (4.13.c) si a • • ir = v [ P / P - ir] Hadjimichalakis shows that in this monetary model, money is non-neutral. But, we show later that this model is unstable, since it implies that the warranted rate is greater than the natural rate on the long-run growth path. The simple Tobin model is a special case of this disequili- brium model with P/P = 0, i.e., when prices are stable and people's expectations of future prices are realized.^ If price stability is the goal, the choice of 0 can be made to depend upon P/P. Case (d) : Money as both and M but with stable prices: this is a generalization of Tobin's model designed to include government investment policy and to study the implications on the steddy state capital path. In this case, the policy choice of a and 0 determine the levels of M and M . respectively. The s2 s± ^Equations (4.10.c) and (4.11.c) with P/P = 0 specify the simple Tobin model. 102 system can be written as: K = sak - (l-3)ms (4.10.3) l-a(l-s) m = mgl + mg2 (4.14.d) s m = aK (4.5.d) s2 m = 0m (4.11.d) s s p/p = u = 0 (4.13.d, 4.14.dr This is Hahn's formulation of the monetary model. Case (e) : As a special case and an alternative to the monetary model, we consider a fiscal policy model, in which the government investment in the public sector is financed by taxation instead of increasing the public debt by printing money. Let us, for simplicity, assume that the total taxes are equal to the government expenditure on invest ment.1^ We write the public sector investment equal to 14 Even if the total tax revenue in the economy is greater than that required to finance the public sec tor investment, we can redefine our income as net of those additional taxes. To study the implications of the public sector growth on the growth path of the total capital stock, only the taxes to finance the government the tax revenue, aK. This case is equivalent to treating • • • aK = mg2 = "Insl our monetarY model. The taxes being negative transfer payments, stands for taxes. Thus, this fiscal policy model is a special case of our mone- • tary model with m =0. s Then, from equation (4.10) , putting mg = 0, we have: K = [sa/(l-a(1-s))]K (4.10.e) When a= 0, i.e., in the.absence of government investment in the economy, the private investment grows at the rate of sa. Such an investment path corresponds to the warranted rate growth path. If, on the other hand,a> 0, the rate of growth of investment is [sa/(1-a(1-s))] > sa. And the investment growth rate is higher than the warranted rate. We show in the next section that such an invest ment growth path does not have the property of long-run stability. Case (f): Finally, we specify a further genera lization of case (d), as the model we consider in our study. This becomes a disequilibrium monetary model with both types of money, namely, money as transfers Mgl, investment are relevant. 104 and money to finance the government purchases of invest ment goods, Mg2» The system of equations for this case are (4.10), (4.11), (4.13), (4.14), and (4.5). For the analysis of equilibrium growth, we assume that labor force grows at a constant rate n. As in Chapter III, let L stand for the labor force. The growth in the labor force can be written as: L = n L (4.18) t t The other equations of this case are: K = saK - (l-s)m„ (4.10.f) l-STT=sf“ m = m [0 - P/P] (4.11.f) s s m = m , + m_9 (4.4.f) s si m _ = aK (4.5.f) s2 TT = [P/P - u] (4 .14 .f) P/P = 8(m - m ) (4.13.f) s d In the next section we show that in both cases (d) and (f) an increase in the share of public sector investment, for any given rate of increase in the 105 real balances leads to increases in the rate of investment. Such a monetary model has non-neutral effects on real growth. We also show that, for a proper choice of a, these two cases have the long-run stability property, namely, the warranted rate and the natural rate become equal on the growth path. Sensitivity of Investment Rate for Changes in a Since the government likes to use the level of public sector investment to shift the capital path, let us examine whether any change in a brings a change in the capital stock. Given the stock of capital and the rate of change of real balances at any time t, from equation (4.10) we see that an increase in a increases the rate of investment, i.e., 3 K/3a > 0. Given the rate of increase of nominal money and stable prices, an increase in a means an increase in the money re quired to finance government investment and hence a de crease in the amount of money distributed as transfers (i.e., a reduction in msi)• This reduces private dis posable income as can be seen from equation (4.6). Since the average propensity to save is less than unity, the private wealth also decreases but not proportionately. We see from equation (4.9J that, for a given m , private s investment decreases. Thus, for an increase in a total 106 investment is higher but there is a reduction in the share of private investment. From (4.10) we have, for given m and K s • • 3 K/3a = (1-s) , K > 0; 1 -a(1-s) and we see that the change in the government investment • • being equal to a[3K/3a + K] is positive and the change in the private investment, being • • (1-a) [ cK/8 a ] - K = -s ^ is negative. However, in the special cases of (a) and (b) where Mg^ = 0, or even when Mg^ > 0, but mg^ =0, • we see that for any given mg, an increase in a implies a decrease in K.15 In these cases the rate of change of real balances is equal to the total government expendi ture on investment. An increased share of public sector investment means a decreased level of total investment. For any given mg, the government's expenditure on invest ment does not change but private investment decreases. If the purpose of government investment, through deficit 15 • * * * Here mg = mg2 = <XK. For any given ms2/ an increase in a implies a decrease in K. Also note that the change in the private investment is negative: (1-a)(K/a) - K < 0. 107 financing, is to raise the rate of investment in the economy, the policy of increasing the government share of investment without any transfer payments, may not be very useful. Thus only the cases (d) and (f) are rele- • > vant to our study, with M > 0, M 0 > 0, m _ _ 0 si si < and mg2 > 0. For a given rate of change in the total supply of real balances, an increase in a increases mg2 (i.e., government expenditure on investment) by reducing mg^ (i.e., transfer payments); and the economy's total investment increases at a faster rate. In case (e) , from equation (4.10.e), we note that an increase in a raises the rate of investment. Thus, the fiscal policy has a non-neutral effect on the investment growth. Stability Properties of the Model In the previous section, we found that only cases (d) and (f) are relevant to our study of a monetary growth model. For its policy implications, we consider fcase (f). Tobin shows tha non-neutrality of money in growth.'1 '6 Hadjimichalakis in his generalization of the Tobin model Tobin, "The Neutrality of Money in Growth Models; A Comment," Economica, XXXIV (February 1967), pp. 69-72; see also H.G. Johnson, "Money in a Neo-Classical One-Sector Growth Model," in Essays in Monetary Economics (New York; Allen and Unwin, 1967), pp. 161-178. 108 introduces a disequilibrium in the money market and shows how the Tobin model becomes unstable when price anticipations different from stable prices are intro duced. Our policy model (f) has both Tobin's money (as transfers) and money which is introduced to finance government investment. Prom case (f) we note that the choice of a determines the amount of money Mg2 required to finance the government investment, and the choice of 0 determines the transfers Mg^. We examine the short-run and long-run stability conditions by evaluating the non neutral effects of money introduced for both transfers and government investment and show that the stability of the model with only transfer money is not possible. Finally we study the sensitivity of changes in the policy parameters a and 9< , upon the equilibrium capital stock, real balances and the price levels. Short-run Equilibrium Analysis Let us investigate the stability properties of the general monetary model (f) in a short-run framework. We .define a short-run as the situation when the capital stock does not change and the labor force does not grow. We treat K as fixed at K and L at L (i.e., n = 0). The monetary model can be written, after some substitutions, as: 109 K * 0 (4 .1 9 ) m = m [0 - 3(m - m,)] (4.20) s s s d tt r = [8(mg - md) - ir] (4.21) L = 0 (4.22) For the local stability of the system we state the following result: Theorem: The necessary and sufficient condition for the local stability of the system (4.19) - (4.22) is that m ^ = 0. The equilibrium solution of the system is given • • by setting mg = 0 and ir = 0. Then we have the solu tions as: K = K (4.23) mg = ms (4.24) i r = if = 0 = 8.(m« - m,) (4.25) s a m, = in. (4.26) d d K, in , in., if are given, s d From equation (4.25) the implication is that the equili brium rate of inflation is equal to the rate of increase 110 in the nominal money. Increases in the nominal money will not affect the equilibrium capital stock (i.e., the real sector) but only the price level. A necessary and sufficient condition for a local stability is that the associated Jacobian determinant be positive and its trace be negative. Prom the equations (4.20) and (4.21) we have: (3m /3m ) = 0 - 20m* + 0m = -0m <0 (4.27) S S Q S (3m /Sir) = 0m m_ < 0 (4 .2 8 ) s s a* (Sir / 3 m ) = v0>O (4 .2 9) s Oir /3ir) = - v-v0 m (4 .3 0 ) dir Denoting the Jacobian matrix of partial derivatives by J, we have: Determinant |J| = v3ms >0 (4.31) Trace of J = -0m - v(l + 0m ] (4.32) s dir Note that if m =0, Trace IJI <0. Again for the air trace to be negative we should have m <_ t (» /v) + (1/0)1 , dir — s since both v and 0 are positive and as v-»-“ and 0-*«> , we should have m ^ > 0. Using equation (4.17.a) the sufficient condition is: Hadjixnichalakis states a similar result as follows: "Proposition I: (a) If both v and $-*■» then, the short-run model is locally unstable. (b) Even if neither v nor 3-*“ , then, money is a perfect substitute for capital, 17 the short-run model is locally unstable." If money is a perfect substitute for capital then the elasticity of the liquidity preference with respect to the real yield on money balances is -® , i.e., = -® . Thus Hadjimichalkis1 proposition I, (b) is a much more rigid requirement for the instability than our condition. If neither v nor 3 - * - “ then, for local instability the requirement is: mdTr < ~ I (®g/v) + (1/0)]. Hence for given v and 3 finite, even a sufficiently high substitutability of money for capital (and vice versa) will be sufficient to make the short-run equilibrium locally unstable. 17 M.G. Hadjimichalakis, p. 466. 112 Long-run Equilibrium Analysis In the long-run analysis of the general monetary model (f) we allow the capital stock to change and the labor force to grow at the rate n. Monetary authorities can change the rate of introduction of money, 9; planners can change the rate of public sector undertakings, a. The long-run equilibrium is defined as the steady state equilibrium. On the steady state path we have: • K = nK (4.34) • m = n in (4.35) s s • L * nL (4.36) tt = 0 (4.37) Solving equations (4.10.f), (4.11.f) and (4.14.f) and substituting equations (4.34) to (4.37), we derive the 18 following set of relations: tt* =0 -n = $(m* - m_) (4.38) s a m* = K* (sa - n(l-a+as)) (4.39) s | U ^ T nt K* = K e (4.40) o i n } ■JO* P/P is eliminated using (4.13.f). 113 where * stands for the steady state solutions. K is o the initial capital stock at the time zero. On the steady state path the equilibrium rate of anticipated inflation t t is equal to the difference between the rate of growth of nominal money 0, and the balanced growth rate n. Non-inflationary growth implies 0= n. As .stated earlier, the non-neutral effect of money on the steady state capital stock can be seen from equation (4.39). An increase in the real balanceson the long- run path will proportionately increase the capital stock at equilibrium. We now state a theorem for the long-run stability of the solutions for m , K, and tt. s Theorem; The necessary and sufficient condition for the long-run equilibrium solutions (4.38), (4.39) and (4.40) to be locally stable is, m ^ = 0. From the system of differential equations (4.10,.f) , (4.11.f), and (4.14.f), for m , K, and tt we have s (9m /9m ) = 0- 28m + 0m, = -0m + n (4.41) s s s d s 0 mg/9 K ) = 0m m^k > 0 (4.42) s 0 m /9tt ) = 0m m, <0 (4.43) s s dTT 114 0K/3m ) = - (1-s) (-0m +n) s I-a+as s = - (1-s) (3m /3m ) 1-a+as s s (3K/3K) = sa (1-s) [0m m,.] 1-a+as 1-a+as s sa __ (1-s) (3m /3K) 1-a+as 1-a+as s (3K/3ir) = (1-s) (0m m„_) “ 1-a+as s dir (1-s) (3m /3tt) 1-a+as s (3 ir/3m ) = v0 > 0 s (3 tt/3K) = -V0 mdk < 0 (3 tt/3 tt) = -;.v0m - v dir Hence, trace of J = -0m + n + sa s 1-a+as -(1-s) (0m m„ ) -v0 m._- v 1-a+as s dk d’1 and determinant, IJI = 0vsa [m -nm_ -(1/0)] 1-a+as s dir ‘ (4.44) (4.45) (4.46) (4.47) (4.48) (4.49) (4.50) (4.51) 115 Then, if m ^ = 0, we fcee that 8-*-» and |j|-M-«> and trace »• and hence the equilibrium solutions are stable. Again whenever m. < (m /n)-(l/B), |j| >0. a it s Since ni < 0, the sufficient condition is m, =0 — dir for Thus, for both the long-run and short-run stability of the solutions, we require m^ = 0. Then the liquidity demand depdnds only on the output level. Monetary deepening means capital deepening and hence, the mone tary model has non-neutral effects on growth.^ Monetary and Non-monetary Analyses For purposes of comparison of monetary and non monetary growth processes and in order to investigate their implications we consider some special cases. The non-monetary one asset model of Solow w can be derived by setting m = 0 in equation (4.10.f) or by s setting m = 0 and hence a=021 in equation (4.39). We 19 See equations (4.10.f) and (4.39). 20 R.M. Solow, ?A Contribution to the Theory of Economic Growth," Quarterly Journal of Economics, LXX (February 1956), pp. 65-94. 21 We assume that the government can increase its expenditure on public investment only through deficit financing. In this sense the monetary policy (deficit financing matched by printing money) is equivalent to a fiscal policy. Hence if m =0, we treat a=0. 9 116 then have the Solow growth path on which the capital stock increases at the rate n. On the Solow intensity path the warranted rate is equal to the natural rate, n. In our case the warranted rate is equal to [s/(l/a)]r the ratio of the marginal propensity to save to the capital output ratio. As a second case, we consider money distributed only as transfer payments. The government does not undertake any public investment to be financed by deficit financing. We then have, m >0, but a=0. In other s • • • words, m _ = 0 and m = m ,. This is our case (c) of S2 s Si a disequilibrium monetary model with only Mgl. Prom equation (4.39) we then have: K*(sa-n) > 0 (lesfcn ds/ (1/a)] > n Then the warranted rate is greater than the natural rate on the growth path. Thus, the general Tobin model with only M is unstable. Because of transfer payments, people have higher disposable income and saving. However, the maximum investment rate with the given rate of labor force growth, is n. Hence the excess of warranted rate of saving cannot be matched. Since real output and investment can grow at most at the or (4.52) 117 natural rate, people cannot engage their savings elsewhere other than as idle balances. One way of bringing the system back to equilibrium is by reducing the transfer payments and by undertaking public expenditures financed by deficit financing. As a third case we consider a>0 with m >0. In s 4 this case M can be zero or positive. This corresponds to cases (d) and (f) of the previous section. With both m and a positive in this monetary model, we have: s [s/(l/a)] > (l-a+as)n (4.53) Since 0 < a 1, the monetary authorities can choose a value of a e (0,1) such that the warranted rate is equal to the natural rate and equation (4.53) holds simultaneous ly. 22 prom equation (4.53) we see that the choice of a is in the range [(n-sa)/n(1-s)J < a < _ 1. Any arbitrary choice of a <[ (n-sa)/n (1-s) ] may not equate the warranted rate to the natural rate; and it may lead either to persistent shortage or excess labor supply. In our special case (e) we have M > 0 and m = 0; s s but the government has a balanced budget such that the public sector investment is totally financed by taxes. ^It is not difficult to show that the choice of a e (0,1) is unique. In the next chapter we show the uniqueness of a during the plan period. 118 For the long-run balanced growth, using equations (4.10.f) and (4.18), we have the solution for the capital path as: (K/K) = [sa/ (1-a (1-s)) ] ■ n We rewrite the same as: a = [ (n-sa)/n(l-s) ] (4.54) If n=sa we then have,a = 0, i.e., on the long-run balanced capital growth path, the public sector investment is zero? and the economy moves along the stable Solow growth path. If a>0, i.e., when n>sa on the long-run path, the natural rate of growth is greater than the warranted rate. Then the long-run growth path is the Keynesian depressionary equilibrium path. Any attempt to increase a tends to diverge the two rates of growth further away from each other. Such a policy choice of a is not desirable in the long-run. Comparative Static Analysis The long-run steady state solutions to the mone tary growth model can be examined on a comparative static basis to study the implications of changing some of the parameters in the system. Basically, we consider the following two cases: (1) the effects of increasing the rate of change of nominal money 0 , upon other real 119 variables in the model, and (2) the effect of changing • the rate of government's share of investment in public sector a upon the economy. Consider the long run solutions (4.38) and (4.39). n = 0 - (3(m -m ) (4.38) s d nK = saK _ (1-s) (nmg) (4.39) 1-a+as 1-a+as * 0 = (m -m,) - it (4.38) s a Consider the system as having three variables, m^, K, and it. Differentiating the above equations with respect { to 0 , we arrive at the following system of differential equations: /(dm^/dS)' 8 -0(dmd/dK) -B (dm /d-rr) d (X\ (dK/d0) -(1-s)n s(a-ja) - n 0 - 0 1-a+as 1-a+as * , (dit/d0) / , 3 -B (dm /dX) d -B (dmd/dir)-| w (4.55) . • 21 The determinant D of the system (4.55) is written as: D = 6 (l-s)n (dm.,/dK) sa + n (4.56) l-a(l-s) d l-a(l-s) The solutions of the system of differential equations (4.55) are: (dm /d0) = sa _ [ 5 (dm„/dir) +1] (4.57) s r-a (l-s) “ n 3 (dK/de) (l-s)n [$(dm /dir)+l] (4.58) 1-a(1-s) s (dir/de) = 1 (4.59) We then have: >0 if;- [0 (dm,/dir) +1] <0 (dms/d0) ) a ( (4.60) <0 if [8 (dm /dir) +1] > 0 a and < 0 i >0 if [8(dm,/dTr) + 1] (dK/d0) ) a ^ (4.61) <0 if [8 (dm^/dir) +1] > oj If the rate of nominal money supply is increased, then the 23 For the stability of the system, the deteminant should be positive. Thus we should have: (dnu/dK) > sa-n(l-*+«s) > 0 d (r-s)n— In the next chapter, we choose the parameters for the demand for real balances such that the above restriction holds. 121 expected rate of inflation increases proportionately. Prom the long-run stability condition, we have, (dm^/dir) = 0, and hence we see that the impact of increas ing the rate of change of the nominal money supply is to reduce the long run equilibrium of the real balances and the capital stock. This is the non-neutral effect of an increased rate of nominal money supply upon the capital stock. Similarly differentiating the equilibrium solu tions (4.38) and (4.39) with respect to a we have, (dm /da) = (dm./dK)(dK/da) (4.62) s a (dir/da) = 0 (4.63) (dK/da) = nK[(1-s)/(l-a(l-s))] (4.64) D Hence, we have: (dK/da) > 0 (4.65) (dm /da) >0 s Increasing the share of public sector investment always increases the steady state capital stock and the real balances. On the other hand,' changing the rate of in crease of nominal money supply can either increase or decrease the capital stock at equilibrium, depending upon whether money is a strong substitute for capital or not. 122 If (dm /dir) = 0, then a decrease in 6 can reduce the d inflationary process and increase the equilibrium capital stock. Thus different choices of a and 0 have differ ent growth implications; and from the policy point of view, they can be used as important policy variables. Conclusions In the monetary model (f) that we considered, the long run stability of the model is important in exercising any monetary policy. The monetary model is stable if the liquidity preference behavior depends on income only. The analysis of non-neutrality of the monetary model suggests the possibility of choosing the policy variable a such that [(n-sa)/n(1-s)]< a <_ 1 and the model has the long-run stability property. Moreover, from the comparative static analysis, we note that the choice of a has the property of increasing the capital stock and hence income. Such a policy model with the choices of a and 0 can be used to stabilize the domes tic capital path when self-sufficiency is to be achieved by reducing the dependency on foreign aid. In the next chapter we consider a planned policy model to attain the self-sufficiency in a minimal time period such that at the end of the plan period, the economy will have attained a stable full employment capital and output path. CHAPTER V AN OPTIMAL MONETARY POLICY PLANNING MODEL FOR SELF-SUFFICIENCY Introduction We consider the general monetary model (f), developed in the previous chapter and investigate the possibilities of constructing an optimal finite time horizon planning model for India. Once again, the goal of the planning model is to attain self-sufficiency with stable domestic capital and saving growth paths during the post plan period. We emphasize a domestic monetary policy with optimal choices of a and 0 to attain self- sufficienfcy in a minimum time. In Chapter III, we treated the time path of aid as a policy choice to minimize the burden of debt. In this chapter any aid received will be treated as stochastic rather than planned and the accumulation of aid will be minimized. Let the demand for real balances be a simple 123 124 function of real income or capital stock. This quantity theory version of the demand for money is a sufficiently close approximation for an economy in which the role of commercial banks is limited, private bonds are negligible, and borrowing and lending market is not well developed. In such an economy with money, the interest rates are quite sticky, and high. Then the demand for real balances can be treated as basically dependent upon the level of transactions with very negligible demand for speculative purposes. Hence, we specify the demand for real balances, defined in equation (4.17) as: m = IK (5.1) d where I is a constant. With the increase in capital stock, and hence in income, the demand for real balances increases proportionately. As defined in the previous chapter, a stands for the fraction of total investment undertaken by the public sector and (1-a) is the fraction of investment in the private sector. The planning authorities may decide to finance part of the public sector investment through foreign borrowing. Let A be the amount of foreign bor- rowing at time t. Then aK-A is the net public sector in vestment financed by the printing of money. From the pre vious chapter we write the equation (i.e., equation 4.5) 125 as: • . , • , • (M _/P) = aK - A = (M /P) - (M ,/P) (5.2) s* s si The equilibrium change in wealth, as in equation (4.9) can then be written as: (1-a)K + (M /P) = s[aK+(M /P)-aK+A] s s or • • K = saK (l-s)mQ + SA (5.3) 1-dTI-s)" “ 1-a (1-s) I-dSF-s)' The total desired investment is equal to savings from three sources, namely, private savings, government dis saving, and foreign borrowing. The domestic investment-saving gap is now matched by government dissaving through a monetary policy and foreign borrowing. In general with such a monetary policy (namely, of creating M £ to finance public sector invest ment) the investment saving gap can be greater, less than, or equal to the balance of trade gap defined in equation (3.13), depending upon whether: sA > l-<*tl-s) < A - (a2+p)N (5.4) 126 Restatement of a Planning Problem The Planning Objective From the analysis of equilibrium monetary growth, we raise the following two questions: (a) What is the minimum time required to reach a stable full employment balanced growth path of capital; and (b) During the plan period, 0 < t <_ T , what is the minimum requirement of foreign borrowing to reach such a balanced growth path at the time T? ' As in Chapter III, we consider self-reliance as the goal of the planning model. However, the choice of domestic policy is such that the full employment target is reached in a minimum time with the capital stock growing on a balanced growth path during the post plan period. On the balanced growth path both capital stock and real balanced grow at the same rate n equal to the sate of population growth. Then, we rewrite equation (5.3) as: or nK = saK (l-s)rnns + sA I-d d '-s T “ 1 - a d - s T l- 'o d - s T m = sa - n[1 - a ( 1 - s ) ] „ . s * /K ^ s ------------------ K + ( l- s ) n A (5-S' On the post plan growth path the goal of self- reliance can be achieved if the dependence on foreign 127 aid is reduced to zero. Let us define: F(m ,K) = m_ - sa-n[l-ot(1-s) ]v (5.6) s 3 — rr=sTn— K From equation (5.4) we write: F(m_,K) = SA (5.6.a) 3 (l-s)n F(mg,K) is a measure of the dependency on aid. F ^ 0 depending upon whether or not A ^ 0. The post plan self- sufficiency is defined by setting F (m , K) = 0 for t > T (5.7) s — From the stability properties of the long-term equilibrium paths of capital and real balances discussed in the previous chapter, the definition of self-reliance as in equation (5.7) stands for an equilibrium condition of the monetary model. Hence, minimizing the terminal 1 aid and making the system self-reliant are consistent with the stability conditions of the post-plan monetary equilibrium growth path. At any time t the amount of aid received to increase the total supply of savings is treated as random rather than as planned. We associate ^Same as minimizing (F(ms7,K^)) as can be seen from equation (5.6.a). 128 a social disutility to such an accumulation of aid. St Let e be an index of the social disutility associated with F(m ,K). We minimize the total social disutility s during the plan period. The total disutility of the accumulation of aid is written as: T St Of P (m ,K)e dt. 0 s On the balanced growth path, full employment is defined as: nt L = bK = L e (5.8) t o With full employment as a targetodf the plan we minimize the employment gap at the terminal time T. The planning objective is to minimize a weighted function of the dis utility of aid during the plan period, the terminal burden of aid, and the terminal employment gap. Policy Choice Variables The planning goal is reached by choosing certain policy variables. Given the institutional structure inhibiting the adjustment of the real balances demand to the supply of real balances, 8 can be taken as a con stant or can be assumed to vary quite slowly. In the long-run, however, 8 which is a measure of the cost of disequilibrium in the money market, may increase making 129 the disequilibrium only instantaneous or temporary. For the purpose of our model, we treat 6 as given and constant. We will vary 3 to test for the sensitivity of adjustment. Monetary authorities have the choice of the rate of increase in nominal money 0 , and the government can choose the fraction a of the public sector investment out of total investment. Hence we treat 0 and a as the two policy variables. From the comparative static analysis of the pre vious chapter, the stability of the system requires: monetary model can be rewritten using equation (5.5) as: (dm^/dK) > sa-n(l-ot+aa) > 0 TT^sTTf (5.9) The long-run equilibrium solution (5.7) of the mg* = = sa-n(1-a+as) (l-s)n (5.7.a) Using equation (5.1), on the equilibrium path we should have: I > sa-n(1-a+as) rr-i]h— or a < (l-s)nft - sa + n . < 1 (i-s)n (5.10) Hence the maximum-value of a is less than unity. We denote a value of a sufficiently close to 130 (l-s)ni-sa + n (l-s)n as amax. In the previous chapter, from equation (4.53) we noted that the lower bound for a is ((n-sa)/n (1-s) ] which we call The choice of a is from the inter val (<xm£nr • We consider aa optimal choice of in our planning problem. From the expression for the equilibrium rate of anticipated inflation in equation (4.38) we write: 0 = tt* + n (5.11) In an inflationary economy like India we can, for empiri cal purposes, assume that the rate of anticipated infla tion is greater than or equal to zero. The minimum value of t t is zero which corresponds to price stability. The maximum value of i r ( = ^max) is bounded and is an empirical constant. Hence the upper and lower limits of 0 are 0max = *max + n and 9min = n, respectively. In general the rate of introduction of nominal money could vary anywhere between these two limits. When the price level is stabilized, the stable equilibrium rate of nominal money supply is the same as the natural rate; and the demand for real money balances grows at the same rate as capital stock. When 0= 0m£n = n, the demand for real balances is equal to the supply of real balances 131 growing at the same rate as the capital stock. Since aid is treated as a residual rather than planned, we do not consider the policy choice of the rate of increase or decrease of aid as considered in Chapter III. The allocative choice of investment resources to the consumption and capital goods sectors, as treated in the third chapter, is also not included in this monetary model since our concern at this stage is the growth and stability of the aggregate capital path through a monetary policy. We discuss in the next chapter, the case of an optimal choice of allocating the invest ment resources to the two sectors. An Optimizing Monetary Policy Model Define sa-(1-a+as) (l-s)n fit (5.12) and t Y = / Z. dt 0 * (5.13) Then we have Y = Z (5.14) (1-a+as)n sa-(1-a+as)n sa „( (5.15) (1-s) n i-a(l-s)K( The planning problem can be stated-as a mathematical optimization problem as follows: The plan period is 0 + t <_ T. Minimize: nT J = X Y + X [(L e /b)-K ] + X Z (5.16) 1 T 2 o T 3 T 2 subject to the equations of motion: m_ = 0m - 3m + 3£m_K (4.11.f) s s s s K = saK - (1-s)(0ms-3ms2 + 3*msK) (4.10.f) 1-a(1-s) 6t ( 2 Z = 6Z + e | sa(0ms-3ms +3&mgK) - (1-a+as)n sa-(l-a+as)n sa v I (5.15) (i-s)n I^T(r-"iT R> in (4.11.f). 20btained after substituting (4.13.f) and (5.1) 133 Y *= Z (5.14) Choice of control variables: 0 t a .5 a a (5.17) min max min max Path conditions; nt bK < L e o \ for t < T (5.18) m > sa-n(1-a+as)„ * (I-sJn K Terminal conditions: m = sa-(1-a+as)„ 3 (l-s)n K nt bK = L e o for t > T (5.7.a) From equations (5.6) and (5.12) we note that fit Z = F(m ,K)e . Hence, Z is the social disutility of t s ^ the burden of aid at time t. Again, from equation (5.13) Y^ is the aggregated social disutility or burden of aid at the end of the plan period. From equation (5.12) we note that dependency upon aid at a later date has a higher disutility in terms of the burden of aid. Z is nT \ T the burden of terminal aid and ) LQe -KT \ measures 134 the surplus of labor force at the terminal time T. The weights X , X , and X reflect the relative impor- 1 2 3 tance of the three components of the objective functidn. plan period is important. If X^ = X2 = 0, then, only then, full employment alone is treated as important, irrespective of the burden of debt. We consider the definition of J in equation (5.16) as the general objec tive function. To formulate a maximizing problem we write the Hamiltonian as: with a scrap value = -J. r, , r„, r , r. are the costate variables. Following the 1 2 3 4 maximizing principle, we have the following equations for the time paths of the costate variables: If X = X„ = 0, then the burden of total aid during the 2 3 the terminal aid is treated as the burden. If X = Xo = 0 1 J (5.19) r = -(9H/3m ) * -(0-23m +B£K) r I s s 1 1-a+as 1-s (r ) A* J . M 0 “ + sa (1-a+as)n fit (d r3) (5.20) 1 135 r = - (3H/3K) 2 ( 6t ) = -earn < r, - 1-s (r0) + sa (e r )> ( 1-a+as (i-a+as)n 3 ) / 5t . - sa ; r - sa-n(l-g+as)e r,( 1-a+as ( 2 (l-s)n j (5.21 r = (-3H/3Z) = -r 6- r (5.22) 3 3 4 r4 = (-3IH/3Y) = 0 X5.23) 3 The terminal conditions on the costate variables are: r4 = T 1 r3 = -X. { (5.24) T J r0 = X T 2 Optimal choice of a and 6 : The intertemporal efficiency is achieved for the choices of a and 0 such that (3H/30) and (3H/3a) are non-negative. Differentiating H with respect to a we have: These are obtained from equation (5.16) by differentiating the scrap value of the objective func tion, -J. 136 (3H/3a) = ( sak - (1-s) (0mg-8ms2+0£msK) J [1-a(1-s)]2 j |(l-s)r2-(sa/n)e | (5.25) and similarly for 0 , we have: (3H/30) = m 5 6t r - Q.-^c2 + sae r3 I (5.26) l-a+as (1-a+as)n ( Then the optimal choices of a and 0 are written as: fit a if (l-s)r - (sa/n)e r > 0 max 2 fit 3 a = )a . if (l-s)r_ - (sa/n)e r,< 0 (5.27) min 2 - J fit a . ( C av < a if (l-s)r2- (sa/n)e r = 0 min max 3 fit I 6max if rx~ s -a - e r, > 9 0 = \ A 1-a+as z (l-a+as)n J fit 0_j_ if r,- (l-s)r«,+ sa e r„ < 0 (5.28) mln 1 2 a-d+asTfi 3 0 . < 0 < 0 if mxn max f - (l-s)r + sa e r = 0 ; 1-a+as 2 (i-a+as)n 3 137 For simplicity we denote: R. = (l-s)r - (sa/n)e r ±t 2 3 fit *3 (5.29) fit R = r - (1-s)r + sa (e r ) 2t 1 1-a+as * (l-a+as)n 3 Solution of the Process: Since the optimal choices of 0 and a at any time t depend upon the levels of the costate variables as given in equations (5.27) and (5.28), we solve for the time paths of the costate variables. From the equation for r4 and r in (5.23) and (5.22) and using the terminal conditions (5.24) we derive: r = —X. for all t (5.30) 4 1 5 (T-t) r3 = (X /6) - [(X /5)+X ]e (5.31) t 1 1 3 Hence we note that: 5T 5t r = (X /5)(1-e )-X e -X (5.31.a) 30 1 1 3 r >0 and ? <0 3 3 The shape of r is illustrated in figure 5.1 below, 3t 138 FIGURE 5.1 3t From equations (5.19) and (5.30) we see that r. is t the marginal benefit of the aid at the time t and is always negative. Also note that r3 , being the marginal t utility of the disequilibrium, is minimized by the ter minal time T. From the definition of H is equation (5.19) r0 is interpreted as the marginal productivity t or the return on the marginal investment. As the stock of capital is increased over time, the rate of return on investment is expected to be decreasing. We now show that the optimum choices of 0 and a are not continuous functions of t. We prove the following two lemmas: 139 fit Lemma 1: R, = (l-s)r - (sa/n)e r is not zero 1t 2 3 for all t in 0 < t < T. Proof: If R a 0 for all t in 0 < t < T, then using equation (5.31) we have: fit 6T r = sa [(X /5)e - [(X./fi)+X ]e ] 2 (i-s)n 1 1 3 Hence, r^ is an increasing function of time. But since is expected to be a decreasing function of time we have a contradiction. Thus, R. is not zero for all t. t Then from expression (5.27) we note that the optimum choices of a are discrete functions of time. A fc Lemma 2: R = r.- (lss)(r?) + sa e r is 2 1-a+as (1-a+as)n 3 not zero for all t in 0 < t < T. Proof: If R =0, for all t, then from equations 2 (5.20) and (5.21) we have: r = 0 implying that r is a constant in 0 < t < T 1 1 ~ and r = - sa ( 2 l-o c + o (S | Since R2 = 0, we have fit r - sa-(l-g+gs)n e r 2 (l-s)n 3| 140 fit r (1-a+as) = (l-s)r -(sa/n)e r and r is a 1 2 3 i constant. Then we have: fit (l-s)r — (sa/n)e r + a constant. 2 3 Since r is an increasing function of t, r becomes an 3 2 increasing function of t and hence a contradiction. Thus, is not zero for all t in 0 <_ t <_ T. Then from (5.28) we note that the optimal choices of 0 are discrete functions of time. Prom the terminal con ditions in (5.24) we have, fiT R. = (l-s)r~ -(sa/n)e r T T T fiT = (l-s)X + (sa/n)e \ (5.32) 2 3 r^ is negative and increasing with time and r^ is decreasing with time, and hence, using the expression for R , we have: 1 R > 0 for all tjT. 1 Then the optimal choice of a is given by (5.27) as: a as a for all 0 £ t £ T (5.33) ^ max In the previous chapter we derived the long-run 141 equilibrium solution for it as ir=0-n. With a long- run non-inflationary growth process, we have, 0 = n, i.e., on the long-run steady state path, the nominal money is increased at the rate n. Treating 0 =n as the terminal choice of 0, from (5.28), we impose a restriction as: 6T V = rl ~ (1-s) r2 + sa e r3 <0 (5.34) T T 1-a+as T (1-a+as)n T However, R2 need not always be negative in 0 £ t £ T. Then there are four possibilities: (a) R 2 is positive for t = 0 and decreases smoothly to become negative at t = T. In other words, R£ changes its sign only once. (b) Starting with a positive value, R changes its sign more than once for t _< T and finally becomes negative at t = T. (c) Starting with a negative value, R2 changes its sign at least twice in OFKt < T to become negative at t * T. (d). R remains negative fo 2 all t < t. Figure 5.2 illustrates the four possibilities. For the cases (a), (b) or (c) to hold, whenever R changes its sign from positive to negative for any 2 t = t^, we should have R^ < 0, i.e., R2 is decreasing in a neighborhood of t when R9 = 0. We now show that 1 & whenever R = 0, we can not have R <0. 2 2 142 Figure 5.2 (a) 2 (b) R (c) 2 (d) R > 0. 2 143 Lemma 3; For any 0 ,_< t _< Tr whenever R = 0, M W Proof: From the differential equations (5.20), (5.21) and (5.22), whenever R = 0, we have 2 r = 0 r = -sa 2 1-a+as 6t r - Tsa-n (1-a+as)le r_ 2 ---(1-sTn-------3 and r = -r 6+ X 3 3 1 After some simplification, we have R = 2 (1-s) (1-a+as) 72 >sar. 6t sa e r 1sa-n(1-a+as) 1-a+as J )(i-a+as)n + X ( sa 1 | (1-a+as)n Since r . < 0 and r > 0 for all t < T, we have 3 2 ” R > 0. 2 Thus, the only possibility of R is negative for 2 all t _< T, as illustrated in case (d) of Figure 5.2. Then, from (5.28), the optimal choice of 6 is given as: 0 = 0 t min for 0 ?xt < T (5.35) , Analysis of Empirical Results for the Indian Economy The monetary policy model with optimal choices of a and 0 as in equations (5.33) and (5.35) is estimated for the Indian economy with 1970-71 as the base year of the plan. Appendix B gives a description of the data used in this analysis. The sensitivity of changing 0 and a upon the capital stock and income are analyzed. The growth paths of income, capital stock, etc., are estimated. Sensitivity and Comparative Static Analysis An increase in a , the government's share of investment, increases the total investment in the economy on the long-run equilibrium capital growth path. Table 5.1 shows the levels of investment after 30 years of planning corresponding to different values of 0 (equal to n) and a . When 0 = 0.0228 and a = 0.0, the investment in the thirtieth year from the beginning of the plan is Rs. 1011.5 crores. For the same choice of 0 , when a is increased to 0.1, the investment rises to Rs.1159.8 crores. Thus, we can see that for any given 0 , an increase in a means a higher rate of investment at equilibrium. 145 TABLE 5.1 Levels of Investment k, after 30 years of planning^ for different values of a and 6. a 9 = n 0.0228 0.03 0.04 0.05 0.0 1011.5 1010.0 1007.9 1005.8 0.1 1159.8 1157.9 1153.3 1152.7 0.2 1354.9 1352.5 1349.2 1345.8 0.3 1621.5 1618.3 1613.9 1609.4 0.35 1677.1 1790.4 1785.2 1780.0 0.4 2003.8 1999.3 1993.1 1986.9 0.5 2588.3 2581.7 2572.6 2563.5 Notes: Investment is in Rs Crores (1960-61 prices). I = 0.0592 6 = 0.084 8 = 1.0 a = 0.2918 146 An increase in 0, the rate of increase in nominal money, reduces the rate of investment for any given choice of o . For example, when a = .0.5, as 9 is increased from 0.0228, to 0.03 the investment decreases from Rs.2588.3 to Rs. 2581.7 crores. Thus, an increase in nominal money without increasing the share of govern ment investment has non-neutral effects on the long-run investment path. In Table 5.2, the levels of capital stock and real balances after 30 years are shown, corresponding to a pair of values of 6 and a . For example, when 0 =0.03 and a=0.02, the level of capital stock in the thirtieth year is Rs.70595 crores and the real balance is Rs.4179 crores. The comparative static effects of changes in 6 and a can be noted. As stated in Chapter IV, an increase in 8, for any given a, reduces the equili brium levels of capital stock and real balances. For example, for a=0.35, an increase of 0 from 0.0 to 0.01 decreases the equilibrium capital stock from Rs.79419 to Rs.79182 crores and the real balances from Rs. 4702 to Rs. 4687 crores. 147 TABLE 5.2 Levels of Capital Stock and Real Balances after 30 Years of Planning for Different Values of a and 9. 0 a 0.0 0.01 0.0228 0.03 0.04 0.05 0.0 642i2 3801 64076 3793 63902 3783 63804 3777 63668 3769 63533 3761 0.1 67258 3982 67103 3972 66905 3960 66793 3954 66638 3944 66438 3935 0.2 71136 4211 70955 4200 70725 4186 70595 4179 70415 4168 70235 4157 0.3 76228 4513 76013 4500 75740 4483 75585 4474 75372 4462 75158 4449 0.35 79419 4702 79182 4687 78881 4669 78711 4659 78475 4645 78240 4631 0.4 83193 4925 82930 4909 82596 4889 82406 4878 82144 4863 81883 4847 0.5 93248 5520 92913 5500 92486 5475 92244 5460 91910 5441 91576 5421 Notes: All figures are in Rs Crores (1960-61 prices), n = 0.02277 a = 0.2918 6 = 0.084 8 = 1.0 For each pair of a and 0, the two entries stand for capital stock and real balances respectively. 148 Empirical Results The optimal choice of a, being amaxr depends upon the capital-output ratio a, I and n (see equation (5.10)). For different values of n (equal to 0 ) and a, we tabulate in Table 5.3 the optimal choice of a. TABLE 5.3 Optimal Choice of a for Given n and a a n=0 0.2918 0.3 0.1918 0.4 0.023 — — 0.378 — 0.03 0.259 0.234 0.565 - 0.04 0.482 0.463 0.711 0.234 0.05 0.616 0.600 0.799 0.417 0.06 0.705 0.693 0.858 I = 0.0592 e = i.o s = 0.084 For example, for n * 0.03 and a = 0.3, the choice of a is 0.234. Since the determinant of the system has to be positive, we see from equation (5.10) that for given I and s, the optimal choice of a , other than 0, does not exist for every combination of n and a. The blanks in_the table represent such jsitu^tions. ________ For the Indian economy with the output-capital ! ratio of 0.2918 and the choice of n = 0.03, the optimal choice of 0.259. The optimal public sector share of ivnestment is about 25 percent of the total economy's investment. For any chosen value of the natural rate of : growth n, the optimal choice of an increase in the nominal money 0, is given by equation (5.35) as 0= n. Then, for given I (equal to 0.0592) , s (equal to 0.084) and a (equal to 0.2918), using the optimal choice of a from Table 5.3 we obtain the time paths of variables : such as supply and demand for real, balances, capital stock, Gross National Product, private and public sector investments, maximum possible dependency on aid and price levels. Given the initial stocks of money and capital, ! the increases in the real cash balances and investment ! are obtained from equations (4.11.f) and (4.10.f) respectively. The Gross National Product (GNP) is es timated from equation (4.7). Using (4.5.f) we estimate the public and private sector investments. The maximum amount of aid that may be borrowed to stay on the balanced growth path during the plan period is derived from equation (5.5). The rate of inflation, as can be seen from equation (4.13.f), depends upon the rate of j 150 price adjustment $ and the excess supply of real cash balances. The time path of the rate of inflation is ob- tained as a normalized measure by rewriting (P/P) as: (P/P> = [(m -*K) /(m -*K)J S w S O where (m - fl-K) is the excess of the real balances at s o time zero. The rate of inflation is thus expressed in percentages of the initial year price changes. The • price stability implies (P/P) = 0; and such normaliza tion does not change the rapidity of convergence of (P/P) to zero. Tables 5.4 to 5.8 show the time paths of the variables for values of 8 from 0.2 up to 1.0 with increments of 0.2 and a = 0.2918, n = 0 = 0.034 and a = 0.25894. The long run equilibrium conditions for the choice | | of 0 = n are that both the excess supply of real cash j I balances and the dependency on aid be zero.5 For 8 = 0.2, j ! I I from Table 5.4.1 we see that the excess supply of money i ; and the dependency on aid are Rs. 201.08 and Rs. 65.78 j crores in the thirtieth year. The GNP will be rising at : i i 4 i For a = 0.2918 and n » 0.02277, as used in I Chapter III, there is no optimal choice of a> 0. See | Table 5.3. so we chose n = 0.03. j | _ i 5See equations (4 .38), (4 .39) and (5.5). 151 TABLE 5.4.1 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 0=0.03; a=0.2589; 3=0.2, a=0.2918 Time Real Balance Index of Inflation Supply Demand Excess 1 3808.76 2404.91 1403.36 95.06 2 3816.09 2481.66 1334.43 90.36 3 3828.72 2560.51 1268.22 85.87 4 3846.47 2641.52 1204.95 81.59 5 3869.17 2724.79 1144.38 77.49 6 3896.69 2810.38 1086.31 73.56 7 3928.93 2898.40 1030.53 69.78 8 3965.82 2988.91 976.91 66.15 9 4007.31 3082.00 925.31 62.66 10 4053.37 3177.76 875.61 59.29 11 4103.99 3276.27 827.72 56.05 12 4159.17 3377.62 781.54 52.92 13 4218.93 3481.91 737.02 49.91 14 4283.31 3589.21 694.10 47.00 15 4352.35 3699.63 652.71 44.20 16 4426.10 3813.27 612.83 41.50 17 4504.64• 3930.22 574.42 38.90 18 4588.02 4050.58 537.44 36.39 19 4676.35 4174.46 501.89 33.98 20 4769.70 4301.96 4 67.-74 31.67 21 4868.17 4433.1,9. 434.98 29.45 22 4971.86 4568^27 403.60 27.33 23 5080.89 4707,31 373.58 25.30 24 5195.35 4850.43 344.92 23.36 25 5315.37 4997.75 317.62 21.51 26 5441.07 5149.41 291.66 19.75 27 5572.56 5305.53 267.03 18.08 28 5709.98 5466.24 243.74 16.50 29 5853.44 5631.68 221.76 15.02 30 6003.08 5802.01 201.08 13.62 Notes: t = 0 for 1970-71; Index of inflation is 100 for t = 0. Real Balances are in Rs. Crores. TABLE 5.4.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates 0=0.03, a=0.2589, 3=0.2, a=0.2918 Time Capital Stock Total Public Investment Private Aid GNP Growth Rate 1 40623.42 1262.65 326.95 935.70 459.26 20311.71 3.15 2 41919.96 1296.54 335.72 960.82 436.55 20959.98 3.19 3 43251.79 1331.82 344.86 986.96 414.89 21625.89 3.18 4 44620.27 1368.48 354.35 1014.13 394.19 22310.13 3.16 5 46026.78 1406.51 364.20 1042.31 374.38 23013.39 3.15 6 47472.70 1445.92 374.40 1071.51 355.38 23736.35 3.14 7 48959.41 1486.71 384.97 1101.74 337.13 24479.70 3.13 8 50488.30 1528.90 395.89 1133.01 319.59 25244.15 3.12 9 52070.81 1572.50 407.18 1165.32 302.71 26030.40 3.11 10 53678.35 1617.54 418.84 1198.70 286.45 26839.17 3.11 11 55342.39 1664.05 430.88 1233.16 270.78 27671.20 3.10 12 57054.43 1712.04 443.31 1268.72 255.68 28527.21 3.09 13 58815.97 1761.54 456.13 1305.41 241.11 29407.99 3.09 14 60628.58 1812.61 469.35 1343.25 227.07 30314.29 3.08 15 62493.83 1865.25 482.99 1382.27 213.53 31246.92 3.08 16 64413.36 1919.53 497.04 1422.49 200.48 32206.68 3.07 17 66388.83 1975.47 511.52 1463.94 187.92 33194.41 3.07 18 68421.94 2033.11 526.45 1506.66 175.82 34210.97 3.06 19 70514.46 2092.52 541.83 1550.68 164.19 35257.23 3.06 20 72668.18 2153.72 557.68 1596.04 153.02 36334.09 3.05 TABLE 5.4.2 (Continued) Capital Investment Growth Time Stock Total Public Private Aid GNP Rate 21 74884.96 2216.78 574.01 1642.77 142.30 37442.48 3.05 22 77166.69 2281.73 590.83 1690.91 132.03 38583.35 3.05 23 79515.34 2348.65 608.16 1740.50 122.21 39757.67 3.04 24 81932.93 2417.59 626.01 1791.58 112.84 40966.47 3.04 25 84421.53 2488.60 644.39 1844.21 103.91 42210.77 3.04 26 86983.28 2561.75 663.33 1898.42 95.41 43491.64 3.03 27 89620.38 2637.10 682.85 1954.26 87.36 44810.19 3.03 28 92335.11 2714.73 702.95 2011.78 79.74 46167.56 3.03 29 95129.81 2794.70 723.65 2071.04 72.55 47564.90 3.03 30 98006.89 2877.08 744.99 2132.09 65.78 49003.44 3.02 Notes: t = 0 for 1970-71. Growth rate is in percentage. All other figures are in Rs. Crores (1960-61 prices). 153 154 Levels of Real Supply of 0=0.03 TABLE Balance Supply Real Balance, a=0.25894 8=0. 5.5.1 , Real Balance and Indices of 4, a = 0.2918 Demand, Excess Inflation Time Real Balance Index of Inflation Supply Demand Excess 1 3696.32 2412.90 1283.42 86.90 2 3617.45 2496.04 1121.41 75.93 3 3563.71 2580.06 983.64 66.61 4 3530.40 2665.34 865,07 58.58 5 3514.15 2752.14 762.02 51.60 6 3512.46 2840.69 671.77 45.49 7 3523.45 2931.19 592.27 40.10 8 3545.68 3023.79 521.89 35.34 9 3578.04 3118.66 459.38 31.11 10 3619.63 3215.91 403.72 27.34 , 11 3669.77 3315.68 354.59 23.98 12 3727.88 3418.09 309.79 20.98 13 3793.52 3523.26 270.27 18.30 14 3866.32 3631.29 235.03 15.91 15 3945.96 3742.32 203.65 13.79 16 4032.20 3856.44 175.76 11.90 17 4124.82 3973.77 151.05 10.23 18 4223.64 4094.43 129.21 8.75 19 4328.52 4218.54 109.98 7.45 20 4439.33 4346.22 93.12 6.31 21 4555.98 4477.58 78.40 5.31 22 4678.37 4612.76 65.61 4.44 23 4806.44 4751.87 54.57 3.70 24 4940.14 4895.06 45.09 3.05 25 5079.44 5042.45 36.99 2.50 26 5224.31 5194.17 30.13 2.04 27 5374.74 5350.38 24.36 1.65 28 5530.74 5511.21 19.53 1.32 29 5692.35 5676.82 15.53 1.05 30 5859.58 5847.34 12.24 0.83 Notes: t = 0 for 1970-71; Index of inflation is 100 for t = 0. Real Balances are in Rs. Crores. TABLE 5.5.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates 0=0.03, a=0.25894, 0=0.4, a=0.2918 Capital Investment Growth Time Stock Total Public Private Aid GNP Rate 1 40758.45 1397.68 361.91 1035.77 419.86 20379.22 3.50 2 42162.83 1404.38 363.65 1040.73 366.86 21081.41 3.45 3 43582.17 1419.34 367.52 1051.82 321.79 21791.08 3.37 4 45022.57 1440.40 372.98 1067.43 283.00 22511.29 3.31 5 46488.78 1466.21 379.66 1086.55 249.29 23244.39 3.26 6 47984.61 1495.84 387.33 1108.51 219.77 23992.31 3.22 7 49513.29 1528.68 395.83 1132.84 193.76 24756.64 3.19 8 51077.59 1564.30 405.06 1159.24 170.73 25538.79 3.16 9 \ -52680.00 1602.41 414.92 1187.48 150.28 26340.00 3.14 10 54322.80 1642.80 425.38 1217.42 132.07 27161.40 3.12 11 56008.13 1685.33 436.40 1248.93 115.84 28004.06 3.10 12 57738.03 1729.90 447.94 1281.96 101.35 28869.02 3.09 13 59514.48 1776.45 459.99 1316.46 88.42 29757.24 3.08 14 61339.43 1824.94 472.55 1352.40 76.89 30669.71 3.07 15 63214.79 1875.36 485.60 1389.76 66.62 31607.40 3.06 16 65142.50 1927.71 499.16 1428.55 57.50 32571.25 3.05 17 67124.48 1981.98 513.21 1468.77 49.41 33562.24 3.04 18 69162.70 2038.22 527.77 1510.45 42.27 34581.35 3*04 19 71259.14 2096.44 542.85 1553.59 35.98 35629.57 3.03 20 73415.82 2156.68 558.45 1598.23 30.46 36707.91 3.03 155 Til 21 22 23 24 25 25 27 28 29 30 No TABLE 5.5.2 (Continued) Capital Investment Growth Stock Total Public Private Aid GNP Rate 75634.79 2218.98 574.58 1644.40 24.65 37817.40 3.02 77918.17 2283.38 591.25 1692.12 21.47 38959.08 3.02 80268.09 2349.93 608.48 1741.44 17.83 40134.05 3.02 82686.77 2418.68 626.29 1792.39 14.75 41343.38 3.01 85176.45 2489.68 644.67 1845.01 12.10 42588.22 3.01 87739.43 2562.99 663 .65 1899.33 9.86 43869.72 3.01 90378.09 2638.66 683.25 1955.41 7.97 45189.04 3.01 93094.84 2716.75 703.47 2013.28 6.39 46547.42 3.01 95892.17 2797.33 724.33 2072.99 5.08 47946.09 3.00 98772.62 2880.45 745.86 2134.59 4.00 49386.31 3.00 t = 0 for 1970-71. Growth rate is in percentage. All other figures are in Rs. Crores (1960-61 prices). 156 157 TABLE 5.6.1 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 0=0.03, a=0.25894, 8=0.6, a = 0.2918 r Real Balance Index of Time Supply Demand Excess Inflation 1 3583.87 2420.89 1162.98 78.75 2 3441.31 2508.82 932.49 63.14 3 3352.01 2595.78 756.23 51.21 4 3300.48 2682.85 617.62 41.82 5 3277.18 2770.72 506.47 34.29 6 3275.91 2859.84 416.07 28.17 7 3292.41 2950.56 341.85 23.15 8 3323.65 3043.15 280.50 18.99 9 3367.42 3137.82 229.60 15.55 10 3422.05 3234.76 187.29 12.68 11 3486.26 3334.14 152.12 10.30 12 3559.03 3436.10 122.93 8.32 13 3639.55 3540.79 98.76 6.39 14 3727.17 3648.34 78.83 5.34 15 3821.35 3758.87 62.48 4.23 16 3921.67 3872.52 49.15 3.33 17 4027.75 3989.41 38.34 2.60 18 4139.32 4109.67 29.65 2.01 19 4256.14 4233.42 22.71 1.54 20 4378.02 4360.79 17.23 1.17 21 4504.84 4491.90 12.94 0.88 22 4636.48 4626.88 9.61 0.65 23 4772.91 4765.85 7.05 0.48 24 4914.07 4908.96 5.12 0.35 25 5059.99 5056.32 3.67 0.25 26 5210.67 5208.08 2.59 0.18 27 5366.18 5364.38 1.81 0.12 28 5526.59 5525.35 1.24 0.08 29 5691.97 5691.13 0.84 0.06 30 5862.45 5861.89 0.56 0.04 Notes: t = 0 for 1970-71; Index of inflation is 100 for t = 0. Real Balances are in Rs. Crores. TABLE 5.6.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates CD I I O • o u > a=0.25894, 8= o • c r > ( D I I O .2918 Time Capital Stock Total Public Investment Private Aid GNP Growth Rate 1 40893.48 1532.71 396.88 1135.83 380.46 20446.74 3.84 2 42378.68 1485.21 384.58 1100.63 305.06 21189.34 3.63 3 43847.65 1468.97 380.37 1088.60 247.39 21923.83 3.47 4 45318.48 1470.82 380.85 1089.97 202.05 22659.24 3.35 5 46802.65 1484.17 384.31 1099.86 165.69 23401.32 3.27 6 48308.07 1505.42 389.81 1115.61 136.12 24154.03 3.22 7 49840.53 1532.46 396.81 1135.65 111.83 24920.26 3.17 8 51404.52 1563.99 404.98 1159.02 91.76 25702.26 3.14 9 53003.72 1599.20 414.09 1185.11 75.11 26501.86 3.11 10 54641.27 1637.55 424.02 1213.52 61.27 27320.63 3.08 11 56319.93 1678.67 434.67 1244.00 49.77 28159.97 3.07 12 58042.26 1722.33 445.98 1276.35 40.21 29021.13 3.06 13 59810.62 1768.36 457.90 1310.47 32.31 29905.31 3.05 14 61627.28 1816.66 470.40 1346.26 25.79 30813.64 3004 15 63494.43 1867.15 483.48 1383.67 20.44 31747.22 3.03 16 65414.22 1919.79 497.11 1422.68 16.08 32707.11 3.02 17 67388.76 1974.54 511.28 1463.26 . 12.54 33694.38 3.02 18 69420.17 2031.41 526.01 1505.40 9.70 34710.08 3.01 19 71510.54 2090.38 541.28 1549.10 7.43 35755.27 3.01 20 73662.01 2151.46 557.10 1594.37 5.64 36831.00 3.01 TABLE 5.6.2 (Continued) Capital Investment Growth Time Stock Total Public Private Aid GNP Rate 21 75876.68 2214.67 573.46 1641.21 4.23 37938.34 3.01 22 78156.72 2280.03 590.39 1689.65 3.14 39087.36 3.00 23 80504.28 2347.56 607.87 1739.69 2.31 40252.14 3.00 24 82921.58 2417.30 625.93 1791.37 1.67 41460.79 3.00 25 85410.85 2489.27 644.57 1844.71 1.20 42705.43 3.00 26 87974.38 2563.53 663.80 i899.73 0.85 43987.19 3.00 27 90614.49 2640.11 683.62 1956.49 0.59 45307.25 3.00 28 93333.56 2719.07 704.07 2015.00 0.41 46666.78 3.00 29 96134.02 2800.46 725.14 2075.31 0.27 48067.01 3.00 30 99018.35 2884.33 746.86 2137.47 0.18 49509.18 3.00 Notes: t = 0 for 1970-71. Growth rate is in percentage. All other figures are in Rs. Crores (1960-61 prices). 159 160 TABLE 5.7.1 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 0=0.03, a^O.25894, 3=0.08, a = 0.2918 Real Balance Index of Time Supply Demand Excess Inflation 1 3471.42 2428.89 1042.54 70.59 2 3286.04 2520.11 765.93 51.86 3 3183.27 2608.40 574.87 38.93 4 3132.37 2695.83 436.54 29.56 5 3116.95 2783.55 333.40 22.58 6 3127.32 2872.26 255.07 17.27 7 3157.33 2962.42 194.91 13.20 8 3202.82 3054.37 148.44 10.05 9 3260.86 3148.39 112.47 7.62 10 3329.35 3244.69 84.66 5.73 11 3406.68 3343.45 63.23 4.28 12 3491.65 3444.84 46.80 3.17 13 3583.32 3549.02 34.30 2.32 14 3680.09 3766.27 17.83 1.21 15 3784.09 3756.12 24.87 1.68 16 3892.22 3879.60 12.62 0.85 17 4005.06 3996.24 8.82 0.60 18 4122.38 4116.31 6.07 0.41 19 4369.97 4239.93 4.12 0.28 20 4369.97 4367.22 2.76 0.19 21 4500.11 4498.30 i;8i 0.12 22 4634.46 4633.29 1.17 0.08 23 4773.06 4772.32 0.74 0:05 24 4915.97 4915.50 0.46 0.03 25 5063.26 5062.98 0.28 0.02 26 5215.05 5214.88 0.17 0.01 27 5371.43 5371.33 :o.io 0.01 28 5532.53 5532.47 0.06 0.00 29 5697.48 5698.45 0.03 0.00 30 5869.42 5869.40 0.02 0.00 Notes: t = 0 for 1970-71; Index of inflation is 100 for t = 0. Real Balances are in Rs. Crores. TABLE 5.7.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates t . m o • o I t © a=0.25894, 6= o • 00 P ) I I o .2918 Time Capital Stock Total Public Investment Private Aid GNP Growth Rate 1 41028.50 1667.73 431.84 1235.89 341.06 20514.25 4.18 2 42569.47 1540.97 399.01 1141.95 250.57 21284.74 3.76 3 44060.75 1491.28 386.15 1105.13 188.07 22030.37 3.50 4 45537.66 1476.91 382.43 1094.48 142.81 22768.83 3.35 5 47019.42 1481.76 383.68 1098.08 109.07 23509.71 3.25 6 48517.82 1498.40 387.99 1110.41 83.44 24258.91 3.19 7 50040.80 1522.98 394.36 1128.62 63.76 25020.40 3.14 8 51594.12 1553.32 402.21 1151.11 48.56 25797.06 3.10 9 53182.27 1588.15 411.23 1176.92 36.80 26591.13 3.08 10 54808.92 1626.65 421.20 1205.45 27.70 27404.46 3.06 11 56477.21 1668.30 431Q98 1236.31 20.69 28238.61 3.04 12 58189.94 1712.73 443.49 1269.24 15.31 29094.97 3.03 13 59949.66 1759.71 455.66 1304.06 11.22 29974.83 3.02 14 61758.72 1809.06 468.43 1340.63 8.14 30879.36 3.02 15 63619.38 1860.66 481.80 1378.87 5.83 31809.69 3.01 16 65533.80 1914.22 495.72 1418.70 4.13 32766.90 3.01 17 67504.08 1970.28 510.18 1460.10 2.88 33752.04 3.01 18 69532.27 2028.20 525.18 1503.02 1.99 34766.14 3.00 19 71620.43 2088.15 540.70 1547.45 1.35 35810.21 3.00 20 73770.57 2150.15 556.74 1593.39 0.90 36885.29 3.00 Tii 21 22 23 24 25 26 27 28 29 30 TABLE 5.7.2 (Continued) Capital Investment Growth Stock Total Public Private Aid GNP Rate 75984.75 2214.17 573.33 1640.84 0.59 37992.37 3.00 78265.01 2280.26 590.45 1689.81 0.38 39132.50 3.00 80613.44 2348.43 608.10 1740.33 0.24 40306.72 3.00 83032.16 2418.72 626.30 1792.42 0.15 41516.08 3.00 85523.32 2491.17 645.06 1846.11 0.09 42761.66 3.00 88089.15 2565.83 664.39 1901.44 0.06 44044.58 3.00 90831.90 2642.75 684.31 1958.44 0.03 45376.95 3.00 93453.91 2722.00 704.83 2017.17 0.02 46726.95 3.00 96257.55 2803.65 725.97 2077.68 0.01 48128.78 3.00 99145.33 2887.74 747.75 2140.00 0.01 49572.65 3.00 t = 0 for 1970-71. Growth rate is in percentage. All other figures are in Rs. Crores (1960-61 prices). 162 163 TABLE 5.8.1 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 0 = 0.03, a = 0.25894, 3 = 1.0, a = 0.2918 Time Real Balance Index of Inflation Supply Demand Excess 1 3358.98 2436.88 922.10 62.44 2 3150.02 2530.04 619.98 41.98 3 3049.22 2618.50 430.72 29.17 4 3009.36 2705.47 303.89 20.58 5 3008.19 2792.49 215.70 14.61 6 3033.55 2880.42 153.13 10.37 7 307B.10 2969.81 108.30 7.33 8 3137.11 3061.04 76.07 5.15 9 3207.36 3154.41 52.96 3.59 10 3286.60 3250.13 36.46 2.47 11 3373.21 3348.41 24.80 1.68 12 3466.04 3449.40 16.64 1.13 13 3564.26 3553.26 11.00 0.74 14 3667.26 3660.11 7.15 0.48 15 3775.66 3770.09 4.57 0.31 16 3886.17 3883.30 2.87 0.19 17 4001.64 3999.88 1.77 0.12 18 4120.99 4119.92 1.07 0.07 19 4244.18 4243.55 0.63 0.04 20 4371.23 4370.87 0.36 0.02 21 4502.21 4502.01 0.21 0.01 22 4637.19 4637.07 0.11 0.01 23 4776.25 4776.10 0.06 0.00 24 4919.51 4919.48 0.03 0.00 25 5067.08 5067.06 0.02 0.00 26 5219.08 5219.07 0.01 0.00 27 5375.65 5375.65 0.00 0.00 28 5536.92 5536.92 0.00 0.00 29 5703.02 5703.02 0.00 0.00 30 5374.11 5874.11 0.00 0.00 Notes: t=0 for 1970-71? Index of inflation is 100 for t=0. Real Balances are in Rs. Crores. TABLE 5.8.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates 0=0.03, a=0.25894, 3=1.0, a=0.2918 Time Capital Stock Total Public Investment Private Aid GNP Growth Rate 1 41163.53 1802.76 466.80 1335.96 301.66 20581.77 4.53 2 42737.15 1573.62 407.47 1166.15 202.82 21368.57 3.82 3 44231.44 1494.29 386.93 1107.36 140.91 22115.72 3.50 4 45700.58 1469.14 380.42 1088.72 99.41 22850.29 3.32 5 47170.46 1469.89 380.61 1089.28 70.57 23585.23 3.22 6 48655.73 1485.26 384.59- 1100.67 50.10 24327.86 3.15 7 50165.66 1509.94 390.98 1118.96 35.43 25082.83 3.10 8 51706.76 1541.10 399.05 1142.05 24.89 25853.38 3.07 9 53283.88 1577.12 408.38 1168.74 17.32 26641.94 3.05 10 54900.88 1617.00 418.70 1198.30 11.'93 27450.44 3.03 11 56560.99 1660.10 429.86 1230.24 8.11 28280.49 3.02 12 58266.97 1705.98 441.74 1264.24 5.44 29133.48 3.02 13 60021.30 1754.33 454.26 1300.07 3.60 30010.65 3.01 14 61826.25 1804.95 467.37 1337.48 2.34 30913.13 3.01 15 63683.93 1857.68 481.02 1376.66 1.50 31841.97 3.00 16 65596.36 1912.43 495.20 1417.23 0.94 32798.18 3.00 17 67565.48 1969.13 509.88 1459.24 0.58 33782.74 3.00 18 69593.23 2027.75 525.06 1502.69 0.35 34796.62 3.00 19 71681.52 2088.29 540.74 1547.55 0.21 35840.76 3.00 20 73832.26 2150.74 556.91 1593.83 0.12 36916.13 3.00 TABLE 5.8.2 (Continued) Time Capital Stock Total Public Investment Private Aid GNP Growth Rate 21 76047.41 2215.15 573.59 1641.56 0.07 38023.70 3.00 22 78328.93 2281.53 590.77 1690.75 0.04 39164.47 3.00 23 80678.85 2349.93 608.49 1741.44 0.02 40339.43 3.00 24 83099.26 2420.40 626.73 1793.67 0.01 41549.63 3.00 25 85592.25 2493.00 645.53 1847.46 0.01 42796.13 3.00 26 88160.03 2567.78 664.89 1902.88 0.00 44080.02 3.00 27 90804.84 2644.81 684.84 1959.96 0.00 45402.42 3.00 28 93528.98 2724.15 705.39 2018.76 0.00 46764.49 3.00 29 96334.85 2805.87 726.55 2079.32 0.00 48167.43 3.00 30 99224.90 2890.05 748.34 2141.70 0.00 49612.45 3.00 Notes: t = 0 for 1970-71. Growth rate is in percentage. All other figures are in Rs. Crores (1960-61 prices). 165 166 Figure 5.3 shows the estimated rates of growth of GNP for different values of 3. Figures 5.4 to 5.8 show the convergence of the supply and demand for real cash balances for different values of 8. When 8=1 as can be seen in Figure 5.8/ the two paths converge by the fifteenth year and the prices will be stabilized. For any excess supply of real balances in any year the price level will be rising depending upon 8. Higher 8's require smaller t's to reach the balanced growth path with stable prices on which both the supply and the demand for real balances grow at the same rate as n. The optimal choice of a for any given output- capital ratio and the rate of increase in nominal money, has the stability property that the growth rate of GNP and the natural rates become equal in a minimal time period; and from then onwards the GNP continues to in crease at the natural rate. Table 5.9 shows the rate of growth of GNP for combinations of a and 0. In all the cases, we see that it takes about 15 years for the economy to reach a stable growth rate equal to the natural rate. From the planning point of view, the implication is that for given capital-output ratio, the optimal policy choices of a and 0 uniquely determine the minimal time required to reach the balanced growth path. Rate of Growth of GNP Figure 5.3 5.0 Time Path of GNP for Different Values of 3 4.0* 3= 1 .0 3= 0.6 5 10 15 20 25 30 Time in years Real Cash Balances (Rs. 10 Figure 5.4 Optimal Time Paths of Supply and Demand for Real Cash Balances: 3 = 0.2 60 Supply Demand 50 40 0.2589 0.03 0.2918 30 20 5 10 15 20 25 30 Time in Years 168 Real Cash Balances (Rs. 10 Figure 5.5 Optimal Time Paths of Supply and Demand for Real Cash Balances: 8 = 0.4 60 Supply Demand a\ 50 40 0.2589 0.03 0.2918 30 20 5 10 15 20 25 30 Time in years 169 Real Cash Balances Figure 5.6 Optimal Time Paths of Supply and Demand for Real Cash Balances: B = 0.6 60 Supply Demand 50 40 0.2589 0.03 0.2918 30 20 5 10 15 20 25 30 Time in years 170 Real Cash Balances (Rs. 10 Figure 5.7 Optimal Time Paths of Supply and Demand for Real Cash Balances: 3=0.8 60 c\ Supply Demand 50 40 30 cc= 0.2589 0= 0.03 a= 0&-2918 20 5 10 15 20 25 30 Time in years 171 Real Cash Balances (Rs. 10 Figure 5.8 Optimal Time Paths of Supply and Demand for Real Cash Balances: 1.0 60 Supply Demand 50 40 0.2589 0.03 0.2918 30 20 5 10 15 20 25 30 Time in Years 172 173 TABLE 5.9 . The GNP Growth Rates (in percentages) for Combinations of 9 and a . Year 0=0.03 a=0.29 "0'=oT0T a=0.29 0=0.05 a=0.29 0=0.04 a=0.4 '"0=0 7(55 a=0.4 1 4.53 6.04 7.55 5.44 6.78 2 3.82 5.09 6.35 4.79 5.98 3 3.50 4.65 5.81 4.48 5.60 4 3.32 4.42 5.52 4.31 5.39 5 3.22 4.28 5.34 4.21 5.26 6 3.15 4.19 5.23 4.15. 5.18 7 3.10 4.13 5.15 4.10 5.12 8 3.07 4v09 5.10 4.07 5.08 9 3.05 4.06 5.07 4.05 5.05 10 3.03 4.04 5.04 4.03 5.04 11 3.02 4.03 5.03 4.02 5.02 12 3.02 4.02 5.02 4.01 5.01 13 3.01 4.01 5.01 4 .01 5.01 14 3.01 4.01 5.01 4.01 5.00 15 3.00 4.00 5.00 4.00 5.00 15 3.00 4.00 5.00 4.00 5.00 17 3.00 0 0 5.00 4.00 5.00 18 3.00 4.00 5.00 4.00 5.00 19 3.00 4.00 5.00 4.00 5.p0 20 3.00 4.00 5.00 4.00 5.00 With such an optimal monetary policy it takes about fif teen years for the Indian economy to reach a full employ ment stable growth path. Technological Change During the Plan Period In Tables 5.10 and 5.11 we present the results for a = 0.2918 and two additional values of n. We interpret a shift in n as the increase in the poten tial full employment growth rate due either to labor saving technological change or increased population growth. For different values of n we can compare the estimates of GNP and the capital stock in any year assuming no technological change (i.e., no change in n) during the plan period. Any technological change during the plan period will imply a corresponding change in n. Table 5.12 shows the estimates of GNP and the capital stocks in the fifteenth year for values of constant n during the plan period. A technological change during the plan period would imply changing n during the plan period. Such a technological change would shift the time paths of GNP and the capital stock as illustrated above'* in Figure 5.9. A technological change during the plan period, from n *■ 0.03 to 0.04 will generate a GNP in the fifteenth ’ year somewhere in 175 TABLE 5.10.1 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 0 = 0.04, a = 0.48193, 6 = 1.0, a = 0.2918 Time Real Balance Index of Inflation Supply Demand Excess 1 3397.05 2472.21 924.83 62.62 2 3218.76 2598.01 620.75 42.03 3 3147.71 2718.92 428.79 29.03 4 3138.64 2839.11 299.53 20.28 5 3170.18 2960.64 209.54 14.19 6 3230.56 3084.70 145.85 9.88 7 3312.66 3212.10 100.56 6.81 8 3411.86 3343.43 68.43 4.63 9 3524.98 3479.17 45.82 3.10 10 3649.83 3619.72 30.11 2.04 11 3784.84 3765.46 19.37 1.31 12 3928.90 3916.72 12.18 0.82 13 4081.27 4073.80 7.46 0.51 14 4241.47 4237.02 4.45 0.30 15 4409.24 4406.67 2.57 0.17 16 4584.48 4583.04 1.44 0.10 17 4767.20 4766.42 0.78 0.05 18 4957.51 4957.10 0.41 0.03 19 5155.61 5155.41 0.20 0.01 20 5361.73 5361.63 0.10 0.01 21 5576.15 5576.10 0.04 0.00 22 5799.17 5799.15 0.02 0.00 23 6031.12 5031.12 0.01 0.00 24 6272.36 6272.36 0.00 0.00 25 6523.26 6523.26 0.00 0.00 26 6784.19 6784.19 0.00 0.00 27 7055.55 7055.55 0.00 0.00 28 7337.78 7337.78 0.00 0.00 29 7631.29 7631.29 0.00 0.00 30 7936.54 7936.54 0.00 0.00 Notes: t = 0 for 1970-71; Index of inflation is 100 for t = 0. Real Balances are in Rs. Crores. TABLE 5.10.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates 0 =0.04, cc=0.48193, 0=1.0, a=0.2918 Capital Investment Growth Time Stock Total Public Private Aid GNP . Rate 1 41760.36 2399.59 1156.43 1243.16 403.40 20880.18 6.04 2 43885.33 2124.97 1024.09 1100.89 270.76 21942.67 5.09 3 45927.69 2042.36 984.27 1058.09 187.03 22963.85 4.65 4 47958.01 2030.32 987.47 1051.85 130.65 23979.01 4.42 5 50010.86 2052.85 989.33 1063.52 91,40 25005.43 4.28 6 52106.49 2095.63 1009.94 1085.68 63.62 26053.24 4.19 7 54258.45 2151.97 1037.09 1114.87 43.86 27129.23 4.13 8 56476.82 2218.37 1069.10 1149.27 29.85 28238.41 4.09 9 58769.70 2292.87 1105.00 1187.87 19.99 29384.85 4.06 10 61143.96 2374.27 1144.23 1230.04 13.13 30571.98 4.04 11 63605.77 2461.81 1186.42 1276.39 8.45 31802.88 4.03 12 66160.76 2554.99 1231.32 1323.66 5; 31 33080.38 4.02 13 68814.23 2653.48 1278.-79 1374.69 '3.26 34407.12 4.01 14 71571.31 2757.08 13 28-.72 1428.36 1.94 35785.65 4.01 15 74436.97 2865.66 1381.04 1484.61 1.12 37218.48 4.00 16 77416.14 2979.17 1435.75 1543.42 0.63 38708.07 4.00 17 80513.77 3097.64 1492.84 1604.79 0.34 40256.89 4.00 18 83734.88 3221.11 1552.35 1668.76 0.18 41867.44 4.00 19 87084.58 3349.70 1614.32 1735.38 0.09 43542.29 4.00 20 90568.12 3483.54 1678.82 1804.72 0.04 45284.06 4.00 176 Til 21 22 23 24 25 26 27 28 29 30 TABLE 5.10.2(Continued) Investment Growth Stock Total Public Private Aid GNP Rate 94190.93 3622.80 1745.94 1876.87 0.02 47095.46 4.00 97948.60 3767.67 1815.75 1951.92 0.01 48979.30 4.00 101876.96 3918.36 1888.37 2029.99 0.00 . 50938.48 4.00 105952.05 4075.09 1963.90 2111.18 0.00 52976.02 4.00 110190.13 4238.08 2042.46 2195.63 0.00 55095.07 4.00 114597.74 4407.61 2124.15 2283.45 0.00 57298.87 4.00 119181.65 4583.91 2209.12 2374.79 0.00 59590.82 4.00 123948.91 4767.27 2297.48 2469.78 0.00 61984.46 4.00 128906.87 4957.96 2389.38 2568.57 0.00 64453.43 4.00 134063.14 5156.27 2484.96 2671.32 0.00 67031.57 4.00 t = 0 for 1970-71. Growth rate is in percentage. All other figures are in Rs. Crores (1960-61 prices). 177 178 TABLE 5.11.1 Levels of Real Balance Supply, Real Balance Demand, Excess Supply of Real Balance, and Indices of Inflation 0 = 0.05, a = 0.61572, 0 = 1.00, a = 0.2918 Time Real Balance index of Inflation Supply Demand Excess 1 3435.12 2507.41 927.71 62.82 2 3288.19 2666.65 621.55 42.09 3 3248.23 2821.53 426.69 28.89 4 3272.04 2977.19 294.84 19.96 5 3339.17 3136.22 202.95 13.74 6 3438.36 3300.20 138.16 9.36 7 3562.77 3470.26 92.51 6.26 8 3707.95 3647.29 60.66 4.11 9 3870.85 3832.08 38.78 2.63 10 4049.39 4025.31 24.08 1.63 11 4242.11 4227.64 14.47 0.98 12 4448.07 4439.69 8.38 0.57 13 4666.75 4662.09 4.66 0.32 14 4897.91 4895.43 2.48 0.17 15 5141.59 5140.34 1.25 0.08 16 5398.03 5397.43 0,60 0.04 17 5667.61 5667.34 0.27 0.02 18 5950.83 5950.72 0.11 0.01 19 6248.31 6248.26 -0.04 0.00 20 6560.70 6560.68 0.02 0.00 21 6888.72 6888.72 0.00 0.00 22 7233.15 7233.15 0.00 0.00 23 7594.81 7594.81 0.00 0.00 24 7974.55 7974.55 0.00 0.00 25 8373.28 8373.28 0.00 0.00 26 8791.94 8791.94 0.00 0.00 27 9231,54 9231.54 0.00 0.00 28 9693.12 9693.12 0.00 0.00 29 10177.77 10177.77 0.00 0.00 30 10686.66 10686.66 0.00 0.00 Notes: t = 0 for 1970-71; Index of inflation is 100 for t = 0. Real Balances are in Rs. Crores. TABLE 5.11.2 Levels of Capital Stock, Investment (both Public and Private), Aid, GNP, and Growth Rates 0 -0.05, a-0.61572, 0=1.0, a=0.2918 Time Capital Stock Total Public Investment Private Aid GNP Growth Rate 1 42354.89 2994.12 1843.55 1150.57 505.82 21177.44 7.55 2 45044.70 2689.81 1656.18 1033.63 338.89 22522.35 6.35 3 47661.03 2616.33 1610.93 1005.39 232.65 23830.51 5.81- 4 50290.44 2629.42 1619.00 1010.42 160.76 25145.22 5.52 5 52976.68 2686.24 1653.98 1032.26 110.65 26488.34 5.34 6 55746.57 2769.89 1705.49 1064.40 75.33 27873.28 5.23 7 58619.19 2872.62 1768.74 1103.88 50.44 29309.59 5.15 8 61609.67 2990.49 1841.32 1149.17 33,07 30804.84 5.10 9 64731.04 3121.36 1921.90 1199.47 21.14 32365.52 5.07 10 67995.05 3264.01 2009.73 1254.28 13.13 33997.53 5.04 11 71412.76 3417.71 2104.37 1313.34 7.89 35706.38 5.03 12 74994.77 3582.01 2205.53 1376.48 4.57 37497.39 5.02 13 78751.47 3756.69 2313.08 1443.61 2.54 39375.73 5.01 14 82693.12 3941.65 2426.97 1514.68 1.35 41346.56 5.01 15 86830.06 4136.94 2547.22 1589.73 0.68 43415.03 5.00 16 91172.79 4342.72 2673.92 1668.80 0.33 45586.39 5.00 17 95732.04 4559.26 2807.24 1752.01 0.15 47866.02 5.00 18 100518.94 4786.89 2947.41 1839.49 0.06 50259.47 5.00 19 105545.01 5026.08 3094.68 1931.40 0.02 52772.51 5.00 20 110822.32 5277.30 3249.36 2027.94 0.01 55411.16 5.00 Tii 21 22 23 24 25 26 27 28 29 30 TABLE 5.11.2 (Continued) Capital Investment Growth Stock Total ' Public Private Aid GNP Rate 116363.45 5541.14 3411.81 2129.33 0.00 58181.73 5.00 122181.63 5818.18 3582.39 2235.79 0.00 61090.81 5.00 128290.71 6109.08 3761.51 2347.57 0.00 64145.36 5.00 134705.25 6414.54 3949.58 2464.95 0.00 67352.62 5.00 141440.51 6735.26 4147.06 2588.20 0.00 70720.26 5.00 148512.54 7072.03 4354.42 2717.61 0.00 74256.27 5.00 155938.16 7425.63 4572.14 2853.39 0.00 77969.08 5.00 163735.07 7796.91 4800.74 2996.16 0.00 81867.53 5.00 171921.82 8186.75 5040.78 3145.97 0.00 85960.91 5.00 180517.91 8596.09 5292.82 3303.27 0.00 90258.96 5.00 t = 0 for 1970-71. Growth rate is in percentage. All other figures are in Rs. Crores (1960-61 prices). GNP (Rs. 10 Figure 5.9 Time Paths of GNP with Different Technological Configurations 900 0.04 0.05 Technological change in the tenth year 800 600 400 200 5 10 15 20 25 30 Time in years 181 182 j | range of Rs. 31842 and Rs. 37218 crores, depending upon | the time when such a change takes place. TABLE 5.12 Capital Stock and GNP after 15 years for Different Values of n. n 0.03 0.04 0.05 Capital Stock 63684 74437 86830 GNP 31842 37218 43415 • * Note: All figures are in Rs. Crores in 1960-61 prices Capital stock and GNP in the year zero (1970-71) are i i i Rs. 21367 and 19691 crores respectively. j Conclusion ! The optimal choices of the rate of supply of nominal money and the share of public sector investment are uniquely determined for given capital-output ratio. With the capital-output ratio of 0.29, the public sector i share of investment is about 1/4. It would take about j I I fifteen years for the economy to reach the full employ- ! i ment stable growth path. The dependency on aid is j I treated only to match the gap between the balanced I growth rate of investment and the supply of domestic 183 saving. But the emphasis on the domestic monetary and fiscal actions can greatly reduce the burden of the ex ternal debt and guarantee a stable growth path. In the next chapter the estimated growth paths of the monetary policy model and the two sector optimal investment policy model of Chapter III are compared and evaluated. CHAPTER VI EVALUATION OF THE POLICY MODELS AND SUMMARY CONCLUSIONS This chapter deals with putting together the conclusions from our models of Chapter III and Chapter IV and evaluating the empirical results from Chapter III and Chapter V. The policy models are evaluated and compared both on the basis of theoretical and empirical contents of the models. Certain observations are made on the limitations of our study and possible generaliza tions and alternative approaches are suggested. A Comparison of the Two Policy Models The two sector investment allocation model of Chapter III and the monetary policy model of Chapter V have been treated as two different approaches to planning. Certain observations can be made on their objectives and implications. Both models show that the economy is capable of 184 185 ! I ; f reaching the balanced growth path in about fifteen years, j : i ; I The investment planning model with only foreign aid emphasizes the allocation of investment goods in an j ’ I optimal pattern. Both capital and output grow at a rate j : i greater than the balanced growth rate during the j first phase of the plan. The rates decrease to the | ■ i i natural rate by the terminal year of the plan. The j i i levels of capital stock and output at the end of fif- j teen years will have more than doubled. On the other ! hand, in the monetary policy model that we considered, the output and the capital stock rise smoothly to reach the balanced growth path in fifteen years. In the mone- ! : ' I tary model, the capital stock and output levels in the j | ^fifteenth year are less than that under the first model. j The following table reveals the comparisons: j TABLE 6.1 | Comparison of the Estimates with the Two Policy Models After Fifteen Years of Planning . i Capital GNP Growth Rate Accumu lated Loans i Before the Plan 39361 19690 - 2754 Investment Policy Model 91022 44370 2.27 I 1749 1 Monetary Policy Model 63684 31842 3.0 * 1 • 339a Note: All figures are in Rs. Crores. aComputed using the estimates of aid from Table 5.8J 186 The accumulation of the loans in the-fifteenth year gives an indication of the restriction on the post plan balance of payments position. As summarized in Chapter III, the heavy burden of debt may lead to a low rate of savings. A gap between the natural and the warranted rates may develop. On the other hand, the monetary policy model stabilizes the investment and the | savings path; repayment of Rs. 339 crores may not cause serious balance of payment difficulty. The stability properties of the monetary fcjrowth model do not change for changes in the production function due to the technological changes. As stated in Chapter V, a labor saving technological change with higher capital j and output growth rates is equivalent to an increase in the balanced growth rate n for the same rate of growth of population. As shown in Table 5.9, the time required ' to reach the balanced growth path is independent of n ; (same as 0), provided the monetary authorities are able ; to adjust their supply of nominal money to changes in n. ! For increases in n, the speed of price adjustment in- : creases so as to reach the stable balanced growth path in fifteen years. The terminal time in the investment allocation i ^ , i • model on the other hand, depends upon the rate of technological change. A labor saving technological change will affect the labor intensive consumer goods sector more than the capital intensive capital goods sector. j Hence, the expected rates of returns r^ and r2 in the two sectors will change as a result of a technor i logical change. Both r and r become functions of n. 2 The optimal time path of u^ as well as the terminal I i time T to reach the balanced growth path will become j i functions of n. Thus, the solution paths, terminal j time and all other properties of the model depend upon n. In view of uncertainty of returns in less developed economies, planning on the basis of such a two sector investment allocation policy may be difficult. Stipu- I lating and controlling the consumption in those economies | j has been found to be very difficult. For reasons like unfair market practices during the time of rationing, presence of the "demonstration effect," absence of per- i feet market information on the prices and the rates of return, and the lack of borrowing, lending and risk bearing financial institutions, the implementation of such! an investment policy becomes difficult. As seen in Chapter IV, the growth of public sector investment, on the other hand, with the non interest bearing government debt, can increase the j investment rate in the economy on a stable path and the implementation of such a policy does not restrict j 188 private consumption. The growth of the public sector's share of in vestment reduces the private sector investment. Such a tool can be used to bid the investment resources away from the consumer and housing goods industries to the reproductive capital goods sector so as to increase the rapidity of capital and employment growth rates. i Scope for Further Study The two models can be combinedcto develop an optimal investment allocation model with monetary policy. With the definitions of u^ and a in chapters III and IV, one can consider the allocation of investment goods to the two sectors with both private and govern ment investments. The choice of at depends upon the savings rate, natural rate of growth, and people's attitude to demand for money balances. The time path of u^ ; depends upon the full employment terminal conditions. As shown in Appendix C, the choice of u does not depend t upon the choices of a and 0. . Hence, a combined opti- t mal policy can be developed as a two phase model with u = 1 and aA = a ,0 = 0 •„ in the first phase and t max t ln u = 0, a . = a , a , = a . in the second phase. Such t max t min a generalization of our planning models has both the . properties of stability and self-sufficiency in growth. | J 189 Another scope of further research is in formula ting the model on a stochastic scheme. The capital-out- put and capital-labor ratios/ and the parameters of the demand for money can be treated as stochastic variables.1 In the models we considered, the parameters are non- linearly related to each other and determining the joint j probability distributions of the parameters is found to be difficult. Simplifying the model to a simple linear system is not found to be useful for planning purposes. Our assumption of fixed capital-output and capital labor ratios can be relaxed to time dependent variables obtained either as expected values of certain stochastic processes of those variables or as due to technological changes. Such a generalization can take into account the shifts in the production and factor demand functions. Tintner, Sengupta and Morrison treat the capital- output ratios as following a 8-distribution. See, J.K. Sengupta, G. Tintner, and.B. Morrison, "Stochastic Linear Programming with Applications to Economic Models," Economica, XXX (August, 1963), pp. 263-273. 190 Summary I i i l The real issues of economic development are low j i rates of saving and inelastic demand for investment opportunities rather than lack of incentives, motivations and high population growth rates. Raising the savings rate above a critical minimum level is essential for i capital formation and economic development on a j ! stable growth path. As much as the classical models with trade as an engine of allocation of resources and growth have become inoperative with the decline of imperialism in this century, the theories of economic development with foreign aid are also found to be obsolete. Aid as an investment resource as well as a supply of saving is questionable on the basis of the experiences of several developing economies. Tied aid, misallocation of investment goods, the "demonstration effect',' and the inability of aid donors to direct domestic policies in the receiving countries are some of the reasons why the savings rate may not rise above the minimum required level to sustain a stable growth rate. Our own findings with a two sector investment allocation planning model for India are that the burden of external debt deteriorates the balance of payments 191 position and the domestic savings rate is not sufficient i to balance the investment and the deficit on trade. With barriers to entry in international trade, domestic policies to stabilize the savings rate and the attainment of self-sufficienfcy are to be emphasized in the developing economies. In absence of a strong tax collecting machinery, a tax policy is often found to be insufficient to raise the saving potential in those economies. Money, as non-interest bearing government debt, has non-neutral effects on economic growth. In addition to the non-neutrality, the stability of a monetary model is important if any monetary policy is to be suggested. A monetary growth model is shown to be stable if the demand for cash balances follows specified behavioral patterns. i With money created through government deficit financing, J l the planners can choose an optimal mix of the cate of j increase of nominal money and the share of government J i spending on investment out of total investment. An optimal monetary policy model for India is i l developed to stabilize the saving and investment rates } l j on the balanced growth path. The stability properties i i of the monetary policy model are found to be invariant J with respect to labor saving technological change. j A comparison of the two policy models for India j 192 suggests the need for concentrating on the public sector and setting the guidelines of investment patterns rather than relying on investment policies left to private investors. Any borrowing from the foreign country can be treated as residual rather than planned for develop ment. An optimal investment pattern in a two sector economy is possible with a proper choice of the share of public sector investment such that a full employment stable growth path can be reached in less than fifteen years. APPENDICES 193 APPENDIX A DESCRIPTION OF THE DATA FROM THE INDIAN ECONOMY, 1970-1971 We consider the beginning of the plan to be 1970- 1971. A brief discussion on the data from the Indian economy used in this research follows. The capital goods and consumer goods sectors are j defined in accordance with the definitions given in the Estimates of National Income 1963-64.^ The capital goods sector is defined as consisting of the following economic activities: mining, factory establishment, small enter prises, communications, railways, commerce and transport. i t The consumer goods sector consists of agriculture, forestry, fishery, domestic services, land, house property and others. •^Government of India, Estimates of National Income, 1963-64 (New Delhi : Government of India Press, March, 1$<>5) , Table 2, p. 2. 194 195 Estimates of Gross National Income Components The gross national product (GNP) in 1969-70 was Rs. 19373 crores measured in 1960-61 prices. Applying an average growth rate of 2.7 percent during the third plan, we estimated the GNP in 1970-71 at Rs. 19690.67 S I crores measured in 1960-61 prices. Prom the estimates of net national product (NNP) by industrial origin, published in the Economic Survey, miming, industry, construction and electricity contribute 23.2 percent ! and transport, communications, trade, storage, etc., J : i contribute 16.0 percent of NNP ift 1969-70. Since the latter includes some activities of the consumer sector, j ; j we estimated the contribution of the capital goods sector j 1 ; i at 35 percent and of the consumer goods sector at 65 j percent. Hence, the estimates of GNP from the capital goods sector is Rs. 6891.73 crores and of the consump tion goods sector is Rs. 12,798.94 crores measured in 1960-61 prices. j Estimation of Output-Capital Ratios in the Two Sectors In the past, several output-capital ratios for the two sectors have been estimated for India. Using j I ------------------------------------------------------------------------- I ? I Government of India, Economic Survey. 1970-71 j (New Delhi: Government of India Press, 1971), Tables 1.2, 1.3, and 1.4; one crore equals 10'. j 196 the estimates given by J. Sandee, Mahalanobis, V.K. 3 Sastry and T.V.S.R. Mohan Rao, we estimated the ratio for the capital goods sector, a , as 0.32254 and for the consumption sector, a2, as 0.7113. Our estimates of the output-capital ratio are consistent with the estimates given by.Sastry for a group of countries. Characteristically, the Indian economy is quite capital intensive in the capital goods sector as compared to the consumption goods sector. The capital-output ratio in the capital goods sector is 3.17 and in the consumption goods sector is 2.32. The estimates given by K. Marwah for the aggregate economy are quite high compared to the estimates we are using.^ Marwah's estimate for the aggregate economy is 3.72. Several estimates of the aggregate incremental output-capital ratio are available. They vary around 0.2918 with a high of 0.3175 estimated by V.K. Sastry and a low of 0.2688 estimated by Marwah.. 3 J. Sandee. A Demonstration Planning Model for India (Calcutta: Asia .Publishing House, 1960) ; P,; C. Mahalanobis, "The Approach of Operational Researcfrvto Planning in India," Sankhya, XVI (1965); V.K. Sastry, A Macro-Economic Model for the Indian Economy, United Nations Conference on Trade and Development (mimeographed)j T.V.S.R. Mohan Rao, Approaches to Economic Policy for Stabilization and Growth f 1968. ! 4K. Marwah, "An? Econometric Model of India: Estimating Prices, Their Role and Sources of Change," Carlton University, 1969)., (mimeographed) , p. 22. 197 5 Manne and Weisskopf projected the ratio for 1969-70 from a high of 0.365 to a low of 0.279. Considering the estimates of Chenery and Strout for a group of less developed countries,6 our estimate of the aggregate out put-capital ratio is 0.2918. Estimating the Capital Stocks in the Two Sectors Using the estimates of the output-capital ratio and the estimates of outputs in the two sectors, we estimated the levels of capital stock in the capital sector and in the consumer goods sector in 1970-71 at Rs. 21367.05 and 17, 993,72 crores measured in 1960-61 prices, respectively. The total stock of capital is Rs. 39360.77. Estimating Labor Statistics We estimated the 1970 population as 548.59 million and the average population trend as 2.27 per- 7 cent. T.V.S.R. Rao estimates the ratio of the full 5 \ \ A.S. Manne and T.E. Weisskopf, A Dynamic Multi sectoral Model for India, 1967-75/' in Input-Output Tech— nigue, Vol. II, ed. A.P. Carter and A.Brody, (Amsterdam: North-Holland Publishing Co., 1971). g H..B. Chenery and.A.M. Strout, "Foreign Assistance and Economic Development." American Economic Review, LVI (September, 1966), pp. 684.mm"" ...........— 1 7 Government of India, Basic Statistics Relating to the Indian Economy, 1951-52 to 1968-69 (New Delhi; Government of India Press, 1970). 198 employment labor population in India in 1964-65 as 68.44 percent. Using the same ratio, we estimated the full employment labor force in 1970-71 as 375.45 million. To estimate the labor force engaged in the consumption and capital sector, we used the information from the O International Labor Organization. In 1970, 57.1 per cent of the Indian male population was economically active and 27.9 percent of the female population was active. 43 percent of the total population was economically active. Again, 72.9 percent of the economically active labor force was in the consumer goods sector and the rest in the capital goods sector. Thus, we estimated the labor employed in the capital goods sector as 63.93 million and in the consumer goods sector, 171.966 million, giving a total of 235.893 million people employed. The estimate of the labor-capital ratio in the capital goods —3 sector is b^ = 0.29918 x 10 and in the consumption -3 goods sector is b2 = 0.9557 x 10 . The estimate of the full employment labor force is to be used with' some suspicion. In 1968 the Planning Commission of India appointed a committee of experts to estimate the potential labor force and the details of employment opportunities. 8International Labor Organization, The Year Book of Labor Statistics (Geneva: United Nations, 1971)", Tables 1 and 2 A. Since the situation in India is characterized by many household and small scale enterprises involving family labor, it is difficult to estimate the potential labor force and its distribution among various activities. We think our estimate is substantially below the potential labor force; however, we do not make any attempt to improve our estimates since the information is not complete. Estimates of Consumption Q The fourth five year plan draft of 1969-74 gives the breakdown of consumption in India in 1968-69. The government consumption and the private consumption in 1968-69 measured in current prices were Rs. 3100 and Rs. 25740 crores, respectively. Applying a six percent growth in consumption we estimated the consumption in 1970-71 measured in 1968-69 prices as Rs. 32400 crores. When converted to 1960-61 prices, our estimate of total consumption in 1970-71 is Rs. 17428.72 crores. With the estimate of GNP, our estimate of saving in constant prices is Rs. 2262 crores. The Manne-Weisskopf model gives an average propentisy to consume of 0.914 and using this, we made an estimate of consumption in 1970-71 of Rs. g t j Government of India, The Fourth Five Year Plan: Draft, 1969-74. (New Delhi; Government of India Press, | pV'Tf."______________ ! 200 ! I 17997.27 crores measured in 1960-61 prices. These two estimates are quite consistent and we use the estimates obtained from the statistics given by the Planning Commission. We use the estimate of the marginal propen sity to consume (mpc) of 0.914. This estimate will be 10 called the DMS estimate. The average propensity to consume from our estimates of consumption and GNP is 0.885. Since the consumption path is stipulated during the period in which optimal capital investment will be exclusively in the capital goods sector, we choose the stipulated rate of consumption growth, m, as six percent. The Planning Commission estimates the private consumption in the next 12 years to increase by 86 percent.^ Our stipulated rate is lower than the Planning Commission's goal, but they are consistent since our stipulated rate is for the entire consumption sector whereas the Planning Commission's expected rate is for private consumption only. We will also consider m = 0.1 for the purposes of sensitivity analysis. ^°Dynamic Multisector Model of Manne and Weisskopf is often referred to as DMS model. Hence, we use the same abbreviation. ^^-Government of India, Fourth Five Year Plan, Draft 1969-74, p. 33. 201 Estimates of Loan and Aid India's foreign debt in 1970-71 is estimated by using the data on the existing debt in 1970, the aid utilized in 1970-71, and the debt services. India's external debt repayable in foreign exchange in 1970 12 was Rs. 50,940 million. The aid utilized in 1970-71 13 was Rs. 7688 million. The fraction of aid to be returned is estimated at 0.937. Hence the repayable aid received is estimated at Rs. 7204 million, the remaining being the PL-480 and other gifts and grants. The debt and the aid received in 1960-61 prices are then estimated at Rs. 2753.51 and 424.28 crores. We assumed the interest rate on the external i assistance, to be six percent. The interest rates differe from country to country. We considered the International Development Authority (IDA) and the United States grants in our estimate of We assumed the discount rate, y on capital accumulation to be ten percent and considered five percent and fifteen percent rates ; of depreciation for the sensitivity analysis. 12 Government of India, External Assistance, 1968-69 and 1969-70 (New Delhi: Government of India ; Press, 19*76), p. 2. " " ' 13 Government of India, Economic Survey, 1970-71, pp. 157-158; see also Table 7.1. 202 The data for 1970-71 and the estimates of the parameters in the model are summarized below: K = 21367.05 crores 10 K = 17993.72 crores 20 K = 39360.77 crores 0 X = 19690.67 crores 0 X = 6891.73 crores 10 X = 12798.94 crores 20 C = 17428.72 crores 0 a = 0.32254; a = 0.7113; a = 0.29180 1 2 a = 0.937; a = 0.06 1 2 y = 0.10; m = 0.06; (1-s) = 0.914 L = 375.45 million 0 L =63.93 million 10 L = 171.97 million 20 n = 0.02277 t = L /K = 0.001757 0 0 10 b = 0.29918 x 10 1 ~3; b = 0.9557 x 10_3 2 N = 2753.51 crores o r 203 A = 424.28 crores 0 (b -b )/(b a ) = 2.13; from equation (3.50) we 2 1 2 1 see that b a T + (b -b ) > 0 2 1 12 Prom the expressions in (3.34) we compute, for / a = 0.1* *2 " a b V(b -b ) (n+M) 538‘9376 » 0 12 2 1 83 = a b -1 ( l A V W n ) ----------- = 876.9535 >0 12 2 1 Hence, both 0 and 0 are non-negative. 2 3 The minimal value of e for any given t is obtained by solving the constraint (3.31.a) with an equality. (m+y) t e = 1 + (m+y) (Cn/Km)e______ (a +y)a Z 2 1 30 From equation (3.50.a) we note that the minimal terminal time to reach full employment terminal condi tions (3.35) and (3.36) depends linearly upon the choice of the switching time t^. Therefor*? we choose the minimal t = t^ and hence the corresponding terminal time T such that (3.35) and (3.36) are satisfied. The optimal choice of e = corresponding to the minimal j j 204 j : choice of t = t is shown for different values of ' 1 y below: w El 0.05 11.86 34.0 0.1 10.16 24.5 0.15 2.91 3.5 APPENDIX B DATA DESCRIPTION FOR THE MONETARY POLICY MODEL The data and the parameters for the monetary model are discussed below: The money supply is defined as currency + demand deposits. Since the monetary institutions in India are not well developed, the inclusion of savings deposits may not be very meaningful. Marwah1 also used the same definition of money supply as we used. The money supply in 1960-61 was Rs. 2869 crores and in 1968-69 was 5779 2 crores. From the same source we estimated the annual increase in money supply from 1961 to 1969 and projected it for 1969 and 1970 at 8 percent and estimated the nominal money supply in 1970-71 as Rs. 7005 crores. The - K. Marwah, "An Econometric Model of India: Es timating Prices, Their Role and Sources of Change," Carleton University, 1969 (mimeographed). 2 Government of India, Basic Statistics Relating to the Indian Economy, 1950-51 to 1968-*69 (Dselhi: Government of India Press, 19*70), Table 73. all India consumer price index is 184 for 1970-71 with j 1960 as the base year. Using this price index we estimated i ! the stock of real money supplyas Rs. 3807'crores. An important parameter in the monetary model to be estimated is the parameter for the demand for real balances. We defined the demand for real balance = IK and a fixed j coefficient aggregate production function is assumed. The Gross National Product can be written as aK where a is the aggregate output-capital ratio. Hence, we : derived £= a/v where v is the velocity of money. From the data taken from Marwah1s study, for the period 1961-65 we estimated the inverse of the velocity of money as ah average of 0.203. As discussed in Appendix A, with the estimate of aggregate output/capital ratio of 0.2918, we estimated S i as equal to 0.0592. Other relevant data used in the chapter are ; already discussed in Appendix A. APPENDIX C INVESTMENT ALLOCATION IN A MONETARY POLICY MODEL Consider the model as: K = uK 1 • • K = (l-u)K 2 • • K = saK - (l-s)ms 1 - ar(l-s) • m = m [0 - 3 (m -&K) ] s s s • • ms2= aK nt Path Conditions: b,K, + b K < L e 11 2 2-o The choice of u indicates the allocation of total invest ment resources to the consumption and capital goods sector independently of the choice of the time path of investment. Investment is determined by the choice of 0 and a Rewrite the equations of motion as: 208 K1 = u saK-(l-s)m [0-8(m -&K)] __________ s______ ______ 1-a(1-s) K = (1-u) jsaK-(l-s)ms[e-e(ms-£K)] I 1 - a(l-s) r i i = m [0-8(m -£K)] S S 5 Define the Hamiltonian H as in Chapter V, equation (5.19) H = r m + r K + r^K + r Z + r Y i s 2 1 3 2 3 4 where Z and Y are defined as in equations (5.13) and (5.12), respectively. Then, the optimal choices of a and u are stated as: u = 1 u * 0 0 < u < 1 if ( 3H/3u) >0 if (3H/3u) < 0 if (3H/3u) = 0 a = a max mm & . < a < a mm max if (3H/3 a) > 0 if (3 H/3 a) < 0 if (3H/3a) = 0 209 ( 3H/3u) = (r.-r-,) saK-(l-s)m [0-3 (m -JlK) ] £ J s s [1-a(1-s)]2 (3 H/3 a) = saK- (l-s)m [0-0(m-AK)] __________ s______ s_____ x [1-a(1-s)]2 6t (1-s)(r2~r3) - (sa/n)e r4 + (l-s)r saK-(l-s)m [0-3(m -£K)] 3 s s [1-a (1-s)]2 Hence, (3H/3a) is independent of u and t3H/3u) does not 2 depend upon a since [l-a(l-s)] is always positive. 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Creator Kadekodi, Gopal Krishna (author)

Core Title Planning For Stability And Self-Reliance: An Evaluation Of Policy Approaches For India

Degree Doctor of Philosophy

Degree Program Economics

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

Tag economics, general,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Tintner, Gerhard (committee chair), Bellman, Richard (committee member), DePrano, Michael E. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-886289

Unique identifier UC11364216

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Legacy Identifier 7331356

Dmrecord 886289

Document Type Dissertation

Rights Kadekodi, Gopal Krishna

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

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