University of Southern California Dissertations and Theses

Planning Under Socialism- And Risk

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Planning Under Socialism- And Risk

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Content PLANNING UNDER SOCIALISM-- AND RISK A Dissertation Presented to the Faculty of the Graduate School The University of Southern California In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy (Economics) by Salwa Ali Soliman Farghali June 1966 U N IVER SITY O F S O U T H E R N C A L IF O R N IA T H E G R A D U A T E S C H O O L U N I V E R S I T Y P A R K L O S A N G E L E S , C A L I F O R N I A 9 0 0 0 7 This dissertation, written by Salwa Ali Soliman Farghali under the direction of h.^.V...Dissertation Com mittee, and approved by all its members, has been presented to and accepted by the Graduate School, in partial fulfillment of requirements for the degree of D O C T O R OF P H I L O S O P H Y D ean Date June,*.. . 1 . 9 . 6 6 ............. DISSERT/lTIO NjCOM M ITTEE !A j . 5 0 A . & Z T TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION ............................... 1 Purpose .................................. 1 Importance of the Study................. 2 Hypotheses....................... 2 Methodology .............................. 3 Major S o u r c e s........................... 3 Definitions of Key Terms .............. 4 Organization of Remainder of Dissertation 6 II. THE SOCIALIST EXPERIENCE IN THE UAR . . 10 A Brief Survey of the Main Features of Egypt’s Economy to 1952 . . . . 10 The Socialist Regime ................. 19 The July 1952 Revolution . . . . 19 The Road to Socialism (1952-1959) . 22 The "Inevitability of the Socialist Solution" (1960--) .............. 27 The Socialist Drive .............. 31 Prospects and Potentialities of the UAR Economy: A Comment .............. 43 Role of the Environment.............. 44 Policy Decisions . 49 ii CHAPTER PAGE III. RISK UNDER CENTRAL PLANNING ............ 54 The Term "Risk" D e f i n e d .............. 56 Risk and the Market System's Performance 58 Plan Underfulfillment in Centrally-Planned S y s t e m s ................. . . . . 61 Errors in Plan Fulfillment . . . . 61 Causes of Plan Underfulfillment . . . 63 Risk in Dynamic Central Planning . . 66 IV. AN APPLICATION OF STOCHASTIC PROGRAMMING TO THE UAR: THE CASE OF RISK .... 70 Statement of the P r o b l e m ............. 70 The Assumptions....................... 72 The D a t a .................. 74 The Model ............................ 78 Results of the Optimum Solutions . . 82 The Five Allocational Policies Compared...................... 192 Comparison with the Actual Achievements in the First Five-Year Plan . . . 198 How to Explain the Discrepancies? . 199 V. SUMMARY AND CONCLUSIONS............ 202 S u m m a r y .................................. 202 Conclusions . . . . . ............ 204 APPENDICES........................................... 209 BIBLIOGRAPHY ....................................... 230 33 34 41 83 84 85 86 88 109 130 151 172 193 LIST OF TABLES Planned Percentage Increase in Production and in Value Added--1964-1965 . Planned Distribution of Investment by Sector ■ • ■ • • • • • • • « • Percentage Distribution of Employment per Sector and Percentage of Employment to Total Population ......................... O/L Agriculture ............................ O/K Agriculture ............................ O/L Industry..................... O/K Industry............................ ... Policy I ................................... Policy II ................................... Policy III . . . ......................... Policy IV ................................... Policy V ................................... Results of the Five Policies .............. CHAPTER I INTRODUCTION PURPOSE Within the framework of central planning, the present study aims at investigating the major difficulties that face the central planners and adversely affect target achievement. A basic question that we attempt to answer in this connection is, how many of these difficulties, if any, are due to the phenomenon of "risk..1* In other words, is "risk” confined to conditions arising out of the market system--as a result of the scarcity of information avail able to the individual entrepreneur, and the lack of coor dination among private business plans--or does it play a similar role in centrally-planned systems? And if it does, how important is that role? Are there other factors that have a significant effect on both decision-making and eco nomic outcome? If so, what are they and what is their importance relative to that of risk? 1 2 IMPORTANCE OF THE STUDY Socialist centrally planned patterns hold an increasing appeal for developing nations as the most prom ising approach to development and economic growth. The present study attempts to shed some light on the attitudes of policy-makers in centrally planned developing nations and explore reasons why these attitudes would be expected to differ from those of the entrepreneur in a market sys tem. HYPOTHESES The main hypothesis of the present study is that the ’’risk” phenomenon is not confined to the market system, although it may play different roles and have varying degrees of importance in connection with decision-making in different economic systems. Our second hypothesis is that under socialist centrally-planned systems, the situations which originally represent cases of "risk" are affected by new conditions that turn them into situations of ’’uncertainty,” and that this fact gives a strong justification to the arbitrariness in decision-making under these systems. 3 METHODOLOGY The empirical study of the present work, as pre sented in Chapter IV, is based on the application of the method of stochastic linear programming: beside usual mathematical procedures for solving linear programming problems, statistical analysis is used to obtain the char acteristics of different allocational policies of factors of production, under the assumption that technical coeffi cients are random variables with a known probability dis tribution. Theoretical discussion and analysis of different aspects of the case study under consideration is the second method used to draw the final conclusions. MAJOR SOURCES The primary theoretical sources of the main part of the dissertation, Chapter IV, are Professor Tintner's works on the use of stochastic analysis for economic plan ning. Figures used in that chapter are mainly from two sources: data published in the United Arab Republic (UAR) First Five-Year Plan book, and our own estimates to fill the gaps in available figures. Details of these estimates are given in the relevant appendices. References pertaining to Egypt's modern history and others on economic theory--especially in the field of economic development--are the major source of the theoreti cal discussions of the present work. static systems where there exists a single known probabil ity distribution of anticipations. factors of production, we define the margin of risk as the difference between the mean value of the objective function and its lower 5 per cent probability level. The bigger this difference, the higher the margin of risk, and vice versa. Uncertainty.--Uncertainty is a phenomenon that arises in nonstatic systems where there exist several pos sible probability distributions of anticipations, perhaps connected by an a priori probability distribution.1 DEFINITIONS OF KEY TERMS Risk.--Risk is a phenomenon which arises in non- Margin of risk.--For a given allocational policy of ^G. Tintner and Econometrics, of Mathematical Economics . 32-69. Leading sector.--The word "sector" is used here to distinguish either economic activity (e.g., agricultural versus industrial sector), or the type of ownership and control (e.g., private versus public sector). We generally define the term "leading sector" as that one which domi nates in shaping the economic structure and performance of a given economy. Industrialization.--Using A. 0. Hirschman's terms,2 we mean by "industrialization" the establishment of eco nomic activities which have backward and/or forward link ages. While this definition includes the creation of rural industries (such dairy-product industries, or any type of manufacturing activities carried out in rural areas), it excludes mere mechanization and the use of modern equipment and techniques for carrying out agricultural activities, such as harvesting end planting, per se. Developing nation.--We call "developing" nations those that have been undertaking serious, persistent, and intensive nationwide drives for economic activities aimed ^A. 0. Hirschman, The Strategy of Economic Develop ment (New Haven: Yale University Press, 1960), pp. 76- 133. 6 at overcoming their problems of backwardness and under development. Their initial failure to achieve a signifi- cant--or even any--increase in the rate of economic growth despite of these efforts is not taken to interfere with the definition. It is rather considered to reflect the existence of a serious economic problem (such as a very high rate of population growth) which must be solved some time in the future under the continuous and intensive pres sures of development programs under way. Errors in plan fulfillment.--We use this term to refer to situations of both over-and under-fulfillment of original plan targets. The first situation is regarded a ’’ negative error,” the second a ’’ positive error.” ORGANIZATION OF REMAINDER OF DISSERTATION In the following chapters we seek to obtain satis factory answers to our questions from the empirical example of central planning in the UAR which, since 1960, presents an interesting case. The contrast between the pre-1952 situation in Egypt, and the post-1960 socialist pattern illustrates a typical example of a small country vigorously attempting to overcome her economic problems and to enter a new stage of development. The path to economic growth, as we shall see later from the UAR experience, is full of handicaps (technical, economic, sociological, institutional, and political) that complicate the solution and make the task of the central planner more difficult. The economic prob lems he must cope with usually have multi-dimensions that require any serious and effective plan to be associated with large-scale preparations, massive mobilization of resources and efforts, economic and social reform, and deliberate implementation of basic projects. The next chapter briefly outlines the recent his torical features of the UAR economy prior to the 1952 revolution, and the new trend which since that year has drastically influenced and shaped the economy into a com pletely new pattern that crystallized finally in the intro- q duction of socialism in 1960. The core of the present q JIn the present context, our concern is not to enter into any conceptual discussions of the word "social ism, M or to compare the UARfs present system with other socialist patterns. This would require an unnecessary, lengthy deviation from the main subject. Suffice it to identify that system as "socialist" by referring to the fact that social ownership is predominant and economic ac tivities and performance are deliberately and systematic ally subjected to comprehensive planning by the state. economic situation is illustrated by the major economic problems and targets as recognized by the First Five-Year Plan (1960-1965). In this light we will examine prospects and potentialities of the UAR economy. The third chapter is preparatory to Chapter IV: it presents the theoretical definition of ’’risk,” its role in the market system, and its adverse effects on economic performance. Then it questions the role and significance-- if any--of risk in socialist centrally-planned economies. While we reach the conclusion that risk will not disappear, although other factors arise and account for new difficul ties, another part of the question is left to be examined in the light of the results of Chapter IV: how significant is risk under centrally-planned systems? In Chapter IV, an empirical study based on data from the UAR's First Five-Year Plan is presented. Using the method of stochastic linear programming, a computa tional process is undertaken for two sectors (agricultural and industrial) and two factors of production (labor and capital) to examine the phenomenon of risk (due to the pre assumption of the randomness of technical coefficients of production) under central planning, and to see how its mar gin varies according to different allocational policies of the factors of production. The study is confined to two sectors because of the extreme difficulty, if not impossibility, of handling more sectors with the stochastic method. These two particular sectors were selected because of their basic importance both in shaping and in solving the economic problems of the UAR. The computations are performed for five different preassumed allocational policies. Unfortunately, the actual policy of the UAR Five-Year Plan is not one of the five. We could not gain access, within the given time, to the required data and information on the actual policy. However, the results obtained from the computations on the other five policies have been analyzed and compared with the achievements of the actual policy. Chapter V contains a brief summary and conclusions from the earlier discussions. CHAPTER II THE SOCIALIST EXPERIENCE IN THE UNITED ARAB REPUBLIC A BRIEF SURVEY OF THE MAIN FEATURES OF EGYPT’S ECONOMY UP TO 1952 Historical Background. The "Egypt of the ’Pashas' was an Edwardian society, with its sharp contrasts of surfeit and starva tion, its luxury and vulgarity."1 That Egypt, was in fact the concluding image of the long era of her modern history which culminated in the revolutionary changes of July 23, 1952. Though Egypt, that year, labored under a stagnant and. ragged economy, loaded, with all the economic text books' long lists of features of backwardness and under- D. Warriner, Land. Reform and. Development in the Middle East, January 1953, p. 63. 10 11 p development, the preceding period, had actually been more of a depression phase in a long series of cyclical fluctua tions : Political events had substantially affected, the country’s sociological and economic conditions. At the beginning of the nineteenth century, Napoleon’s invasion and the subsequent three years of French occupation were the first important political events in Egypt's modern history to awaken her traditionally agricultural economy by exposing it strongly to the "demonstration effect" of European civilization, thus putting an end. to the long- stagnant Mameluke era. At the same time, the advent, in 1805, of Mohammad. Ali Pasha (the head, of the family that ruled. Egypt since that year until 1952) laid, the foundation of a new stage in Egypt's modern history. His arrival marked, the starting point of concentration of wealth (particularly land, owner 2 See B. Higgins’ Economic Development: Principles, Problems, and Policies (New York: W. W. Norton and Co., Inc., 1959), pp. 11-21; J. Viner's "The Economics of Devel opment," published in Th^ Economics of Underdevelopment by A. N. Agarwala and. S. P. Singh (ed.s.), (Oxford. University Press, 1958), pp. 9-31; and. H. Leibenstein's Economic Back wardness and. Economic Growth (New York: John Wiley and. Sons, 1957), chapter iv. 12 ship, in the form of huge estates) held by members of the royal family, together with a few other families.^ Under his rule, Egypt also gained internal independence from the Ottoman Empire, and a new stage of social and economic change was abruptly introduced.1 ^ In general, Mohammad Ali Pasha’s era was charac terized by the emergence of a strong monarchy and sharp class differentiation, the appearance of a class of bureau crats, and the establishment of military factories to meet the needs of his expansionist ambitions. These develop ments also prompted the formation of a class of industrial and agricultural laborers who lived on subsistence wages, working long hours under unfavorable conditions and with inadequate health, educational, and housing facilities.5 3 For example, of the total area appropriated in the first Land Reform Law of 1952, about one-third had been the property of the royal family, and another major portion belonged to fifteen to twenty other families. See D. Warri- ner's Land Reform and Development in the Middle East (Lon don and New York: Royal Institute of International Affairs, 1957), pp. 14-15. A A. A. El-Greitly, History of Industry in Egypt During the First Half of the 19th Century ( Arabic) (Cairo: 1952; A. A. Crouchley, Economic Development of Modern Egypt 5R. El-Barrawy and H. Eleysh, The Economic History of Egypt, Cairo. 13 Because of the linkage between the Pasha's dreams of conquest and the pace of new activities, the latter halted, as the ruler's expansionist ambitions ended. This was the starting point in a new downturn, and. a phase of stagnation continued, for about three decades after the end of his rule. With the 1870's came a new wave of awareness, stimulated, by slow changes in the preceding decades, and. culminating in Oraby’s bourgeois revolution of 1882 against the ruling family. Among other important factors, the movement had. behind it the peasants' search for greater freedom, the ambitions of the new class of Egyptian land owners, the emergence of a merchant class, and the spread of education and. democratic ideas. But this new popular voice of revival was quickly forced, into the silence of a traditional colonial economy when British troops intervened, to crush the revolution. This was the start of a period, of forced, stability that meant and. required, the preservation of a typical backward economy. General Conditions of the Economy Prior to 1952 As was exemplified, by the odd. mixture of the afflu- 14 ence of the royal family and the landed aristocracy, co existing with mass poverty, ignorance, illiteracy, and diseases, Egypt of this period fitted perfectly the stereo type of the typical traditional society.6 A substantial sector of the economy was engaged in producing primary products, mainly for export, thus providing no opportunity for further "linkages” ^ of economic activity, beyond cul tivation, that would have pulled the economy out of stag nation. Even worse was the fact that the agricultural sector, with all its sufferings from growing seasonal and Q disguised unemployment, and technical and institutional backwardness, was the leading productive sector in the economy. In 1952, it contributed two-fifths of the national income. Furthermore, the cultivable area of roughly six million acres, was inhabited and worked by 18 million out of the total population of 21.5 million,^ 6W. W. Rostow, The Stages of Economic Growth (Cambridge University Press, 1960), chapter ii, pp. 4-6. See A. O. Hirschman's The Strategy of Economic Development (Yale University Press, 1960), chapter vi. Q R. Nurkse, Problems of Capital Formation in Under developed Countries (Oxford University Press, 1958), p. 36. ^Statistical Year Book, 1962, The Egyptian Statis tical and Census Department, Cairo. 15 engaging one-half of the working population. The major source of agricultural income was spe cialization in cotton cultivation, subjecting the economy to inherent economic instability because of the dependence of that crop on an ever-changing international market. Extreme mal-distribution of land ownership was another feature of the agricultural sector. In 1952, 0.6 per cent of all landowners possessed one-fifth of the total cultivable area; 70 per cent owned one acre or less each.lO Very high land rent left a meagre residual, if any, for some 2.3 million peasants.11 Under the circumstances, mass poverty was common, since there was no other alternative for labor outside the agricultural sector, and the bulk of the increment of the labor force continued its increasing pressure on land,12 adding more disguised unemployment and depressing the over all productivity of labor to a very low level. 10Statistical Pocket Year Book, Cairo, 1952. ^^See National Bank of Egypt (NBE), Economic Bulletin. Vol. Ill, 1951. 12 Leibenstein, op. cit., pp. 159-164. 16 Indeed, population pressure has been a major eco nomic problem for Egypt: with a constant birth rate and a declining mortality rate, the Egyptian population more than doubled since the beginning of the twentieth century, while cultivated area increased by only 30 per cent from 1897 to 1952. Per capita income declined from about $200 in 1945 to about $100 in 1952.13 The low per capita income provided practically no market for any potential industrial activity, imposing a major obstacle to economic develop ment . 14 The saving capacity of the Egyptian society as a whole,15 with its vast inequality in income distribution, was quite large and was concentrated in very few hands.^ * 1 O ^Probably the average for 90 per cent of the popu lation was even below $70. F. Harbison, Human Resources for Egyptian Enterprises, 1953, p. 78. l^Nurkse, op. cit. , chapter i. l5Savings capacity in a certain society is not the decisive factor: inducement and ability to invest are the critical ones. See N. Rozenberg’s ’ ’ Capital Formation in Underdeveloped Countries,” American Economic Review, (Sep tember 1960); and Hirschman, op. cit., chapter ii, pp. 35- 39. l^The effect of inequality of income distribution on the economy’s savings may be illustrated by the finding that the marginal propensity to consume in Egypt during the second World War was 0.4. Although part of the expla- 17 Had these savings been directed into productive activities, rather than spent on luxury imports and land investment, Egypt might have had less substantial economic problems to cope with in 1 9 5 2 .-^ The open-market policy for foreign trade, imposed upon the country during the colonial era following the British intervention against the 1882 revolution, made it impossible for any significant national industry to stand on its own feet in the face of competition from strong foreign industries. It was not until November 1930, when law number 2/1930 was enacted, that Egypt regained her nation might be the scarcity of consumption goods in this period, the fact that, generally speaking, the rich became even richer and the poor poorer during the war, is undenia ble. (The data we used in calculating the marginal pro pensity to consume was taken from a Ph.D. dissertation by M. A. Anis, published in L'Egypte Contemporaine, November 1950.) 17 The history of the industrial revolution in England provides us with very good examples of the effec tive role of landlords in providing industry with both entrepreneurship and capital. See T. S. Ashton's The In dustrial Revolution, 1760-1830 (Oxford University Press, 1960); H. Heaton's "Financing the Industrial Revolution," Bulletin of the Business Historical Society, February 1937; and C. Wilson's "The Entrepreneur in the Industrial Revolu tion in Britain," Explorations in Entrepreneurial History, Vol. II, 1955, pp. 129-145. freedom to implement a new tariff compatible with her in terests.18 Nevertheless, this was by no means a sufficient condition for industrial progress. The final result rested on the attitude of the would-be industrial investors and entrepreneurs. Unfortunately, those individuals continued to spend their savings mainly on luxuries or land invest ment, and shied away from industrial ventures. Accord ingly, the industrial sector remained small, weak, and neglected. A considerable portion of it was small shops1^ contributing with less than 5 per cent of total employ ment .20 A modest industrial sector had been in existence in 1952, with a total production amounting to about 11 per cent of the national income, and employing 273,156 per sons. 21 The textile industry was the most important, con tributing one-fourth of the net industrial income, and - J Q A. A. El-Greitly, The Structure of Modern Indus try in Egypt (Cairo, 1948). ~ ■^Grunwald and Ronall, Industrialization in the Middle East, p. 189. 20See Harbison, op. cit., p. 138. 21 Central Statistical Committee, Basic Statistics, (January 1962), p. 80. 19 providing employment for 89,743 of total industrial workers. Food industries were next in importance. The backward status of the country's industry was caused by a number of major difficulties: scarcity of raw materials such as fuel and minerals, limited quality and quantity of entrepreneurial talent, scarcity of adequate skills, and dim prospects for industrial growth due to marketing problems. The weakness and backwardness of this sector was most reflected in the very low productivity of n p industrial labor, where the above difficulties shared the responsibility with unfavorable institutional factors of a legal, sociological, and cultural nature. THE SOCIALIST REGIME The July 23, 1952 Revolution We have not preoccupied ourselves with theories in search for our life; rather, we have been preoccu pied with our life itself in search for theories: Freedom of work has been the introduction for theo retical ideology; and this came later as a natural result. Gamal Abdel-Hasser 22 Factors contributing, at that time, to low labor productivity in industrial sector are surveyed in an arti cle by G. Saied, "Productivity of Labor in Egyptian Indus try," L*Egypte Contemporaine, April 1952. Pragmatic Approach If nothing else, the quotation by Abdel-Nasser emphasizes that Egypt's main and compelling concern handi capped as she was by missing the chance for progress for so many years, has been simply to find out the most direct pragmatic answer to her economic problems of backwardness, and not to live in the ivory tower utopias of theoretical/ ideological debates and struggles. Such a practical outlook has been mandatory from the very beginning. The revolutionary movement of the Egyptian army was a direct reaction to a long-time dis satisfaction with all aspects of life in the country--po- litical, sociological, and economic. On July 23, 1952, the leaders of the coup d'etat were preoccupied with the single goal of successful termination of the country's controlling regime. It was too early to ask, "What to do next?" let alone to expect a clear and definite answer to such a question. They simply wanted something better; a correction to the wrongs of many years' duration, an im provement of the country's economic, political, and social conditions. The choice of the specific methods of action was something to be borne of practical necessities and learned through experience. 21 Determination of the Principles After the achievement of the introductory "nega tive" goal of the revolution--the successful overthrow of the monarch--it was necessary to prepare for the "positive" steps of the construction of the new Egypt by outlining principles for future actions. These principles can be summarized in three words: Freedom, Security, and Welfare. Freedom.--Both for the individual citizen within O Q the society, and for the nation as a whole. Security.--The individual citizen must have the right to be sure of his future, his job, and a peaceful life. The nation should also have the right and the abil ity to protect herself against foreign threat, at any time. Welfare.--Rapid growth and development of the pro ductive capacity and the level of economic performance of the whole economy are necessary, so that, given the high rate of population growth, every individual citizen will p Q “The specific definition of the individual's free dom, especially in the economic sense, has been later made in the light of the finally established socialist pattern of the economy. 22 be able to improve continuously his economic, social, and cultural standard. These three ’’deduced" principles have been implied^ since 1952, in the declaration of the six goals of the revolution; namely: 1. Termination of foreign domination. 2. Termination of "feudalism." 3. Termination of monopoly and the dominance of political and executive power by private capital. 4. Establishment of "social justice." 5. Establishment of a strong national army. 6. Establishment of a true democratic life. The Road to Socialism: 1952-1959 The period from 1952 to 1959 was one of experimen tation and preparation, full of scattered political and economic events that deeply affected the economy and shaped its future. Land reform.--Before the land reform of 1952, as we have learned, land ownership was concentrated in the hands of a very small group where it was a source of wealth and political influence. Judiciary and executive powers were dominated by the wealthy landowners, and directed to 23 the benefit of the rich class without any consideration for the interest of the majority of the working peasants. It was therefore natural that the new leaders labeled re distribution of land ownership an indispensable necessity for reform, and a prerequisite to the next stages of eco nomic action. The first Land Reform Law (Number 178), issued in 1952, limited land ownership to a maximum of 200 "feddans" per owner.2^ The land appropriated from holdings exceeding this amount was distributed among landless peasants, in parcels not exceeding five feddans. Former owners of the expropriated lands were compensated through long-term state bonds. Political conditions and government policy.--During the years 1952-1959, the UAR1s economic policy was the product of a period of important political developments and successive trial-and-error economic experiments. It was not until the launching of the first comprehensive Five-Year Plan of 1960-1965, and the declaration of the July, 1961 socialist laws that the socialist features of 24 One "feddan" = 1.038 acres. 24 the Egyptian economy became unmistakably clear.25 The years 1951 and 1952 left behind a heavy burden of both budget and balance of payment deficits. In an attempt to reverse that situation, the government followed a policy of austerity in the next two years. Government 2 ^ expenditures were reduced from -L.E.232.85 m. in 1951/1952 to -E.E.199.70 m. in 1953/1954**7 and tight import restric tions were imposed. Up until that time, Egyptian leaders had not even considered the idea of central planning. The implementa tion of economic and social projects was confined to study councils2® where their effects were scattered and mild. 25It should be noted, however, that Egypt's first attempt at government planning on a large scale came with the introduction of the Industrial Five-Year Plan in 1957. For a detailed survey of development policies in Egypt during the period 1952-1957, see UAR, Institute of National Planning (INP), I. H. Abdel-Rahman, Memo No. 63: Planning for Balanced Social and Economic Development in the UAR (Egypt), August 1961. 2^"JL.E.m." refers to "millions of Egyptian Pounds." The official exchange rate with the United States Dollar is 1 t.E. = $2,872. See Central Bank of Egypt, Economic Re view, Vol. Ill, No. 3, Cairo, 1963, p. 366. 27Where a deficit of -t.E.38.774 m. in 1951/1952 was reversed into a surplus of t.E.6.668 m. in 1953/1954. See UAR, Statistical Pocket Year Book, 1957, Table 52, p. 75. 28Namely, The Supreme Council for Development of 25 "Conservatism" was thus the best description for the government's policy for economic development from 1952 to 1954. No drastic socialist economic measure, other than the 1952 first Land Reform Law, was undertaken. The year of 1955 marked a turning point in the previous conservative trend. A number of factors led the government to engage in deficit financing and develop a large balance of payment deficit. Among these factors, the following were most important: 1. The government's hopes that the average standard of living could be improved were frustrated by the rapid rate of population growth,29 and the argument for a "more effective" government role in economic development began to win ground. 2. The increased demand for public expenditures was also responsible for the creation of deficits in the government budget. National Production; and The Supreme Council for Social Services. 29It is not possible to compare Egypt's national income for the years before and after 1954 due to change in methods of estimation since that year. (The available figures show 0.7 per cent and 6 per cent increases in national income for the years 1953 and 1954 respectively.) The rate of population growth was 2.5 per cent and 2.2 per cent for those two years. See National Bank of Egypt, Economic Bulletin, Vol. XVII, No. 1, 1964, p. 29. 26 3. The political crisis of the Suez war put a heavy strain on the balance of payments. Together with the severe setback effect on Egypt's exports, import prices increased, and the value of the Egyptian pound abroad deteriorated. The net result was a reversal of 1954's small balance of payment surplus to a large deficit throughout the period 1955-1957. The Suez war had an even more positive and direct effect on the emergence of the public sector as a major power in business activities. <The nationalization of numerous French and British business in Egypt, for the most part banks and insurance companies, came as a direct reac tion to the war, and was followed by the establishment of the Economic Development Organization to manage the govern ment's business interests. Nationalization and the formation of a major public sector paved the road for a big push towards socialism, increased the attractiveness of the method of central plan ning, and led to the introduction of an industrial five- year plan at the close of 1957. Events connected with the establishment of the United Arab Republic (Syria-Egypt), culminated in 1958, slowed Egypt's proj'ected pace of economic development to some extent. However the period 1957-1960 was generally marked by a considerable economic improvement, due to both 27 the industrialization drive and favorable agricultural conditions.30 The "Inevitability of the Socialist Solution” (1960---)^ An independent path.--Having settled on a "social- ist pattern" for the country, Egyptian leaders always em phasize that such a conclusion is the independent outcome of the practical necessities and specific conditions and circumstances of the country, and is by no means a blind imitation or application of others’ experiences. "The need for a new road . . . arises from the fact that the Arab Revolution is now facing new circumstances; therefore, demanding more suitable solutions; (it) cannot afford to copy what others have achieved."32 Egyptian leaders do not, however, deny the inter dependence of nations’ experiences. "(We) must by no means deny (ourselves) access to the rich storehouse of experi 30It should be noticed, however, that when the July 1960 First Comprehensive Five-Year Plan was launched, about one-fourth of the previous industrial plan was not yet ful filled, and was included in the new comprehensive plan. 3^UAR Information Department, The Charter, p. 43. 32Ibid., pp. 12-13. See also President Abdel- Nasser’s speech, February 1965, at the Parliamentary Com- 28 ence gained by other striving peoples in their similar struggles. . . . Social experiences . . . are capable of passing from one place to another, but not of being blindly copied."33 Central Planning as a Method; w h y ? 3 4 Efficient socialist planning is the sole method which guarantees the use of all national resources . . . in a practical, scientific and humane way, aimed at realizing the common good of the masses, and ensuring a life of prosperity for them. Charter, p. 45. The decision to employ central planning for solving the country's economic problems was reached through several logical steps: (1) Before the individual citizen can be mittee meeting of the Arab Socialist Union. 33The Charter, op. cit. , pp. 14-15. 34 In addition to the policy of centralized plan ning, the government, plans to implement the principle of decentralization of plan execution through the application of the system of "Local Administration," and is making considerable efforts to push the system into an effective role. See UAR, INP, I. H. Abdel-Rahman, Memo No. 12, Plan Centralization and Execution Decentralization (Observations Concerning the General Economic Development Plan and Its Relation to Local Administration Organs), November 20, 1960. Also UAR, INP, I. H. Abdel-Rahman, Memo No. 48, Role of Local Societies in National Development, June 2, 1961. 29 politically free, he must first be helped to improve his economic standard of living. "The freedom of voting with out the freedom of earning a living and a guarantee to this freedom, (looses) all its value, and (becomes) a deceit, misleading the people."33 (2) To achieve this economic goal, two conditions must be present: a) Social justice must be available to all-- a guarantee of equal opportunity for all citizens. To this end, differences among individuals must be reduced to their mini mum limits through more equal distribution of income and wealth. b) The base of wealth must be widened through economic development, so that more equal distribution of income would be accompanied by higher average standard of living. The second condition is obviously the more critical and positive side of the solution. Its fulfillment, on the desired scale and at the desired speed, has been found to be possible only through central planning. The reasons are given as follows: 1. Central planning is the only means of channeling national efforts and resources in the right direction, in order to give the economy a fast "big push" toward the path of development. In other words, deliberate central planning is the only choice for the achievement of rapid growth 35The Charter, p. 35. 30 required to meet the country’s target of doubling national income every ten years. The private sector, particularly in underdeveloped countries, is not powerful or organized enough to carry out the job. 2. Social benefits and private benefits do not al ways coincide.36 For example: a) Major public utility projects, ’’collective goods,” which are of utmost importance for developments are usually not attractive to private business. b) Modern techniques would be unattractive to private business when their application means high replacement costs. But this attitude is inconsistent with society’s interests if the application of such modern techniques can in the long run achieve high levels of efficiency and economic perform ance . 3. The lack of harmony between private business plans is not conducive to a balance of needs and resources; the consequence is economic crises.3? 4. Provision of adequate work opportunities for the labor force requires a comprehensive plan for all economic activities. 36 See H. B. Chenery's "The Application of Invest ment Criteria," Quarterly Journal of Economics, February 1953, pp. 76-96; and A., E. Kahn's "Investment Criteria in Development Programs," Quarterly Journal of Economics, February 1951, pp. 38-61. 37 See B. A. Balassa's The Hungarian Experience in Economic Planning (New Haven: Yale University Press, 1959), pp. 9-10. 31 5. The reduction of income inequalities cannot be left to the conscience of private business and the wealthy class. O Q 6. The "telescopic faculty" (the fact that pri vate savers are unable to size up their future satisfactions from future goods) necessitates reliance on centrally-planned decisions, in order to accumulate savings to provide needed amounts of domestic capital. The Socialist Drive The First Five-Year Plan: Goals The battle of production is the true challenge in which the Arab man will justify his worthy position under the sun. Charter, p. 53. Finally, the early questions found definite answers. Production--increased production and its rate of growth--is the challenge, and central planning is the way to meet it. Being sure of both the goal and the method, the next logical step must be action. The first comprehensive plan for economic and social development was launched on July 1, 1960, marking the starting point in the application of central planning in Egypt and the 38 A. C. Pigou, The Economics of Welfare (London: Macmillan, 1932), p. 26. 32 economy’s radical transformation into socialism. The Plan was framed on the basis of certain major targets: 1. To achieve an average growth rate of the national product which would exceed the rate of population growth. Specifically, the national income was to be doubled in ten years (1960-1970). Forty per cent of the planned increase was assigned to the First Five-Year Plan (1 9 6 0 -1 9 6 5 ).39 2. To free the economy from its traditional rigid agricultural structure,40 and to establish a structure compatible with the goals of economic development and rapid growth. Such a target necessitated an increase in the role and impor tance of the industrial sector and other non-raw material-producing sectors.41 This new emphasis on industry can be seen in Tables I and II, which illustrate the comparative role of different eco nomic sectors in production and value added tar gets, and the relative importance given to each of them in terms of investment allocation. 3. At the same time, the plan aims at a comprehen sive agricultural expansion and development, in harmony with other sectors of the economy. This goal was found to require an increase in both average land productivity and in cultivated area (i.e., "vertical" and "horizontal" expansions). 39see Government of the UAR, Five-Year Plan, Cairo, 1960. 40See UAR, INP, E. E. Hammam, Memo No. 169, Our Plan for Agriculture, Part I, March 31, 1962. 41UAR, INP, I. H. Abdel-Rahman and N. Deif, Memo No. 76, The Social Aspects of Development Planning in UAR, November 3, 1961, pp. 1-2. 33 TABLE I PLANNED PERCENTAGE INCREASE IN PRODUCTION AND IN VALUE ADDED IN 1964-1965, IN RELATION TO 1959-1960a Sector Planned Percentage Increase in Total Production Planned Percentage Increase in Value Added Agr iculture 28.2 28.0 Industry 65.8 97.8 Construction 6.1 1.9 Services 25.2 24.2 Total 42.6 40.0 Government of the UAR, Five-Year Plan, Cairo,1960, p. 46. 34 TABLE II PLANNED DISTRIBUTION OF INVESTMENT BY SECTOR3 (In -L.E.M. ) Sector 1960/1965 Per Cent 1965/70 Per Cent Agriculture, Irri gation and Drain age 392.0 24.9 412.0 23.9 Industry and Electricity 578.7 36.7 555.0 32.0 Services 111.0 7.0 160.0 9.0 Transportation and Communication, Housing and Pub lic Utilities 495.2 31.4 590.0 35.1 Total 1576.9 lOO 1717.0 lOO Government of the UAR, Five-Year Plan, Cairo, 1960, p. 18. Percentages are ours. 35 (The agricultural sector, though not expected to retain its dominant position, will continue to be important in the expanding economy. More over , the government wishes to be fair to the rural population by including them in the over all development drive.) 4. The fourth major goal of the Plan is to free the economy from excessive dependence on foreign products by accelerating the pace of industriali zation, changing the composition of imports and e x p o r t s ,42 and establishing the proper pattern for the country's foreign trade. Within the framework of the above four major tar gets, further decisions and conclusions have been reached on specific economic questions; most important of which are those concerning the decision on the leading sector, the agricultural, industrial, and employment plans, and the question of consumption versus investment goods. We shall devote a few brief words to each of these five issues. The First Five-Year Plan; Strategic Decisions The leading sector.--Egyptian planners have agreed that the public sector--"being the one owned by the peo ple"- -must take the lead. However, such a "subjective" 42see UAR,INP, Abdel-Rahman, Memo No. 238, Compre hensive Economic Planning in the UAR, September 23, 1962, p. 5. 36 statement is useful only in justifying actions such as massive nationalization and central planning which are apt to strengthen the public sector. But since these actions have already been taken, the relevant justification for the public sector’s lead is that such is the logical and expected outcome under existing conditions. Whatever the justification may be, the public sector’s prominence means that it has to bear the major burden in the achievement of the goals of the P l a n . Agriculture.--Two types of agricultural expansion are planned for the ten-year period--1960-1970. They are: 1. In the First Five-Year Plan (1960-1965), vertical expansion of agricultural production, where investment assigned for this purpose amounts to L.E.57 m. y e a r l y , 44 is to be carried to its opti mum level, but "without exerting pressure on the farmers and their limited r e s o u r c e s . "45 2. Horizontal expansion (which is associated with irrigation, drainage, and High Dam projects) is 43uaR, INP, M. M. El-Imam, Memo No. 201, Prepara tion of the General Framework of the Plan (Arabic), July 10, 1962, pp. 50-52. 44 UAR, INP, Hammam, op. cit., p. 8. 45uAR, INP, I. H. Abdel-Rahman, Memo No. 238, Com prehensive Economic Planning in the UAR, September 23, 1962, pp. 3-4. For figures on the distribution of funds among 37 to start in the second Five-Year Plan, "when land productivity will have been carried to its optimum level" in the First Five-Year Plan. Industry.--As we have seen, the UAR development plans have been based on the conclusion that industry, due to its progressive and dynamic nature as compared to that of agriculture, is the only road to economic development and continuous progress. "Industry is the strong support of the national build-up. . . . it is capable of enlarging the production base in a revolutionary and decisive manner, and in a very short time. . . . Our approach to industry must be deliberate. . . ."46 Industrial expansion, however, necessitates two major requirements to be met as follows: 1. Fixed capital--to be provided through foreign loans (these amount to -L.E.646 m., out of total investment requirements of -E.E.1576.9 m. in the First Five-Year Plan, and-L.E.549 m., out of total investment requirements of -E.E.1717 m. in the Second Five-Year Plan), domestic savings,47 and mobilization of the country's exports for the importation of needed equipment and machinery. specific projects of vertical expansion, see UAR, INP, Hammam, op. cit., p. 8. The Charter, p. 57. ^See UAR, INP, Abdel-Rahman, Memo No. 238, op. cit. pp. 8-10. 38 2. Working capital a) Skills--in the beginning, the plan is to rely mainly on foreign experts and technicians, while at the same time carrying out large- scale programs to train both workers and experts, at home and abroad, so that self- sufficiency can gradually be achieved. b) Raw materials--to adequately meet the needs for raw materials, the Plan stresses the need to expand extracting industries and import materials unavailable domestically. c) Energy--the critical importance of this factor for successful industrialization has led to special attention to the develop ment of electric power. Investment goods versus consumers1 goods.--In order to establish a solid industrial base, the Plan stresses the necessity of expanding investment goods industries. However, consumers' goods are by no means neglected. The Plan included sizeable expansion in their production.^® Heavy industry no doubt provides the solid founda tion for the gigantic industrial set-up. . . . Yet . . . it must not hamper the progress of consumer industries. The mass of our people have long been deprived; to mobilize them completely for . . . build ing . . . heavy industry and overlook their consumer needs is incompatible with their established right to make up for their long deprivation.49 4®See UAR, INP, F. R. Fahmi, Memo No. 386, Growth Pattern of Manufacturing Sector in Egypt (1950-1970), pp. 7-8 and Tables I, II, and III. 49The Charter, p . 58. 39 Employment.--In stressing the necessity of en larging the economy's productive capacity, the Plan's ulti mate goal is obviously to improve the average citizen's standard of living and to raise the level of employment of the labor force. At present, there is much more labor on land than is actually needed.Since the goal for agricultural development during the First Five-Year Plan centers on vertical expansion, agricultural real employment is not expected to increase significantly during this period. Not until the horizontal expansion stage begins during the Second Five-Year Plan will the increased cultivable area provide more jobs for peasants, and thus absorb part of the excess agricultural labor. Furthermore, the increase in employment resulting from industrialization will be relatively small because of the capital-intensive nature of modern industry. In other words, no solution to the labor problem ^See UAR, INP, M. M. El-Imam, Memo No. 201, Prepa ration of the Framework of the Plan (Arabic), June 10, 1962, pp. 49-50. 51UAR, INP, I. H. Abdel-Rahman, Memo No. 296, Man power Planning in the UAR, May 15, 1963, pp. 2-4. 40 outside the countryside can be predicted for the foresee able future.^ Table III shows the estimates for the per centage distributions of employment per sector, and the percentages of total employment to total population at the end of the First and the Second Five-Year Plans respec tively, as compared to the figures of the base year (1959/ 1960). The July 1961 Socialist Laws Central planning and the introduction of the First Five-Year Plan was not the only mark of socialist trans formation in Egypt. An equally important event was the passage of socialist laws initiated February 1960 with wide-scale nationalizations, putting the major part of business activities into the hands of the government. With the declaration of the July 1961 Laws, a major proportion of Egypt's business was wholly or par tially nationalized. The government took over all import trade, and monopolized cotton and other important export trades. A new land reform law was introduced, reducing maximum holdings from 200 feddans per owner to 100 feddans 52xhe Charter, p. 56. 41 TABLE III PERCENTAGE DISTRIBUTIONS OF EMPLOYMENT PER SECTOR AND PERCENTAGES OF EMPLOYMENT TO TOTAL POPULATION21 Sector 1959/60 1964/65 1969 Agriculture 54.3 54.3 49.9 Industry 10.6 12.1 11.7 Construction 2.8 2.3 2.5 Sectors ’’ Supporting the Economic Structure”*3 8.4 7.9 7.9 Commerce 10.6 10.4 11.9 Services 13.3 13.0 16.1 Total 100.0 100.0 100.0 Per Cent of Total Employ ment to Total Population 23.5 24.7 28.2 Government of the UAR, Five-Year Plan, Cairo, 1960 p. 77. ^These include housing, public utilities, trans portation and communication, defense, police, justice, and administrative governmental services. 42 per family. Incomes of more than E.E.10,000 per year were sub jected to a new progressive income tax rate of 90 per cent. Maximum salary from any fir,m or organization was limited to t.E.5,000 per year. Workers' benefits were beyond their aspirations. Probably the most drastic of all was that workers and employees were given the right to elect representatives from among themselves to participate in their firms' boards of management, and to share in 25 per cent of their establishments' net distributed profits. "Two basic aims" for the July 1961 laws are given by the National Charter 1. The creation of some form of economic equality among the citizens . . . , and . . . to . . . (dissolve) . . . class distinctions in a way that . . . paves the way for democratic solu tions to the major problems confronting the process of development. 2. . . . to step up the efficiency of the public sector . . ., to consolidate its capacity to shoulder the responsibility of planning and to enable it to play its leading role in industrial development on a socialist basis. 53Ibid., p. 60. 43 PROSPECTS AND POTENTIALITIES OF THE UAR ECONOMY: A COMMENT After the above survey of UAR planners' attitudes towards the country's economic problems, we shall base the following comments on the general aspects of existing economic conditions and policy inclinations. The first fact that we must emphasize here is that the economic problems which face countries like the UAR have their roots deep in the sociological, cultural, and traditional makeup of the society. These environmental conditions interact with the country's economic retarda tion to perpetuate all aspects of her backwardness. In other words, existing conditions cannot autonomously pro vide a way out from within. The solution must be delib erately imposed by a new and powerful outside force--an organized, comprehensive drive for economic, social, and cultural change. And this is the most important role to be played by central planning. The effectiveness of central planning is greater-- the less the obstacles and difficulties presented by the economic and social environment. No successful develop ment program can rely solely on centralized directives, 44 rules, plans and orders. Indeed, positive public partici pation is crucial; it makes the organizational system within which the central plan is to be carried out run smoothly and effectively. To wit, the success and effectiveness of central planning in achieving development goals depend on two main factors: the role of the environment and policy decisions. We shall attempt a brief evaluation of the UAR case in the light of these two issues. Role of the Environment Structure and Attitudes No serious effort for economic development can be initiated and maintained in a vacuum. It must be accom panied, to some degree or another, by harmonious and smooth communication between the directives and instructions of the planners and the reactions and attitudes of the public who constitute the effective members of the economic, cul tural, and sociological environment. A prerequisite to that is the capability and willingness of the environment to rise up to the developmental goals set by the central planners. Indeed the necessity of meeting this condition is the real impasse that faces developing nations today. 45 Together with pure economic targets, the planners must give equal initial attention to issues such as education and health standards, population growth, and saving habits. In the case of the UAR, noticeable efforts have been devoted to the social aspect of economic development especially in the field of education. However, the popu lation problem still represents the greatest threat and handicap to the country's economic efforts, and no per sistent, serious drive has ever been made to slow the rising population tide which in itself is likely to thwart the UAR's hopes for future economic progress. Business mentality and the attitude of the general public towards savings represent another point of weakness. The average Egyptian citizen has always shown a high ten dency to spend. Household savings are ordinarily aimed at buying durable consumers' goods in the near future, rather than investing in shares or small business activi ties. This phenomenon is unlikely to change autonomously. Nothing less than strict control of consumption pattern by central authorities will lead to any reasonable accumu lation of domestic savings.^ 5^In spite of an increase of about 34 per cent in 46 Egyptian private capital also tends to prefer investment in buildings rather than commercial or indus trial activities. This attitude cannot be defended through claims that it is due to lack of confidence as a result of the socialist measures that have swept the business sector since 1961. This attitude on the part of private capital is nothing new; it was born long before 1961. Moreover, socialist measures (such as rent limitations) have equally reached the construction sector and still it retains its traditional relative attractiveness to private capital. Motivational Systems The UAR socialist system does not abolish private economic activity, private ownership, or income inequal ities, which are necessary for the encouragement of self- interest motivation. It is true that to some extent, certain private initiative has been discouraged by recent socialist national income during the period from 1960 to 1964, the percentage of domestic savings to national income remained constant. See El-Kaisoni, A., Deputy Premier for Financial and Economic Affairs, A Report to the National Assembly on the New Budget, 1965, (an "undated" reprint, in Arabic, by the United Arab Republic Education Bureau, Washington, D.C.) p. 4. 47 changes but this loss is actually of no significance. The changes affected a small minority of capitalists, among whom an even smaller minority were engaged in industrial activities. Moreover, this part has been more than com pensated for by government projects. The greater propor tion of the now estranged capital went to land investments, construction activities, spending in foreign countries, and luxury imports, none of which satisfied the country’s crucial investment needs. The discouragement of this group may therefore be deemed a net economic gain. In the major government-owned establishments, one might well expect to encounter the motivational weaknesses (e.g., bureaucracy, apathy, favoritism, and so on) that are usually attributed to the very nature of centrally planned patterns. However, in view of the fact that in countries like the UAR, private business activities and motives have proved not to be capable of achieving eco nomic development, the motivational disadvantages under central planning are likely to be less costly than simple acceptance of the original state of backwardness and eco nomic stagnation. Moreover, these very disadvantages are equally likely to characterize the huge private enterprise com- 48 plexes (in which private profit motivation, in its classic sense, no longer plays a significant role) which are apt to develop in any free market economy that reaches an advanced stage of economic progress. As for the system of workers and employees profit sharing in the UAR, it would prove a hasty and short sighted attitude to confine the appraisal of its future effect to the apparent role of its monetary motivational nature. The fact that, as will be repeated later, the central planners’ choice will not necessarily be guided by the projects’ expected profitability makes inadequate any generalized application of the profit sharing method. In some cases, where the planner selects a project whose returns are certainly expected to be more or less below its high costs, a proper success indicator should be estab lished according to the expected margin of loss. However, even after taking such a realistic attitude, we may still face other difficulties due to plan revisions, such that the initial norm of success--determined by the original planned margin of loss or profit--may no longer be appro priate. To sum up, the application of profit sharing methods without due consideration to the above mentioned 49 difficulties would only give a distorted picture of the economy’s actual economic ability and performance. Policy Decision Economic Structure The UAR central planners* approach to the main productive sectors seems to be the only reasonable one, in view of Egypt's problems and economic conditions: 1. Egypt's agricultural production used to consti tute the main source of national income. As a result, the economy has always been exposed to all the vulnerabilities (e.g., economic in stability, social backwardness, weakness of business and industrial attitudes, et cetera) that usually characterize rural, agricultural economic structures. 2. Moreover, arable land has been exploited to capacity and there is no significant potential in increasing total agricultural output by raising what is already one of the world's highest land productivities . 3. The rapid population increase has already pro duced a tremendous oversupply of agricultural labor, and pressure on rural areas will con tinue to increase as long as there are no employment opportunities outside the agricul tural sector. Furthermore, if the present D. Warriner, Land Reform and Development in the Middle East (A Study of Egypt, Syria, and Iraq) (London, New York: Royal Institute of International Affairs, 1957), p. 19. 50 high rate of population growth--2.3 per cent-- continues, the new arable land which will be added by the High Dam project is likely to be more than absorbed by population increase, so that the problem of surplus agricultural labor will remain unsolved. In other words, the agricultural sector cannot provide the solution to Egypt’s problem of unemployment and economic retardation. Thus, the UAR policy emphasizing the necessity for industrialization seems to be consistent with the country's major problems and economic conditions. However, the present tendency to adopt mainly capital intensive techniques will not provide a solution for unemployment in the near future. Not before the next industrial expan sionary stage, which is expected to follow the initial stage of establishing basic industries, will considerable new work opportunities be created in the industrial sector. And even at that time, assuming that the present pace of population growth continues, the country may still face the same question: Are the existing employment opportuni ties enough? In summary, there are two major weaknesses in the present UAR economic policy: 1. Industrialization, as stressed by the planning authorities, is no doubt an indispensable and urgent necessity for the development of the UAR economy. Yet, in addition to capital intensive 51 industries, due consideration should also be given to labor intensive ones. A potentially successful approach could be a long-run program for a carefully planned and co-ordinated nation wide spread of small and very specialized rural labor-intensive factories. The generation of hydro-electric power from the High Dam will provide, at tremendous cost advantage, ample power that could be economically used to drive simple equipment in such rural factories. The high degree of labor specialization would also facilitate, without need for costly technical training programs, an efficient utilization of the rural workers' low-level industrial skills. 2. The problem that frustrates all hopes for eco nomic progress, and will continue to do so, is the high rate of population growth. Ignoring the solution to this problem and concentrating only on economic programs for development and industrialization, is like attempting to blow up a torn balloon. Time Preference: Consumption versus Investment Goods As we saw earlier, the National Charter's explana tion (page 58) of the Egyptian planners' approach to indus trialization is reasonably realistic, logical, and humani tarian : Heavy industry no doubt provides the solid founda tion for . . . the industrial set-up. Yet, . . . it must not hamper the progress of consumer industries. . . . The masses of our people have long been de prived, . . . (they have an) established right to make up for their long deprivation .... At least during the initial stages of economic development, the logical, realistic, and humanitarian measures (those that would make up for the "long depriva tion" of the masses of the people) would be to increase the supply and availability of consumer goods which meet their necessary needs. For a population the majority of which live for so long at subsistence levels, the defini tion of "provision of necessities" might reasonably encom pass better health measures, free education, proper housing facilities, extension of electricity and purified water to rural areas, and reasonable expansion of necessary consump tion goods such as foodstuffs and clothing. But to carry out the interpretation of the Charter’s statement as far as to bring domestically manufactured consumer's durables within easy reach of the average-income citizen (through very easy installment arrangements) is quite inconsistent with the desire to establish a sound industrial expansion that would promise, and guarantee, future development and economic growth. A country like Egypt, with all its economic prob lems and difficulties (paramount among which is the scarc ity of capital), can by no miracle achieve its development goals while starting with an expansion in the consumption of durables that are--by that country's average standard of living--nothing less than luxuries. 53 Fortunately, this weakness has now been recognized by the UAR planners, and the trend is likely to be cor rected in the Second Five-Year Plan (1965-1970). Probably the best thing about this experience is the hope that it would be a step ahead to economic development, along the indispensable path of trial-and-error. CHAPTER III RISK UNDER CENTRAJL PLANNING In the previous chapter, we presented an overall picture for the UAR economy, with special emphasis on its recent experience in the field of central planning. In the concluding part of that chapter--the com ment- -it was made clear that the results and achievements of economic planning are a direct outcome of policy deci sions and the criteria adopted by the planners in their attempts to provide adequate economic solutions. One interesting method for economic planning is that advocated by Professor Gerhard Tintner and which accounts for the phenomenon of risk in connection with situations of central planning. Our purpose is to apply this method to the UAR case, and to attempt to evaluate its adequacy for guiding policy makers in centrally-planned developing nations. The present chapter attempts to provide a theoret ical introduction to the empirical work which follows in Chapter IV, the result of which will then be used in the 54 55 final chapter to evaluate the role and significance of risk under conditions of central planning. As far as the term "risk'' is concerned, we simply want to show that, in its established economic definition, this phenomenon is not confined to economic decision-making under independent atomistic plans of market system. Its role and effect in a centrally-planned economy could be equally important and significant as far as economic per formance of the system is concerned. The subject under consideration falls within the vast boundaries of what may be called "economic failures”- 1 ' under dynamic economic systems; i.e., under cases which involve planning for future periods of time, irrespective of what may be the particular type of economic system under discussion. Within this point of view of the phenomenon of risk, our limited concern excludes market systems and in corporates only the centrally-planned systems which have "TDhe term is an analogy to the one used by F. M. Bator in his article, "The Anatomy of Market Failure," published in the Quarterly Journal of Economics, (August 1958) which singles out some aspects of economic failures under market systems. 56 recently been gaining an increasing appeal to many "devel oping”^ nations as the most promising method of achieving rapid solutions to their economic problems. However, due to the long-established, tradition among economists of connecting the concept of risk with the market system, let us first look briefly at the main argument on the effects of "risk" on the economic outcome of the market system. Then the same question will be raised in connection with centrally-planned, economies. The Term "Risk" Defined. "Risk" is a phenomenon which arises in non-static systems.^ To make this statement clearer, we should, first go back to Professor Hicks' classification of economic sys tems, namely: 2 See definition in Chapter I, p. 5. 3 G. Tintner, Methodology of Mathematical Economics and Econometrics (First Draft), pp. 50-69; "A Contribution to the Non-Static Theory of Choice," Quarterly Journal of Economics, Vol. 56, (1942), pp. 274-306; "The Theory of Production Under Non-Static Conditions," Journal of Politi cal Economy, Vol. 50, pp. 645-667; "The Theory of Choice Under Subjective Risk and. Undercertainty," Econometrica, Vol. 9, (1941), pp. 298-304. 57 1 . Statics--"where we do not trouble about dating." 2. Dynamics--"where every quantity must be dated.."4 Professor Tintner proceeds from this start and. gives two other classifications for economic systems 1. Statics, in the definition of Hicks. 2. Non-statics, which, following Professor F. H. Knight,^1 he classifies into three sub-groups: a) Dynamics--in the sense of Hicks; i.e., single-valued anticipations. b) Risk--existence of a single known probabil ity distribution of anticipations. c) Uncertainty--existence of several possible probability distributions of anticipations, perhaps connected by an a priori probabil ity distribution.7 It has thus become customary since the publication of Knight's book to draw a line of distinction between "risk" and "uncertainty," where in the case of risk there 4 J. R. Hicks, Value and Capital (Oxford.: The Chalendon Press, 1939), p. 115. ^Tintner, op. cit. , pp. 32-69. 6 F. H. Knight, Risk, Uncertainty, and. Profit (Boston and New York: Houghton Mifflin Co., 1921) , re printed. by the London School of Economics, London, 1933. 7Tintner, op. cit. , p. 51. 58 is available an adequate number of previous cases which enable us to calculate the probabilities of various possi ble outcomes. On the other hand, uncertainty exists when we can base our expectations only on our own experience, intuition, and guesswork. In other words, it is that situation in which no objective estimate--on the basis of past experience--can be made for future events. Risk and the Market System’s Performance In a private enterprise system, the effect of risk on economic outcomes can be seen through the attitude of the individual decision maker (the entrepreneur). The possibility of computing the probability dis tributions and their characteristics (e.g., means, vari ances, et cetera) for alternative long-run investment policies, give the businessman an allowance of choice. His personal attitudes, preferences, and psychology deter mine what specific future policy he may follow. Regardless of what this specific choice may be, the important thing is that it will always hold true that the consideration of risk allowance as a future discount factor when planning for long-run investment activities will always shorten the economic horizons of his future plans. This could mean 59 the unattractiveness of major long-run investment projects to the private businessman.® The fact that future decision-making requires anticipations and involves a certain margin of error or another (risk) is the basis of many economists’ arguments against the efficiency of the market system’s economic performance 1. That private business, with its limited resources (as compared to those of central planning organs) and limited accessibility to necessary informa tion, would shy away from undertaking certain long-run investment projects that are of vital importance to the economy. 2. The lack of coordination among individual busi ness plans would, lead, to conflicting require ments and. decisions, economic instability, and. waste of resources. Besides pointing out these weaknesses, it has also been customary to suggest that a solution exists in cen- g See R. H. Hicks, op. cit., chapter x; and. M. Kalecki, "The Principle of Increasing Risk," Economica, November 1937, pp. 440-447. ^See for example, T. Scitovsky's Welfare and Com petition, chapter x, (1951); Kalecki, op. cit.; M. Ezekeil, "The Cobweb Theorem," Quarterly Journal of Economics, Feb ruary 1938; N. Buchanan, "A Reconsideration of the Cobweb Theorem," Journal of Political Economy, February 1939, pp. 67-81; A. Alchian, "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, (1950), pp. 211-221. 60 tralized economic systems:^ that enough information on the whole picture of business activities would be available and no plan conflicts would arise. In other words, the central planning agency would have all the requirements for the "optimum" future plan which would, therefore lead, to the "optimum" outcome, without the risk of facing unexpected situations that might conflict with or slow down the planned, course of economic activities. While we accept the criticisms directed, to the market system regarding the effect of "risk" on its final economic performance, we do not accept the optimistic con clusion which implies that "risk" and. its adverse effects ■ 1 ‘0The most important ideas along these lines have been presented by the works of E. Heimann, Mehrwert k und Gemeinwirtschaft (Berlin: H. R. Engelmann, 1922); Sozialistische Wirtschafts-und. Arbeitsordnung (Potsdam: Alfred. Prott, 1932); F. M. Taylor, "The Guidance of Produc tion in a Socialist State," a presidential address to the American Economic Association in 1928, reprinted, in On the Economic Theory of Socialism, Benjamin Lippincott (ed.), (Minneapolis: University of Minnesota Press, 1938); H. D. Dickinspn, "Price Formation in a Socialist Communijty," The Economic Journal, XLIII (June 1933); Economics of Social ism (London: Oxford University Press, 1939); O. Lange, "On the Economic Theory of Socialism," in Benjamin Lippincott, (ed.) On the Economic Theory of Socialism (Minneapolis: University of Minnesota Press, 1938). Also in Review of Economic Studies, IV, No.l, (October 1936), IV, No.2, (Feb ruary 1937); A. P. Lerner, "Economic Theory and. Socialist Economy," Review of Economics Studies, II (October 1934); The Economics of Control (New York: Macmillan, 1944). 61 on economic outcomes would have no place in a centrally planned economy. Risk is not confined to the market sys tems. Even with the guarantee of plan coordination and the availability of the "maximum possible" amount of infor mation, risk--as defined above--cannot be ruled out of the sphere of centralized economic planning. PLAN UNDERFULFILLMENT IN CENTRALLY PLANNED SYSTEMS The experiences of many countries in the field of central planning provide ample evidence of deviation of plan achievements from original targets. Such deviations have, in many cases, been in the form of underfulfillment of plan targets; a fact that has two important implica tions : 1. That centralized systems, though could be superior to market systems in plan coordination and avail ability of information, may not achieve the as pired level of perfection as far as future expec tations and targets are concerned. 2. The sign of this imperfection is to be found in plan underfulfillment, a phenomenon which must be due to causes inherent in the system itself. One of these causes, as we shall see later, is a typical "risk" situation. Errors in plan fulfillment.--Under centralized sys- 62 terns where the plan covers a number of time periods, plan underfulfillment is represented by the margin of error between plan targets and plan achievements. Such a dis crepancy reflects the imperfection of predictions, even when the "maximum possible" amount of information is available to the central planner. Needless to say, the discrepancy between plan achievement and target does not necessarily mean that the error must be always of a nega tive sign. Cases of overfulfillment could also be found in empirical cases of central planning. Nevertheless, overfulfillments are more likely to occur in partial plans, rather than in the central plan as a whole. In such cases, we may consider the margin of "negative error" as a sort of "windfall social gain. At the same time, we identify plan underfulfillment as a "positive error." The use of these terms is based on the following simplifying assump tions : 1. The central planner (or central planning agency) is thought of as an efficient and experienced -^This is in the sense that it is caused by factors behind man's control, such as favorable weather conditions and on the assumption that an overfulfillment in a certain partial plan does not occur at the expense of underfulfill ment somewhere else. 63 entrepreneur who wants to achieve maximum output with a given amount of input. 1 2 2. We also take the planner’s preference for granted as if it always reflects the "most rational choice" for the society as a whole. 3. The case of plan underfulfillment (i.e., positive errors) is our present concern. Stressing this type of error is not merely a typical economist's pessimistic attitude. More important is that since our previous assumptions were that the most favorable conditions are available to the central planner, he would be expected to formulate the optimum plan whose targets, if achieved, would be the optimum results. Therefore, underfulfill ment, rather than overfulfillment, would be more likely to occur. Causes of Plan Underfulfillment Plan underfulfillment in centrally-planned systems generally stems from two factors: Imperfect conditions of plan execution.--These con ditions could be imperfect in the sense of being more or less unfavorable so that they adversely affect the stand ards of target achievements. Such unfavorable conditions could arise in the form of new random elements due to the nature of the system of central planning itself. Most im portant among these elements are: I Q In other words, we mean strictly "technical effi ciency," avoiding the complications of getting into the distinction between it and "economic efficiency." 64 1. Organizational factors--the organizational set up of the system of planning may not be well- suited. for the particular situation.13 Such a disparity would, result in malperformance, delays and wastes at different levels and. in various aspects of plan execution (e.g., production processes, systems of supervision and. control, plan coordination, et cetera). 2. Human factors--the motivations and reactions of people to situations, systems, or rules have an important bearing on the implementation of those systems or rules. If those asked, to carry out the plan react negatively (e.g., with dissatis faction or resistence), or even if they are neutral (e.g., careless or indifferent), or any mixture of both, the plan cannot be executed, as smoothly and efficiently as projected.14 13A suitable example could, be found, in the 1957 reform of the Russian system of industrial planning. The autarky of the old. ministerial system--which dated back to 1932--proved to be inadequate for the development of new regions and the provision of proper coordinating authority in the face of the growing complexity of the industrial structure. Therefore, a switch to a new system based, on territorial principle (regional economic planning councils "Sovnorkhozy") was found, to be more suitable to the new situation. This, however, is not, and will not be, the last in the series of* organizational changes in search for adequate conditions of plan execution. See O. Hoeffding, ”The Soviet Industrial Reorganization of 1957,” American Economic Review (Proceedings), XLIX, No. 2 (1959), pp. 65- 77; P. J. D. Wiles, ”Rationality, the Market, Decentraliza tion and. the Territorial Principle,” Value and. Plan, G. Grossman (ed..), (University of California Press, 1960), pp. 184-203; M. Kaser, ”The Reorganization of Soviet Industry and Its Effect on Decision Making,” Value and Plan, pp. 213-234; A. Nove, The Soviet Economy (New York: Preager University Series, 1961), chapter ii. 14 Probably one of the best examples here is the 65 Risk.--Under central planning, information needed for predictions could be made more abundant than in a mar ket system but it is never perfect or complete. Thus, predictions could be more accurate, but the actual behavior of variables in the future remains to be seen. Risk of faulty expectations can never be ruled out. Through our explanation of plan underfulfillment in terms of the above two main reasons, we have attempted to show that "positive errors" under central planning need not be wholly due to cases of risk. Risk is identified only when available data from past experience enables the Yugoslav agricultural experience which started under Tito’s regime in 1945 by a strong drive towards a Russian-style collectivization system. The resistence of the farmers forced the government in 1953 to adopt a completely differ ent agricultural system based on voluntary cooperation and private ownership of land, that would be acceptable to the peasants and, therefore, more favorable to the achievement of agricultural targets. See G. Hoffman and F. Neal, Yugoslavia and the New Communism (New York: Twentieth Century Fund, 1962), pp. 113-173 and pp. 265-298; Royal Institute of International Affairs, The Soviet-Yugoslav Dispute (London: Oxford Uni versity Press, 1948); D. Warriner, Revolution in Eastern Europe (London: Turnstile Press, 1950); E. Ames, Economic Development in Yugoslavia, a memo, of Seminar notes, Decem ber 10, 1954, Russian Research Center, Harvard University; J. Tomasevich, Peasants, Politics and Economic Change in Yugoslavia (Palo Alto: Stanford University Press, 1955). 66 planner to make an approximate calculation of the varia bles1 future values. But this is possible only when we deal with calculable variables such as prices, quantities, values of technical coefficients, et cetera. But the factors which represent "imperfection in the conditions of plan execution" are uncalculable 'random variables.' There is no way to obtain approximate numerical estimates for their behavior in the future. Therefore, it would be more accurate to classify these "conditions of imperfec tion" as factors of uncertainty rather than risk. All we can do about them when planning for the future is to rely on our own value judgments, intuition, and guesswork. Risk in Central Planning We have seen that risk is one of the factors that could be responsible for plan underfulfillment. The reason is that target-setting in dynamic central planning requires estimation of the future values of quantitative variables. These estimates are based on samples from the past, and may not coincide with the actual values of the variables in the future. Such deviations affect the level of plan achievement. For example, an overestimation of future values of average productivities of factors of production 67 may lead to the setting of targets that cannot be actually fulfilled. This case of risk is what we shall empirically examine in detail in the following chapter. The subject of the study is taken from the UAR's first experience in the field of central planning: The First Comprehensive Five-Year Plan (1960-1965). The example shows a dynamic situation in which "estimates" based on scarce data are used for future expectations and calculations of what would be the final plan achievement levels. The random variables are the technical coefficients of production, where the different levels of plan achieve ments under different allocational policies of factors of production are caused by preassumed deviations of the co efficients from their average estimates that would be used in setting the targets if the coefficients were considered as fixed values rather than random variables. Under a given allocational policy, the absolute margin of risk is represented by the difference between the expected mean value of plan achievement and the value of its 5 per cent lower probability point. The relative margin of risk is the percentage of the value of the absolute margin of risk to the expected mean value of the given allocational policy. 68 The method used--Stochastic Linear Programming-- follows closely a previous treatment by Professor Tintner of an Indian case.^ However, the scopes and dimensions of the two cases are not identical. Professor Tintner's example uses one factor of production--capital--and two types of industries--consumer goods and investment goods industries. Thus, for Professor Tintner's example, the technical coefficients are two: output-capital ratio in consumption industries and output-capital ratio in invest ment industries. In the present case we have two sectors (agricul tural sector and industrial sector) and two productive factors to be allocated among them (capital and labor). Thus, our technical coefficients are four: output-labor ratio in agricultural sector; output-labor ratio in industrial sector; output-capital ratio in agricultural sector; and output-capital ratio in industrial sector. There are two reasons for choosing these two sec tors and two factors of production for the present study: "^G. Tintner, The Econometrics of Development and Planning (First Draft), pp. 631-646. 69 1. In attempting to achieve the country's goals tor economic development the UAR planners put the main emphasis on the necessity of changing the structure of the economy from its predominantly agricultural pattern into an industrial one. At the same time, they do not underestimate the importance of agricultural production, both as a considerable source of national income and foreign exchange, and as an increasingly impor tant source for the requirements of the growing industrial sector. As a result, the target of doubling national income in ten years must be reached through both the development of a strong industrial sector and the optimum utilization of present and potential agricultural resources. 2. The question of sectoral development cannot be separated from that of the choice of investment criterion, where two factors of production basically shape the problem: scarce capital and abundant labor. The traditional argument for economizing in the use of the scarce factor and adopting labor-intensive methods weakens in the face of the planners* strong desire to achieve rapid initial growth through modern tech nology (mainly for basic industries), and to launch major long-run projects (such as the High Dam) which require intensive use of capital. At the same time, this last approach, though very appealing as far as the goal of rapid growth is concerned, does not provide the means, at least in the foreseeable future, of achieving the equally important goal of solving the serious problem of unemployment. These two questions, of sectoral development and of investment criteria, underline the dilemma that is the core of the problem facing the UAR in her recent persistent and vigorous drive for rapid economic growth. CHAPTER IV AN APPLICATION OF STOCHASTIC PROGRAMMING TO THE UAR: THE CASE OF RISK Statement of the Problem The involvement of random variables the values of which could be approximated on the basis of samples from the past, for use in future economic decisions, indicates that the expected economic performance is not a single sure value, but rather a number of them that fall within a certain range determined by the characteristics of the statistical distribution of the random elements. That is what we have identified as a situation of risk. In application to UAR data, the results of the present calculations for five different allocational pol icies that involve risk make it clear that the level of plan fulfillment may attain any of a multiplicity of final output values, each with a certain probability, and that the number of these values (i.e., the optimum solutions) rapidly multiplies as the system approaches reality; i.e., as it includes more sectors and more variables. 70 71 The present study illustrates this fact in the most simplified way, and attempts to use the results of the calculations to analyze and evaluate the allocational policy and the economic performance of the UAJR’s First Five-Year Plan (1960-1965) with respect to the agricultural and industrial sectors. In view of the tremendous complications and very lengthy steps of the applied method of the Stochastic process, we could make the subject manageable only by limiting the calculations to two sectors, rather than extending them to the whole economy. We arbitrarily assume five different allocational policies where the core of the problem is to calculate, under the specific assumptions of our model, the total maximum output that could be derived from both the agri cultural and industrial sectors at the end of the fifth year of the Plan; i.e., to maximize: + S 5 = W 5 where: Acj : is the value of agricultural output at the end of 1965. : is the value of industrial output at the end of 1965. W5 : is the value of total output of both sectors at the end of 1965. The final results are then contrasted and compared 72 with the achievements of the actual UAR policy. The Assumptions The numerical model used for the present work is based on three main assumptions: 1. Two factors of production are considered: a) Total labor force available for both sectors together over the Plan period. b) Total capital available for investment for the two sectors together, over the Plan period. 2. The output/input coefficients: b^l* ^°\2 ’ ^21* t>22 are assumed to be normally distributed random variables that could deviate from their preesti mated fixed values where: b n : Output/Labor ratio in the agricultural sector: (0 /LA ) b ^ 2 : Output/Capital ratio in the agricultural sector: (O/K^); and, * Output/Labor ratio in the industrial sector: (O/Lg) t*22 : Output/Capital ratio in the industrial sector: (O/Kg) This second assumption is made under another restrictive premise that the probability distribution of the technical coefficients is Known (case of technical 73 risk) 1 such that we can pre-estimate their possible values when they deviate from their fixed means. 3. A priori determination of sectoral allocation of factors of production; where each set of arbi trarily-determined values of each of: U-^, ui2 ’ U21> and U2 2 represents a certain allocational policy that is to be tested and evaluated on the basis of its final numerical results. Where: U n : is the percentage of labor devoted to agriculture each year; U 1 2 : is the percentage of labor devoted to industry each year; such that: Also: U11 + U12 = 1 U2i : is the percentage of capital devoted to agriculture each year; U2 2 ; is the percentage of capital devoted to industry each year; such that: U21 + U22 = X ^See G. Tintner, The Econometrics of Development and Planning (First Draft), pp. 618-628; "The Use of Sto chastic Linear Programming in Planning," Indian Economic Review, Vol. V, (1960), pp. 159-167. 74 Under these three basic assumptions, the final purpose is to determine the "best"^ allocation of the two factors of production among the two sectors over the plan years, so that W 5 is a maximum. The Data One of the major difficulties which face us in undertaking the present study is the scarcity of necessary data. Our sources are partly published figures of the UAR's First Five-Year Plan, and--to fill the gaps and make up for the deficiencies--partly our own estimates and cal culations, which we have to base on certain arbitrary assumptions due to lack of sufficient information. Published figures of the First Five-Year Plan that are of interest to us are confined to investment data. Nothing is mentioned on capital or labor supplies. Other basic statistics, such as those of consump tion, which could have enabled us to form a better model, are unfortunately non-existent. O Obviously, the word "best” could lead to a number of different choices according to different preferences and value judgments. Therefore, our actual task will be limited to the exposition of the different aspects and merits of each policy, while the final decision is to be based on the specific, arbitrarily chosen, allocational policy. 75 Only one choice is left to us where we have to estimate--using the scant data available, together with our own calculations and simplifying assumptions--the sup plies of capital and of labor available to both sectors together in each year of the Plan, and use these values as givens in each of the five policies that we have worked out. Capital supply data.--The following are the esti mates of the supply of capital--of both sectors together-- in each year of the Plan,^* in millions of Egyptian pounds (•L.E.m.): First year (1960/61): K 0 = 225.1200 Second year (1961/62): * H I I 324.6152 Third year (1962/63): K 2 = 477.8306 Fourth year (1963/64): k3 = 711.7174 Fifth year (1964/65): * I I 1014.6487 Where ( t = 0, 1, 2, 3, 4) is lagged by one time period to refer to capital supply at the beginning of each planning year. Labor supply data.--The estimates of total labor % e e Appendix I, p. 210. 76 supplies available— to both sectors together--each year of the Plan give the following figures in millions of work- 4 ers First year: = 4.428 045 Second year: L-^ = 4.523 450 Third year: L2 = 4.618 857 Fourth year: Lg = 4.686 088 Fifth year: = 4.766 094 Where, again, (t = 0, 1, 2, 3, 4) lagged by one period to refer to the beginning of each year. Output/input coefficients.--Here, again, we rely both on published data5 and on our own derivations and calculations,^ whence we get the following values: 1. Agricultural sector: Mean Value Standard Error of the Mean b 1 1 : 1.91228 0.027741 b 1 2 : 0.45500 0.004729 4 See Appendix II, p. 214. ^UAR, INP, M. M. El-Imam, Memo No. 255, Models Used in Drafting the 20-Year Plan (1959-1978), (December 1962). See Appendix III, p. 217. 77 2. Industrial sector: Mean Value Standard Error of the Mean b2 1 : 10.00000 0.51515 b2 2 : 0.29000 0.06340 The assumed allocational policies.--The following calculations are made under five different pre-assumed policies for allocating available capital and labor among agricultural and industrial sectors. In the light of their final results, these policies are then discussed and con trasted with each others and with actual policy and achievements of the UAR First Five-Year Plan regarding these two sectors. The five allocational policies are: Policy I : U11 = 2/3 U2i = 1/4 U 1 2 = 1/3 U2 2 = 3/4 Policy II : U11 = 2 / 3 u2 i = 1/3 U1 2 = 1/3 U2 2 = 2/3 Policy III : Uji = 3/4 ^21 = 1/4 U1 2 = 1/4 U2 2 = 3/4 78 Policy IV: U11 = 3/4 U12 = 1/4 Policy V : U11 = 1/2 Ui2 = 1/2 U 21 U 22 1/2 1/2 U 21 U 22 1/2 1/2 The Model Assuming that the above given technical coeffi cients, ^ijj are normally distributed, random variables, our problem is to find, out the set of policy variables, Uij, which maximizes the objective function: + S5; under the conditions that: A1 ^ A0 + *11 U11 (L0) + b12 U21 (K0) si :$C so + b21 U12 (bo) + b22 u22 (K0) A2 <C a i + bll U11 (Lx) + b12 U21 (KX) S2<gSl + b21 U12 (bl) + b22 U22 (KX) A3 <C A2 + bll Ull (l2) + b12 U21 (k2) S3 ^ S2 + b21 U12 (l2) + b22 U22 (K2) A4 <C A3 + bll U11 (l3) + b12 b21 (k 3) S4 < S3 + b21 U12 (L3) + b22 U22 (K3) 79 A5^ A 4 + bi;L U X 1 (L4) + b 1 2 U2i (K4) S5< S4 + b2 1 U 1 2 (b4) ^ b22 U22 (K4) Ax^> 405 Where 405 is the empirical A 2 405 value of agricultural output in the year just Ag 405 before the first year of the Plan. A4 ^ 4 0 5 a 5 ^ 405 S i > 266.1 Where 266.1 is the empirical S 2 266.1 value of industrial output in the year just before 266.1 the first year of the Plan, 5 4 ^ 266.1 5 5 ^ 266.1 KQ + + K2 + K 3 + K4.<^ total supply of capital available for the two sectors together over the Plan years. LQ + + L2 + L3 + L4 total supply of labor available to the two sectors together over the Plan years. J^Note that for A^ and the subscripts 1 , 2 , 3 , 4, 5 refer to the end of each of the five years of the Plan, while the subscripts 0, 1, 2, 3, 4 of and are lagged 80 by one time period to refer to the beginning of each of the same five years, respectively.j But we have the following Knowns: K^ 1 s : are given estimates. L^'s : are given estimates. U-^j 1 s : are assumed policy variables which are determined a priori. b^j's : are random variables with Known distri bution such that their values can be estimated and are thus given in each problem. Aq and Sq : each has its Known value from empiri cal data of the year 1959/1960. These Knowns reduce the model to one of maximizing the objective function W 5 = A 5 + S5 under the conditions that: A 1 < C 1 Sl < C 2 - Ax + A2^ C3 - sx + s2 <^ c4 - a2 + a 3^; c 5 - S2 + s3 < C6 81 “ A3 + C7 - Sg + Cg - A 4 + A 5 ^ Cg - s4 + s5<c; c10 Where: , C2 , Cg, to C1Q are constants. This extremely simple form makes the maximization solutions of the problems very simple: they are always obtained by a zero slack vector; i.e., the values of the constants to C^q always attain the upper limit of the inequality. However, this situation only technically simplifies the solutions of the great number of linear programming problems at hand. It in no way undermines the significance of the two basic assumptions of the present study, namely: 1. The randomness of the technical coefficients. 2. The pre-determined allocational policies from which we are to select one. It is now even more important and interesting--as well as far more manageable--to assume more values for the random variables and more choices of decision policies: i.e., to put more weight on our basic assumptions. This is precisely what we intend to do. 82 Results of the Optimum Solutions To derive the approximate distribution of the ob jective function W r = A_ + S_ --under different alloca- 5 5 5 tional policies of labor and. capital between the two sec tors; i.e., under pre-determined. sets of values for (lK_.’s) --we assume that the coefficients b ^ > b2 1 ’ b 2 2 bave the following independent normal distributions which are derived, from their means and. standard, errors (pages 76-77) : p < b n > = P(b ) = v 12} P<b21> P<b22> = 1/V 2 7T (0.027741) 1 / V 2 7 T ~ (0.004729) 1/V 2 7 T (0.51515) 1/V 2 7T (0.06340) <bll — 1.91228 2 (0 .027741)2 CM H £ - 0.455)2 2 (0 .004729)2 ( b 2 1 1 H o """to 2 (0 .51515)2 (b 2 2 — 0.2900)2 2(0.06340)2 83 For each coefficient we assume five standardized values: 0 , + 1 , + 2 and calculate their corresponding values, comulative probabilities, and probabilities, as follows: TABLE 1-A O/L = AGRICULTURE . 1 1 ) ........................ , m ............... ..................................(3) ................... (4) Standardized Values b n Values Comulative Probabilities Probabilities - 2 1.856 798 0.0228 0.0215 — 1 1.884 539 0.1587 0.1359 0 1.912 280 0.5000 0.3413 + 1 1.940 021 0.8413 0.3413 + 2 1.967 762 0.9772 0.1359 84 TABLE 1-B O/K: AGRICULTURE (1) (2) (3) (4) Standardized ^>12 Values Comulative Probabilities Values Probabilities — 2 0.445 542 0.0228 0.0215 - 1 0.450 271 0.1587 0.1359 0 0.455 000 0.5000 0.3413 + 1 0.459 729 0.8413 0.3413 + 2 0.464 458 0.9772 0.1359 85 TABLE 1-C O/L: INDUSTRY (1)_____________(2)______________(3)______________(4)________ Standardized b21 Values Comulative Probabilities Values Probabilities - 2 9.969 700 0.0228 0.0215 — 1 9.484 850 0.1587 0.1359 0 10.000 000 0.5000 0.3413 + 1 10.515 150 0.8413 0.3413 + 2 11.030 300 0.9772 0.1359 86 TABLE 1-D O/K: INDUSTRY (1 ) (2 ) (3) (4) Standardized Values b2 2 Values Comulative Probabilities Probabilities — 2 0.163 200 0.0228 0.0215 — 1 0.226 600 0.1587 0.1359 0 0.290 000 0.5000 0.3413 + 1 0.353 400 0.8413 0.3413 + 2 0.416 800 0.9772 0.1359 j^In later uses of the coefficients bn, b^2 , b2]_, and b2 2 (Columns 2 ), we shall use, for simplicity’s sake, the symbols: 1, 2, 3, 4, 5, for the values of b ^ corresponding to 0 , +1 , —1 , +2 , — 2 , respectively; a, b, c, d, e, for the values of b 1 2 corresponding to 0 , +1 , — 1 , +2 ,— 2 , respectively; I, II, III, IV, V, for the values of b2^ correspond ing to O, +1, — 1, +2,~ 2 , respectively; and A, B, C, D, E, for the values of b2 2 corresponding to 0 , +1 , — 1 , +2 , — 2 , respectively.j 87 To derive the distribution of the objective func tion (W^) under each of the five allocational policies, we first estimate the probabilities of getting each value of W5 --as shown in the following tables, 2-A to 2-E, for the assumed policies. This probability equals the joint probabilities of the relevant combination of coefficients "columns (4), tables 1-A to 1-D." We th'en use the values of P(W^) to calculate the means and. standard deviations under each policy. The following are the five policies and their final results: Policy I: U n = . 6 6 6 G H CO I I .333 U 2 1 = .25 I I CM CM D .75 The twenty values of the coefficients "columns (2), tables 1-A to 1-D," give (5)^ = 625 combinations "Table 2-A," each of which is used, for a linear programming prob lem whose final optimum solution is W 5 "Table 2-A," which is the value of total output of both sectors at the end of the fifth year of the plan. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 TABLE 2-A POLICY I U11 = 2/3 U2i = 1/4 U12 = 1/3 U22 = 3/4 Combinations' Values Optimum Value bll b12 b21 b22 of W5 1 a I A 1 699.655 003 1 a I B 1 832.030 964 1 a I C 1 567.279 042 1 a I D 1 964.406 927 1 a I E 1 434.903 073 1 a II A 1 703.616 262 1 a II B 1 835.992 223 1 a II C 1 571.240 299 1 a II D 1 968.368 186 1 a II E 1 438.864 337 1 a III A 1 695.693 744 1 a III B 1 828.069 705 1 a III C 1 563.317 781 1 a III D 1 960.445 6 6 8 1 a III E 1 430.941 819 1 a IV A 1 707.577 520 1 a IV B 1 839.953 481 1 a IV C 1 575.201 557 1 a IV D 1 972.329 444 1 A IV E 1 442.825 595 1 a V A 1 699.422 0 1 0 1 a V B 1 831.797 971 1 a V C 1 567.046 047 1 a V D 1 964.173 934 1 a V E 1 434.670 085 89 TABLE 2-A (Continued) Problem Combinations1 Values Optimum Value p(w5) Number bll bi2 b 2 1 b 2 2 of W 5 26 1 b I A 1 702.946 306 .0135690 27 1 b I B 1 835.322 267 .0135690 28 1 b I C 1 570.570 345 .0054030 29 1 b I D 1 967.698 230 .0054030 30 1 b I E 1 438.194 381 .0008548 31 1 b II A 1 706.907 565 .0135690 32 1 b II B 1 839.283 526 .0135690 33 1 b II C 1 574.531 602 .0054030 34 1 b II D 1 971.659 489 .0054030 35 1 b II E 1 442.155 640 .0008548 36 1 b III A 1 698.985 047 .0054030 37 1 b III B 1 831.361 008 .0054030 38 1 b III C 1 566.609 084 .0021514 39 1 b III D 1 963.736 971 .0021514 40 1 b III E 1 434.233 1 2 2 .0003404 41 1 b IV A 1 710.868 823 .0054030 42 1 b IV B 1 843.244 784 .0054030 43 1 b IV C 1 578.492 860 .0021514 44 1 b IV D 1 975.620 747 .0021514 45 1 b IV E 1 446.116 898 .0003404 46 1 b V A 1 702.713 313 .0008548 47 1 b V B 1 835.089 274 .0008548 48 1 b V C 1 570.337 350 .0003404 49 1 b V D 1 967.465 237 .0003404 50 1 b V E 1 437.961 388 .0000538 51 1 c I A 1 696.363 699 .0054030 52 1 c I B 1 828.739 660 .0054030 53 1 c I C 1 563.987 738 .0021514 54 1 c I D 1 961.115 623 .0021514 55 1 c I E 1 431.611 774 .0003404 56 1 c II A 1 700.324 958 .0054030 57 1 c II B 1 832.700 919 .0054030 uml 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 TABLE 2-A (Continued) Combinations’ Values Optimum Value '11 b 1 2 b 2 1 b_ _ 2 2 of W 5 1 c II C 1 567.948 995 1 c II D 1 965.076 882 1 c II E 1 435.573 033 1 c III A 1 692.402 440 1 c III B 1 824.778 401 1 c III C 1 560.026 477 1 c III D 1 957.154 364 1 c III E 1 427.650 515 1 c IV A 1 704.286 216 1 c IV B 1 836.662 177 1 c IV C 1 571.910 253 1 c IV D 1 969.038 140 1 c IV E 1 439.534 291 1 c V A 1 696.130 706 1 c V B 1 828.506 667 1 c V C 1 563.754 743 1 c V D 1 960.882 630 1 c V E 1 431.378 781 1 d I A 1 706.268 556 1 d I B 1 838.644 517 1 d I C 1 573.892 595 1 d I D 1 971.020 480 1 d I E 1 441.516 631 1 d II A 1 710.229 815 1 d II B 1 842.605 776 1 d II C 1 577.853 852 1 d II D 1 974.981 739 1 d II E 1 445.477 890 1 d III A 1 702.307 297 1 d III B 1 834.683 258 1 d III C 1 569.931 334 1 d III D 1 967.059 2 2 1 1 d III E 1 437.555 372 91 92 93 94 95 96 97 98 99 100 lOl 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 TABLE 2-A (Continued) Combinations’ Values Optimum Value '11 b 1 2 b 2 1 b 2 2 of W 5 1 d IV A 1 714.191 073 1 d IV B 1 846.567 034 1 d IV C 1 581.815 1 1 0 1 d IV D 1 978.942 997 1 d IV E 1 449.439 148 1 d V A 1 706.034 563 1 d V B 1 838.411 524 1 d V C 1 573.659 600 1 d V D 1 970.787 487 1 d V E 1 441.283 638 1 e I A 1 693.072 395 1 e I B 1 825.448 356 1 e I C 1 560.696 434 1 e I D 1 957.824 319 1 e I E 1 428.320 470 1 e II A 1 697.033 654 1 e II B 1 829.409 615 1 e II C 1 564.657 691 1 e II D 1 961.785 578 1 e II E 1 432.281 729 1 e III A 1 689.Ill 136 1 e III B 1 821.487 097 1 e III C 1 556.735 173 1 e III D 1 953.863 060 1 e III E 1 424.359 2 1 1 1 e IV A 1 700.994 912 1 e IV B 1 833.370 873 1 e IV C 1 568.618 949 1 e IV D 1 965.746 836 1 e IV E 1 436.242 987 1 e V A 1 692.839 402 1 e V B 1 825.215 363 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 92 TABLE 2-A (Continued) Combinations' Values Optimum Value P(W^) '11 b 1 2 b 2 1 b 2 2 of W 5 1 e V C 1 560.463 439 .0000214 1 e V D 1 957.591 326 .0000214 1 e V E 1 428.087 477 .0000034 2 a I A 1 699.919 052 .0135690 2 a I B 1 832.295 013 .0135690 2 a I C 1 567.543 091 .0054030 2 a I D 1 964.770 976 .0054030 2 a I E 1 435.167 127 .0008548 2 a II A 1 703.880 311 .0135690 2 a II B 1 836.256 272 .0135690 2 a II C 1 571.504 348 .0054030 2 a II D 1 968.632 235 .0054030 2 a II E 1 439.128 386 .0008548 2 a III A 1 695.957 793 .0054030 2 a III B 1 838.333 754 .0054030 2 a III C 1 563.581 830 .0021514 2 a III D 1 960.709 717 .0021514 2 a III E 1 431.205 8 6 8 .0003404 2 a IV A 1 707.841 569 .0054030 2 a IV B 1 840.217 530 .0054030 2 a IV C 1 575.465 606 .0021514 2 a IV D 1 972.593 493 .0021514 2 a IV E 1 443.089 644 .0003404 2 a V A 1 699.686 059 .0008548 2 a V B 1 832.062 0 2 0 .0008548 2 a V C 1 567.310 096 .0003404 2 a V D 1 964.437 983 .0003404 2 a V E 1 434.934 134 .0000538 2 b I A 1 703.210 355 .0135690 2 b I B 1 835.586 316 .0135690 2 b I C 1 570.’834 394 .0054030 2 b I D 1 967.962 279 .0054030 2 b I E 1 438.458 430 .0008548 93 TABLE 2-A (Continued) Problem Combinations* Values Optimum Value p (w 5) Number bll b 1 2 b 2 1 b 2 2 of W 5 156 2 b II A 1 707.171 614 .0135690 157 2 b II B 1 839.547 575 .0135690 158 2 b II C 1 574.795 651 .0054030 159 2 b II D 1 971.923 538 .0054030 160 2 b II E 1 442.419 689 .0008548 161 2 b III A 1 699.249 096 .0054030 162 2 b III B 1 831.625 057 .0054030 163 2 b III C 1 566.873 133 .0021514 164 2 b III D 1 964.001 0 2 0 .0021514 165 2 b III E 1 434.497 171 .0003404 166 2 b IV A 1 711.132 872 .0054030 167 2 b IV B 1 843.508 833 .0054030 168 2 b IV C 1 578.756 909 .0021514 169 2 b IV D 1 975.884 796 .0021514 170 2 b IV E 1 446.380 947 .0003404 171 2 b V A 1 702.977 362 .0008548 172 2 b V B 1 835.353 323 .0008548 173 2 b V C 1 570.601 399 .0003404 174 2 b V D 1 967.729 286 .0003404 175 2 b V E 1 438.225 437 .0000538 176 2 c I A 1 696.627 748 .0054030 177 2 c I B 1 829.003 709 .0054030 178 2 c I C 1 564.251 787 .0021514 179 2 c I D 1 961.379 672 .0021514 180 2 c I E 1 431.875 823 .0003404 181 2 c II A 1 700.589 007 .0054030 182 2 c II B 1 832.964 968 .0054030 183 2 c II C 1 568.213 044 .0021514 184 2 c II D 1 965.340 931 .0021514 185 2 c II E 1 435.837 082 .0003404 186 2 c III A 1 692.666 489 .0021514 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 TABLE 2-A (Continued) Combinations’ Values Optimum Value >11 b12 b21 b22 of W5 2 c III B 1 825.042 450 2 c III C 1 560.290 526 2 c III D 1 957.418 413 2 c III E 1 427.914 564 2 c IV A 1 704.550 265 2 c IV B 1 836.926 226 2 c IV C 1 572.174 302 2 c IV D 1 969.302 189 2 c IV E 1 439.798 340 2 c V A 1 696.394 755 2 c V B 1 828.770 716 2 c V C 1 564.018 792 2 c V D 1 961.146 679 2 c V E 1 431.642 830 2 d I A 1 706.532 605 2 d I B 1 838.908 566 2 d I C 1 574.156 644 2 d I D 1 971.284 529 2 d I E 1 441.780 680 2 d II A 1 710.493 864 2 d II B 1 842.869 825 2 d II C 1 578.117 901 2 d II D 1 975.245 788 2 d II E 1 445.741 939 2 d III A 1 702.571 346 2 d III B 1 834.947 307 2 d III C 1 570.195 383 2 d III D 1 967.323 270 2 d III E 1 437.819 421 2 d IV A 1 714.455 122 2 d IV B 1 846.831 083 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 95 TABLE 2-A (Continued) Combinations' Values Optimum Value P(W5) bll b12 b21 b22 of W5 2 d IV c 1 582.079 159 .0008566 2 d IV D 1 979.207 046 .0008566 2 d IV E 1 449.703 197 .0001355 2 d V A 1 706.299 612 .0003404 2 d V B 1 838.675 573 .0003404 2 d V c 1 573.923 649 .0001355 2 d V D 1 971.051 536 .0001355 2 d V E 1 441.547 687 .0000214 2 e I A 1 693.136 443 .0008548 2 e I B 1 825.712 404 .0008548 2 e I C 1 560.960 482 .0003404 2 e I D 1 958.088 367 .0003404 2 e I E 1 428.584 518 .0000538 2 e II A 1 697.297 702 .0008548 2 e II B 1 829.673 663 .0008548 2 e II C 1 564.921 739 .0003404 2 e II D 1 962.049 626 .0003404 2 e II E 1 432.545 777 .0000538 2 e III A 1 689.375184 .0003404 2 e III B 1 821.751 145 .0003404 2 e III C 1 556.999 2 2 1 .0001355 2 e III D 1 954.127 108 .0001355 2 e III E 1 424.623 259 .0000214 2 e IV A 1 701.258 960 .0003404 2 e IV B 1 833.634 921 .0003404 2 e IV C 1 568.882 997 .0001355 2 e IV D 1 966.010 884 .0001355 2 e IV E 1 436.507 035 .0000214 2 e V A 1 693.103 450 .0000538 2 e V B 1 825.479 411 .0000538 2 e V C 1 560.727 487 .0000214 2 e V D 1 957.855 374 .0000214 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 TABLE 2-A (Continued) Combinations' Values Optimum Value >11 b 1 2 b 2 1 b 2 2 of W5 2 e V E 1 428.351 525 3 a I A 1 699.068 348 3 a I B 1 831.444 309 3 a I C 1 566.692 387 3 a I D 1 963.820 272 3 a I E 1 434.316 423 3 a II A 1 703.029 607 3 a II B 1 835.405 568 3 a II C 1 570.653 644 3 a II D 1 967.781 531 3 a II E 1 438.277 682 3 a III A 1 695.107 089 3 a III B 1 827.483 050 3 a III C 1 562.731 126 3 a III D 1 959.859 013 3 a III E 1 430.355 164 3 a IV A 1 706.990 865 3 a IV B 1 839.366 826 3 a IV C 1 574.614 902 3 a IV D 1 971.742 789 3 a IV E 1 442.238 940 3 a V A 1 698.835 355 3 a V B 1 831.211 316 3 a V C 1 566.459 392 3 a V D 1 963.587 279 3 a V E 1 434.083 430 3 b I A 1 702.359 651 3 b I B 1 834.735 612 3 b I C 1 569.983 690 3 b I D 1 967.111 575 3 b I E 1 437.607 726 97 TABLE 2-A (Continued) Problem Combinations' Values Optimum Value P(Wnj) fumber bll b 1 2 b 2 1 b 2 2 of W 5 281 3 b II A 1 706.320 910 .0054030 282 3 b II B 1 838.696 871 .0054030 283 3 b II C 1 573.944 947 .0021514 284 3 b II D 1 971.072 834 .0021514 285 3 b II E 1 441.568 985 .0003404 286 3 b III A 1 698.398 392 .0021514 287 3 b III B 1 830.774 353 .0021514 288 3 b III C 1 566.022 429 .0008566 289 3 b III D 1 963.150 316 .0008566 290 3 b III E 1 433.646 467 .0001355 291 3 b IV A 1 710.282 168 .0021514 292 3 b IV B 1 842.658 129 .0021514 293 3 b IV C 1 577.906 205 .0008566 294 3 b IV D 1 795.034 092 .0008566 295 3 b IV E 1 445.530 243 .0001355 296 3 b V A 1 702.126 658 .0003404 297 3 b V B 1 834.502 619 .0003404 298 3 b V C 1 569.750 695 .0001355 299 3 b V D 1 966.878 582 .0001355 300 3 b V E 1 437.374 733 .0000214 301 3 c I A 1 695.777 044 .0021514 302 3 c I B 1 828.153 005 .0021514 303 3 c I C 1 563.401 083 .0008566 304 3 c I D 1 961.528 968 .0008566 305 3 c I E 1 431.025 119 .0001355 306 3 c II A 1 699.738 303 .0021514 307 3 c II B 1 832.114 264 .0021514 308 3 c II C 1 567.362 340 .0008566 309 3 c II D 1 964.490 227 .0008566 310 3 c II E 1 434.986 378 .0001355 311 3 c III A 1 691.815 785 .0008566 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 TABLE 2-A (Continued) Combinations’ Values Optimum Value '11 b 1 2 b 2 1 b 2 2 of W 5 3 c III B 1 824.191 746 3 c III C 1 559.439 822 3 c III D 1 956.567 709 3 c III E 1 427.063 860 3 c IV A 1 703.699 561 3 c IV B 1 836.075 522 3 c IV C 1 571.323 598 3 c IV D 1 968.451 485 3 c IV E 1 438.947 636 3 c V A 1 695.544 051 3 c V B 1 827.920 0 1 2 3 c V C 1 563.168 088 3 c V D 1 960.295 975 3 c V E 1 430.792 126 3 d I A 1 705.681 901 3 d I B 1 838.057 862 3 d I C 1 573.305 940 3 d I D 1 970.433 825 3 d I E 1 440.929 976 3 d II A 1 709.643 160 3 d II B 1 842.019 1 2 1 3 d II C 1 577.267 197 3 d II D 1 974.395 084 3 d II E 1 444.891 235 3 d III A 1 701.720 642 3 d III B 1 834.096 603 3 d III C 1 569.344 670 3 d III D 1 966.472 566 3 d III E 1 436.968 717 3 d IV A 1 713.604 418 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 TABLE 2-A (Continued) Combinations’ Values Optimum Value ’1 1 b 1 2 b 2 1 b 2 2 of W 5 3 d IV B 1 845.980 379 3 d IV C 1 581.228 455 3 d IV D 1 978.356 342 3 d IV E 1 448.852 493 3 d V A 1 705.448 908 3 d V B 1 837.824 869 3 d V C 1 573.072 945 3 d V D 1 970.200 432 3 d V E 1 440.696 983 3 e I A 1 692.485 740 3 e I B 1 824.861 701 3 e I C 1 560.109 779 3 e I D 1 957.237 664 3 e I E 1 427.733 815 3 e II A 1 696.446 999 3 e II B 1 828.822 960 3 e II C 1 564.071 036 3 e II D 1 961.198 923 3 e II E 1 431.695 074 3 e III A 1 688.524 481 3 e III B 1 820.900 442 3 e III C 1 556.148 518 3 e III D 1 953.276 405 3 e III E 1 423.772 556 3 e IV A 1 700.408 257 3 e IV B 1 832.784 218 3 e IV C 1 568.032 294 3 e IV D 1 965.160 181 3 e IV E 1 435.656 332 3 e V A 1 692.252 747 3 e V B 1 824.628 708 3 e V C 1 559.876 784 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 TABLE 2-A (Continued) Combinations' Values Optimum Value >11 b 1 2 b 2 1 b 2 2 of W 5 3 e V D 1 957.004 671 3 e V E 1 437.500 822 4 a I A 1 700.344 406 4 a I B 1 832.720 367 4 a I C 1 567.968 445 4 a I D 1 965.106 330 4 a I E 1 435.592 481 4 a II A 1 704.305 665 4 a II B 1 836.681 626 4 a II C 1 571.929 702 4 a II D 1 969.056 589 4 a II E 1 439.553 740 4 a III A 1 696.383 147 4 a III B 1 827.759 108 4 a III C 1 564.007 184 4 a III D 1 961.135 071 4 a III E 1 431.631 2 2 2 4 a IV A 1 708.266 923 4 a IV B 1 840.642 884 4 a IV C 1 575.890 960 4 a IV D 1 973.018 847 4 a IV E 1 443.514 998 4 a V A 1 700.111 413 4 a V B 1 832.487 374 4 a V C 1 567.735 450 4 a V D 1 964.863 337 4 a V E 1 435.359 488 4 b I A 1 703.635 709 4 b I B 1 836.011 670 4 b I C 1 571.259 748 4 b I D 1 968.387 633 4 b I E 1 438.883 784 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 TABLE 2-A (Continued) Combinations’ Values Optimum Value >11 b 1 2 b 2 1 b 2 2 of W 5 4 b II A 1 707.596 968 4 b II B 1 839.972 929 4 b II C 1 575.221 005 4 b II D 1 972.348 892 4 b II E 1 442.845 043 4 b III A 1 699.674 450 4 b III B 1 832.050 411 4 b III C 1 567.298 487 4 b III D 1 964.426 374 4 b III E 1 434.922 525 4 b IV A 1 711.558 226 4 b IV B 1 843.934 187 4 b IV C 1 579.182 263 4 b IV D 1 976.310 150 4 b IV E 1 446.806 301 4 b V A 1 703.402 716 4 b V B 1 835.778 677 4 b V C 1 571.026 753 4 b V D 1 968.154 640 4 b V E 1 438.650 791 4 c I A 1 697.053 1 0 2 4 c I B 1 829.429 063 4 c I C 1 564.677 141 4 c I D 1 961.805 026 4 c I E 1 432.301 177 4 c II A 1 701.014 361 4 c II B 1 833.390 322 4 c II C 1 568.638 398 4 c II D 1 965.766 285 4 c II E 1 436.262 436 4 c III A 1 693.091 843 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 TABLE 2-A (Continued.) Combinations' Values Optimum Value •11 b 1 2 b 2 1 b 2 2 of W 5 4 c III B 1 825.467 804 4 c III C 1 560.715 880 4 c III D 1 957.843 767 4 c III E 1 428.339 918 4 c IV A 1 704.975 619 4 c IV B 1 837.351 580 4 c IV C 1 572.599 656 4 c IV D 1 969.727 543 4 c IV E 1 440.223 694 4 c V A 1 696.820 109 4 c V B 1 829.196 070 4 c V C 1 564.444 146 4 c V D 1 961.572 033 4 c V E 1 432.068 184 4 d I A 1 706.957 959 4 d I B 1 839.333 920 4 d I C 1 574.581 998 4 d I D 1 971.709 883 4 d I E 1 442.206 034 4 d II A 1 710.919 218 4 d II B 1 843.295 179 4 d II C 1 578.543 255 4 d II D 1 975.671 142 4 d II E 1 446.167 293 4 d III A 1 702.996 700 4 d III B 1 835.372 661 4 d III C 1 570.620 737 4 d III D 1 967.748 624 4 d III E 1 438.244 775 4 d IV A 1 714.880 476 4 d IV B 1 847.256 437 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 TABLE 2-A (Continued) Combinations’ Values Optimum Value >11 t>12 t>21 t>22 of W 5 4 d IV C 1 582.504 513 4 d IV D 1 979.632 400 4 d IV E 1 450.128 551 4 d V A 1 706.724 966 4 d V B 1 839.100 927 4 d V C 1 574.349 003 4 d V D 1 971.476 890 4 d V E 1 441.973 041 4 e I A 1 574.498 537 4 e I B 1 706.874 498 4 e I C 1 442.122 576 4 e I D 1 839.250 461 4 e I E 1 309.746 612 4 e II A 1 578.459 796 4 e II B 1 710.835 757 4 e II C 1 446.083 833 4 e II D 1 843.211 720 4 e II E 1 313.707 871 4 e III A 1 570.537 278 4 e III B 1 702.913 239 4 e III C 1 438.161 315 4 e III D 1 835.289 2 0 2 4 e III E 1 305.785 353 4 e IV A 1 582.421 054 4 e IV B 1 714.797 015 4 e IV C 1 450.045 091 4 e IV D 1 847.172 978 4 e IV E 1 317.669 129 4 e V A 1 574.265 544 4 e V B 1 706.641 505 4 e V D 1 441.889 581 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 TABLE 2-A (Continued) Combinations’ Values Optimum Value '11 b 1 2 b 2 1 b 2 2 of W 5 4 e V D 1 839.017 468 4 e V E 1 309.513 619 5 a I A 1 698.642 993 5 a I B 1 831.018 954 5 a I C 1 566.267 032 5 a I D 1 963.394 917 5 a I E 1 433.891 068 5 a II A 1 702.604 252 5 a II B 1 834.980 213 5 a II C 1 570.228 289 5 a II D 1 967.356 176 5 a II E 1 437.852 327 5 a III A 1 694.681 734 5 a III B 1 827.057 695 5 a III C 1 562.305 771 5 a III D 1 959.433 658 5 a III E 1 429.929 809 5 a IV A 1 706.565 510 5 a IV B 1 838.941 471 5 a IV C 1 574.189 547 5 a IV D 1 971.317 434 5 a IV E 1 441.813 585 5 a V A 1 698.410 0 0 0 5 a V B 1 830.785 961 5 a V C 1 566.034 037 5 a V D 1 963.161 924 5 a V E 1 433.658 075 5 b I A 1 701.934 296 5 b I B 1 834.310 257 5 b I C 1 569.558 335 5 b I D 1 966.686 2 2 0 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 TABLE 2-A (Continued) Combinations' Values Optimum Value '11 b 1 2 b 2 1 b 2 2 of W 5 5 b I E 1 437.182 361 5 b II A 1 705.895 555 5 b II B 1 838.271 516 5 b II C 1 573.519 592 5 b II D 1 970.647 479 5 b II E 1 441.143 630 5 b III A 1 697.973 037 5 b III B 1 830.348 998 5 b III C 1 565.597 074 5 b III D 1 962.724 961 5 b III E 1 433.221 1 1 2 5 b IV A 1 709.856 813 5 b IV B 1 842.232 774 5 b IV C 1 577.480 850 5 b IV D 1 974.608 737 5 b IV E 1 455.104 8 8 8 5 b V A 1 701.701 303 5 b V B 1 834.077 264 5 b V C 1 569.325 340 5 b V D 1 966.453 227 5 b V E 1 436.949 378 5 c I A 1 695.351 689 5 c I B 1 827.727 650 5 c I C 1 562.975 728 5 c I D 1 960.103 613 5 c I E 1 430.599 764 5 c II A 1 699.312 948 5 c II B 1 831.688 909 5 c II C 1 566.936 985 5 c II D 1 964.064 872 5 c II E 1 434.561 023 106 TABLE 2-A (Continued) Problem Number Combinations1 Values bll b 1 2 b 2 1 b 2 2 Optimum Value of W 5 p(w5) 561 5 c III A 1 691.390 430 .0001355 562 5 c III B 1 823.766 391 .0001355 563 5 c III C 1 559.014 467 .0000540 564 5 c III D 1 956.142 354 .0000540 565 5 c III E 1 426.638 505 .0000085 566 5 c IV A 1 703.274 206 .0001355 567 5 c IV B 1 835.650 167 .0001355 568 5 c IV C 1 560.898 243 .0000540 569 5 c IV D 1 968.026 130 .0000540 570 5 c IV E 1 438.522 281 .0000085 571 S c V A 1 695.118 696 .0000214 572 5 c V B 1 827.494 657 .0000214 573 5 c V C 1 562.742 733 .0000085 574 5 c V D 1 959.870 620 .0000085 575 5 c V E 1 430.366 771 .0000014 576 5 d I A 1 705.256 546 .0003404 577 5 d I B 1 837.632 507 .0003404 578 5 d I C 1 572.880 585 .0001355 579 5 d I D 1 970.008 470 .0001355 580 5 d I E 1 440.504 621 .0000214 581 5 d II A 1 709.217 805 .0003404 582 5 d II B 1 841.593 766 .0003404 583 5 d II C 1 576.841 842 .0001355 584 5 d II D 1 973.969 729 .0001355 585 5 d II E 1 444.465 880 .0000214 586 5 d III A 1 701.295 287 .0001355 587 5 d III B 1 833.671 248 .0001355 588 5 d III C 1 568.919 324 .0000540 589 5 d III D 1 966.047 2 1 1 .0000540 590 5 d III E 1 436.543 362 .0000085 591 5 d IV A 1 713.179 063 .0001355 592 5 d IV B 1 845.555 024 .0001355 tob Numl 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 TABLE 2-A (Continued Combinations' Values Optimum Value '11 b 1 2 b 2 1 b 2 2 of W 5 5 d IV C 1 580.803 1 0 0 5 d IV D 1 977.930 987 5 d IV E 1 448.427 138 5 d V A 1 705.023 553 5 d V B 1 837.399 514 5 d V C 1 572.647 590 5 d V D 1 969.775 477 5 d V E 1 440.271 628 5 e I A 1 692.060 385 5 e I B 1 824.436 346 5 e I C 1 559.684 424 5 e I D 1 956.812 309 5 e I E 1 427.308 460 5 e II A 1 696.021 644 5 e II B 1 828.397 605 5 e II C 1 563.645 681 5 e II D 1 960.773 568 5 e II E 1 431.269 719 5 e III A 1 688.099 126 5 e III B 1 820.475 087 5 e III C 1 555.723 163 5 e III D 1 952.851 050 5 e III E 1 423.347 2 0 1 5 e IV A 1 699.982 902 5 e IV B 1 832.358 863 5 e IV C 1 567.606 939 5 e IV D 1 764.734 826 5 e IV E 1 435.230 977 5 e V A 1 691.827 392 5 e V B 1 824.203 353 5 e V C 1 559.451 429 5 e V D 1 956.579 316 5 e V E 1 427.075 467 108 From these 625 values of we derive: Mean value = 1 741.703 263 -L.E.m, Standard deviation = 219.204 936 Lower 5% probability level = 1 724.517 596 and the approximate distribution of the objective function W5 is given by: (x- 1741.703263)2 f (x) = 1/V 2TT(219.204936) 2(219.204936)2 Policy II: U 11 = . 666 I I CM r —1 D .333 U21 = .333 U22 = . 666 Again the 625 combinations of the technical coeffi cients give the same number of linear programming problems, where the two factors of production are allocated among the two sectors according to the present policy. This gives 625 values for W5. These optimum values are presented in Table 2-B as follows: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 TABLE 2-B POLICY II U11 = 2/3 °21 = 1/3 U12 = 1/3 U22 = 2/3 Combinations' Values Optimum Value b- ’ 11 b12 b21 b22 of 1 a I A 1 737.780 945 1 a I B 1 855.507 300 1 a I C 1 620.054 589 1 a I D 1 973.233 656 1 a I E 1 502.328 234 1 a II A 1 741.742 204 1 a II B 1 859.468 559 1 a II C 1 624.015 848 1 a II D 1 977.194 915 1 a II E 1 506.289 493 1 a III A 1 733.819 686 1 a III B 1 851.546 041 1 a III C 1 616.093 330 1 a III D 1 969.272 397 1 a III E 1 894.366 975 1 a IV A 1 745.703 463 1 a rv B 1 863.429 818 1 a IV C 1 627.977 107 1 a IV D 1 981.156 174 1 a IV E 1 510.250 752 1 a V A 1 737.547 952 1 a V B 1 855.274 307 1 a V C 1 519.821 596 1 a V D 1 973.000 663 1 a V E 1 502.095 241 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 TABLE 2-B (Continued) Combinations1 Values Optimum Value 11 b12 b21 b22 of /Ws 1 b I A 1 742.164 962 1 b I B 1 860.891 317 1 b I c 1 624.438 606 1 b I D 1 977.617 673 1 b I E 1 506.712 251 1 b II A 1 746.126 221 1 b II B 1 863.852 576 1 b II C 1 628.399 865 1 b II D 1 980.578 932 1 b II E 1 510.673 510 1 b III A 1 738.203 703 1 b III B 1 855.930 058 1 b III C 1 620.477 347 1 b III D 1 973.656 414 1 b III E 1 898.750 992 1 b IV A 1 750.087 480 1 b IV B 1 867.813 845 1 b IV C 1 632.361 124 1 b IV D 1 985.540 191 1 b IV E 1 514.634 769 1 b V A 1 741.931 969 1 b V B 1 859.658 324 1 b V C 1 524.205 613 1 b V D 1 977.384 680 1 b V E 1 506.479 258 1 c I A 1 731.396 929 1 c I B 1 851.123 284 1 c I C 1 615.670 573 1 c I D 1 968.849 640 1 c I E 1 497.944 218 1 c II A 1 737.358 188 1 c II B 1 855.084 543 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 TABLE 2-B (Continued) Combinations1 Values Optimum Value ’ 11 b12 b21 b22 of W5 1 c II C 1 619.631 832 1 c II D 1 972.810 899 1 c II E 1 501.905 477 1 c III A 1 729.435 670 1 c III B 1 847.162 025 1 c III C 1 611.709 314 1 c III D '' 1 964.888 381 1 c III E 1 889.982 959 1 c IV A 1 741.319 447 1 c IV B 1 859.045 802 1 c IV C 1 623.593 091 1 c IV D 1 976.772 158 1 c IV E 1 505.866 736 1 c V A 1 733.263 936 1 c V B 1 850.890 291 1 c V C 1 515.437 580 1 c V D 1 968.616 647 1 c V E 1 497.711 225 1 d I A 1 746.548 978 1 d I B 1 864.275 333 1 d I C 1 628.822 622 1 d I D 1 982.001 689 1 d I E 1 511.096 267 1 d II A 1 750.510 237 1 d II B 1 868.236 592 1 d II C 1 632.783 880 1 d II D 1 985.962 948 1 d II E 1 515.057 526 1 d III A 1 742.587 719 1 d III B 1 861.314 078 1 d III C 1 624.861 363 1 d III D 1 978.040 430 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 TABLE 2-B (Continued) Combinations' Values Optimum Value '11 b12 b21 b22 of W5 1 d III E 1 903.135 008 1 d IV A 1 754.471 496 1 d IV B 1 872.197 851 1 d IV C 1 636.745 140 1 d IV D 1 989.924 207 1 d IV E 1 519.018 785 1 d V A 1 746.315 985 1 d V B 1 864.042 340 1 d V C 1 528.589 629 1 d V D 1 981.768 696 1 d V E 1 510.863 274 1 e I A 1 729.012 912 1 e I B 1 846.739 267 1 e I C 1 611.286 556 1 e I D 1 964.465 623 1 e I E 1 493.560 201 1 e II A 1 732.974 171 1 e II B 1 850.699 526 1 e II C 1 615.247 815 1 e II D 1 968.426 882 1 e II E 1 497.521 460 1 e III A 1 725.051 653 1 e III B 1 842.778 008 1 e III C 1 607.325 287 1 e III D 1 960.504 364 1 e III E 1 885.598 942 1 e IV A 1 736.935 430 1 e IV B 1 854.661 785 1 e IV C 1 619.209 074 1 e IV D 1 972.388 141 1 e IV E 1 501.482 719 1 e V A 1 728.779 919 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 TABLE 2-B (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W5 1 e V B 1 846.506 274 1 e V C 1 511.053 563 1 e V D 1 964.232 630 1 e V E 1 493.327 208 2 a I A 1 738.044 999 2 a I B 1 855.771 354 2 a I C 1 620.318 643 2 a I D 1 973.497 710 2 a I E 1 702.592 288 2 a II A 1 742.006 258 2 a II B 1 859.732 613 2 a II C 1 624.279 902 2 a II D 1 977.458 969 2 a II E 1 506.553 547 2 a III A 1 734.083 740 2 a III B 1 851.810 095 2 a III C 1 616.357 384 2 a III D 1 969.536 451 2 a I IT E 1 894.631 029 2 a IV A 1 745.967 517 2 a IV B 1 863.693 872 2 a IV C 1 628.241 161 2 a IV D 1 981.420 228 2 a IV E 1 510.514 806 2 a V A 1 737.812 006 2 a V B 1 855.538 361 2 a V C 1 520.085 560 2 a V D 1 973.264 717 2 a V E 1 502.359 295 2 b I A 1 742.429 016 2 b I B 1 860.155 371 2 b I C 1 624.702 760 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 TABLE 2-B (Continued) Combinations1 Values Optimum Value ’ 11 i —l £ b21 b22 of W5 2 b I D 1 977.881 727 2 b I E 1 506.976 305 2 b II A 1 746.390 275 2 b II B 1 864.116 630 2 b II C 1 628.663 919 2 b II D 1 981.842 986 2 b II E 1 510.937 564 2 b III A 1 738.467 757 2 b III B 1 856.194 112 2 b III C 1 620.741 4Q1 2 b III D 1 973.920 468 2 b III E 1 899.015 046 2 b IV A 1 750.351 534 2 b IV B 1 868.077 889 2 b IV C 1 632.625 178 2 b IV D 1 985.804 245 2 b IV E 1 514.898 823 2 b V A 1 742.196 023 2 b V B 1 859.922 378 2 b V C 1 524.469 667 2 b V D 1 977.648 734 2 b V E 1 506.743 312 2 c I A 1 733.660 983 2 c I B 1 851.387 338 2 c I C 1 615.934 627 2 c I D 1 969.113 694 2 c I E 1 498.208 272 2 c II A 1 737.622 242 2 c II B 1 855.348 597 2 c II C 1 619.895 885 2 c II D 1 973.074 953 2 c II E 1 502.169 531 2 c III A 1 729.699 724 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 TABLE 2-B (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W5 2 c III B 1 847.426 079 2 c III C 1 611.973 368 2 c III D 1 965.152 435 2 c I IT E 1 890.247 013 2 c IV A 1 741.583 501 2 c IV B 1 859.309 856 2 c IV C 1 623.857 145 2 c IV D 1 977.036 212 2 c IV E 1 506.130 790 2 c V A 1 733.427 990 2 c V B 1 851.154 345 2 c V C 1 515.701 634 2 c V D 1 968.880 701 2 c V E 1 497.975 279 2 d I A 1 746.813 032 2 d I B 1 864.539 387 2 d I C 1 629.086 676 2 d I D 1 982.265 743 2 d I E 1 511.360 321 2 d II A 1 750.774 291 2 d II B 1 868.500 646 2 d II C 1 633.047 935 2 d II D 1 986.227 002 2 d II E 1 515.321 580 2 d III A 1 742.851 773 2 d III B 1 860.578 128 2 d III C 1 625.125 417 2 d III D 1 978.304 484 2 d III E 1 903.399 062 2 d IV A 1 754.735 550 2 d IV B 1 872.461 905 2 d IV C 1 636.009 194 -rob: Numl 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 TABLE 2-B (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W5 2 d IV D 1 990.188 261 2 d IV E 1 519.282 839 2 d V A 1 746.680 039 2 d V B 1 864.306 394 2 d V C 1 528.853 683 2 d V D 1 981.032 750 2 d V E 1 511.127 328 2 e I A 1 729.276 966 2 e I B 1 847.003 321 2 e I C 1 611.550 610 2 e I D 1 964.729 677 2 e I E 1 493.824 255 2 e II A 1 733.238 225 2 e II B 1 850.964 580 2 e II C 1 615.511 869 2 e II D 1 968.690 936 2 e II E 1 497.785 514 2 e III A 1 725.315 707 2 e III B 1 843.042 062 2 e III C 1 607.589 351 2 e III D 1 960.768 418 2 e III E 1 885.862 996 2 e IV A 1 737.199 484 2 e IV B 1 854.925 839 2 e IV C 1 619.473 128 2 e IV D 1 972.652 195 2 e IV E 1 501.746 773 2 e V A 1 729.043 973 2 e V B 1 846.770 328 2 e V C 1 511.317 617 2 e V D 1 964.496 684 2 e V E 1 493.591 262 117 TABLE 2-B (Continued) Problem Combinations’ Values Optimum Value p(w5) Number bll b12 b21 b22 of W5 251 3 a I A 1 737.194 295 .0054030 252 3 a I B 1 854.920 650 .0054030 253 3 a I C 1 619.467 939 .0021514 254 3 a I D 1 972.647 006 .0021514 255 3 a I E 1 501.741 584 .0003404 256 3 a II A 1 741.156 554 .0054030 257 3 a II B 1 858.881 909 .0054030 258 3 a II C 1 623.429 198 .0021514 259 3 a II D 1 976.609 265 .0021514 260 3 a II E 1 505.702 843 .0003404 261 3 a III A 1 733.333 036 .0021514 262 3 a III B 1 850.959 391 .0021514 263 3 a III C 1 615.506 680 .0008566 264 3 a III D 1 968.685 747 .0008566 26 5 3 a III E 1 893.780 325 .0001355 266 3 a IV A 1 745.116 813 .0021514 267 3 a IV B 1 862.843 168 .0021514 268 3 a IV C 1 627.390 457 .0008566 269 3 a IV D 1 980.569 524 .0008566 270 3 a IV E 1 509.664 102 .0001355 271 3 a V A 1 736.961 302 .0003404 272 3 a V B 1 854.687 657 .0003404 273 3 a V C 1 519.234 946 .0001355 274 3 a V D 1 972.414 013 .0001355 275 3 a V E 1 501.508 591 .0000214 276 3 b I A 1 741.578 312 .0054030 277 3 b I B 1 859.304 667 .0054030 278 3 b I C 1 523.851 956 .0021514 279 3 b I D 1 977.031 023 .0021514 280 3 b I E 1 506.125 601 .0003404 281 3 b II A 1 745.539 671 .0054030 282 3 b II B 1 863.265 926 .0054030 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 TABLE 2-B (Continued) Combinations’ Values Optimum Value ’11 b12 b21 b22 o£ W5 3 b II C 1 627.813 215 3 b II D 1 980.992 282 3 b II E 1 510.086 860 3 b III A 1 737.617 153 3 b III B 1 855.343 408 3 b III C 1 619.890 697 3 b III D 1 973.069 764 3 b III E 1 898.164 342 3 b IV A 1 749.500 830 3 b IV B 1 867.227 185 3 b IV C 1 631.774 474 3 b IV D 1 984.953 541 3 b IV E 1 514.048 119 3 b V A 1 741.345 319 3 b V B 1 859.071 674 3 b V C 1 523.618 963 3 b V D 1 976.798 030 3 b V E 1 505.892 608 3 c I A 1 732.810 279 3 c I B 1 850.636 634 3 c I C 1 615.083 923 3 c I D 1 968.262 990 3 c I E 1 497.357 568 3 c II A 1 736.771 538 3 c II B 1 854.497 893 3 c II C 1 629.045 182 3 c II D 1 972.224 249 3 c II E 1 501.318 827 3 c III A 1 728.849 020 3 c III B 1 846.575 375 3 c III C 1 611.122 664 3 c III D 1 964.302 731 3 c III E 1 889.396 309 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 TABLE 2-B (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of W5 3 c IV A 1 740.732 797 3 c IV B 1 858.459 152 3 c IV C 1 623.006 441 3 c IV D 1 976.185 508 3 c IV E 1 505.280 086 3 c V A 1 732.577 286 3 c V B 1 850.303 641 3 c V C 1 514.850 930 3 c V D 1 968.029 997 3 c V E 1 497.124 575 3 d I A 1 745.962 328 3 d I B 1 863.688 683 3 d I C 1 628.235 972 3 d I D 1 981.415 039 3 d I E 1 510.509 617 3 d II A 1 749.923 587 3 d II B 1 867.649 942 3 d II C 1 632.197 231 3 d II D 1 985.376 298 3 d II E 1 514.470 876 3 d III A 1 742.001 069 3 d III B 1 859.727 424 3 d III C 1 624.274 713 3 d III D 1 977.453 780 3 d III E 1 902.548 358 3 d IV A 1 753.884 846 3 d IV B 1 871.611 201 3 d IV C 1 636.158 490 3 d IV D 1 989.337 557 3 d IV E 1 518.432 135 3 d V A 1 745.729 335 3 d V B 1 863.455 690 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 TABLE 2-B (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of W5 3 d V C 1 528.001 979 3 d V D 1 981.182 046 3 d V E 1 510.276 624 3 e I A 1 728.426 262 3 e I B 1 846.152 617 3 e I C 1 610.699 906 3 e I D 1 963.878 973 3 e I E 1 492.973 551 3 e II A 1 732.387 521 3 e II B 1 850.113 876 3 e II C 1 614.661 165 3 e II D 1 967.840 232 3 e II E 1 496.934 810 3 e III A 1 724.465 003 3 e III B 1 842.191 358 3 e III C 1 606.738 647 3 e III D 1 959.917 714 3 e III E 1 885.012 292 3 e IV A 1 736.348 780 3 e IV B 1 854.075 135 3 e IV C 1 618.622 424 3 e IV D 1 971.801 491 3 e IV E 1 500.896 069 3 e V A 1 728.193 269 3 e V B 1 845.919 624 3 e V C 1 510.466 913 3 e V D 1 963.645 980 3 e V E 1 492.740 558 4 a I A 1 738.470 353 4 a I B 1 856.196 708 4 a I C 1 620.743 997 4 a I D 1 973.923 064 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 121 TABLE 2-B (Continued) Combinations' Values Optimum Value P(W^) bll b12 b21 b22 of W5 4 a I E 1 503,017 642 .0003404 4 a II A 1 742,431 612 .0054030 4 a II B 1 860.157 967 ,0054030 4 a II C 1 624,705 256 .0021514 4 a II D 1 977.885 323 ,0021514 4 a II E 1 506,978 901 .0003404 4 a III A 1 734.509 094 .0021514 4 a III B 1 852.235 449 .0021514 4 a III C 1 616.782 738 .0008566 4 a III D 1 969.961 805 .0008566 4 a III E 1 895.056 383 .0001355 4 a IV A 1 746.392 871 .0021514 4 a IV B 1 864.119 226 .0021514 4 a IV C 1 628.666 515 .0008566 4 a IV D 1 981.845 582 .0008566 4 a IV E 1 510.940 160 .0001355 4 a V A 1 738.237 360 .0003404 4 a V B 1 855.963 715 .0003404 4 a V C 1 520.511 004 .0001355 4 a V D 1 973.690 071 .0001355 4 a V E 1 502.784 649 .0000214 4 b I A 1 742.854 370 .0054030 4 b I B 1 860.580 725 .0054030 4 b I C 1 625,128 014 .0021514 4 b I D 1 978.307 081 .0021514 4 b I E 1 507.401 659 .0003404 4 b II A 1 746.815 629 .0054030 4 b II B 1 864.541 984 .0054030 4 b II C 1 629.089 273 .0021514 4 b II D 1 982.268 340 .0021514 4 b II E 1 511.362 918 .0003404 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 TABLE 2-B (Continued) Combinations' Values Optimum Value ’11 b12 b21 b22 of W5 4 b III A 1 738.893 111 4 b III B 1 856.619 466 4 b III C 1 621.166 755 4 b III D 1 974.345 822 4 b III E 1 899.440 400 4 b IV A 1 750.776 888 4 b IV B 1 868.503 243 4 b IV C 1 633.050 532 4 b IV D 1 986.229 599 4 b IV E 1 515.324 177 4 b V A 1 742.621 377 4 b V B 1 860.347 732 4 b V C 1 524.895 021 4 b V D 1 986.229 599 4 b V E 1 507.168 666 4 c I A 1 734.086 337 4 c I B 1 851.812 692 4 c I C 1 616.359 981 4 c I D 1 969.539 048 4 c I E 1 498.633 626 4 c II A 1 738.047 596 4 c II B 1 855.773 951 4 c II C 1 620.321 240 4 c II D 1 973.500 307 4 c II E 1 502.594 885 4 c III A 1 730.125 078 4 c III B 1 847.851 433 4 c III C 1 612.398 722 4 c III D 1 965.577 789 4 c III E 1 890.672 367 4 c IV A 1 742.008 855 4 c IV B 1 859.735 210 123 TABLE 2-B (Continued) Problem Combinations1 Values Optimum Value P(W5) Number ^11 ^*12 ^*21 ^*22 ^5 443 4 c IV c 1 624.282 499 .0003411 444 4 c IV D 1 977.461 566 .0003411 445 4 c IV E 1 506.556 144 .0000540 446 4 c V A 1 733.853 344 .0001355 447 4 c V B 1 851.579 699 .0001355 448 4 c V C 1 516.126 988 .0000540 449 4 c V D 1 969.306 055 .0000540 450 4 c V E 1 498.400 633 .0000085 451 4 d I A 1 747.238 386 .0021514 452 4 d I B 1 864.964 741 .0021514 453 4 d I C 1 629.512 030 .0008566 454 4 d I D 1 982.691 097 .0008566 455 4 d I E 1 511.785 675 .0001355 456 4 d II A 1 751.199 645 .0021514 457 4 d II B 1 868.926 OOO .0021514 458 4 d II C 1 633.473 289 .0008566 459 4 d II D 1 986.652 356 .0008566 460 4 d II E 1 515.746 934 .0001355 461 4 d III A 1 743.277 127 .0008566 462 4 d III B 1 861.003 482 .0008566 463 4 d III C 1 625.550 771 .0003411 464 4 d III D 1 978.729 838 .0003411 465 4 d III E 1 923.824 416 .0000540 466 4 d IV A 1 755.160 904 .0008566 467 4 d IV B 1 872.887 259 .0008566 468 4 d IV C 1 637.434 548 .0003411 469 4 d IV D 1 990.613 615 .0003411 470 4 d IV E 1 519.708 193 .0000540 471 4 d V A 1 747.005 393 .0001355 472 4 d V B 1 864.731 748 .0001355 473 4 d V C 1 529.279 037 .0000540 474 4 d V D 1 982.458 104 .0000540 475 4 d V E 1 511.552 682 .0000085 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 TABLE 2-B (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of W5 4 e I A 1 729.702 320 4 e I B 1 847.428 675 4 e I C 1 611.975 964 4 e I D 1 965.155 031 4 e I E 1 494.249 609 4 e II A 1 733.663 579 4 e II B 1 851.389 934 4 e II C 1 615.937 223 4 e II D 1 969.116 290 4 e II E 1 498.210 868 4 e III A 1 725.741 061 4 e III B 1 843.467 416 4 e III C 1 608.014 705 4 e III D 1 961.193 772 4 e III E 1 886.288 350 4 e IV A 1 737.624 838 4 e IV B 1 855.351 193 4 e IV C 1 619.898 482 4 e IV D 1 973.077 549 4 e IV E 1 502.172 127 4 e V A 1 729.469 327 4 e V B 1 847.196 682 4 e V C 1 511.742 971 4 e V D 1 964.922 038 4 e V E 1 494.016 616 5 a I A 1 736.768 940 5 a I B 1 854.495 295 5 a I C 1 619.042 584 5 a I D 1 972.221 651 5 a I E 1 501.316 229 5 a II A 1 740.730 199 5 a II B 1 858.456 554 5 a II C 1 623.003 843 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 TABLE 2-B (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of W5 5 a II D 1 976.182 910 5 a II E 1 505.277 488 5 a III A 1 732.807 781 5 a III B 1 850.534 036 5 a III C 1 615.081 325 5 a III D 1 968.260 392 5 a III E 1 893.354 970 5 a IV A 1 744.691 458 5 a IV B 1 862.417 813 5 a IV C 1 626.965 102 5 a IV D 1 980.144 169 5 a IV E 1 509.238 747 5 a V A 1 736.535 947 5 a V B 1 854.262 302 5 a V C 1 518.809 591 5 a V D 1 971.988 658 5 a V E 1 501.083 236 5 b I A 1 741.152 957 5 b I B 1 858.879 312 5 b I C 1 623.426 601 5 b I D 1 976.605 668 5 b I E 1 505.700 246 5 b II A 1 745.114 216 5 b II B 1 862.840 571 5 b II C 1 627.387 860 5 b II D 1 980.566 927 5 b II E 1 509.661 505 5 b III A 1 737.191 698 5 b III B 1 854.918 053 5 b III C 1 619.465 342 5 b III D 1 972.644 409 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 TABLE 2-B (Continued) Combinations' Values Optimum Value '11 b12 b21 b2 2 of W5 5 b III E 1 897.738 987 5 b IV A 1 749.075 475 5 b IV B 1 866.801 830 5 b IV C 1 631.349 119 5 b IV D 1 984.528 186 5 b IV E 1 513.622 764 5 b V A 1 740.919 964 5 b V B 1 858.646 319 5 b V C 1 523.193 608 5 b V D 1 976.372 675 5 b V E 1 505.467 253 5 c I A 1 732.384 924 5 c I B 1 850.Ill 279 5 c I C 1 614.658 568 5 c I D 1 967.837 635 5 c I E 1 496.932 213 5 c II A 1 736.346 183 5 c II B 1 854.072 538 5 c II C 1 618.619 827 5 c II D 1 971.798 894 5 c II E 1 500.893 472 5 c III A 1 728.423 665 5 c III B " 1 846.150 020 5 c III C 1 610.697 309 5 c III D 1 963.876 376 5 c III E 1 888.970 954 5 c IV A 1 740.307 442 5 c IV B 1 858.033 797 5 c IV C 1 622.581 086 5 c IV D 1 975.760 153 5 c IV E 1 504.854 731 5 c V A 1 732.151 931 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 TABLE 2-B (Continued) Combinations' Values Optimum Value '11 b12 b21 b22 of W5 5 c V B 1 849.878 286 5 c V C 1 514.435 575 5 c V D 1 967.604 642 5 c V E 1 495.699 220 5 d I A 1 745.536 973 5 d I B 1 863.263 328 5 d I C 1 627.810 617 5 d I D 1 980.989 684 5 d I E 1 510.084 262 5 d II A 1 749.498 232 5 d II B 1 867.224 587 5 d II C 1 631.771 876 5 d II D 1 984.950 943 5 d II E 1 514.045 521 5 d III A 1 741.675 714 5 d III B 1 859.302 069 5 d III C 1 623.849 358 5 d III D 1 977.028 425 5 d III E 1 902.123 003 5 d IV A 1 753.459 491 5 d IV B 1 871.185 846 5 d IV C 1 635.733 135 5 d IV D 1 988.912 202 5 d IV E 1 518.006 780 5 d V A 1 745.303 980 5 d V B 1 863.030 335 5 d V C 1 527.577 624 5 d V D 1 980.755 691 5 d V E 1 509.851 269 5 e I A 1 728.000 907 5 e I B 1 845.727 262 5 e I C 1 610.274 551 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 TABLE 2-B (Continued) Combinations' Values Optimum Value 11 b12 b21 b22 of W5 5 e I D 1 963.453 618 5 e I E 1 492.548 196 5 e II A 1 731.962 166 5 e II B 1 849.688 521 5 e II C 1 614.235 809 5 e II D 1 967.414 877 5 e II E 1 496.509 455 5 e III A 1 724.039 648 5 e III B 1 841.766 003 5 e III C 1 606.213 292 5 e III D 1 959.492 359 5 e III E 1 884.586 937 5 e IV A 1 735.923 425 5 e IV B 1 853.649 780 5 e IV C 1 618.197 069 5 e IV D 1 971.376 136 5 e IV E 1 500.470 714 5 e V A 1 727.767 914 5 e V B 1 845.494 269 5 e V C 1 510.041 558 5 e V D 1 963.220 625 5 e V E 1 492.315 203 129 From the above 625 solutions we then derive for the objective function W5: Mean value = 1 794.526 292 Standard deviation = 120.551 803 Lower 5% probability level = 1 785.075 031 and the approximate distribution of W^_ is given by: f(x) = l/V2 TC (120.551803) (x- 1794.526292)' 2(120.551803)2 Policy III: I I rH H D .75 G H CO I I .25 U21 = .25 U22 = .75 Under this new allocational policy we again solve for 625 problems, each based on a different combination of the four technical coefficients. The optimum solutions for are listed in Table 2-C as follows: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 130 TABLE 2-C POLICY III UH = 3/4 U12= 1/4 U2i = 1/4 U22 = 3/4 Combinations' Values Optimum Value P(W5) bll b12 b21 b22 of W5 1 a I A 1 684.034 562 .0135690 1 a I B 1 816.410 524 .0135690 1 a I C 1 551.658 599 .0054030 1 a I D 1 948.780 486 .0054030 1 a I E 1 419.282 636 .0008548 1 a II A 1 686.999 577 .0135690 1 a II B 1 819.375 539 .0135690 1 a II C 1 554.623 614 .0054030 1 a II D 1 951.751 501 .0054030 1 a II E 1 422.247 651 .0008548 1 a III A 1 681.069 547 .0054030 1 a III B 1 813.445 509 .0054030 1 a III C 1 548.693 584 .0021514 1 a III D 1 945.821 471 .0021514 1 a III E 1 416.317 621 .0003404 1 a IV A 1 689.964 589 .0054030 1 a IV B 1 821.340 551 .0054030 1 a IV C 1 557.588 626 .0021514 1 a IV D 1 954.716 513 .0021514 1 a IV E 1 425.212 663 .0003404 1 a V A 1 683.860 167 .0008548 1 a V B 1 816.236 129 .0008548 1 a V C 1 551.484 204 .0003404 1 a V D 1 948.612 091 .0003404 1 a V E 1 419.108 241 .0000538 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 TABLE 2-C (Continued) Combinations1 Values Optimum Value '11 b12 b21 b22 of W5 1 b I A 1 687.327 865 1 b I B 1 819.701 827 1 b I C 1 554.949 902 1 b I D 1 952.071 789 1 b I E 1 422.573 939 1 b II A 1 690.290 880 1 b II B 1 822.666 842 1 b II C 1 557.914 917 1 b II D 1 955.042 804 1 b II E 1 425.538 954 1 b III A 1 684.360 850 1 b III B 1 816.736 812 1 b III C 1 551.984 887 1 b III D 1 949.112 774 1 b III E 1 419.608 924 1 b IV A 1 693.255 892 1 b IV B 1 824.631 854 1 b IV C 1 560.879 929 1 b IV D 1 958.007 816 1 b IV E 1 428.503 966 1 b V A 1 687.151 470 1 b V B 1 819.527 432 1 b V C 1 554.775 507 1 b V D 1 951.903 394 1 b V E 1 422.399 544 1 c I A 1 680.743 258 1 c I B 1 813.119 220 1 c I C 1 548.367 295 1 c I D 1 945.489 182 1 c I E 1 415.991 332 1 c II A 1 683.708 273 1 c II B 1 816.084 235 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 TABLE 2-G (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of W5 1 c II C 1 551.332 310 1 c II D 1 948.460 197 1 c II E 1 418.956 347 1 c III A 1 677.778 243 1 c III B 1 810.154 204 1 c III C 1 545.402 280 1 c III D 1 942.530 167 1 c III E 1 413.026 317 1 c IV A 1 686.673 285 1 c IV B 1 818.049 247 1 c IV C 1 554.297 322 1 c IV D 1 951.425 209 1 c IV E 1 421.921 359 1 c V A 1 680.568 863 1 c V B 1 812.944 825 1 c V C 1 548.192 900 1 c V D 1 945.320 787 1 c V E 1 415.816 937 1 d I A 1 690.648 115 1 d I B 1 823.024 077 1 d I C 1 558.272 152 1 d I D 1 955.394 039 1 d I E 1 425.896 189 1 d II A 1 693.613 130 1 d II B 1 825.989 092 1 d II C 1 561.237 167 1 d II D 1 958.365 054 1 d II E 1 428.861 204 1 d III A 1 687.683 100 1 d III B 1 820.059 062 1 d III C 1 555.307 137 1 d III D 1 952.435 024 1 d III E 1 422.931 174 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 133 TABLE 2-C (Continued) Combinations' Values Optimum Value P(W5) '11 b12 b21 b22 of W5 1 d IV A 1 696.578 142 .0021514 1 d IV B 1 827.954 104 .0021514 1 d IV C 1 564.202 179 .0008566 1 d IV D 1 961.330 066 .0008566 1 d IV E 1 431.826 216 .0001355 1 d V A 1 690.473 720 .0003404 1 d V B 1 822.849 682 .0003404 1 d V C 1 558.097 757 .0001355 1 d V D 1 955.225 644 .0001355 1 d V E 1 425.721 794 .0000214 1 e I A 1 677.451 954 .0008548 1 e I B 1 809.827 916 .0008548 1 e I C 1 545.075 991 .0003404 1 e I D 1 942.197-878 .0003404 1 e I E 1 412.700 028 .0000538 1 e II A 1 680.416 969 .0008548 1 e II B 1 812.792 931 .0008548 1 e II C 1 548.041 006 .0003404 1 e II D 1 945.168 893 .0003404 1 e II E 1 415.665 043 .0000538 1 e III A 1 674.486 939 .0003404 1 e III B 1 806.862 901 .0003404 1 e III C 1 542.110 976 .0001355 1 e III D 1 939.238 863 .0001355 1 e III E 1 409.735 013 .0000214 1 e IV A 1 683.381 981 .0003404 1 e IV B 1 814.757 943 .0003404 1 e IV C 1 551.006 018 .0001355 1 e IV D 1 948.133 905 .0001355 1 e IV E 1 418.630 055 .0000214 1 e V A 1 677.277 559 .0000538 1 e V B 1 809.653 521 .0000538 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 TABLE 2-C (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W5 1 e V C 1 544.901 596 1 e V D 1 942.029 483 1 e V E 1 412.525 633 2 a I A 1 684.331 916 2 a I B 1 816.707 878 2 a I C 1 551.955 953 2 a I D 1 949.077 840 2 a I E 1 419.579 990 2 a II A 1 687.296 931 2 a II B 1 819.672 893 2 a II C 1 554.920 968 2 a II D 1 952.048 855 2 a II E 1 422.545 005 2 a III A 1 681.366 901 2 a III B 1 813.742 863 2 a III C 1 548.990 938 2 a III D 1 946.118 825 2 a III E 1 416.614 975 2 a IV A 1 690.261 943 2 a IV B 1 821.637 905 2 a IV C 1 557.885 980 2 a IV D 1 955.013 867 2 a IV E 1 425.510 017 2 a V A 1 684.157 521 2 a V B 1 816.533 483 2 a V C 1 551.781 558 2 a V D 1 948.909 445 2 a V E 1 419.405 595 2 b I A 1 687.623 219 2 b I B 1 819.999 181 2 b I C 1 555.247 256 2 b I D 1 952.369 143 135 TABLE 2-C (Continued) Problem Combinations’ Values Optimum Value p(w5) Number bll b12 b21 b22 of W5 155 2 b I E 1 422.871 293 .0008548 156 2 b II A 1 690.588 234 .0135690 157 2 b II B 1 822.964 196 .0135690 158 2 b II C 1 558.212 271 .0054030 159 2 b II D 1 955.340 158 .0054030 160 2 b II E 1 425.836 308 .0008548 161 2 b III A 1 684.658 204 .0054030 162 2 b III B 1 817.034 166 .0054030 163 2 b III C 1 552.282 241 .0021514 164 2 b III D 1 949.410 128 .0021514 165 2 b III E 1 419.906 278 .0003404 166 2 b IV A 1 693.553 246 .0054030 167 2 b IV B 1 824.929 208 .0054030 168 2 b IV C 1 561.177 283 .0021514 169 2 b IV D 1 958.305 170 .0021514 170 2 b IV E 1 428.801 320 .0003404 171 2 b V A 1 687.448 824 .0008548 172 2 b V B 1 819.824 786 .0008548 173 2 b V C 1 555.072 861 .0003404 174 2 b V D 1 952.200 748 .0003404 175 2 b V E 1 422.696 898 .0000538 176 '2 c I A 1 681.040 612 .0054030 177 2 c I B 1 813.416 574 .0054030 178 2 c I C 1 548.664 649 .0021514 179 2 c I D 1 945.786 536 .0021514 180 2 c I E 1 426.288 686 - .0003404 181 2 c II A 1 684.005 627 .0054030 182 2 c II B 1 816.381 589 .0054030 183 2 c II C 1 551.629 664 .0021514 184 2 c II D 1 948.757 551 .0021514 185 2 c II E 1 419.253 701 .0003404 186 2 c III A 1 678.075 597 .0021514 136 TABLE 2-C (Continued) Problem Combinations’ Values Optimum Value p(w5) Number bll b12 b21 b22 of W5 187 2 c III B 1 810.451 559 .0021514 188 2 c III c 1 545.699 634 .0008566 189 2 c III D 1 942.827 521 .0008566 190 2 c III E 1 413.323 671 .0001355 191 2 c IV A 1 686.970 639 .0021514 192 2 c IV B 1 818.346 601 .0021514 193 2 c IV C 1 554.594 676 .0028566 194 2 c IV D 1 951.722 563 .0028566 195 2 c IV E 1 422.218 713 .0021355 196 2 c V A 1 680.886 217 .0003404 197 2 c V B 1 813.242 179 .0003404 198 2 c V C 1 548.490 254 .0001355 199 2 c V D 1 945.618 241 .0001355 200 2 c V E 1 416.114 291 .0000214 201 2 d I A 1 690.945 469 .0054030 202 2 d I B 1 823.321 431 .0054030 203 2 d I C 1 558.569 506 .0021514 204 2 d I D 1 955.691 393 .0021514 205 2 d I E 1 426.193 543 .0003404 206 2 d II A 1 693.910 484 .0054030 207 2 d II B 1 826.286 446 .0054030 208 2 d II C 1 561.534 521 .0021514 209 2 d II D 1 958.662 408 .0021514 210 2 d II E 1 429.158 558 .0003404 211 2 d III A 1 687.980 454 .0021514 212 2 d III B 1 820.356 416 .0021514 213 2 d III C 1 555.604 491 .0008566 214 2 d III D 1 952.732 378 .0008566 215 2 d III E 1 423.228 528 .0001355 216 2 d IV A 1 696.875 496 .0021514 217 2 d IV B 1 828.251 458 .0021514 218 2 d IV C 1 564.499 533 .0008566 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 TABLE 2-C (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W5 2 d IV D 1 961.627 420 2 d IV E 1 432.123 570 2 d V A 1 690.771 074 2 d V B 1 823.147 036 2 d V C 1 558.395 111 2 d V D 1 955.522 998 2 d V E 1 426.019 148 2 e I A 1 677.749 308 2 e I B 1 810.125 270 2 e I C 1 545.373 345 2 e I D 1 942.495 232 2 e I E 1 412.997 382 2 e II A 1 680.714 323 2 e II B 1 813.090 285 2 e II C 1 548.338 360 2 e II D 1 945.466 247 2 e II E 1 415.962 397 2 e III A 1 674.784 293 2 e III B 1 807.160 255 2 e III C 1 542.408 330 2 e III D 1 939.536 217 2 e III E 1 410.032 367 2 e IV A 1 683.679 335 2 e IV B 1 815.055 297 2 e IV C 1 551.303 372 2 e IV D 1 948.431 259 2 e IV E 1 418.927 410 2 e V A 1 677.574 913 2 e V B 1 809.950 875 2 e V C 1 545.198 950 2 e V D 1 942.326 937 2 e V E 1 412.822 987 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 TABLE 2-C (Continued) Combinations’ Values Optimum Value '11 b 12 b 21 CM CM £ of W_ 3 a I A 1 683.373 913 3 a I B 1 815.749 875 3 a I C 1 550.997 950 3 a I D 1 948.119 837 3 a I E 1 418.621 987 3 a II A 1 686.338 928 3 a II B 1 818.714 890 3 a II C 1 553.962 965 3 a II D 1 951.090 852 3 a II E 1 421.587 002 3 a III A 1 680.408 898 3 a III B 1 812.784 860 3 a III C 1 548.032 935 3 a III D 1 945.160 822 3 a III E 1 415.656 972 3 a IV A 1 689.303 940 3 a IV B 1 820.679 902 3 a IV C 1 556.927 977 3 a IV D 1 954.055 864 3 a IV E 1 424.552 014 3 a V A 1 683.199 518 3 a V B 1 815.575 480 3 a V C 1 550.833 555 3 a V D 1 947.951 442 3 a V E 1 418.447 592 3 b I A 1 686.665 216 3 b I B 1 819.041 178 3 b I C 1 554.289 253 3 b I D 1 952.411 140 3 b I E 1 421.913 290 3 b II A 1 689.629 231 3 b II B 1 822.006 193 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 TABLE 2-C (Continued) Combinations' Values Optimum Value '11 b12 b21 b22 of W5 3 b II C 1 557.254 268 3 b II D 1 954.382 255 3 b II E 1 424.878 305 3 b III A 1 683.700 201 3 b III B 1 8i6.076 163 3 b III C 1 551.324 238 3 b III D 1 948.452 125 3 b III E 1 418.948 275 3 b IV A 1 692.595 244 3 b IV B 1 823.971 205 3 b IV C 1 560.219 280 3 b IV D 1 957.347 167 3 b IV E 1 427.843 317 3 b V A 1 686.490 821 3 b V B 1 818.866 783 3 b V C 1 554.114 858 3 b V D 1 951.342 745 3 b V E 1 421.738 895 3 c I A 1 680.082 609 3 c I B 1 811.458 571 3 c I C 1 547.706 646 3 c I D 1 944.828 533 3 c I E 1 415.330 683 3 c II A 1 683.047 624 3 c II B 1 815.423 586 3 c II C 1 550.671 661 3 c II D 1 947.799 548 3 c II E 1 418.295 698 3 c III A 1 677.117 594 3 c III B 1 809.493 556 3 c III C 1 544.741 631 3 c III D 1 941.869 518 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 TABLE 2-C (Continued) Combinations' Values Optimum Value '11 b12 b21 b22 of W5 3 c III E 1 412.365 668 3 c IV A 1 686.012 636 3 c IV B 1 817.388 598 3 c IV C 1 553.636 673 3 c IV D 1 950.764 560 3 c IV E 1 421.360 710 3 c V A 1 679.908 214 3 c V B 1 812.284 176 3 c V C 1 547.532 251 3 c V D 1 944.760 138 3 c V E 1 415.156 288 3 d I A 1 689.987 466 3 d I B 1 822.363 428 3 d I C 1 557.611 503 3 d I D 1 954.733 390 3 d I E 1 425.235 540 3 d II A 1 692.952 481 3 d II B 1 825.328 443 3 d II C 1 560.576 518 3 d II D 1 957.704 405 3 d II E 1 428.200 555 3 d III A 1 687.022 451 3 d III B 1 819.398 413 3 d III C 1 554.646 488 3 d III D 1 951.774 375 3 d III E 1 322.270 525 3 d IV A 1 695.917 493 3 d IV B 1 827.293 455 3 d IV C 1 563.541 530 3 d IV D 1 960.669 417 3 d IV E 1 431.165 567 3 d V A 1 689.813 071 3 d V B 1 822.184 033 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 TABLE 2-C (Continued) Combinations1 Values Optimum Value 1 11 b12 b21 b22 of W5 3 d V c 1 557.437 108 3 d V D 1 954.564 995 3 d V E 1 425.061 145 3 e I A 1 676.791 305 3 e I B 1 809.167 267 3 e I C 1 544.415 342 3 e I D 1 941.537 229 3 e I E 1 412.039 379 3 e II A 1 649.756 320 3 e II B 1 812.132 282 3 e II C 1 547.380 357 3 e II D 1 944.508 244 3 e II E 1 415.004 394 3 e III A 1 673.826 290 3 e III B 1 806.202 252 3 e III C 1 541.450 327 3 e III D 1 938.578 214 3 e III E 1 409.074 364 3 e IV A 1 682.721 332 3 e IV B 1 814.097 294 3 e IV C 1 550.345 369 3 e IV D 1 947.473 256 3 e IV E 1 417.969 406 3 e V A 1 676.616 910 3 e V B 1 808.992 872 3 e V C 1 544.240 947 3 e V D 1 941.368 834 3 e V E 1 411.864 984 4 a I A 1 684.810 917 4 a I B 1 817.186 897 4 a I C 1 552.434 954 4 a I D 1 949.556 841 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 142 TABLE 2-C (Continued) Combinations’ Values Optimum Value P(W5) '11 b12 b21 b22 of W5 4 a I E 1 420.058 991 .0003404 4 a II A 1 687.776 032 .0054030 4 a II B 1 820.151 894 .0054030 4 a II C 1 555.399 969 .0021514 4 a II D 1 952.527 856 .0021514 4 a II E 1 423.024 006 .0003404 4 a III A 1 681.845 902 .0021514 4 a III B 1 814.221 864 .0021514 4 a III C 1 449.469 939 .0008566 4 a III D 1 946.597 826 .0008566 4 a III E 1 417.093 976 .0001355 4 a IV A 1 690.740 944 .0021514 4 a IV B 1 822.116 906 .0021514 4 a IV C 1 558.364 981 .0008566 4 a IV D 1 955.492 868 .0008566 4 a IV E 1 325.989 018 .0001355 4 a V A 1 684.636 522 .0003404 4 a V B 1 817.012 484 .0003404 4 a V C 1 552.260 559 .0001355 4 a V D 1 949.388 446 .0001355 4 a V E 1 419.884 596 .0000214 4 b I A 1 688.102 220 .0054030 4 b I B 1 820.478 182 .0054030 4 b I C 1 555.726 257 .0021514 4 b I D 1 952.848 144 .0021514 4 b I E 1 423.350 294 .0003404 4 b II A 1 691.067 235 .0054030 4 b II B 1 823.443 197 .0054030 4 b II C 1 558.691 272 .0021514 4 b II D 1 955.819 158 .0021514 4 b II E 1 426.315 309 .0003404 4 b III A 1 685.137 205 .0021514 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 TABLE 2-C (Continued) Combinations' Values Optimum Value > 11 b12 b21 b22 of W5 4 b III B 1 817.513 167 4 b III C 1 552.761 242 4 b III D 1 949.889 129 4 b III E 1 420.385 279 4 b IV A 1 694.032 247 4 b IV B 1 825.408 209 4 b IV C 1 561.656 284 4 b IV D 1 958.784 171 4 b IV E 1 429.280 321 4 b V A 1 687.927 825 4 b V B 1 820.303 787 4 b V C 1 555.551 862 4 b V D 1 952.679 749 4 b V E 1 423.175 899 4 c I A 1 681.519 613 4 c I B 1 813.895 575 4 c I C 1 549.143 650 4 c I D 1 946.265 537 4 c I E 1 416.767 687 4 c II A 1 684.484 528 4 c II B 1 816.860 590 4 c II C 1 552.108 665 4 c II D 1 949.236 552 4 c II E 1 419.732 702 4 c III A 1 678.554 598 4 c III B 1 810.930 560 4 c III C 1 546.178 635 4 c III D 1 943.306 522 4 c III E 1 413.802 672 4 c IV A 1 687.449 640 4 c IV B 1 818.825 602 4 c IV C 1 555.073 677 4 c IV D 1 952.201 564 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 TABLE 2-C (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of 4 c IV E 1 422.697 714 4 c V A 1 681.345 218 4 c V B 1 813.721 180 4 c V c 1 548.969 255 4 c V D 1 946.097 142 4 c V E 1 416.593 292 4 d I A 1 671.424 470 4 d I B 1 823.800 432 4 d I C 1 559.048 507 4 d I D 1 956.170 394 4 d I E 1 426.672 544 4 d II A 1 694.389 485 4 d II B 1 826.765 447 4 d II C 1 562.013 522 4 d II D 1 959.141 409 4 d II E 1 429.637 559 4 d III A 1 688.459 455 4 d III B 1 820.835 417 4 d III C 1 556.083 492 4 d III D 1 953.211 379 4 d III E 1 423.707 529 4 d IV A 1 697.354 497 4 d IV B 1 828.730 459 4 d IV C 1 564.978 534 4 d IV D 1 962.106 421 4 d IV E 1 432.602 571 4 d V A 1 691.250 075 4 d V B 1 823.626 037 4 d V C 1 558.874 112 4 d V D 1 956.001 999 4 d V E 1 426.498 149 4 e I A 1 678.228 309 Prol Nui 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 TABLE 2-C (Continued) Combinations’ Values Optimum Value ‘ 11 b12 b21 b22 of W5 4 e I B 1 810.604 271 4 e I c 1 545.852 346 4 e I D 1 942.974 233 4 e I E 1 413.476 383 4 e II A 1 681.193 324 4 e II B 1 813.569 286 4 e II C 1 548.817 361 4 e II D 1 945.945 248 4 e II E 1 416.441 398 4 e III A 1 675.263 294 4 e III B 1 807.639 256 4 e III C 1 542.887 331 4 e III D 1 940.015 218 4 e III E 1 410.511 368 4 e IV A 1 684.158 336 4 e IV B 1 815.534 298 4 e IV C 1 551.782 373 4 e IV D 1 948.910 260 4 e IV E 1 419.406 410 4 e V A 1 678.053 914 4 e V B 1 810.429 876 4 e V C 1 545.677 951 4 e V D 1 942.805 838 4 e V E 1 413.301 988 5 a I A 1 682.894 912 5 a I B 1 815.270 874 5 a I C 1 550.518 949 5 a I D 1 947.640 836 5 a I E 1 418.142 986 5 a II A 1 685.856 927 5 a II B 1 818.235 889 5 a II C 1 553.483 964 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 TABLE 2-C (Continued) Combinations’ Values Optimum Value '11 17 H to b21 b22 of W c 5 a II D 1 950.611 851 5 a II E 1 421.108 OOl 5 a III A 1 679.929 897 5 a III B 1 812.305 859 5 a III C 1 547.553 934 5 a III D 1 944.681 821 5 a III E 1 415.177 971 5 a IV A 1 688.824 939 5 a IV B 1 820.200 901 5 a IV C 1 556.448 976 5 a IV D 1 953.576 863 5 a IV E 1 424.173 013 5 a V A 1 682.720 517 5 a V B 1 815.096 479 5 a V C 1 550.344 554 5 a V D 1 947.472 441 5 a V E 1 417.968 591 5 b I A 1 686.186 215 5 b I B 1 818.562 177 5 b I C 1 553.810 252 5 b I D 1 950.932 139 5 b I E 1 421.434 289 5 b II A 1 689.151 230 5 b II B 1 821.527 192 5 b II C 1 556.785 267 5 b II D 1 953.903 154 5 b II E 1 424.399 304 5 b III A 1 683.221 200 5 b III B 1 815.597 162 5 b III C 1 550.845 237 5 b III D 1 947.973 124 5 b III E 1 418.469 274 N uj 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 TABLE 2-C (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W5 5 b IV A 1 692.116 342 5 b IV B 1 823.492 204 5 b IV C 1 559.740 279 5 b IV D 1 956.868 166 5 b IV E 1 427.364 316 5 b V A 1 686.011 820 5 b V B 1 818.387 782 5 b V C 1 553.635 857 5 b V D 1 950.763 744 5 b V E 1 421.259 894 5 c I A 1 679.604 608 5 c I B 1 811.979 570 5 c I C 1 547.227 645 5 c I D 1 944.349 532 5 c I E 1 414.851 682 5 c II A 1 682.568 623 5 c II B 1 814.944 585 5 c II C 1 550.192 660 5 c II D 1 947.320 547 5 c II E 1 417.816 697 5 c III A 1 676.638 593 5 c III B 1 809.014 555 5 c III C 1 554.262 630 5 c III D 1 941.390 517 5 c III E 1 411.886 667 5 c IV A 1 685.533 635 5 c IV B 1 816.909 597 5 c IV C 1 553.157 672 5 c IV D 1 950.285 559 5 c IV E 1 420.781 710 5 c V A 1 679.429 213 5 c V B 1 811.805 173 148 TABLE 2-C (Continued) Problem Combinations’ Values Optimum Value P(W ) Number b b b n b of W 11 12 21 22 5 573 5 c V c 1 547.053 250 .0000085 574 5 c V D 1 944.181 137 .0000085 575 5 c V E 1 414.677 287 .0000014 576 5 d I A 1 689.508 465 .0003404 577 5 d I B 1 821.884 427 .0003404 578 5 d I C 1 557.132 502 .0001355 579 5 d I D 1 954.254 389 .0001355 580 5 d I E 1 424.756 539 .0000214 581 5 d II A 1 692.473 480 .0003404 582 5 d II B 1 824.849 442 .0003404 583 5 d II C 1 560.097 517 .0001355 584 5 d II D 1 957.225 404 .0001355 585 5 d II E 1 427.721 554 .0000214 586 5 d III A 1 686.543 450 .0001355 587 5 d III B 1 818.919 412 .0001355 588 5 d III C 1 554.167 487 .0000540 589 5 d III D 1 951.295 474 .0000540 590 5 d III E 1 421.791 524 .0000085 591 5 d IV A 1 695.438 492 .0001355 592 5 d IV B 1 826.814 454 .0001355 593 5 d IV C 1 563.062 529 .0000540 594 5 d IV D 1 960.190 416 .0000540 595 5 d IV E 1 430.686 566 .0000085 596 5 d V A 1 689.334 070 .0000214 597 5 d V B 1 821.710 032 .0000214 598 5 d V C 1 556.958 107 .0000085 599 5 d V D 1 954.085 994 .0000085 600 5 d V E 1 424.582 144 .0000014 601 5 e I A 1 676.312 304 .0000538 602 5 e I B 1 808.688 266 .0000538 603 5 e I C 1 543.936 341 .0000214 604 5 e I D 1 941.058 228 .0000214 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 TABLE 2-C (Continued) Combinations' Values Optimum Value '11 b12 b21 b22 of W5 5 e I E 1 411.560 378 5 e II A 1 679.277 319 5 e II B 1 811.653 281 5 e II C 1 546.901 357 5 e II D 1 944.029 243 5 e II E 1 414.525 393 5 e III A 1 673.347 289 5 e III B 1 805.723 251 5 e III C 1 540.971 326 5 e III D 1 938.099 213 5 e III E 1 408.595 363 5 e IV A 1 682.242 331 5 e IV B 1 813.618 293 5 e IV C 1 549.866 368 5 e IV D 1 946.994 255 5 e IV E 1 417.490 405 5 e V A 1 676.137 909 5 e V B 1 808.513 871 5 e V C 1 543.761 946 5 e V D 1 940.889 833 5 e V E 1 411.385 983 150 Using the 625 values and their corresponding prob abilities under this policy, we derive for W^: Mean Value = 1 745.690 063 Standard deviation = 148.002 836 Lower 5% probability level = 1 734.086 641 and the approximate distribution of the objective function "W5" is: (x-1745.690063)2 2(148.002836)2 f (x) = 1 ^\[W( (148 .002836) Policy IV: U11 = .75 U12 = .25 U21 = .50 U22 = .50 The obtained values of under this allocational policy are listed in Table 2-D as follows: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 TABLE 2-D POLICY IV U11 = 3/4 U21 = 1/2 U12 = 1/4 U22 = 1/2 Combinations' Values Optimum Value b- '11 b12 b21 b22 of W5 1 a I A 1 791.998 568 1 a I B 1 880.249 209 1 a I C 1 703.747 926 1 a I D 1 968.499 850 1 a I E 1 615.497 285 1 a II A 1 794.963 583 1 a II B 1 883.214 224 1 a II C 1 706.712 941 1 a II D 1 971.464 865 1 a II E 1 618.462 300 1 a III A 1 789.033 553 1 a III B 1 877.284 194 1 a III C 1 700.782 911 1 a III D 1 965.534 835 1 a III E 1 612.532 270 1 a IV A 1 797.928 595 1 a IV B 1 886.179 236 1 a IV C 1 709.677 953 1 a IV D 1 974.429 877 1 a IV E 1 621.427 312 1 a V A 1 791.823 903 1 a V B 1 880.074 814 1 a V C 1 703.573 531 1 a V D 1 968.325 455 1 a V E 1 615.322 890 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 152 TABLE 2-D (Continued) Combinations' Values Optimum Value P(W^) bll b12 b21 b22 0lf W5 1 b I A 1 804.454 359 .0135690 1 b I B 1 892.705 000 .0135690 1 b I C 1 716.203 717 .0054030 1 b I D 1 980.955 641 .0054030 1 b I E 1 627.953 076 .0008548 1 b II A 1 807.419 374 .0135690 1 b II B 1 895.670 015 .0135690 1 b II C 1 719.168 732 .0054030 1 b II D 1 983.920 656 .0054030 1 b II E 1 630.918 091 .0008548 1 b III A 1 801.489 344 .0054030 1 b III B 1 889.739 985 .0054030 1 b III C 1 713.238 702 .0021514 1 b III D 1 977.990 626 .0021514 1 b III E 1 624.988 061 .0003404 1 b IV A 1 810.384 386 .0054030 1 b IV B 1 898.635 027 .0054030 1 b IV C 1 722.133 744 .0021514 1 b IV D 1 986.885 668 .0021514 1 b IV E 1 633.883 103 .0003404 1 b V A 1 804.279 694 .0008548 1 b V B 1 892.530 605 .0008548 1 b V C 1 716.029 322 .0003404 1 b V D 1 980.781 246 .0003404 1 b V E 1 627.778 681 .0000538 1 c I A 1 792.289 145 .0054030 1 c I B 1 880.539 786 .0054030 1 c I C 1 704.038 503 .0021514 1 c I D 1 968.790 427 .0021514 1 c I E 1 615.787 862 .0003404 1 c II A 1 795.254 160 .0054030 1 c II B 1 883.504 801 .0054030 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 TABLE 2-D (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W^_ 1 c II C 1 707.003 518 1 c II D 1 971.755 442 1 c II E 1 618.752 877 1 c III A 1 789.324 130 1 c III B 1 877.574 771 1 c III C 1 701.073 488 1 c III D 1 965.825 412 1 c III E 1 612.822 847 1 c IV A 1 798.219 172 1 c IV B 1 886.469 813 1 c IV C 1 709.968 530 1 c IV D 1 974.720 454 1 c IV E 1 621.717 889 1 c V A 1 792.114 480 1 c V B 1 880.365 391 1 c V C 1 703.864 108 1 c V D 1 968.616 032 1 c V E 1 615.613 467 1 d I A 1 812.036 965 1 d I B 1 900.287 606 1 d I C 1 723.786 323 1 d I D 1 988.538 247 1 d I E 1 635.535 682 1 d II A 1 815.001 980 1 d II B 1 903.252 621 1 d II C 1 726.751 338 1 d II D 1 991.503 262 1 d II E 1 638.500 697 1 d III A 1 809.071 950 1 d III B 1 897.322 591 1 d III C 1 720.821 308 1 d III D 1 985.573 232 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 TABLE 2-D (Continued) Combinations' Values Optimum Value ► 11 b12 b21 b22 of 1 d III E 1 632.570 667 1 d IV A 1 817.966 992 1 d IV B 1 906.217 633 1 d IV C 1 729.716 350 1 d IV D 1 994.468 274 1 d IV E 1 641.465 709 1 d V A 1 811.862 300 1 d V B 1 900.113 211 1 d V C 1 723.611 928 1 d V D 1 988.363 852 1 d V E 1 635.361 287 1 e I A 1 785.706 540 1 e I B 1 873.957 181 1 e I C 1 697.455 898 1 e I D 1 962.207 822 1 e I E 1 609.205 257 1 e II A 1 788.671 555 1 e II B 1 876.922 196 1 e II C 1 700.420 913 1 e II D 1 965.172 837 1 e II E 1 612.170 272 1 e III A 1 782.741 525 1 e III B 1 870.992 166 1 e III C 1 694.490 883 1 e III D 1 959.242 807 1 e III E 1 606.240 242 1 e IV A 1 791.636 567 1 e IV B 1 879.887 208 1 e IV C 1 703.385 925 1 e IV D 1 968.137 849 1 e IV E 1 615.135 284 1 e V A 1 785.531 875 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 TABLE 2-D (Continued) Combinations' Values Optimum Value '11 b12 b21 b22 of W^_ 1 e V B 1 873.782 786 1 e V C 1 697.281 503 1 e V D 1 962.033 427 1 e V E 1 609.030 862 2 a I A 1 799.169 107 2 a I B 1 887.419 748 2 a I C 1 710.918 465 2 a I D 1 975.670 389 2 a I E 1 622.667 824 2 a II A 1 802.134 122 2 a II B 1 890.384 763 2 a II C 1 713.883 480 2 a II D 1 978.635 404 2 a II E 1 625.632 839 2 a III A 1 796.204 092 2 a III B 1 884.454 733 2 a III C 1 707.953 450 2 a III D 1 972.705 374 2 a III E 1 619.702 809 2 a IV A 1 805.099 134 2 a IV B 1 893.349 775 2 a IV C 1 716.848 492 2 a IV D 1 981.600 416 2 a IV E 1 628.597 851 2 a V A 1 798.994 442 2 a V B 1 887.245 353 2 a V C 1 710.744 070 2 a V D 1 975.495 994 2 a V E 1 622.493 429 2 b I A 1 805.751 713 2 b I B 1 894.002 354 2 b I C 1 717.501 071 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 TABLE 2-D (Continued) Combinations’ Values Optimum Value ’ 11 b12 b21 b22 of W_ 5 2 b I D 1 982.252 995 2 b I E 1 629.250 430 2 b II A 1 808.716 728 2 b II B 1 896.967 369 2 b II C 1 720.466 086 2 b II D 1 985.218 010 2 b II E 1 632.215 445 2 b III A 1 802.786 698 2 b III B 1 891.037 339 2 b III C 1 714.536 056 2 b III D 1 978.287 980 2 b III E 1 626.285 415 2 b IV A 1 811.681 740 2 b IV B 1 899.932 381 2 b IV C 1 723.431 098 2 b IV D 1 988.183 022 2 b IV E 1 635.180 457 2 b V A 1 805.577 048 2 b V B 1 893.827 959 2 b V C 1 717.326 676 2 b V D 1 982.078 600 2 b V E 1 629.076 035 2 c I A 1 792.586 499 2 c I B 1 880.837 140 2 c I C 1 704.335 857 2 c I D 1 969.087 781 2 c I E 1 616.085 216 2 c II A 1 795.551 514 2 c II B 1 883.802 155 2 c II C 1 707.300 872 2 c II D 1 972.052 796 2 c II E 1 619.050 231 157 TABLE 2-D (Continued) Problem Combinations1 Values Optimum Value p(w^) Number b-^ b-^ ^21 ^22 °^ ^5 186 2 c III A 1 789.621 484 .0021514 187 2 c III B 1 877.872 125 .0021514 188 2 c III C 1 701.370 842 .0008566 189 2 c III D 1 966.122 766 .0008566 190 2 c III E 1 613.120 201 .0001355 191 2 c IV A 1 798.516 526 .0021514 192 2 c IV B 1 886.767 167 .0021514 193 2 c IV C 1 710.265 884 .0028566 194 2 c IV D 1 975.017 808 .0028566 195 2 c IV E 1 622.015 243 .0021355 196 2 c V A 1 792.411 834 .0003404 197 2 c V B 1 880.662 745 .0003404 198 2 c V C 1 704.161 462 .0001355 199 2 c V D 1 968.913 386 .0001355 200 2 c V E 1 615.910 821 .0000214 201 2 d I A 1 812.334 319 .0054030 202 2 d I B 1 900.584 960 .0054030 203 2 d I C 1 724.083 677 .0021514 204 2 d I D 1 989.835 601 .0021514 205 2 d I E 1 635.833 036 .0003404 206 2 d II A 1 815.299 334 .0054030 207 2 d II B 1 903.549 975 .0054030 208 2 d II C 1 727.048 692 .0021514 209 2 d II D 1 991.800 616 .0021514 210 2 d II E 1 638.798 051 .0003404 211 2 d III A 1 809.369 304 .0021514 212 2 d III B 1 897.619 945 .0021514 213 2 d III C 1 721.118 662 .0008566 214 2 d III D 1 985.870 586 .0008566 215 2 d III E 1 632.868 021 .0001355 216 2 d IV A 1 818.264 346 .0021514 217 2 d IV B 1 906.514 987 .0021514 218 2 d IV C 1 730.013 704 .0008566 Prol Nui 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 158 TABLE 2-D (Continued) Combinations' Values Optimum Value P(W^) bll b12 b21 b22 of W5 2 d IV D 1 994.765 628 .0008566 2 d IV E 1 641.763 063 .0001355 2 d V A 1 812.159 654 .0003404 2 d V B 1 900.410 565 .0003404 2 d V C 1 723.909 282 .0001355 2 d V D 1 988.661 206 .0001355 2 d V E 1 635.658 641 .0000214 2 e I A 1 786.003 894 .0008548 2 e I B 1 874.254 535 .0008548 2 e I C 1 697.753 252 .0003404 2 e I D 1 962.505 176 .0003404 2 e I E 1 609.502 611 .0000538 2 e II A 1 818.968 909 .0008548 2 e II B 1 877.219 550 .0008548 2 e II C 1 700.718 267 .0003404 2 e II D 1 965.470 191 .0003404 2 e II E 1 612.467 626 .0000538 2 e III A 1 783.038 879 .0003404 2 e III B 1 871.289 520 .0003404 2 e III C 1 694.788 237 .0001355 2 e III D 1 959.540 161 .0001355 2 e III E 1 606.537 596 .0000214 2 e IV A 1 791.933 921 .0003404 2 e IV B 1 880.184 562 .0003404 2 e IV C 1 703.683 279 .0001355 2 e IV D 1 968.435 203 .0001355 2 e IV E 1 615.432 638 .0000214 2 e V A 1 785.829 229 .0000538 2 e V B 1 874.080 140 .0000538 2 e V C 1 697.578 857 .0000214 2 e V D 1 962.330 781 .0000214 2 e V E 1 609.328 216 .0000034 3 a I A 1 798.211 104 .0054030 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 TABLE 2-D (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of W,- 3 a I B 1 886.461 745 3 a I c 1 709.960 462 3 a I D 1 974.712 386 3 a I E 1 621.709 821 3 a II A 1 801.176 119 3 a II B 1 889.426 760 3 a II C 1 712.925 477 3 a II D 1 977.677 401 3 a II E 1 624.674 836 3 a III A 1 795.246 089 3 a III B 1 883.496 730 3 a III C 1 706.995 447 3 a III D 1 971.747 371 3 a III E 1 618.744 806 3 a IV A 1 804.141 131 3 a IV B 1 892.391 772 3 a IV C 1 715.890 489 3 a IV D 1 980.642 413 3 a IV E 1 627.639 848 3 a V A 1 798.036 439 3 a V B 1 886.287 350 3 a V C 1 709.786 067 3 a V D 1 974.537 991 3 a V E 1 621.535 426 3 b I A 1 804.793 710 3 b I B 1 893.044 351 3 b I C 1 716.543 068 3 b I D 1 981.294 992 3 b I E 1 628.292 427 3 b II A 1 807.758 725 3 b II B 1 896.009 366 3 b II C 1 719.508 083 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 TABLE 2-D (Continued) Combinations' Values Optimum Value '11 b12 b21 b22 of W5 3 b II D 1 984.260 007 3 b II E 1 631.257 442 3 b III A 1 801.828 695 3 b III B 1 890.079 336 3 b III C 1 713.578 053 3 b III D 1 978.329 977 3 b III E 1 625.327 412 3 b IV A 1 810.723 737 3 b IV B 1 898.974 378 3 b IV C 1 722.473 095 3 b IV D 1 987.225 019 3 b IV E 1 634.222 454 3 b V A 1 804.619 045 3 b V B 1 892.869 956 3 b V C 1 716.368 673 3 b V D 1 981.120 597 3 b V E 1 628.118 032 3 c ' I A 1 791.628 496 3 c I B 1 879.879 137 3 c I C 1 703.377 854 3 c I D 1 968.129 778 3 c I E 1 615.127 213 3 c II A 1 794.593 511 3 c II B 1 882.844 152 3 c II C 1 706.342 869 3 c II D 1 971.094 793 3 c II E 1 628.092 228 3 c III A 1 788.663 481 3 c III B 1 876.914 122 3 c III C 1 700.412 839 3 c III D 1 965.164 763 3 c III E 1 612.162 198 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 TABLE 2-D (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of 3 c IV A 1 797.558 523 3 c IV B 1 885.809 164 3 c IV C 1 709.307 883 3 c IV D 1 974.059 805 3 c IV E 1 621.057 240 3 c V A 1 791.453 831 3 c V B 1 879.704 732 3 c V C 1 703.203 459 3 c V D 1 967.955 383 3 c V E 1 614.952 818 3 d I A 1 811.376 316 3 d I B 1 899.626 957 3 d I C 1 723.125 674 3 d I D 1 987.877 598 3 d I E 1 634.875 033 3 d II A 1 814.341 331 3 d II B 1 902.591 972 3 d II C 1 726.090 689 3 d II D 1 990.842 613 3 d II E 1 637.840 048 3 d III A 1 808.411 301 3 d III B 1 896.661 942 3 d III C 1 720.160 659 3 d III D 1 984.912 583 3 d III E 1 631.910 018 3 d IV A 1 817.306 343 3 d IV B 1 905.556 984 3 d IV C 1 729.055 701 3 d IV D 1 993.807 625 3 d IV E 1 640.805 060 3 d V A 1 811.201 651 3 d V B 1 899.452 562 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 TABLE 2-D (Continued) Combinations' Values Optimum Value '11 b 1 2 b2 l b 2 2 of W 5 3 d V C 1 722.951 279 3 d V D 1 987.703 203 3 d V E 1 634.700 638 3 e I A 1 785.045 891 3 e I B 1 873.296 532 3 e I C 1 696.795 249 3 e I D 1 961.547 173 3 e I E 1 608.544 608 3 e II A 1 788.010 906 3 e II B 1 876.261 547 3 e II C 1 699.760 264 3 e II D 1 964.512 188 3 e II E 1 611.509 623 3 e III A 1 782.080 876 3 e III B 1 870.331 517 3 e III C 1 693.830 234 3 e III D 1 958.582 158 3 e III E 1 605.579 593 3 e IV A 1 790.975 918 3 e IV B 1 879.226 559 3 e IV C 1 702.725 276 3 e IV D 1 967.477 2 0 0 3 e IV E 1 614.474 635 3 e V A 1 784.871 226 3 e V B 1 873.122 137 3 e V C 1 696.620 854 3 e V D 1 961.372 778 3 e V E 1 608.370 213 4 a I A 1 799.648 108 4 a I B 1 887.898 749 4 a I C 1 711.397 466 4 a I D 976.149 390 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 TABLE 2-D (Continued) Combinations* Values Optimum Value '11 b12 b21 b22 of W5 4 a I E 1 623.146 825 4 a II A 1 802.613 123 4 a II B 1 890.863 764 4 a II C 1 714 362 481 4 a II D 1 979.114 405 4 a II E 1 626.111 840 4 a III A 1 796.683 093 4 a III B 1 884.933 734 4 a III C 1 708.432 451 4 a III D 1 973.184 375 4 a III E 1 620.181 810 4 a IV A 1 805.578 135 4 a IV B 1 893.828 776 4 a IV C 1 717.327 493 4 a IV D 1 982.079 417 4 a IV E 1 629.076 852 4 a V A 1 799.473 443 4 a V B 1 887.724 354 4 a V C 1 711.223 071 4 a V D 1 975.974 995 4 a V E 1 622.972 430 4 b I A 1 806.230 714 4 b I B 1 894.481 355 4 b I C 1 717.980 072 4 b I D 1 982.731 996 4 b I E 1 629.729 431 4 b II A 1 809.195 729 4 b II B 1 897.446 370 4 b II C 1 720.945 087 4 b II D 1 985.697 011 4 b II E 1 632.694 446 4 b III A 1 803.265 699 164 TABLE 2-D (Continued) Problem Combinations’ Values Optimum Value p(w5) Number bll b12 b21 b22 of W5 412 4 b III B 1 891.516 340 .0021514 413 4 b III C 1 715.015 057 .0008566 414 4 b III D 1 979.766 981 .0008566 415 4 b III E 1 626.764 416 .0001355 416 4 b IV A 1 812.160 741 .0021514 417 4 b IV B 1 900.411 382 .0021514 418 4 b IV C 1 723.910 099 .0008566 419 4 b IV D 1 988.662 023 .0008566 420 4 b IV E 1 635.659 458 .0001355 421 4 b V A 1 806.056 049 .0003404 422 4 b V B 1 894.306 960 .0003404 423 4 b V C 1 717.805 677 .0001355 424 4 b V D 1 982.557 601 .0001355 425 4 b V E 1 629.555 036 .0000214 426 4 c I A 1 793.065 500 .0021514 427 4 c I B 1 881.316 141 .0021514 428 4 c I C 1 704.814 858 .0008566 429 4 c I D 1 969.566 782 .0008566 430 4 c I E 1 616.564 217 .0001356 431 4 c II A 1 796.030 515 .0021514 432 4 c II B 1 884.281 156 .0021514 433 4 c II C 1 707.779 873 .0008566 434 4 c II D 1 972.531 797 .0008566 435 4 c II E 1 619.529 232 .0001355 436 4 c III A 1 790.100 485 .0008566 437 4 c III B 1 878.351 126 .0008566 438 4 c III C 1 701.849 843 .0003411 439 4 c III D 1 966.601 767 .0003411 440 4 c III E 1 613.599 202 .0000540 441 4 c IV A 1 798.995 527 .0008566 442 4 c IV B 1 887.246 168 .0008566 165 TABLE 2-D (Continued) Problem Number Combinations’ Values bll b12 b21 b22 Optimum Value of W5 p(w5) 443 4 c IV c 1 710.744 885 .0003411 444 4 c IV D 1 975.496 809 .0003411 445 4 c IV E 1 622.494 244 .0000540 446 4 c V A 1 792.890 835 .0001355 447 4 c V B 1 881.141 746 .0001355 448 4 c V C 1 704.640 463 .0000540 449 4 c V D 1 979.392 387 .0000540 450 4 c V E 1 616.389 822 .0000085 451 4 d I A 1 812.813 320 .0021514 452 4 d I B 1 901.063 961 .0021514 453 4 d I C 1 724.562 678 .0008566 454 4 d I D 1 989.314 602 .0008566 455 4 d I E 1 636.311 037 .0001355 456 4 d II A 1 815.778 335 .0021514 457 4 d II B 1 904.028 976 .0021514 458 4 d II C 1 727.527 693 .0008566 459 4 d II D 1 992.279 617 .0008566 460 4 d II E 1 639.277 052 .0001355 461 4 d III A 1 809.848 305 .0008566 462 4 d III B 1 898.098 946 .0008566 463 4 d III C 1 721.597 663 .0003411 464 4 d III D 1 986.349 587 .0003411 465 4 d III E 1 633.347 022 .0000540 466 4 d IV A 1 818.743 347 .0008566 467 4 d IV B 1 906.993 988 .0008566 468 4 d IV C 1 730.492 705 .0003411 469 4 d IV D 1 995.244 629 .0003411 470 4 d IV E 1 642.242 064 .0000540 471 4 d V A 1 812.638 655 .0001355 472 4 d V B 1 900.889 566 .0001355 473 4 d V C 1 724.388 283 .0000540 474 4 d V D 1 989.140 207 .0000540 166 TABLE 2-D (Continued) Problem - Number Combinations’ Values bll b12 b21 b22 Optimum Value of W5 p(w5) 475 4 d V E 1 636.037 642 .0000085 476 4 e I A 1 786.483 395 .0003404 477 4 e I B 1 874.734 036 .0003404 478 4 e I C 1 698.232 753 .0001355 479 4 e I D 1 962.984 677 .0001355 480 4 e I E 1 609.982 112 .0000214 481 4 e II A 1 789.448 410 .0003404 482 4 e II B 1 877.699 051 .0003404 483 4 e II C 1 701.197 768 .0001355 484 4 e II D 1 965.949 692 .0001355 485 4 e II E 1 612.947 127 .0000214 486 4 e III A 1 783.518 380 .0008566 487 4 e III B 1 871.769 021 .0008566 488 4 e III C 1 695.267 738 .0000540 489 4 e III D 1 960.019 662 .0000540 490 4 e III E 1 607.017 097 .0000085 491 4 e IV A 1 792.413 422 .0008566 492 4 e IV B 1 880.664 063 .0008566 493 4 e IV C 1 704.162 780 .0000540 494 4 e IV D 1 968.914 704 .0000540 495 4 e IV E 1 615.912 139 .0000085 496 4 e V A 1 786.308 730 .0000214 497 4 e V B 1 874.559 641 .0000214 498 4 e V C 1 698.058 358 .0000085 499 4 e V D 1 962.810 282 .0000085 500 4 e V E 1 609.707 717 .0000014 501 5 a I A 1 797.732 103 .0008548 502 5 a I B 1 885.982 744 .0008548 503 5 a I C 1 709.481 461 .0003404 504 5 a I D 1 974.233 385 .0003404 505 5 a I E 1 621.230 820 .0000538 506 5 a II A 1 800.697 118 .0008548 167 TABLE 2-D (Continued) Problem Combinations' Values Optimum Value P(W^) Number b ^ b±2 b2± b22 of W5 507 5 a II B 1 888.947 759 .0008548 508 5 a II C 1 712.446 576 .0003404 509 5 a II D 1 977.198 400 .0003404 510 5 a II E 1 624.195 835 .0000538 511 5 a III A 1 794.767 088 .0003404 512 5 a III B 1 883.017 729 .0003404 513 5 a III C 1 706.516 446 .0001355 514 5 a III D 1 971.268 370 .0001355 515 5 a III E 1 618.265 805 .0000214 516 5 a IV A 1 803.662 130 .0003404 517 5 a IV B 1 891.912 771 .0003404 518 5 a IV C 1 715.411 488 .0001355 519 5 a IV D 1 980.163 412 .0001355 520 5 a IV E 1 627.260 847 .0000214 521 5 a V A 1 797.557 438 .0000538 522 5 a V B 1 885.808 349 .0000538 523 5 a V C 1 709.307 066 .0000214 524 5 a V D 1 974.058 990 .0000214 525 5 a V E 1 621.056 425 .0000034 526 5 b I A 1 804.314 709 .0008548 527 5 b I B 1 892.565 350 .0008548 528 5 b I C 1 716.064 067 .0003404 529 5 b I D 1 980.815 991 .0003404 530 5 b I E 1 627.813 426 .0000538 531 5 b II A 1 807.279 724 .0008548 532 5 b II B 1 895.530 365 .0008548 533 5 b II C 1 719.029 082 .0003404 534 5 b II D 1 983.781 006 .0003404 535 5 b II E 1 630.778 441 .0000538 536 5 b III A 1 801.349 694 .0003404 537 5 b III B 1 889.600 335 .0003404 538 5 b III C 1 713.099 052 .0001355 539 5 b III D 1 977.850 976 .0001355 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 TABLE 2-D (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W5 5 b III E 1 624.848 411 5 b IV A 1 810.244 736 5 b IV B 1 898.495 377 5 b IV C 1 721.994 094 5 b IV D 1 986.746 018 5 b IV E 1 633.743 453 5 b V A 1 804.140 044 5 b V B 1 892.390 955 5 b V C 1 715.889 672 5 b V D 1 980.641 596 5 b V E 1 627.639 031 5 c I A 1 791.149 495 5 c I B 1 879.400 136 5 c I C 1 702.898 853 5 c I D 1 967.650 777 5 c I E 1 614.648 212 5 c II A 1 794.114 510 5 c II B 1 882.365 151 5 c II C 1 705.863 868 5 c II D 1 970.615 792 5 c II E 1 617.613 227 5 c III A 1 788.184 480 5 c III B 1 876.435 121 5 c III C 1 699.933 838 5 c III D 1 964.685 762 5 c III E 1 611.683 197 5 c IV A 1 797.079 522 5 c IV B 1 885.330 163 5 c IV C 1 708.828 380 5 c IV D 1 973.580 804 5 c IV E 1 620.578 239 5 c V A 1 790.974 830 5 c V B 1 879.225 741 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 TABLE 2-D (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W5 5 c V c 1 702.724 458 5 c V D 1 967.476 382 5 c V E 1 614.473 817 5 d I A 1 810.897 315 5 d I B 1 899.147 956 5 d I c 1 722.646 673 5 d I D 1 987.398 597 5 d I E 1 634.396 032 5 d II A 1 813.862 330 5 d II B 1 902.112 971 5 d II C 1 725.611 688 5 d II D 1 990.363 612 5 d II E 1 637.361 047 5 d III A 1 807.932 300 5 d III B 1 896.182 941 5 d III C 1 719.681 658 5 d III D 1 984.433 582 5 d III E 1 631.431 017 5 d IV A 1 816.827 342 5 d IV B 1 905.077 983 5 d IV C 1 728.576 700 5 d IV D 1 993.328 624 5 d IV E 1 640.326 059 5 d V A 1 810.722 650 5 d V B 1 898.973 561 5 d V C 1 722.472 278 5 d V D 1 987.224 202 5 d V E 1 634.221 637 5 e I A 1 784.566 890 5 e I B 1 872.817 531 5 e I C 1 696.316 248 5 e I D 1 961.068 172 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 TABLE 2-D (Continued) Combinations1 Values Optimum Value '11 b12 b21 b22 of 5 e I E 1 608.065 607 5 e II A 1 787.531 905 5 e II B 1 875.782 546 5 e II C 1 699.281 263 5 e II D 1 964.033 187 5 e II E 1 611.030 622 5 e III A 1 781.601 875 5 e III B 1 869.852 516 5 e III C 1 693.351 233 5 e III D 1 958.103 157 5 e III E 1 605.100 592 5 e IV A 1 790.496 917 5 e IV B 1 878.747 558 5 e IV C 1 702.246 275 5 e IV D 1 966.998 199 5 e IV E 1 613.995 634 5 e V A 1 784.392 225 5 e V B 1 872.643 136 5 e V C 1 696.141 853 5 e V D 1 960.893 777 5 e V E 1 607.891 212 171 These values of W,- and their probabilities give the following moments for the objective function: Mean value = 1 841.936 306 Standard deviation = 77.433 857 Lower 5% probability level = 1 835.865 492 Finally the approximate distribution of W5 is: f(x) = l/yiTT (77.432857) (x- 1841.936306)2 2(77.433857)2 Policy V: U n = .50 U12 = -50 U21 = *50 U22 = *50 We obtain the following optimum solutions for W^_ , as shown in Table 2-E: 1 2 3 4 5 6 7 8 9 lO 11 12 13 14 15 16 17 18 19 20 21 22 23 24 TABLE 2-E POLICY V U1:L = 1/2 U21 = 1/2 U12 = 1/2 U22 = 1/2 Combinations' Values Optimum Value bll b12 b21 b22 of W5 1 a I A 1 855.361 160 1 a I B 1 933.611 801 1 a I C 1 757.110 518 1 a I D 2 021.862 442 1 a I E 1 668.859 877 1 a II A 1 851.291 189 1 a II B 1 939.541 830 1 a II C 1 763.040 547 1 a II D 2 027.792 471 1 a II E 1 674.789 906 1 a III A 1 839.431 161 1 a III B 1 927.681 772 1 a III C 1 751.180 489 1 a III D 2 015.932 413 1 a III E 1 662.929 848 1 a IV A 1 857.221 217 1 a IV B 1 945.471 858 1 a IV C 1 768.970 575 1 a IV D 2 033.722 499 1 a IV E 1 680.719 934 1 a V A 1 845.012 369 1 a V B 1 933.263 010 1 a V C 1 756.761 727 1 a V D 2 020.513 651 1 a V E 1 668.511 086 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 TABLE 2-E (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of W5 1 b I A 1 851.943 766 1 b I B 1 940.194 407 1 b I C 1 763.693 124 1 b I D 2 028.445 048 1 b I E 1 675.442 483 1 b II A 1 857.873 795 1 b II B 1 946.124 436 1 b II C 1 769.623 153 1 b II D 2 034.375 077 1 b II E 1 681.372 512 1 b III A 1 846.013 737 1 b III B 1 934.264 378 1 b III C 1 757.763 095 1 b III D 2 022.515 019 1 b III E 1 669.512 454 1 b IV A 1 863.803 823 1 b IV B 1 952.054 464 1 b IV C 1 775.553 181 1 b IV D 2 040.305 105 1 b IV E 1 687.302 540 1 b V A 1 851.594 975 1 b V B 1 939.845 616 1 b V C 1 763.344 333 1 b V D 2 027.096 257 1 b V E 1 675.093 692 1 c I A 1 838.778 552 1 c I B 1 927.029 193 1 c I C 1 750.527 910 1 c I D 2 015.279 834 1 c I E 1 662.277 269 1 c II A 1 844.708 581 1 c II B 1 932.959 222 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 174 TABLE 2-E (Continued) Combinations’ Values Optimum Value P(W ) b b b b of W 11 12 21 22 5 1 c II C 1 756.457 939 .0021514 1 c II D 2 021.209 863 .0021514 1 c II E 1 668.207 298 .0003404 1 c III A 1 832.848 523 .0021514 1 c III B 1 921.099 164 .0021514 1 c III C 1 744.597 881 .0008566 1 c III D 2 009.349 805 .0008566 1 c III E 1 656.347 240 .0001355 1 c IV A 1 850.638 609 .0021514 1 c IV B 1 938.889 250 .0021514 1 c IV C 1 762.387 967 .0008566 1 c IV D 2 027.139 891 .0008566 1 c IV E 1 674.137 326 .0001355 1 c V A 1 838.439 761 .0003404 1 c V B 1 926.680 402 .0003404 1 c V C 1 750.179 119 .0001355 1 c V D 2 013.931 043 .0001355 1 c' V E 1 661.928 478 .0000214 1 d I A 1 858.526 372 .0054030 1 d I B 1 946.777 013 .0054030 1 d I C 1 770.275 730 .0021514 1 d I D 2 035.027 654 .0021514 1 d I E 1 682.025 089 .0003404 1 d II A 1 864.456 401 .0054030 1 d II B 1 952.707 042 .0054030 1 d II C 1 776.205 759 .0021514 1 d II D 2 040.957 683 .0021514 1 d II E 1 687.955 118 .0003404 1 d III A 1 852.596 343 .0021514 1 d III B 1 940.846 984 .0021514 1 d III C 1 764.345 701 .0008566 1 d III D 2 029.097 625 .0008566 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 TABLE 2-E (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of Wj_ 1 d III E 1 676.095 060 1 d IV A 1 870.386 429 1 d IV B 1 958.637 070 1 d IV C 1 782.135 787 1 d IV D 2 046.887 711 1 d IV E 1 693.885 146 1 d V A 1 858.177 581 1 d V B 1 946.428 222 1 d V C 1 769.926 939 1 d V D 2 033.678 863 1 d V E 1 681.676 298 1 e I A 1 832.195 947 1 e I B 1 920.446 588 1 e I C 1 743.945 305 1 e I D 2 008.697 229 1 e I E 1 655.694 664 1 e II A 1 838.125 976 1 e II B 1 926.376 617 1 e II C 1 749.875 334 1 e II D 2 014.627 258 1 e II E 1 661.624 693 1 e III A 1 826.265 918 1 e III B 1 914.516 559 1 e III C 1 738.015 276 1 e III D 2 002.767 200 1 e III E 1 649.764 635 1 e IV A 1 844.056 004 1 e IV B 1 932.306 645 1 e IV C 1 755.805 362 1 e IV D 2 020.557 286 1 e IV E 1 667.554 721 1 e V A 1 831.847 156 176 TABLE 2-E (Continued) Problem Combinations1 Values Optimum Value P(W5) Number b.^ b12 b21 b22 of W5 122 1 e V B 1 920.097 797 .0000538 123 1 e V C 1 743.596 514 .0000214 124 1 e V D 2 007.348 438 .0000214 125 1 e V E 1 655.345 873 .0000034 126 2 a I A 1 845.559 396 .0135690 127 2 a I B 1 933.810 037 .0135690 128 2 a I C 1 757.308 754 .0054030 129 2 a I D 2 022.060 678 .0054030 130 2 a I E 1 669.058 113 .0008548 131 2 a II A 1 851.489 425 .0135690 132 2 a II B 1 939.740 066 .0135690 133 2 a II C 1 763.238 783 .0054030 134 2 a II D 2 027.990 707 .0054030 135 2 a II E 1 674.988 142 .0008548 136 2 a III A 1 839.629 367 .0054030 137 2 a III B 1 927.880 008 .0054030 138 2 a III C 1 751.378 725 .0021514 139 2 a III D 2 016.130 649 .0021514 140 2 a III E 1 663.128 084 .0003404 141 2 a IV A 1 857.419 453 .0054030 142 2 a IV B 1 945.670 094 .0054030 143 2 a IV C 1 769.168 811 .0021514 144 2 a IV D 2 033.920 735 .0021514 145 2 a IV E 1 680.918 170 .0003404 146 2 a V A 1 845.210 605 .0008548 147 2 a V B 1 933.461 246 .0008548 148 2 a V C 1 756.959 963 .0003404 149 2 a V D 2 020.711 887 .0003404 150 2 a V E 1 668.709 322 .0000538 151 2 b I A 1 852.142 002 .0135690 152 2 b I B 1 940.392 643 .0135690 153 2 b I C 1 763.891 360 .0054030 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 3-85 TABLE 2-E (Continued) Combinations1 Values Optimum Value '11 b12 b21 b22 of W5 2 b I D 2 028.643 284 2 b I E 1 675.640 719 2 b II A 1 858.072 031 2 b II B 1 946.322 672 2 b II C 1 769.821 389 2 b II D 2 034.573 313 2 b II E 1 681.570 748 2 b III A 1 846.211 973 2 b III B 1 934.462 614 2 b III C 1 757.961 331 2 b III D 2 022.713 255 2 b III E 1 669.710 690 2 b IV A 1 864.002 059 2 b IV B 1 952.252 700 2 b IV C 1 775.751 417 2 b IV D 2 040.503 341 2 b IV E 1 687.500 776 2 b V A 1 851.793 211 2 b V B 1 940.043 852 2 b V C 1 763.542 569 2 b V D 2 027.294 493 2 b V E 1 675.291 928 2 c I A 1 838.976 788 2 c I B 1 927.227 429 2 c I C 1 750.726 146 2 c I D 2 015.478 070 2 c I E 1 662.475 505 2 c II A 1 844.906 817 2 c II B 1 933.157 458 2 c II C 1 756.656 175 2 c II D 2 021.408 099 2 c II E 1 668.405 534 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 TABLE 2-E (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W,_ 2 c III A 1 833.046 759 2 c III B 1 921.297 400 2 c III c 1 744.796 117 2 c III D 2 009.548 041 2 c III E 1 656.545 476 2 c IV A 1 850.836 845 2 c IV B 1 939.087 486 2 c IV C 1 762.586 203 2 c IV D 2 027.338 127 2 c IV E 1 674.335 562 2 c V A 1 838.627 997 2 c V B 1 926.878 638 2 c V C 1 750.377 355 2 c V D 2 014.129 279 2 c V E 1 662.126 714 2 d I A 1 858.724 608 2 d I B 1 946.975 249 2 d I C 1 770.473 966 2 d I D 2 035.225 890 2 d I E 1 682.223 325 2 d II A 1 864.654 637 2 d II B 1 952.905 278 2 d II C 1 776.403 995 2 d II D 2 041.155 919 2 d II E 1 688.153 354 2 d III A 1 852.794 579 2 d III B 1 941.045 220 2 d III C 1 764.543 937 2 d III D 2 029.295 861 2 d III E 1 676.293 296 2 d IV A 1 870.584 665 2 d IV B 1 958.835 306 179 TABLE 2-E (Continued) Problem Combinations’ Values Optimum Value P(W^) Number b ^ b12 b21 b22 of W5 218 2 d IV c 1 782.334 023 .0008566 219 2 d IV D 2 047.085 947 .0008566 220 2 d IV E 1 694.083 382 .0001355 221 2 d V A 1 858.375 817 .0003404 222 2 d V B 1 946.626 458 .0003404 223 2 d V C 1 770.125 175 .0001355 224 2 d V D 2 033.877 099 .0001355 225 2 d V E 1 681.873 534 .0000214 226 2 e I A 1 832.394 184 .0008548 227 2 e I B 1 920.644 825 .0008548 228 2 e I C 1 744.143 542 .0003404 229 2 e I D 2 008.895 466 .0003404 230 2 e I E 1 655.892 901 .0000538 231 2 e II A 1 838.324 213 .0008548 232 2 e II B 1 926.574 854 .0008548 233 2 e II C 1 750.073 571 .0003404 234 2 e II D 2 014.825 495 .0003404 235 2 e II E 1 661.822 930 .0000538 236 2 e III A 1 826.464 155 .0003404 237 2 e III B 1 914.714 796 .0003404 238 2 e III C 1 738.213 513 .0001355 239 2 e III D 2 002.965 437 .0001355 240 2 e III E 1 649.962 872 .0000214 241 2 e IV A 1 844.254 241 .0003404 242 2 e IV B 1 932.504 882 .0003404 243 2 e IV C 1 756.003 599 .0001355 244 2 e IV D 2 020.755 523 .0001355 245 2 e IV E 1 667.752 958 .0000214 246 2 e V A 1 832.045 393 .0000538 247 2 e V B 1 920.296 034 .0000538 248 2 e V C 1 743.794 751 .0000214 249 2 e V D 2 007.546 675 .0000214 250 2 e V E 1 655.544 110 .0000034 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 TABLE 2-E (Continued) Combinations' Values Optimum Value '11 b12 b21 b22 of W5 3 a I A 1 844.920 728 3 a I B 1 933.171 369 3 a I C 1 756.670 086 3 a I D 2 021.422 010 3 a I E 1 668.419 445 3 a II A 1 850.850 757 3 a II B 1 939.101 398 3 a II C 1 762.600 115 3 a II D 2 027.352 039 3 a II E 1 674.349 474 3 a III A 1 838.990 699 3 a III B 1 927.241 340 3 a III C 1 750.740 057 3 a III D 2 015.491 981 3 a III E 1 662.489 416 3 a IV A 1 856.780 785 3 a IV B 1 945.031 426 3 a IV C 1 768.530 143 3 a IV D 2 033.282 067 3 a IV E 1 680.279 502 3 a V A 1 844.571 937 3 a V B 1 932.822 578 3 a V C 1 756.321 295 3 a V D 2 020.073 219 3 a V E 1 668.070 654 3 b I A 1 851.503 334 3 b I B 1 939.753 975 3 b I C 1- 763.252 692 3 b I D 2 028.004 616 3 b I E 1 675.002 051 3 b II A 1 857.433 363 3 b II B 1 945.684 004 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 181 TABLE 2-E (Continued) Combinations' Values Optimum Value p(W5) bll b12 b21 b22 of W5 3 b II C 1 769.182 721 .0021514 3 b II D 2 033.934 645 .0021514 3 b II E 1 680.932 080 .0003404 3 b III A 1 845.573 305 .0021514 3 b III B 1 933.823 946 .0021514 3 b III C 1 757.322 663 .0008566 3 b III D 2 022.074 587 .0008566 3 b III E 1 669.072 022 .0001355 3 b IV A 1 863.363 391 .0021514 3 b IV B 1 951.614 032 .0021514 3 b IV C 1 775.112 749 .0008566 3 b IV D 2 039.864 673 .0008566 3 b IV E 1 686.862 108 .0001355 3 b V A 1 851.154 543 .0003404 3 b V B 1 939.405 184 .0003404 3 b V C 1 762.903 901 .0001355 3 b V D 2 026.655 825 .0001355 3 b V E 1 674.653 260 .0000214 3 c I A 1 838.338 120 .0021514 3 c I B 1 926.588 761 .0021514 3 c I C 1 750.087 478 .0008566 3 c I D 2 014.839 402 .0008566 3 c I E 1 661.836 837 .0001355 3 c II A 1 844.268 149 .0021514 3 c II B 1 932.518 790 .0021514 3 c II C 1 756.017 507 .0008566 3 c II D 2 020.769 431 .0008566 3 c II E 1 667.766 866 .0001355 3 c III A 1 832.408 091 .0008566 3 c III B 1 920.658 732 .0008566 3 c III C 1 744.157 449 .0003411 3 c III D 2 008.909 373 .0003411 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 TABLE 2-E (Continued) Combinations' Value Optimum Value ’ 11 b12 b21 b22 of W5 3 c III E 1 655.906 808 3 c IV A 1 850.198 177 3 c IV B 1 938.448 818 3 c IV C 1 761.947 535 3 c IV D 2 026.699 459 3 c IV E 1 673.696 894 3 c V A 1 837.989 329 3 c V B 1 926.239 970 3 c V C 1 749.738 687 3 c V D 2 013.490 611 3 c V E 1 661.488 046 3 d I A 1 858.085 940 3 d I B 1 946.336 581 3 d I C 1 769.835 298 3 d I D 2 034.587 222 3 d I E 1 681.584 657 3 d II A 1 864.015 969 3 d II B 1 952.266 610 3 d II C 1 775.765 327 3 d II D 2 040.517 251 3 d II E 1 687.514 686 3 d III A 1 852.155 911 3 d III B 1 940.406 552 3 d III C 1 763.905 269 3 d III D 2 028.657 193 3 d III E 1 675.654 628 3 d IV A 1 869.945 997 3 d IV B 1 958.196 638 3 d IV Q 1 781.695 355 3 d IV D 2 046.447 279 3 d IV E 1 693.444 714 3 d V A 1 857.737 149 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 TABLE 2-E (Continued) Combinations' Values Optimum Value bll b12 b21 b_ _ 22 of W5 3 d V B 1 945.987 790 3 d V C 1 769.486 507 3 d V D 2 033.238 431 3 d V E 1 681.235 866 3 e I A 1 831.755 515 3 e I B 1 920.006 156 3 e I C 1 743.504 873 3 e I D 2 008.256 797 3 e I E 1 655.254 232 3 e II A 1 837.685 644 3 e II B 1 925.936 185 3 e II C 1 749.434 902 3 e II D 2 014.186 826 3 e II E 1 661.184 261 3 e III A 1 825.825 486 3 e III B 1 914.076 127 3 e III C 1 737.574 844 3 e III D 2 002.326 768 3 e III E 1 649.324 203 3 e IV A 1 843.615 572 3 e IV B 1 931.866 213 3 e IV C 1 755.364 930 3 e IV D 2 020.116 854 3 e IV E 1 667.114 289 3 e V A 1 831.406 724 3 e V B 1 919.657 365 3 e V C 1 743.156 082 3 e V D 2 006.908 006 3 e V E 1 654.905 441 4 a I A 1 845.878 730 4 a I B 1 934.129 371 4 a I C 1 757.628 088 4 a I D 2 022.380 012 184 TABLE 2-E (Continued) Problem Combinations' Values Optimum Value p ( w 5 ) Number bll b12 b21 b22 O f W ej 380 4 a I E 1 669.377 447 .0003404 381 4 a II A 1 851.808 759 .0054030 382 4 a II B 1 940.059 400 .0054030 383 4 a II C 1 763.558 117 .0021514 384 4 a II D 2 028.310 041 .0021514 385 4 a II E 1 675.307 476 .0003404 386 4 a III A 1 839.948 701 .0021514 387 4 a III B 1 928.199 342 .0021514 388 4 a III C 1 751.698 059 .0008566 389 4 a III D 2 016.449 983 .0008566 390 4 a IIT E 1 663.447 418 .0001355 391 4 a IV A 1 857.748 787 .0021514 392 4 a IV B 1 945.989 428 .0021514 393 4 a IV C 1 769.488 145 .0008566 394 4 a IV D 2 034.240 069 .0008566 395 4 a IV E 1 681.237 504 .0001355 396 4 a . V A 1 845.529 939 .0003404 397 4 a V B 1 933.780 580 .0003404 398 4 a V C 1 757.279 297 .0001355 399 4 a V D 2 021.031 221 .0001355 400 4 a V E 1 669.028 656 .0000214 401 4 b I A 1 852.461 336 .0054030 402 4 b I B 1 940.711 977 .0054030 403 4 b I C 1 764.210 694 .0021514 404 4 b I D 2 028.962 618 .0021514 405 4 b I E 1 675.960 053 .0003404 406 4 b II A 1 858.391 365 .0054030 407 4 b II B 1 946.642 006 .0054030 408 4 b II C 1 770.140 723 .0021514 409 4 b II D 2 034.892 647 .0021514 410 4 b II E 1 681.890 082 .0003404 411 4 b III A 1 846.531 307 .0021514 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 TABLE 2-E (Continued) Combinations* Values Optimum Value 'll b12 b21 b22 of W5 4 b III B 1 934.781 948 4 b III C 1 758.280 665 4 b III D 2 023.032 589 4 b III E 1 670.030 024 4 b ' IV A 1 864.321 393 4 b IV B 1 952.572 034 4 b IV C 1 776.070 751 4 b IV D 2 040.822 675 4 b IV E 1 687.820 110 4 b V A 1 852.112 545 4 b V B 1 940.363 186 4 b V C 1 763.861 903 4 b V D 2 027.613 827 4 b V E 1 675.611 262 4 c I A 1 839.296 122 4 c I B 1 927.546 763 4 c I C 1 751.045 480 4 c I D 2 015.797 404 4 c I E 1 662.794 839 4 c II A 1 845.226 151 4 c II B 1 933.476 792 4 c II C 1 756.975 509 4 c II D 2 021.727 433 4 c II E 1 668.724 868 4 c III A 1 833.366 093 4 c III B 1 921.616 734 4 c III C 1 745.115 451 4 c III D 2 009.867 375 4 c III E 1 656.864 810 4 c IV A 1 851.156 179 4 c IV B 1 939.406 820 4 c IV C 1 762.905 537 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 TABLE 2-E (Continued) Combinations' Values Optimum Value ’11 b12 b21 b22 of W c 4 c IV D 2 027.657 461 4 c IV E 1 674.654 896 4 c V A 1 838.947 331 4 c V B 1 927.197 972 4 c V C 1 750.696 689 4 c V D 2 014.448 613 4 c V E 1 662.446 048 4 d I A 1 859.043 942 4 d I B 1 947.294 583 4 d I C 1 770.793 300 4 d I D 2 035.545 224 4 d I E 1 682.542 659 4 d II A 1 864.973 971 4 d II B 1 953.224 612 4 d II C 1 776.723 329 4 d II D 2 041.475 253 4 d II E 1 688.472 688 4 d III A 1 853.113 913 4 d III B 1 941.364 554 4 d III C 1 764.863 271 4 d III D 2 029.615 195 4 d III E 1 676.612 630 4 d IV A 1 870.903 999 4 d IV B 1 959.154 640 4 d IV C 1 782.653 357 4 d IV D 2 047.405 281 4 d IV E 1 694.402 716 4 d V A 1 858.695 151 4 d V B 1 946.945 792 4 d V C 1 770.444 509 4 d V D 2 034.196 433 4 d V E 1 682.193 868 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 TABLE 2-E (Continued) Combinations1 Values Optimum Value ’1 1 b 1 2 b 2 1 b 2 2 of W5 4 e I A 1 832.713 517 4 e I B 1 920.964 158 4 e I C 1 744.462 875 4 e I D 2 009.214 799 4 e I E 1 656.212 234 4 e II A 1 838.643 546 4 e II B 1 926.894 187 4 e II C 1 750.392 904 4 e II D 2 015.144 828 4 e II E 1 662.142 263 4 e III A 1 826.783 488 4 e III B 1 915.044 129 4 e III C 1 738.532 846 4 e III D 2 003.284 770 4 e III E 1 650.282 205 4 e IV A 1 844.573 574 4 e IV B 1 932.824 215 4 e IV C 1 756.322 932 4 e IV D 2 021.074 856 4 e IV E 1 668.072 291 4 e V A 1 832.364 726 4 e V B 1 920.615 367 4 e V C 1 744.114 084 4 e V D 2 007.866 008 4 e V E 1 655.863 443 5 a I A 1 844.601 392 5 a I B 1 932.852 033 5 a I C 1 756.350 750 5 a I D 2 0 2 1 . 1 0 2 674 5 a I E 1 6 6 8 . 1 0 0 109 5 a II A 1 850.531 421 5 a II B 1 938.782 062 188 TABLE 2-E (Continued) Problem Combinations' Values Optimum Value p(w5) Number bll b12 b21 b22 of W5 508 5 a II c 1 762.280 779 .0003404 509 5 a II D 2 027.032 703 .0003404 510 5 a II E 1 674.030 138 .0000538 511 5 a III A 1 838.671 363 .0003404 512 5 a III B 1 926.922 004 .0003404 513 5 a III C 1 750.420 721 .0001355 514 5 a III D 2 015.172 645 .0001355 515 5 a III E 1 662.170 080 .0000214 516 5 a IV A 1 856.461 449 .0003404 517 5 a IV B 1 944.712 090 .0003404 518 5 a IV C 1 768.210 807 .0001355 519 5 a IV D 2 032.962 731 .0001355 520 5 a IV E 1 679.960 166 .0000214 521 5 a V A 1 844.252 601 .0000538 522 5 a V B 1 932.503 242 .0000538 523 5 a V C 1 756.001 959 .0000214 524 5 a V D 2 019.753 883 .0000214 525 5 a V E 1 667.751 318 .0000034 526 5 b I A 1 851.183 998 .0008548 527 5 b I B 1 939.434 637 .0008548 528 5 b I C 1 762.933 356 .0003404 529 5 b I D 2 027.685 280 .0003404 530 5 b I E 1 674.682 715 .0000538 531 5 b II A 1 857.114 027 .0008548 532 5 b II B 1 945.364 668 .0008548 533 5 b II C 1 768.863 385 .0003404 534 5 b II D 2 033.615 309 .0003404 535 5 b II E 1 680.612 744 .0000538 536 5 b III A 1 845.253 969 .0003404 537 5 b III B 1 933.504 610 .0003404 538 5 b III C 1 757.003 327 .0001355 539 5 b III D 2 021.755 251 .0001355 N m 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 TABLE 2-E (Continued) Combinations' Values Optimum Value ’ 11 b12 b21 b22 of W5 5 b III E 1 668.752 686 5 b IV A 1 863.044 055 5 b IV B 1 951.294 696 5 b IV C 1 774.793 413 5 b IV D 2 039.545 337 5 b IV E 1 686.542 772 5 b V A 1 850.835 207 5 b V B 1 939.085 848 5 b V C 1 762.584 565 5 b V D 2 026.336 489 5 b V E 1 674.333 924 5 c I A 1 838.118 784 5 c I B 1 926.369 425 5 c I C 1 749.868 142 5 c I D 2 014.620 066 5 c I E 1 661.617 501 5 c II A 1 844.048 813 5 c II B 1 932.299 454 5 c II C 1 755.798 171 5 c II D 2 020.550 095 5 c II E 1 667.547 530 5 c III A 1 832.188 755 5 c III B 1 920.439 396 5 c III C 1 743.938 113 5 c III D 2 008.690 037 5 c III E 1 655.687 472 5 c IV A 1 849.978 841 5 c IV B 1 938.229 482 5 c IV C 1 761.728 199 5 c IV D 2 026.480 123 5 c IV E 1 673.477 558 5 c V A 1 837.769 993 190 TABLE 2-E (Continued) Problem Combinations' Values Optimum Value P(W5) Number bll b12 b21 b22 of 572 5 c V B 1 926.020 634 .0000214 573 5 c V C 1 749.519 351 .0000085 574 5 c V D 2 013.271 275 .0000085 575 5 c V E 1 661.268 710 .0000014 576 5 d I A 1 857.766 604 .0003404 577 5 d I B 1 946.017 245 .0003404 578 5 d I C 1 769.515 962 .0001355 579 5 d I D 2 034.267 886 .0001355 580 5 d I E 1 681.265 321 .0000214 581 5 d II A 1 863.696 633 .0003404 582 5 d II B 1 951.947 274 .0003404 583 5 d II C 1 775.445 991 .0001355 584 5 d II D 2 040.197 915 .0001355 585 5 d II E 1 687.195 350 .0000214 586 5 d III A 1 851.836 575 .0001355 587 5 d III B 1 940.087 216 .0001355 588 5 d III C 1 763.585 933 .0000540 589 5 d III D 2 028.337 857 .0000540 590 5 d III E 1 675.335 292 .0000085 591 5 d IV A 1 869.626 661 .0001355 592 5 d IV B 1 957.877 302 .0001355 593 5 d IV C 1 781.376 019 .0000540 594 5 d IV D 2 046.127 943 .0000540 595 5 d IV E 1 693.125 378 .0000085 596 5 d V A 1 857.417 813 .0000214 597 5 d V B 1 945.668 454 .0000214 598 5 d V C 1 769.167 171 .0000085 599 5 d V D 2 032.919 095 .0000085 600 5 d V E 1 680.916 530 .0000014 601 5 e I A 1 831.436 179 .0000538 602 5 e I B 1 919.686 820 .0000538 603 5 e I C 1 743.185 537 .0000214 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 TABLE 2-E (Continued) Combinations’ Values Optimum Value '11 b12 b21 b22 of W5 5 e I D 2 007.937 461 5 e I E 1 654.934 896 5 e II A 1 837.366 208 5 e II B 1 925.616 849 5 e II C 1 749.115 566 5 e II D 2 013.867 490 5 e II E 1 660.864 925 5 e III A 1 825.506 150 5 e III B 1 913.756 791 5 e III C 1 737.255 508 5 e III D 2 002.007 432 5 e III E 1 649.004 867 5 e IV A 1 843.296 236 5 e IV B 1 931.546 877 5 e IV C 1 755.045 594 5 e IV D 2 019.797 518 5 e IV E 1 666.794 953 5 e V A 1 831.087 388 5 e V B 1 919.338 029 5 e V C 1 742.836 746 5 e V D 2 006.588 670 5 e V E 1 654.586 105 192 Again we derive for : Mean value = 1 890.596 221 Standard deviation = 228.450 362 Lower 5% probability level = 1 872.685 713 Then the approximate distribution of the objective function "W^M is given by: f(x) = 1 / V 2 7 7 (228.450362) (x—1890.596221)2 2(228.450362)2 The Five Allocational Policies Compared Table 3-A summarizes the five policies and their obtained results. In view of these results, we compare the five pol icies as follows: Policy I versus Policy II.--The allocational pro portions of labor are the same in both cases, but agricul ture is more capital intensive under Policy II than under Policy I. In view of these results, Policy II is prefer able ; it gives a higher mean value for and. a smaller standard error. Policy II versus Policy III.--Clearly Policy II is TABLE 3-A p o w5 Abso Rela 1 (1) (2) (3) lute tive 1 un U12 U21 °22 Mean Value Standard Lower 5% Risk Risk c Error Probability Margin: Margin: y & Level (1) —(3) % to (1) i . 666 .333 .25 .75 1 741.703 263 219.204 936 1 724.517 596 17.186 0.987% ii .666 .333 .333 .666 1 794.526 292 120.551 803 1 785.075 031 9.451 0.527% h i .75 .25 .25 .75 1 745.690 063 148.002 836 1 734.086 641 11.603 0.665% IV .75 .25 .50 .50 1 841.936 306 77.433 857 1 835.865 492 6.071 0,330% V .50 .50 .50 .50 1 890.596 221 228.450 362 1 872.682 713 17.914 0.948% H vO U ) 194 also preferable to Policy III, since it has a higher aver age value of W^_ with smaller standard error than Policy III. But these two conclusions appear to be paradoxical when we compare the results of the two movements away from Policy I: once to Policy II, which has a more capital intensive agriculture and a more labor intensive industry than Policy Ij and once to Policy III, where agriculture becomes more labor intensive and industry more capital intensive than Policy I. The apparent paradox is due to the fact that these two opposite movements away from the factor proportions of Policy I both lead to higher averages and smaller standard errors for W^. In other words, any of these movements brings factor allocation to more proper proportions. Actually, this is no paradox; it simply implies the existence of a hierarchy of fixed-proportions tech- 7 niques, where any allocational policy becomes more effi- 7 See R. S. Eckaus, "The Factor-Proportions Problem in Underdeveloped Areas," in The Economics of Underdevelop ment , by A. N. Agarwala and S. P. Singh (eds.), (Oxford University Press, 1958), pp. 348-380; and H. Leibenstein, "Technical Progress, The Production Function and Dualism," (Institute of Industrial Relations, University of Califor nia, Berkeley, 1962). 195 cient when it approaches the proper factor proportions of any of these techniques. The results of the movements are also consistent with the values that we have for the output/input coeffi cients and their standard errors (pages 76-77): 1. The movement from I to II (i.e., towards a more capital-intensive agriculture and a less capital-in tensive industry) leads to an increase in average total income by approximately b.E.53 m. Noting that output/capital ratio in agricultural sector is higher than in industry by only .165, one may conclude that the big increase in Wcj reflects not only the differences in capital productivity among the two sectors, but also--and probably much more significantly--the avoid ance of the waste of Policy I’s nonproper proportions. The lower value of the standard deviation of W5 under Policy II is consistent with the fact that the stand ard. error of the agricultural output/capital ratio is much smaller (.004729) than in industry (.06340). 2. The movement from I to III is towards a less capital-intensive technology in the agricultural sector (and. vice versa in the industrial sector) than under Policy I. The better results obtained by this movement indi cate that under Policy I factor allocation is out of proper proportions, where more labor than needed is engaged in industry. More efficient factor proportions are achieved by making industry even less labor intensive (as, for in stance, because of the application of more advanced tech nology), and thus, making agriculture even more labor intensive than under Policy I. The smaller standard error under Policy III than under Policy I is consistent with the smaller standard deviation (.027741) of average output/ labor ratio in agricultural sector than in industrial sec tor (.51515). Finally, the minor increase in average W^_ (^b.E.5 m. ) could be taken as an indication that the move ment from Policy I to another policy of less capital in tensive agriculture (Policy III) is less productive than the movement to a policy of a more capital-intensive agri culture (Policy II). Policy IV versus Policy V .--For the two policies, proportional allocation of capital is the same in both sec tors (.5 and .5). But under Policy V, agriculture is less 197 labor intensive, and industry is more labor intensive than Policy IV. If we imagine a movement from Policy IV to Policy V, the result will be an increase in the average value of W5 by approximately -L.E.48m. But the corresponding value of the standard error increases from 77 to 228. It is clear then that Policy V is more productive than Policy IV (and this is again consistent with our first finding that the combination of less capital-intensive industry and more capital-intensive agriculture leads to higher total output). However, Policy V is more risky. Agriculture becomes too capital-intensive and industry becomes too labor-intensive. Although this means much higher output (since O/L in industry = 10, while it is in agriculture = 1.9228), it also means greater risk: the value of the standard error of O/L in industry = .51515, while in agri culture it is = .027741. Which policy is preferable? Policy IV with its smaller average value of (= 1,842 -L.E.m.) and a very low margin of risk (=0.330%), or Policy V with its higher aver age value of W5 (=1,891 i.E.m.) and a much higher margin of risk (=0.948%), indeed the second risky policy among 198 the five ones considered? The answer depends on preference and value-judg ment . Let us assume that we prefer the safer policy; i.e., Policy IV. Now the final question is--which policy is the better of the two best--Policy II or Policy IV? The answer is definitely Policy IV, which devotes higher percentages of both labor and capital to agricultur al sector than Policy II. Policy IV has a higher mean value of W5 and a lower standard, deviation (W^= 1,842 L.E.m. & = 77) than Policy II (W5= 1,794 L.E.m.; Cf = 120). Thus, the final conclusion is that Policy IV is probably the best. Comparison With the Actual Achievements In the First Five-Year Plan Policy IV versus the actual policy achievements of UAR First-Five-Year Plan.--Our rough estimations give the following values for the proportions of capital and labor actually devoted to each sector:8 U1:L = 85% U1 2 = 15% U2 1 = 44% U2 2 = 56% 8See Appendices IV and V, pp. 219-222. 199 Our estimate of the total output achievement at the end of the fifth year of the plan^ is given by: W5 = 2489.120 E.E.m. The first thing we observe is the very high value of W5 , relative to the mean values of that we found by our tested policies. The second observation is that none of our five policies is identical to the one that is "supposed" to have been actually adopted in the UAR. Nevertheless, we can say, very roughly, that the allocational policy closest to it is Policy IV. This could somewhat be a justification of saying, very roughly, that the policy (supposedly) adopted in UAR is, on these grounds, a proper choice. How to explain the discrepancies?--We can give no clear and definite answer to this question. For example: our results show that the movement from any of the first three policies to Policy IV (which, of any of the five pol icies , devotes the highest proportions of both labor and capital to agriculture) will always be preferable; the mean ^See Appendix IV, p. 219. 200 value of W5 is always higher, and the risk margin is always the least. But in contrast to this conclusion, Policy V, which devotes less of both labor and capital to agriculture than does Policy IV, gives a higher average value for W5, though with greater risk. Thus, we cannot say whether the proportions esti mated for the actual policy should have led. to a greater or a smaller value for than that of Policy IV. Nevertheless, the big difference between the actual policy's estimated, value of (= 2489 E.E.m.) and the highest average value attained, by any of the five policies (= 1891 E.E.m.) would, reasonably enough, tempt us to place at least a major part of the burden of the explanation on data difficulties. This last statement refers not only to the expected inaccuracy of the data obtained from various publications, but also to the fact that the lack of very necessary data has often led us to estimations that have always required simplifying, and at the same time arbitrary and limiting, assumptions. Thus, our conclusion can only be a very rough one: that if our estimates of the actual allocational policy somewhat reflect the true picture, and. if all the assump- tions we have had to make are not untrue or too limiting, then the estimated actual allocational policy is a proper one because of its relative closeness to Policy IV which we have chosen to be "the best." CHAPTER V SUMMARY AND CONCLUSIONS Summary The findings of the previous chapter's calculations undoubtedly make it clear that as long as random variables are involved in planning for future action, target expecta tion cannot be a sure single value; regardless of whether we deal with a market or centrally planned system. It is, instead, a whole range of possible levels of achievement; each of which has a certain probability to occur. In other words, there is no way of ruling out the risk of setting forth unachievable targets. This fact is illustrated by the different values of total output at the end of the fifth year (W^), when the coefficients deviate from their original fixed aver ages . The magnitudes of the absolute margins of risk, as represented by the difference between the mean value of and its lower 5 per cent probability level, depend on the 202 203 particular allocational decision. This is because a par ticular policy (Ujj) assigns different roles to alternative output/input ratios, which have different standard errors. These differences, in turn, are reflected both on the level of the final output and the magnitude of risk of its achievement. In comparison with fixed coefficients methods, the applied method of stochastic linear programming is superior in its advantage of presenting to the policy maker a more realistic picture of what would be the outcomes of differ ent policies. In other words, it provides him with addi tional information which enables him to make "better” (in terms of his own scale of preference and value judgment) forecasts about the results of alternative choices. As we have just seen in the previous chapter, the numerical results would be very favorable if they are to be taken at face value for evaluating the achievements of the actual UAR policy. But such an attitude cannot be con vincing. The UAR organizational and motivational systems of planning cannot be expected to be perfect; and the 1960- 1965 Five-Year Plan is the Egyptian planners' first expe rience. It cannot be expected to be free from technical errors and policy mistakes. Indeed, the very high value 204 of the actual policy's Wj---relat ive to the results of the five tested policies--is a reasonable enough source of doubt about the accuracy of the published data, or our own estimates, or--more likely--both. The limiting arbitrary assumptions, difficulties, and shortcomings which sur rounded data estimation and collection make one very hesi tant to place significant weight on the numerical discrep ancies between the results of the assumed policies and the actual policy. If such data difficulties are typical for most developing countries, one would have good reason to ques tion the degree of usefulness which such countries can derive from the additional information offered by the sto chastic method. Conclusions As for our basic concern of examining the role and significance of the phenomenon of risk in centrally planned systems, we may give the following conclusions: A. It may not be possible to evaluate risk for different policies under centrally planned developing econ omies- -even if it could be practically isolated--with rea- 205 sonable degree of accuracy, because of: 1) The deficiency and scarcity of necessary data. 2) The improbability that the adequate technical facilities needed to carry out a highly com plicated stochastic program to estimate the characteristics of different choices will be available. B. Risk, as a phenomenon whose consideration would affect future decision-making, may not be (again even if it were possible to isolate it) of significant role or relevance in centrally planned developing economies. The knowledge of risk margins is in itself addi tional information which helps in making "better" choices. But in the case of these countries, priorities would be so clear that the possibility of choices becomes very limited. Such a limitation implies the necessity of a priori accept ance of the risk involved in following the particular growth path. For example, the central planners could be quite aware that the scarcity of industrial skills--quali- tatively and quantitatively--will, in the short run, in volve high production costs and even waste; yet they accept that risk because they believe that it is unavoidable if they really want future industrialization that will streng then the economy's structure and enlarge its productive 206 capacity, two necessary prerequisites for long run economic growth and sustained increase in national income. C. By the same logic, it should be added that at later stages of development, when choices become less limited and priorities not so clearly defined, the stochas tic method, with its consideration of risks involved in different policy decisions, becomes of real usefulness and relevance. Moreover, at such a higher stage of develop ment, the greater adequacy of both available data (quanti tatively and qualitatively) and the technical facilities needed to carry out a complicated stochastic program would make it possible to make reliable calculations for the characteristics of different policies. This, in turn, means more usefulness of the additional information which the stochastic method provides. D. Under conditions of central planning, whether we are discussing a developing or developed economy, un- calculable random variables (discussed in Chapter III under the heading of "Conditions of Plan Execution") may inter fere in a way which invalidates, to one degree or another, the accuracy of predictions of the consulted theoretical findings of the selected policy. For example, the central 207 planner may decide to apply a policy that uses capital intensive techniques in agriculture. But when it comes to practical application, certain non-technical factors may affect the expected final achievements. In other words, abstract knowledge of, for instance the labor-capital ratio, may prove an insufficient condition for reaching a completely reliable policy recommendation. Equally impor tant could be the knowledge of the particular system within which the policy is to be undertaken. For instance, a co operative system that rents machines and equipment to small landowners may turn out to be more or less efficient--given the labor-capital ratio--than a system which stresses mechanization on big government-controlled-and-managed estates. These factors, which are held constant under theo retical calculations, are of special importance under con ditions of central planning, and are likely to affect the actual level of technical efficiency of a certain alloca- tiona3. policy. The important implication of this argument is that under central planning, uncalculable random elements (e.g., organizational or motivational factors) which cannot be isolated in practice from the calculable ones (e.g., 208 prices, quantities, technical coefficients, et cetera) could play an important role in affecting plan achieve ments. Under such circumstances, the actual situation which faces the policy maker may turn out to be closer to one of uncertainty rather than risk. This conclusion should not be considered as a denial of the usefulness of the stochastic approach to economic planning. Rather, it should provide an objective justification for the acceptance of planners* choice and value-judgment. APPENDICES APPENDIX I Steps Followed in Estimating the Supply of Capital--tor Both Sectors--in Each Year of the Plan 1. Total investment planned for the two sectors- in 1959-1960 prices--over the five years 1960-1965.^ (In millions of -L.E. ) Agricultural sector: 392.0 Industrial sector: 578.7 Total: 970.7 2. Investments in agricultural and industrial sec tors in each of the first four years of the Plan.^ (As shown in Table A.) - ’ -Council of National Planning, Outline of the Gen eral Plan for Economic and Social Development for the Five Years--July 1960-June 1965. (1960), p. 18. 2 UAR Ministry of Planning, Progress Under Planning (1964), p. 28. 210 211 TABLE A Year Agricultural Sector Industrial Sector Total 1960/1961 38.2 73.4 1 1 1 . 6 (achieved) 1961/1962 51.9 56.6 108.5 (achieved) 1962/1963 73.8 92.4 166.2 (achieved) 1963/1964 1 0 0 . 2 152.8 253.0 (planned) Total of the first four years 639.3 The remaining _ for 1964/1965 *'u./ - ■ 639.3 = 331.4 Note: The way in which we derive the amount of investment remaining for the fifth year is obviously based on the assumption that there is no change in the original plan for total investment in the two sectors over the plan period. 212 3. From published data we get: Total capital formation in 1958 = 135.5 L.E.m.^ Depreciation coefficient = .4^ Total investment in 1959/1960 = 171.4^ Investment in the two sectors in 1959/1960 = 85.0 Thus, the percentage of investment--in both sec tors-- to total investment, in 1959, is = 49.59%. Using the relation: where Kt = 1t + Kt- 1 - d<Kt-l> (!) 1^ : investment in period t; K^: capital in period t; d. : depreciation coefficient (= 4%); 3 UAR, INP, A. H. Ahmed, Memo No. 211, Financxng Capital Formation in UAR (August 1962), p. 25. ^UAR, INP, M. M. El-Iman, Memo No. 255, Models Used, in Drafting the 20-Year Plan (1959-1978) (December 1962), p. 9. 5 Progress Under Planning, loc, cit. 6 Ibid.. 213 we estimate the total capital formation in 1959, thus K5 9 = 171.4 + 135.5 - (.04)(135.5) = 301.48 Then, assuming that in 1959, the percentage of capital formation in the two sectors to total capital formation is the same as that of investment in the two sectors to total investment, we calculate: ^301 4 8 W 49 SO^ Kj-g (Agriculture + Industry) = ^ ‘1^ = 149.5 Finally, using equation (1), we calculate capital formation --in both sectors together--in each of the five years of the Plan: 1960/1961 1961/1962 1962/1963 1963/1964 1964/1965 : 255.1200 324.6152 477.8306 711.7174 1014.6487 APPENDIX II Steps Followed in Estimating the Supply of Labor Force--for Both Sectors--in Each Year of the Plan 1. Rural and urban population estimates; TABLE B* Year Per Cent of Rural to Total Population Per Cent of Urban Popula tion 1917/1918 79.2 1927/1928 77.0 1937/1938 76.0 1947/1948 69.6 1957/1958 64.2 1960/1961 63.6 36.4 1961/1962 63.2 36.8 1962/1963 62.8 37.2 1963/1964 62.4 37.6 1964/1965 62.0 38.0 *The figures for 1917/1918 to 1960/1961 taken from: Central Statistical Committee, Basic Statistics, January I960, p. 38 and May 1963, p. 17, were used to extrapolate, by least squares method, the figures of 1960/1961-1964/1965. 214 215 From the obtained percentages, together with total population figures, we calculate the absolute numbers of rural versus urban population for 1960/1961--1964/1965, in millions: TABLE C Year Total Population Rural Population Urban Population 1960/1961 26 059 000 16 581 342 9 477 658 1961/1962 26 716 000 16 889 855 9 826 145 1962/1963 27 373 000 17 195 719 10 177 281 1963/1964 27 8 6 6 951 17 394 551 10 472 400 1964/1965 28 443 012 17 637 512 10 805 500 2. Agricultural and. industrial labor force: from published, data, we have for 1960:^ Total labor force (entire economy): 6,720,362 Agricultural labor force: 3,689,845 Industrial labor force: 738,200 and. from figures in Table C, we calculate: a) Percentage of agricultural labor to rural population in 1960: = 22.25%; and. ‘ '"UAR, INP, M. Hamely (ed..), Memo No. 431, Manpower Requirements for the UAR for the Period. 1960-1985 (May 1964), p. 60. 216 b) Percentage of industrial labor to urban population in 1960: = 7.79%. Assuming these percentages are the same for the years 1960/1961--1964/1965, we obtain the following values: TABLE D Year Agricultural Industrial Labor Force Labor Force Labor Force in Both Sectors 1960/1961 1961/1962 1962/1963 1963/1964 1964/1965 3 689 845 3 757 993 3 826 047 3 870 288 3 924 346 738 200 765 457 792 810 815 800 841 748 4 428 045 4 523 450 4 618 857 4 686 088 4 766 094 APPENDIX III From published figures of eighteen estimates of average capital/output and capital/labor ratios for each of the two sectors and for several industries independ ently,-*- we estimated the corresponding output/labor and output/capital ratios. From these we picked the average coefficients (population means) in each sector: average output/labor in agricultural sector = 1.91228 average output/capital in agricultural sector = 0.45500 average output/labor in industrial sector = 10.0000 average output/capital in industrial sector = 0.29000. As for the standard errors of the means, we selected two samples from the eighteen values. By this UAR, INP, M. M. El-Imam, Memo No. 255, Models Used in Drafting the 20-Year Plan--(1959-1978), (December 1962), pp. 15-33. 217 218 arbitrary selection our aim was to obtain the suitable sample--from the point of view of factor proportions--for each sector. We then estimated the following standard errors: S of O/L in agricultural sector = 0.027741 x S_ of O/K in agricultural sector = 0.004729 x S_ of O/L in industrial sector = 0.51515 x S_ of O/K in industrial sector = 0.06340. APPENDIX IV Steps Followed in Estimating the Average Percentage of Labor Force Devoted to Each Sector in Every Year of the Plan 1. From published data we got the values of aver age weekly wages (in Piasters) in the industrial sector for the years 1953-1957 and 1959-1962.1 2. Then, by least-square method, we estimated two values for 1958, once using the data of 1953-1957, and then the data of 1959-1962. The average of the two values was taken as an estimate for 1958. 3. The remaining figures (1963-1965) are extra polations using the data of 1953-1962. 4. These weekly wage figures were then multiplied by 52 and divided by 10O to obtain the annual wage rates in terms of Egyptian Pounds. ^Basic Statistics, January 1960, p. 49; and May 1963, p. 37. Statistical Pocket Year Book, 1957, p. 50; 1958, p. 54; and 1960 and 1961, p. 54. 219 220 5. The values of annual wage bills in the indus- trial sector for the years 1960/1961--1964/1965 were divided by the corresponding values of annual wage rates to make estimates for industrial employment each year. 6. Finally, we estimated the yearly percentages of industrial employment using these industrial employment figures and the previously estimated values of the total 3 labor force available each year for both sectors together. The average of the five percentages was taken for the whole period. Table E is a summary of these steps. UAR, Ministry of Planning, Progress Under Plan ning (1964), p. 31 3 See Appendix II, p. 217. 221 TABLE E (1) (2) (3) Year Weekly Wage in pias Annual Wage in t.E. (1)x52 Wage Bill L.E.m, Indus trial Employ ment (3)4(2) Average % over the 5 years in indus trial sector 1953 296 153.9 1954 314 163.3 1955 342 177.8 1956 349 181.5 1957 331 172.1 1958 344* 178.9 1959 333 173.2 1960/ 1961 332 172.6 817 473 349 1961/ 1962 336 174.7 939 537 493 1962/ 1963 338 175.8 1,293 735 495 1963/ 1964 346* 179.9 1,417 787 660 1964/ 1965 349* 181.5 1,550 853 995 1965/ 1966 352* 183.0 Therefore, the percentage of labor in the agricul tural sector is approximately 85 per cent. *Estimate. APPENDIX V Steps Followed in Estimating the Average Percentage of Capital Devoted to Each Sector in Every Year of the Plan A. Industrial Sector Estimates 1. Investment achieved in industrial sector as a percentage of its original target, in each of the first three years of the Plan: Per Cent Achievement^ 1960/1961 77% of target 1961/1962 52.05% of target 1962/1963 61.8 % of target 2. Thus, average percentage over the three years = 63.62%. 3. What would be achieved out of the fourth year's ^H. Omar, Planning in the Socialist Society (Arabic) Kamak Publishers, 1963, p. 127. 222 223 target2 is calculated by multiplying the target by 63.62%. This gives: Estimated investment achievement in 1963/1964 = 97.21136 4. For planned investment in the industrial sector q over the five years, we have the value 578.7. 5. And we have the following values for investment achievements in industry in the first four years:4 1960/1961 73.4 1961/1962 56.6 1962/1963 92.4 1963/1964 97.2 (our estimate) Total achieved: 319.6 -E.E.m. 6. Thus, what is planned for the fifth year is: = 578.7 — 319.6 = 259.1; and out of this planned value, ^Progress Under Planning, p. 28. 3 See Appendix I, p. 210. 4 See Appendix I, p. 211 for the first three values; the fourth is our estimate. 224 we estimate the achievement at 63.62%: (259.1)(63.62) 100 = 164.8 B. Agricultural Sector Estimates 1. Percentages of investment achievement in agri cultural sector, out of original plans, for the first three years are: Per Cent Achievement^ 1960/1961 64.4% of planned 1961/1962 95 % of planned 1962/1963 119.4% of planned j . . Average per cent = 92.9% The great increase in this percent age is due to rapid work on the High Dam. 2. Thus, the estimate of investment achievement in agriculture in the fourth year: = (planned investment in agriculture in the fourth year) (92.9%) = (100.2)(92.9) = 93>1 t.E.m. 100 6 c : Omar, oja. cat., p. 127. 6See Appendix I, p. 212. 225 3. Total achieved in the first four years: = 38.2 + 51.9 + 73.8 + 93.1 = 257. 4. What would be planned for investment in agri culture in the fifth year: = Total planned for the five years — total achieved in the first four years, thus: = 392 - 257 = 135 L.E.m. 5. Therefore, estimate of achieved investment in the fifth year = (135)(92.9%) = 125.4 -L.E.m. Table F summarizes the estimates of allocational percentages of capital among the two sectors. 7 See Appendix I, p. 210. TABLE F Year Invest ment achieved in Agricul ture Invest ment achieved in Industry Total Invest ment Per cent of invest ment in Industry Average per cent over the five years 1960/61 38.2* 73.4* 111.6 65.8% > 1961/62 51.9* 56.6* 108.5 52.2% 56.3% 1962/63 73.8* 92.4* 166.2 55.6% ) 7^/56% 1963/64 93.11 97.21 190.3 51.1% 1964/65 125.4~ 164.81 290.2 56.8% ' Thus, the average percentage of investment devoted yearly to agricultural sector ^>44%. Note: The capital depreciation coefficient for the estimation of capital supply3- is 4 per cent for all sectors. And since we are concerned here only with the allocational policy in terms of percentages, not absolute values, we used the investment figures to reflect the ten dency of the actual allocational policy of capital among the two sectors. * Empirical data. 1 Our estimates. aAppendix I, p. 213. APPENDIX VI Steps Followed in Estimating Total Output Achieved at the End of the Fifth Year of the Plan A. Estimate of Agricultural Output Achievement 1. Level of output achieved in agricultural sec tor, as a percentage of the original target, in each of the first three years of the Plan:"*" Per Cent Achievement 1960/1961 97.2% of target 1961/1962 88.7% of target 1962/1963 95.1% of target Thus, average per cent of achievement over the three years = 93.666% £^93.7%. 2. Using this percentage, we estimate in 1959 1H. Omar, Planning in the Socialist Society (Arabic) Karnak Publication, 1963, p. 116. 227 228 prices the achievements in the fourth and fifth yearst Target^ Estimated achievement 1963/1964 676.9 634.2553 -L.E.m. 1964/1965 736 689.6320 L.E.m. B. Estimate of Industrial Output Achievement 1. Level of output achieved in industrial sector, as a percentage of the original target, in each of the first three years of the Plan: O Per Cent Achievement 1960/1961 98.50% of target 1961/1962 99.55% of target 1962/1963 99.65% of target Thus, average percentage of achievement over the three years = 99.2%. 2. Using this percentage, we estimate the achieve- p UAR, Ministry of Planning, Progress Under Plan ning (1964), p. 22. 3 Omar, o£. cit., p. 116. 229 ments in the fourth and the fifth years: Target^ Estimated achievement 1963/1964 1514.7 1502.5824 1964/1965 1814.0 1799.4880 From estimates of output achievements in the fifth year in each sector, we get the value of total output achieved by both sectors at the end of the Plan: = 1799.488 + 689.632 = 2489.120 4 Progress Under Planning, loc. cit, p. 22. BIBLIOGRAPHY BIBLIOGRAPHY BOOKS Agarwala, A. N. and Singh, S. P. (eds.), The Economics of Underdevelopment. London: Oxford University Press, 1958. Arrow, K. Social Choice and Individual Values. New York: John Wiley and Sons, Inc., 1951. Ashton, T. S. The Industrial Revolution, 1760-1830. London: Oxford University Press, 1960. Balassa, B. A. The Hungarian Experience in Economic Plan ning . New Haven: Yale University Press, 1959. Bellman, R. Dynamic Programming. 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Taylor, F. M. "The Guidance of Production in a Socialist State," in On the Economic Theory of Socialism, Benjamin Lippincott (ed.). Minneapolis: Univer sity of Minnesota Press, 1938. Wiles, P. J. D. "Rationality, the Market, Decentralization and the Territorial Principle," in Value and Plan, G. Grossman (ed.). California: University of California Press, 1960. PUBLICATIONS OF THE GOVERNMENT, LEARNED SOCIETIES AND OTHER ORGANIZATIONS United Arab Republic, Institute of National Planning. Memo No. 238, by I. H. Abdel-Rahman, Comprehensive Eco nomic Planning in the UAR, September 1962. _________. Memo No. 296, by I. H. Abdel-Rahman, Manpower Planning in the UAR, May 15, 1963. _________. Memo No. 12, by I. H„ Abdel-Rahman, Plan Cen tralization and Execution Decentralization (Obser vation Concerning the General Economic Development Plan and Its Relation to Local Administration Organs), November 20, 1960. _________. Memo No. 63, by I. H. Abdel-Rahman, Planning for Balanced Social and Economic Development in the UAR (Egypt), August 1961. _________. Memo No. 48, by I. H. Abdel-Rahman, Role of Local Societies in National Development (ARabic), June 2, 1961. _________. Memo No. 76, by I. H. Abdel-Rahman, The Social Aspects of Development Planning in UAR, November 1961. United Arab Republic, Institute of National Planning. Memo No. 211, by A. H. Ahmed, Financing Capital Formation in UAR, August 1962. _________ . Memo No. 255, by M. M. El-Imam, Models Used in Drafting the 20-Year Plan (1959-1978), December 1962. _________ . Memo No. 201, by M. M. El-Imam, Preparation of the General Framework of the Plan (Arabic), July 10, 1962. _________ . Memo.No. 386, by F. R. Fahmi, Growth Pattern of Manufacturing Sector in Egypt (1950-1970). _________ . Memo No. 431, by M. Hamdy (ed.), Manpower Re quirements for the UAR for the Period 1960-1985, May 1964. _________ . Memo No. 169, by E. E. Hammam, Our Plan for Agriculture, Part I, March 1962. United. Arab Republic, Council of National Planning. Out line of the General Plan for Economic and Social Development for the Five Years; July 1960— June 1965, (Arabic), 1960. UAR, Central Statistical Committee, Basic Statistics, January 1960. UAR, Central Statistical Committee, Basic Statistics, January 1962. _________ . Basic Statistics, May 1963. UAR, Information Department, The Charter. UAR Ministry of Planning. Progress Under Planning, (Arabic) 1964. UAR, National Bank of Egypt. Economic Bulletin, Vol. Ill, 1951. _________ . Economic Bulletin, Vol. XVII, No. 1, 1964. 237 United Arab Republic. Statistical Pocket Year Book, Ca; 1952. Statistical Pocket Year Book, 1957. Statistical Pocket Year Book, 1958. Statistical Pocket Year Book, 1960 and 1961. UAR, The Egyptian Statistical and Census Department. Statistical Year Book, 1962. ARTICLES AND PERIODICALS Alchian, A. "Uncertainty, Evolution, and Economic Theory,'1 Journal of Political Economy, (1950). Archibald, G. C. "Utility, Risk, and Linearity," Journal of Political Economy, Vol. LXVII, No. 5, (1959). Arrow, K. J. "Alternative Approaches to the Theory of Choice in Risk-Taking Situations," Econometrica, Vol. XIX, No. 4, (1951). Babbar, M. M. "Distribution of Solutions of a Set of Linear Equations," Journal of the American Statis tical Association, Vol. 50, (1955). Bator, F. M. "The Anatomy of Market Failure," Quarterly Journal of Economics, August 1958. _________ • "The Simple Analytics of Welfare Maximization," American Economic Review, Vol. XLVII, No. 1, (1957). Bergson, A. "On the Concept of Social Welfare," The Quarterly Journal of Economics, Vol. LXVIII, No. 2, (1954). Buchanan, N. "A Reconsideration of the Cobweb Theorem," Journal of Political Economy, (February 1939). Chenery, H. B. "The Application of Investment Criteria," Quarterly Journal of Economics, (February 1953). 238 Dantzig, J. B. "Linear Programming Under Certainty," Management Science, Vol. I, (1955). Dickinson, H. D. "Price Formation in a Socialist Commu nity," The Economic Journal, Vol. XLIII, (June 1933) Eckstein, O. "Investment Criteria for Economic Develop ment and the Theory of Intertemporal Welfare Eco nomics," Quarterly Journal of Economics, Vol. LXXI, No. 1, (February 1957). Edwards, W. "The Reliability of Probability Preferences," American Journal of Psychology, Vol. LXVII, (1954). _________ . "The Theory of Decision-Making," Psychological Bulletin, Vol. LI, No. 4, (1954). Elmaghraby, S. E. "An Approach to Linear Programming Under Certainty," Operations Research, Vol. X, (1959). Ezekeil, M. "The Cobweb Theorem," Quarterly Journal of Economics, (February 1938). Freund, R. T. "The Introduction of Risk into a Program ming Model," Econometrica, Vol. XXIV, (1956). Graaff, J. and Baumol, W. "Three Notes on ’Expectation in Economics'," Economica, New Series, Vol. XVI, (November 1949). Hanson, M. A. 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"Dynamic Programming Under Certainty with Quadratic Criterion Function," Econometrica, Vol. XXVI, (1956). 240 Streeten, P. "Economics and Value Judgments," Quarterly Journal of Economics, Vol. LXIV, No. 4, (November 1950). Theil, H. Econometric Models and Welfare Maximization," Weltwirtschaftliches Archiv, Vol. LXXII, (1954). Tintner, G. "A Contribution to the Non-Static Theory of Choice," Quarterly Journal of Economics, Vol. LVI, (1942). ___________. "Foundations of Probability and Statistical Inference," Journal of Royal Statistical Society, Vol. CXII, Part III, (1949). __________. "A Note on Stochastic Linear Programming," Econometrica, Vol. XXVIII, (1960). __________. "Stochastic Linear Programming with Application to Agricultural Economics." Second Symposium in Linear Programming, Proceedings, Vol. I, (1955). __________. "The Pure Theory of Production Under Technolog ical Risk and Uncertainty," Econometrica, Vol. IX, (1941). . 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Creator Farghali, Salwa Ali Soliman (author)

Core Title Planning Under Socialism- And Risk

Degree Doctor of Philosophy

Degree Program Economics

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

Tag Economics, theory,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Tintner, Gerhard (committee chair), Elliott, John E. (committee member), Ford, James S. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-219299

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Rights Farghali, Salwa Ali Soliman

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