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"1‘ ‘ II .14 ‘4"‘I““'“1‘““"‘““"‘4“ 4‘44'4? I ‘ I' “ I' ‘I ‘4“ ‘4“ 44'4 444M414 44 44! ' 1n‘.h"4L 1.” 4441 i““““““ IIIXI“4‘..I ‘44‘4 1 4 1.44. “‘ .W 411 ‘1 “4‘“? [“1144‘14 Hill ll I!“ I! 1293 100 "lllmull; lllsllllllllsll J" “1 79 This is to certify that the thesis entitled IMPACTS OF ALTERNATIVE TECHNOLOGIES ON PRODUCTION AND RESOURCE ALLOCATION IN SOUTHERN BRAZILIAN AGRICULTURE, 1970-1980 presented by Joao Eustaquio de Lima has been accepted towards fulfillment of the requirements for Ph.D. Agricultural Economics degree in Major professor (George E. Rossmiller) Date £1,1sz @4477 0-7639 ‘5 '"7' ' " vs" UN J __, / IMPACTS OF ALTERNATIVE TECHNOLOGIES ON PRODUCTION AND RESOURCE ALLOCATION IN SOUTHERN BRAZILIAN AGRICULTURE, 1970—1980 By Joao Eustaquio de Lima A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics l977‘ ABSTRACT IMPACTS OF ALTERNATIVE TECHNOLOGIES ON PRODUCTION AND RESOURCE ALLOCATION IN SOUTHERN BRAZILIAN AGRICULTURE, l970-l980 By Joao Eustaquio de Lima The planning of agricultural research and the implementation of technology policy require knowledge of the impacts and adjustments that take place as a result of the introduction of new technologies. In essence, the effects of improved technology can be characterized by impacts on the cost structure or the product mix of individual firms, shifts in industry demand curves for factors of production, shifts in product supply curves, and impacts on the growth and distri- bution of total and per capita income. The analysis of these effects provides useful information to the decision-making process in setting guidelines for research policy and in planning research activities. ,The main purpose of this study has been to contribute informa- tion on the potential impacts of alternative technologies on production and resource allocation in Southern Brazilian agriculture. Specifi- cally, the objectives of the study were: I. To determine optimal land use and production patterns through time for farmswith different sizes in the state of Rio Grande do Sul, Brazil. Ge Joao Eustaquio de Lima 2. To evaluate the effects of introducing alternative agricultural technology on production, income, employment, resource allocation, and income distribution among different farm size groups. In this context the study focused on: a) Evaluating the effects of introducing high-yield varieties with higher biological potential and higher capacity to respond to fertilizer application, and b) Evaluating the effects of changing the level of mechanization by varying the combination of labor, animal power, and tractor requirements in production activities. The focus of this study concerned the development of an analyt- ical framework which could be used to analyze the potential impacts of a set of assumed varietal and mechanical technologies. High-yield crop varieties with higher capacity to respond to fertilizer applica- tion, were analyzed by means of a number of alternative assumptions with respect to yield per hectare for annual crops. High-yield varie- ties are supposed to facilitate substitution of fertilizer for land, thus changing resource proportion and resulting in substantial increases in output. Mechanical technology was analyzed on the basis of its effects on changes in labor, draft animal, and tractor input requirements for production activities. Tractor services were assumed to substitute for labor and draft animals, permitting more efficient combination of factors and resulting in higher returns to farm resources. A regional model of production and resource allocation was developed to allow the observation of the time profile of optimal land Joao Eustaquio de Lima use and cropping patterns, production, farm income, and derived demand for farm inputs under a selected set of yield and mechanization assump- tions. The model has three components: a) a yield component which estimates crop yields on the basis of yield-nutrient response functions; b) a resource allocation.component consisting of a Recursive Linear Programming model which allocates land and other farm resources to alternative farm enterprises, and c) a production and accounting compo- nent which computes production levels and other performance criteria by commodity, farm size, and regional aggregates. The model is ap- plied to the total area of the state of Rio Grande do Sul in Brazil. Model results indicated that in response to technological change farmers can change, to a certain extent their land utilization, production, input demand, and income patterns over time. With the introduction of high-yield varieties and improved mechanization, the model projects significant increases in area and production of wheat and soybeans. Net returns to resources in farming can be increased significantly with improvements in crop yields and mechanization. Income of large farms showed higher projected growth rate than that of small farms. Thus, improved technology tends to increase the income gap between farm size groups over time. This study suggests that technology policy should be based on a well-defined set of Objectives. The choice of technology to be implemented would have differential impacts on the relative competi- tive position of the various farm enterprises and on the income accru- ing to the different producing groups. Dedicated to: my father, JOAQUIM NORONHA DE LIMA (in memory) and my mother, JACINTA MARIA DE JESUS with love and care. ii ACKNOWLEDGMENTS I would like to express my special gratitude to Professor George E. Rossmiller for his interest and guidance throughout my graduate program and for his assistance and encouragement in the development of this study. Also, I wish to express my appreciation to Drs. Larry J. Connor, Lester Manderscheid, Harren Vincent, Thomas Manetsch, and John M. Hunter for their assistance as members of my guidance and thesis committees. I am grateful to the Secretaria de Planejamento e Orcamento (SUPLAN) of the Ministry of Agriculture of Brazil for providing me the opportunity to pursue advanced graduate studies in the United - States. Also, I want to thank the U.S. Agency for International Development for providing the financial support for my graduate pro- gram. I am thankful to Mr. Gary R. Ingvaldson for his invaluable help in writing the computer program and for his assistance with gen- eral computer work. Special appreciation is extended to Mrs. Lucy Wells for typing the first draft of the thesis and for her assistance with other secre- tarial matters. Also, I wish to thank Mrs. Noralee Burkhardt and Miss Linda Stephens for typing the final manuscript. A very special thanks goes to Ms. Barbara J. Cullinane for her editorial assistance and for her precious support and encour- -agement which greatly contributed to the completion of this work. Finally, I am sincerely grateful to my mother, and my brothers and sisters for their love and unwavering support throughout my educa- tion and my life. iv LIST OF TABLES ..... ‘ ..................... ix LIST OF FIGURES .......................... xi PART A BACKGROUND AND DESCRIPTION OF THE STUDY CHAPTER I: INTRODUCTION ..................... I General Problem Setting ................ 3 Problem Situation and Statement ............ 8 Research Objectives .................. l8 Focus and Scope of the Study ............. 19 Organization of Thesis ................ 2] CHAPTERII: REVIEW OF LITERATURE ......... .g ........ 22 ~ CHAPTERIII: THE REGIONAL SETTING OF THE STUDY ........... 42 The Geographic Setting ................ 42 Some Characteristics of Agriculture . in Rio Grande do Sul ................ 44 PART B THE FARM RESOURCE ALLOCATION AND PRODUCTION MODEL CHAPTER IV: THE CONCEPTUAL APPROACH OF THE MODEL ......... 57 Introduction ..................... 57 Some Useful Concepts of Production Theory ....... 59 Technological Change in the Linear Model ; ...... 63 Aggregation Bias and Farm Size Considerations ..... 66 General Description of Model Structure ........ 69 Alternative Approach for Modeling Resource Allocation ..................... 75 CHAPTER V: MATHEMATICAL STRUCTURE OF THE MODEL .......... 78 Yield Component. . . . ................ 78 Resource Allocation Component ............. 82 Mathematical Programming Model ........... 82 Structure of a Periodic Linear Programming Model ................ 84 Objective Function ............... 85 Activities ................... 87 Constraints ................... 91 Summary of the Model .............. 97 TABLE OF CONTENTS Dynamic Feedback Mechanisms and Exogenous Variables ............. 99 Objective Function Coefficients ........ 99 Constraint Elements .............. 101 Input-Output Coefficients ........... 111 Production and Accounting Component ......... 111 Land Use Pattern ................. 111 Production .................... 112 Income . . .................... 114 Resource Utilization ............... 116 Input-Output Ratios ................ 119 Resource Productivities .............. 120 Product and Input Prices Expectations ........ 120 Data Requirements and Sources ............ 126 ~ PART C MODEL APPLICATION AND ANALYSIS CHAPTER VI: EMPIRICAL RESULTS .................. 129 A Note on Model Operation .............. 130 Technology Alternatives Designed for Experiment ................... 131 Alternative Varietal Technology .......... 131 Alternative Mechanical Technology ......... 137 Simulated Model Results ............... 141 The Impacts of Varietal Technology ........ 141 Land Use and Cropping Patterns ......... 142 Production ................... ‘145 Employment and Input Utilization ........ 146 Income and Factor Productivities ........ 151 The Impacts of Mechanical Technology ....... 154 Land Use and Cropping Patterns ......... 155 Production ................... 157 Employment and Input Utilization ........ 159 Income and Factor Productivities ........ 162 Model Evaluation ................... 164 CHAPTER VII: SUMMARY AND CONCLUSIONS ............... 171 Summary of Problem, Objectives and Methodology .................. 171 Summary of Findings, Conclusions and Implications for Development and Technology Policy ................. 176 Limitations and Suggestions for Further Research .................. 184 BIBLIOGRAPHY ........................... 189 vi APPENDIX The Structure of the Recursive Linear Programming Model ............. 194 Sample of the Yearly Output from the Model ..................... 205 Computer Program ................. 209 vii Table I-1. I-2. III-1. III-2. III-3. III-4. III-5. III-6. III-7. V-l. VI-l. VI-Z. VI-3. VI-4. LIST OF TABLES Performance of Selected Macro-economic Variables, Brazil, 1961-1970 .................. Average Yields of Major Brazilian Crops for Selected Years ............... Estimated Domestic Income by Sectors, South Region of Brazil, 1968 (Cr$ 1,000) .......... Agricultural Gross Product by Subsectors, South Region of Brazil, 1969 (1,000 Cr$) ....... Some characteristics of Agriculture in Rio Grande do Sul, Brazil, 1960-1970 ......... Percent Distribution of Land by Farm Sizes, Rio Grande do Sul, Brazil, 1960 and 1970 (Percent). . . . Harvested Area for Four Field Crops, Rio Grande do Sul, 1960-1976 (Hectares) ......... Production of Four Field Crops, Rio Grande do Sul, 1960-1976 (Metric Tons) ........... Calendar of Operations ................ Summary of Activities and Constraints in the Resource Allocation Component ......... Summary of Alternative Technology Runs ........ Optimal Land Use and Crepping Patterns for 1980 Under Different Yield Alternatives and a 50 Percent Mechanization Level ............ Optimal Production Levels for 1970 and 1980 Under Different Yield Alternatives and a 50 Percent Mechanization Level ................. Optimal Input Use for 1980 Under Different Yield Alternatives and a 50 Percent Mechanization Level . . . viii Page 13 16 43 44 45 46 49 50 55 98 140 143 147 . 149 VI-S. VI-B. VI-9. VI-10. VI-11. VII-1. Net Farm Income and Factor Productivities for 1980 Under Different Yield Alternatives and a 50 Percent Mechanization Level ......... Optimal Land Use and Cropping Patterns for 1980 Under Different Mechanization Alternatives and Base Yield Levels ................ Optimal Production Levels for 1980 Under Different Mechanization Alternatives and Base Yield Levels ................ Optimal Input Use for 1970 and 1980 Under Different Mechanization Alternatives and Base Yield Levels ................ Net Farm Income and Factor Productivities for 1980 Under Different Mechanization Alternatives and Base Yield Levels .......... Optimal Area and Production Levels Under TWO Sets of Price Assumptions, Alternative IA, 1970-1980 ............ Actual and Estimated Area and Production Levels, 1970-1976 ............. Sample of Output Results Comparing the Impacts . . 152 .. . 160 . . 163 . 166 . . 168 of Varietal and Mechanical Technologies in 1980 ..... 178 ix LIST OF FIGURES Figure ‘ Page IV-l. Input and Output Flows of the Model ........... 73 IV-2. Farm Size Disaggregation for a Periodic Linear Programming Model ............ 74 PART A BACKGROUND AND DESCRIPTION OF THE STUDY CHAPTER I INTRODUCTION Modernization of traditional agriculture has been an impor- tant thrust of most existing theories of agricultural development. An effective strategy for economic development depends on the capacity to generate new technologies which will contribute to growth in agricultural productivity. The strategy to modernize agriculture is usually taken as the basic means of strengthening the role of agriculture in the general process of economic development. Thus, the concept of technological change becomes a focal theme in understanding agricultural development. Its potential con- tribution to development has been recognized for some time. But the study of its sources and the adjustments in the system under- going structural changes arising from the continuous process of technological change will remain an important economic area of in- quiry. The generation and diffusion of agricultural technology is a rather complex problem. Market forces have become effective in speeding agricultural transformation, but other mechanisms such as public policies, projects, and programs have also been very efficient in increasing the technological level in agriculture. In the case of developing countries where there is a great deal of government intervention in the market system, the transformation of traditional agriculture has occurred mainly as the result of public investment in research, extension, and education. Public investment in agricultural research generates technical knowledge which, having been diffused and adopted, has great potential as a source of increasing production and productivity in the agri- cultural sector. Such investments involve the use of scarce re- sources. The task of planning agricultural research should consider the efficient use of these resources. The objectives of agricultural research should emphasize the usefulness of its results to society and, in particular, to the rural community. The problem of defining research objectives is a rather difficult one. Clearly, such objectives are dependent upon the gen- eral objectives of development in a country. Research priorities need to be adjusted to the goals of development.1 Analysis of the economic situation and knowledge of objectives and goals of an over- all strategy of development can serve as a basis to adjust research priorities to development needs. The planning of agricultural research or the implementation of agricultural research policy requires knowledge of the impacts and adjustments that take place as a result of the introduction of new technologies. Different approaches can be followed in order to carry out an analysis of research programs. One approach is to analyze a specific technological improvement after it has been in- troduced and its results have already occurred. Another approach is to look at the current economic situation and investigate the possible impacts and adjustments that could take place if certain well-defined types of technology were developed and introduced. This approach can deal with different objectives related to types of technology that are feasible for a region or a country. It attempts to provide useful insights into the possible impacts that are likely to happen in different parts of the agricultural sector. This study, which applies the second approach, is concerned mainly with the impacts and adjustments in resource allocation, pro- duction, and income distribution that are most likely to occur follow- ing changes in agricultural production technology. In order to do this, a dynamic production and resource allocation model is devel- oped which is assumed to represent the production relationships of the agricultural sector of the region. The model is then used to generate simulation results through time given changes in its structural parameters. The model is developed for one region with disaggregation in two farm size groups. The changes in structural parameters to be simulated are those which represent changes in pro- duction technology. Specifically, this involves changes in yields, fertilizer application rates, and technical coefficients related to the use of labor, animal and mechanical power. General Problem Setting In a general context this study is related to the economics of technological change. It is concerned with the impacts of innovations that could be generated through public investments in research and would be feasible for adoption by farmers. This approach to technological change differs from the typical one because, at least implicitly, it considers the effects of inputs such as research and extension, which are unconventional inputs of a production process. The increasing interest in the economics of technological change after the early 1960's is, in most part, due to the recogni- tion of the crucial role such change plays in economic growth and development.1 This growing interest is the result of the impact of early studies which started with the observation that the gloomy predictions of the classical economists concerning growth were not corroborated by contemporary reality, at least in the developed countries.2 The classical approach to growth neglected the fact that significant increase in labor productivity was not explained by the increase in capital per worker.3 An important contribution in the area of measurement of technological change was made by Robert Solow whose work laid the foundation for subsequent research in economic growth.4 Solow 1For examples of contributions which have emphasized the role of technological change in economic growth and development see: T.H. Schultz, Transforming Traditional Agriculture (New Haven: Yale University Press, 1964); Yujiro Hayami and Vernon H. Ruttan, Agria cultural Development: An International Perspective (Baltimore: The Johns Hopkins Press, 1971)} Zvi Griliches, "The Sources of Measured Productivity Growth: United States Agriculture, 1940-60," Journal of Political Economy 71(4):331-346, August 1963. 2Lester B. Lave, Technological Change: Its Conception and Measurement (Englewood Cliffs: Prentice-Hall, Inc., 1966), pp. 3-5. 3Robert Solow, "Technical Change and the Aggregate Production Function," Review of Economics and Statistics 30 (1957): 312-20. 4For a comprehensive survey of modern formal growth theories see F.H. Hahn and R.G.0. Matthews, "The Theory of Economic Growth: A Survey," Economic Journal 74 (December 1964): 779-902. 5 defined technological change as those increases in output per man that could not be explained by increases in capital per man. How- ever, this increase in productivity was in fact a "residual", and for this particular reason, Solow's approach was much criticized in subsequent works on the subject.5 For the most part, the debates over technological change concentrated around measurement aspects. No attempt was made to redefine the concepts and to understand the process by which tech- nical progress is induced by economic forces. After several years economists turned to different approaches which emphasized uncon- ventional variables such as research, extension, and education as major sources of increased productivity.6 Over time technology became an increasingly important element affecting growth and development. This notion is demon- strated by the new theories of agricultural development which emphasize technological, institutional, and human changes. T.H. 7 Schultz argues that significant growth in productivity cannot be 5Among others see T.H. Schultz, Transforming Traditional Agri- culture (New Haven: Yale University Press, 1964); Zvi Griliches, "The Sources of Measured Productivity Growth: United States Agri- culture, 1940-60," Journal of Political Economy 71(4): 331-346, August 1963. ‘TI 6See Robert E. Evenson, "The Contributions of Agricultural Re- search and Extension to Agricultural Productivity," Unpublished Ph.D. dissertation, University of Chicago, 1968; Zvi Griliches, "Research Expenditures, Education, and the Aggregate Agricultural Production Function," American Economic Review, 54 (December 1964): 961-974; P.L. Cline,’"Sources of Prodittivity Change in U.S. Agriculture,“ Unpublished Ph.D. dissertation, Oklahoma State University, 1975. 7T.H. Schultz, Transforming Traditional Agriculture (New Haven: Yale University Press, 1964): 6 brought about by the reallocation of resources in traditional agri- culture. Transformation is dependent on the decision to invest in agriculture to make modern high-pay-off inputs available to farmers. Mellor8 emphasizes the process of agricultural modernization as a condition for development. He states that "a dynamic contribution to economic development from the agricultural sector and significant improvement in rural welfare depend upon the modernization of agri- culture through technological change." He further suggests that there is a need to generate new inputs of technological change which increase the productivity of traditional inputs. Modernization is a process of increasing the productivity of inputs and of introducing new and improved inputs. In their important contribution to the literature of agricultural development Hayami and Ruttan9 have treated technical and institutional changes as endogenous to the economic system, and have emphasized the process by which a new and improved factor is supplied. The inducement of changes in technology, institutions, and human nature is an important policy variable. This process has been the preoccupation of most governments of developing countries and of international donor organizations which have invested large amounts of resources in order to induce transformations that can increase 8J.H. Mellor, The Economics of Agricultural Development (Ithaca: Cornell University Press, 1966), p. 223. 9V. Hayami and V.H. Ruttan, Agricultural Development: An International Per§pective (Baltimore: The Johns Hopkins Press, 1971). 1+ production of food, the efficiency of use of resources, and improve the welfare of people. The basic problem decision-makers face in inducing trans- formations is the determination of the forms of investment that a government can make in agriculture in order to foster development. This point, in fact, is made by Schultz who states that “basically, this transformation is dependent on investing in agriculture. Thus it is an investment problem. But it is not primarily a problem of capital supply. It is rather a problem of.determining the forms this investment must take, forms that will make it profitable to in- vest in agriculture."10 This implies that the inducement of trans- formations in agriculture should come about through investments that can create conditions for new investments to take place. This, in turn, emphasizes the need to identify those sectors or subsectors of the agricultural economy which have a greater potential to induce changes as the result of investments. The variable technological innovation in agriculture has be- come an important factor in the development process. The planning and organization of the research sector and the identification of research programs that can affect technological change is presently a significant problem. To do so requires a great deal of informa- tion about the structure of production and the major interrelationships 1OTJV. Schultz, Transformigg Traditional Agriculture (New Haven: Yale University Press, 1964), p. 4. among markets, commodities, producing units, and other economic forces in the agricultural sector. Problem Situation and Statement Basically this study concerns itself with the problem of how research programs can be directed to affect technological change to increase productivity of scarce resources and increase total pro- duction of major commodities. Public investment in agricultural re- search generates technical knowledge that, after being diffused and adopted, will change the resource base of farmers and the structure of production of a region or a country. A whole series of impacts and adjustments will take place following the introduction of new technologies. Of particular interest are changes in the structure of use of and demand for agricultural inputs, changes in income and production patterns, and impacts on the income distribution among different farm size groups. The problem of resource allocation to agricultural research has received increased attention over the past years. This concern may be seen as the result of: (a) the need to increase the produc- tion of food to meet increased demand due to population and income growth; (b) the increased levels of privateandlnflflic investment in research; (c) the recognition of the potential contribution of tech- nological change to development; (d) the actual level of knowledge about the generation of new technology for some specific geographical areas; (e) the absence of knowledge about the nature of returns to research investments; (f) the increased concern about a systematic way to deal with the problem of establishing research priorities, and (g) the lack of.satisfactory results in respect to actual im- provements in production and productivity in the agricultural sector. These factors have contributed to the growing concern over the organization and planning of research programs in developing countries. Specifically, major reforms have taken place in the organization of research activities in Brazil in recent years.11 The concern over the agricultural research system in Brazil arose from the importance attached to the modernization of agriculture. The performance of this system was considered very unsatisfactory in respect to generation and maintenance of a flow of research out- comes that would be able to meet the needs of the overall process of development. The process of reform started with the analysis and diagnosis of problems of the current situation that led to the formulation of a new approach involving the institutional, administrative, and financial organization of the research system. The reorganization involved the creation of the Empresa Brasileira de Pesquisa Agropecuaria (EMBRAPA), an agency whose objectives were the planning and coordinating of research programs in accordance with the policies of the Federal Government in respect to technology and socio-economic development. EMBRAPA was allowed adequate administrative and finan- cial flexibility to execute a national plan of agricultural research nSee Helio Tollini, "Planning Agricultural Research: Concepts and Practice," in The Future of Agriculture: Technology, Policies and Adjustments, Collection of Papers and Reports of the Fifteenth International Conference of Agricultural Economists, Sao Paulo, Brizil, August 1973. 10 and to coordinate the activities of other organizations such as universities, secretaries of agriculture, and other government agencies, as well as the private sector. The responsibility of EMBRAPA is to establish and maintain research activities throughout the country. Its orientation has been toward commodity and basic resources. It has established Regional Research Centers in different regions with the objective of concentrating efforts on major problems of each region. One example of basic resource oriented research is the case of "campos cerrados." The upland savanas, or "campos cerrados,“ represent extensive areas which at the present time contribute little to the economy of Brazil. A Regional Research Center has been created to develop field experiments and carry out systematic examination of the soils of the "campos cerrados" in order to create technical know- ledge that would make these areas capable of supporting a much more intensive agriculture than they do at the present time. Other Regional Research Centers have been created in major producing areas to carry out research programs related to products that are important for the regional economy. In most cases the centers concentrate research efforts on one commodity or a few re- lated commodities. Questions arise concerning the viability of the commodity- orientation approach because of the widely scattered distribution of production of major commodities and the difficulties of transferring technological innovations from one region to another due to marked differences in environmental conditions. This orientation can 11 affect the relative comparative advantages among regions, induce transference of resources, and have great impacts on income dis- tribution within the agricultural sector. At any rate, the responsibility of the research system is to strengthen the role of agriculture in the development process. Brazil, as well as other developing countries, is facing the basic problem of increasing production of food and avoiding the debilitat- ing effects of malnutrition. Historically, the major source of output growth in the agricultural sector has been the expansion of the frontier with incorporation of new land, labor, and associated capital. As land becomes more scarce, increases in production will have to rely more on productivity growth. Brazil is a large country with marked diversities. Its area has been estimated at 851,000,000 hectares by the National Council of Geography, and at 846,000,000 hectares by the population census. According to the 1960 census, only 3.5 percent of the total area of the country was cultivated, and only some 30 percent of the total area of the country was counted as land in farms.12 The 1970 census estimated the population of the country to be 94,508,000 inhabitants, and classified 44 percent as rural. The population distribution is very uneven with high concentration on the East Coast and in the Central-South region. During the 1960-70 period total population grew by about 3.0 percent per year. Rural population grew at less 126. Edward Schuh, The Agricultural Development of Brazil (New York: Praeger Publishers, Inc., 1970), p. 124. 12 than 1 percent per year and urban population grew at an average 13 Rural- greater than 5 percent per year during the same period. urban migration is the basic factor determining the rate of growth of the urban population. The performance of some macroeconomic variables related to the Brazilian economy during the 1961-70 period is shown in Table 1.1. The annual growth rate and the rate of inflation give a good idea of the performance of the economy during that period. The economy experienced sharp decreases in the rate of growth and high inflation rates until 1965, mainly because of a political crisis in the early 1960's which led to a revolution and the take-over by the military in March 1964. The new government initiated a set of economic policies designed to speed up economic progress and control the rate of inflation. As a result, inflation was much lower after 1965, and the rate of growth indicated a strong economic performance by the end of the decade. Agriculture has been a major sector of the Brazilian economy. It-has provided a major source of employment opportunities, produced a substantial portion of the gross national product, and has been a significant source of export earnings. For example, in 1970 agri- culture generated about 15 percent of the Brazilian gross domestic 13Ruy Miller Paiva, et al., Setor Agricola do Brasil (Rio de Janeiro: Editora Forense Universitaria, Ltda., 1973), p. 286. 13 .Fump .muzmwpmpmm m mingmomw mubgwm—megm 0.9:»?me omomuczm .7595 on cowpmwuwpmm 2:522 ”mugaom m.m_ m.F_m.om 0.8 m.mm. m.m m.m m.mmm ~.Nem cam, m.- m.eom.kp o.m c.4mp 4.x o.m m.omm o.me~ soap m.km m.m~o.ep w.m m.¢LF m.~ m.m “.mom “.mON mmm_ _.- ¢.PPO.PF m.~ «.map m.e m.¢ 4N.mm ~.m¢o Lam. m.mm m.m~o.m m.P “.mop e.“ F.m m.me~ m.mpa mom. ¢.mm m.m¢~.m e.o- m.mm_ N.A L.N e.mm~ m.mmm meme m.~m o.w_o.m ~.o- e.oc_ m.~ m.~ m.m¢~ m.m~m eem_ o.mk A.mm_.m m.F- m.oop m.“ m.P m.~¢~ m.emm mom, m.¢m ¢.NON.F P.N m.mmp 4.5 m.m m.mm~ o.m¢m Nom_ m.mm m.mhk 5.8 o.oo~ N.N m.op m.m- o.PNm Fma_ Axv oopum¢m_ Aav oopumemp (Awao ewe ANMW oopnmem_ (dwcu coc_Pcs ecu, Laa> cowpmpmcm moorucu guzocw mmuwucH mmowca guzocw mmowucm moupcm mo mama wows; «PomoFozz Pmacc< Fem“ ucmpmcou Fmacc< Puma acmpmcou Fame mea_ Foam mes, nuance; mmocw muwmnu cw; uuauoca Pacowumz mmocu .onmpupmmp .FVNMLm .mopnmwcm>.uPEocoumocumz umuompmm mo wocmsgomcma "~.H m4mv mama .Pwmmcm cu oowpm_umumm owcmac< "mucaom wmp mwp mm, om~.F Nwo.P mnw.~ moo.p mpacmma NFF opp mop owe «me Fuw wmw coupou mPP mFF mop Pmm.mv Pop.m¢ mo¢.pe No¢.wm mcmugmmam Fm mm em mum mmm mmm woe mouou mm mm mm ppm new mvo.P mpm.p wmemou mvp mmp m—P mmo.n mmm.o mo¢.m omm.¢ mmoumuom :meH mmp opp mm mvm mum. mmm mmn paws: NFF mop mm Noo.¢P ¢¢~.¢F mmm.mp mmoqmp oomcmz No no ma «mm moo Fem owe mcmmm mop mop mm mom.~ Nmm.F ¢m~.F mn~.p :sou mm mm mm woe.~ mmm.~ emm.~ mam.p mowm onnwmmp mmuemmp ooummmp onuwmmp wmuvmmp oouommp Pmnmvmp maogo Aoop u pmunvmpv mmxmucH m;\mx cw mupaw> mcmm> vmuoopmm com maocu cmwnwnmgm Lona: mo mupmw> mmmgm>< .N.H momcmx cha< vco cowpmcogmco F:om mcwumm>coz mewumo>coz mcwumm>coz coco: zgmscnom Mu mcwacopo Mu my acmacmq .u. o5 .H .%. ow. cc 5239:. h... h u. :8 u. m. 28588 w. m. a mcwpmm>cmz coasm>oz mcwpcmpo marpco—o mcwpcmpa Lmnopoo new ago new cowumcoamca .J cowpmcmamco covumcmnmca :8 .fln :8 :8 28538 b”: 2.553 .M 532 new mu corumcmnmco .u Fwom xpza mcapmoo mcsummo “concoamucH poms: cmpcwz cmesam cmmnxom \cmmnxom poms: :cou mowm mcpcoz mcowpocoao mo covcmFou ”N.HHH ofinoh 56 In conclusion, this chapter shows that the state of Rio Grande do Sul is one of the most important producers of agricultural products in the South Region and also in the country. A major char- acteristic of its agriculture in the past fifteen years.has been a shift from the traditional range livestock production on extensive natural pastures to intensive cropping systems. Increases in crop yields have not been significant in the past. Basically, increases in production have resulted from increased use of land rather than from the improvement in yield per hectare. PART B THE FARM RESOURCE ALLOCATION AND PRODUCTION MODEL CHAPTER IV THE CONCEPTUAL APPROACH OF THE MODEL Introduction The agricultural production system of Rio Grande do Sul has experienced very significant changes during the past fifteen years. These changes have been related to levels and composition of re- sources used and output. There have been great changes in the quality and quantity of inputs used; new inputs in the form of improved seeds, fertilizer, and machinery have been introduced and used in rapidly increasing amounts. Also, real agricultural output has grown considerably, and production patterns have changed signif- icantly, resulting in a transformation of the regional economy from range livestock production to intensive crop production. Technological change has been a most strategic factor in the transformation of traditional agriculture. The complexity of choices involved in agricultural production is further increased when new technologies are introduced. In Rio Grande do Sul rapid increase in mechanization has been the major characteristic of technological advance. Other technologies such as biological innovations have not contributed as much as they could to the growth process. Yields per hectare and per annual remained relatively stagnant throughout the 1960's and early 1970's. 57 58 It is difficult to predict how this transformation will develop in the future. It is true, however, that the future of agri- culture in Rio Grande do Sul will depend on government policies to- ward the agricultural sector and to market adjustments to supply and demand shifts. Despite the uncertainties in respect to market con- ditions, it has to be recognized that the performance of the agri- cultural sector will depend on the extent of government participation which alters the environment within which farmers make their decisions. As Singh and Ahn1 point out, government intervention may occur in three ways: a) by directly controlling scarce economic and physical resources through controls over their distribution or access to them (distribution of seeds, fertilizers, or credit are examples); b) by intervention in product or factor markets either directly through the purchase or sales 0f inputs or outputs or indirectly through price controls and taxes (price support programs, excise and sales taxes, transportation levies, land taxes, and input price subsidies are examples); and c) through changes in the economic and social infra- structure within and with which farmers operate, thus reducing the costs of farm production or increasing (in quantity and quality) the real resource base (including knowledge) of the farm sector. Given these considerations, three underlying assumptions are maintained in this study: a) in spite of significant changes that have occurred in the past, resource reallocation within agriculture 11. Singh and C.Y. Ahn, "A Dynamic Multi-commodity Model of the Agricultural Sector: A Regional Application in Brazil," Studies in Employment and Rural Development No. 37, IBRD, Washington, D.C., 1977, (Mimeo). p. 6. 59 and changes in production structure will continue in the future; b) technological change will continue as an important factor in the process of transformation and will be characterized by different types of innovations, and c) government participation in its various forms will continue as a major factor affecting the economic environ- ment within which farmers make their decisions. The primary objective of this study is to develop an aggregate sector level model for one region with disaggregation in two farm size groups which take into account the economic behavior of farmers as decision-makers in the agricultural sector. The basic approach is to model the activities of farm firms as behavioral decision units competing for regional resources. The model is used to project adjustments and structural changes in resource allocation and production. This chapter presents a conceptual description of the theory and logic behind the model. Detailed model formulation is presented in the next chapter. Some Useful Concepts of Production Theory In a broad sense, production may be defined as the trans- formation of inputs into outputs, and technology is the set of technical opportunities that defines the basic relationships of this transformation. Considering a process as represented by a vector of input-output coefficients, that'hs,a particular method or technique of converting resources into a product, technology may be defined as the complete set of processes available or potentially available for production. Processes can be defined as the different ways or 60 sequences in which production can be carried out. A process is characterized by certain ratios of the quantities of the inputs to each other and to the quantities of each of the outputs.2 The concept of a production function is one of the most im- portant in the theory of production economics. It formalizes the relationship between output and inputs in a production system. A production function is defined as "a schedule showing the maximum amount of output that can be produced from any specified set of inputs, given the existing technology."3 The concept is associated with a particular technological process. It expresses the relation between input and output, as well as the relation among inputs themselves. It also implies that a technical maximization problem has been solved. In mathematical form it can be represented by Y = f(X],...,Xj/Xj+1,...,Xn) (1) where Y is output, X],...,Xj ,Xn are fixed inputs. Specification of the variables in are variable inputs and Xj+],... the production function and the form of the function are based on the nature of the process or phenomenon described by the function. The available quantities of the factors specify the values of the variables, and the maximal output specifies the value assumed by the function. The complete specification of the relationship be- tween inputs and output defines a function or surface in the case of 2R.H. Day, Recursive Programming and Production Response, (Amsterdam: North-Holland Publishing Company,1963), pp. 61-62. 3C.E. Ferguson, Microeconomic Theory, 3rd ed. (Homewood, Illinois: Richard D. Irwin, Inc., 1972), p. 136. 61 more than one variable input. Changes in the quantity of a vari- able factor will define movement along the production function or surface upward or downward depending on the nature of the change. Further elaboration of the concept of production function distinguishes between two situations of production concerning the nature of the relationships among inputs. One situation refers to those cases in which the set of technically possible factor com- binations is unrestricted, allowing for continuous substitution among factors. This situation defines what is known as production under conditions of variable proportions. The ratio of input quantities may vary, and it is necessary to determine not only the level of output to produce but also the optimal proportion in which to combine inputs. The other situation involves cases in which some factors can only be combined, within the technological principle involved, in fixed ratios to each other. This situation defines what is known as production under conditions of fixed pro- portions. If output is expanded or contracted, all inputs must be expanded or contracted so as to maintain the fixed input ratio. It is a truism of economic analysis that the familiar curvature of production functions is generated by changes in the scale of application of any one process.4 Situations in which pro- duction is characterized by conditions of variable proportions are represented by continuous production functions and continuous isoquants 4R. Dorfman, Application of Linear Programming to the Theory of the Firm, (Berkeley: University of California Press, 1951). 62 with the possibility of substitution between factors. In a case of fixed proportions, the corresponding production function has kinks at the points where the ratios of available factor quantities coincide with the technical ratios specific to the process in question. This study is concerned with production that involves many activities. The efficient combination of activities will be de- termined by an established optimizing criteria. Technology choices available are assumed to be linear in nature. The analysis of pro- duction involving many activities and a linear form for the tech- nology is presented by Koopmans5 in a model of production in which the following circumstances or considerations are treated formally as distinct elements of the production problem: a) the purely technical possibilities of production; b) the quantitative limita- tions on basic resources (primary factors of production) available to the economy; c) the general goal or objective to be served by production, and d) the optimizing choice whereby the technical possibilities are exploited in a coordinated manner toward that ob- jective. The input structure of a given production process is repre- sented by a column vector of coefficients, denominated technical coefficients, which defines the amounts of input used and output produced for a given unit of a process. The vector includes input coefficients and output coefficients. .The set of all vectors 5T.C. Koopmans, "Analysis of Production as an Efficient Combina- tion of Activities," in T.C. Koopmans, ed. Activity Analysis of Production and Allocation (New York: John Wiley and Sons, Inc., 1951), Chapter III. 63 representing the processes available can be adjoined to form the technological matrix. This matrix describes the technical oppor- tunities available for a given point in time. Technological Change in the Linear Model In traditional economic theory a clear distinction is made between "substitution" and "technological change." The former con- cept is used to designate choices related to a given production function, and the latter to changes in the production function it- self. Then, technological change is simply defined as changes in one or more of the parameters of the relevant production function. This distinction is relevant in the case of production under con- ditions of variable proportions.6 The concept of technological change in this context is somewhat narrow, mainly because it only encompasses production of existing commodities and use of existing resources. Observing the variation in context in which technological change is referred to, it is clear that this concept has been given a wide range of meanings and interpretations. This shows the difficulties of defining technological change, because of the great number of relationships that it involves. In general terms, technological change may be defined as any change in the methods of production used. Basically, the change 6For a formal treatment of technological change within the con- text of continuous production functions see M. Brown, On the Theory and Measurement of Technological Change, (Cambridge University Press, 1966). 64 may result from: a) improvement in existing processes permitting commodities to be produced at lower cost; b) partial or total sub- stitution of an old resource by a new one, and c) production of new products. This more general view of technological change can be in- corporated in a linear model of production of the type presented by Koopmans,7 which is based on the framework of linear programming. One advantage of this approach is that it permits the analysis of different meanings of technological change and the possible inter- action among them. Basically, the problem is to deal with the changing structure of the economy which can be analyzed through changes in the structure of an input-output model. The introduction of new technology can be represented by changes in the elements of the model. Of course, a major problem is to work out a mechanism that makes these changes operational. It is necessary to understand the nature of the new structure with new technology and how the structure changes through time. Carter8 approaches this problem by incorporating process substitution in a linear model by means of equations that describe the rate at which the input-output coefficients change as new tech- niques gradually replace older or average techniques. 7T.C. K00pmans, op. cit. 8Anne P. Carter, "A Linear Programming System Analyzing Embodied Technological Change," in Anne P. Carter and A. Brody, eds. Erg- ceedipgs of the Fourth International Conference on Input-Ogtput Tech- niguesTAmsterdam: North-Holland Publishing Company, 1970). put Cl binat descr time. ideas nolog ways. Chang reso for excl also cons r881 def thi 110 as ana 65 In the last section a process is denoted by a vector of in- put coefficients and output coefficients such as yields. The com- bination of a number of vectors form the technological matrix which describes the technical opportunities available at one period of time. Once the structure of this matrix is understood, the basic ideas of technological change in the linear model can be introduced. Innovation can be viewed as the existence of a new tech- nological matrix which can differ from the previous one in several ways. The structure of the matrix changes over time as a result of changes in the technical coefficients, changes in types of scarce resources, and changes of processes. Expansion of the matrix allows for the introduction of new processes, while contraction allows for exclusion of processes which have been abandoned. The matrix can also change in order to accomodate changes in the nature of the constraints. Asprocess or techniques of production change, new resources are developed and become a constraining element. Changes in input and output coefficients for a unit level of a process will define changes in the proportions in which resources are used and this will basically define new processes. In a real sense, innova- tion is a continuous process and the technological matrix is defined as a function of time. An analysis of technological change using an approach analogous to parametric programming is presented by Simon.9 He 9H.A. Simon, "Effects of Technolgoical Change in a Linear Model," in T.C. Koopmans, ed. Activity Analysis of Production and Allocation (New York: John Wiley and Sons, Inc., 1951), Chapter XV. 66 analyzes the effects of changing technical coefficients and re- source scarcities on the economy of production activities and on in- come. He also emphasizes process substitution, but does not elaborate a mechanism that operationalizes the structural changes over time. Technological change can be characterized by three com- ponents: invention, innovation, and diffusion. Invention is the process of creating new knowledge. It is of crucial importance in the growth process, but cannot be treated by existing tools of economic analysis. For this reason, treatment of technological change must include the second component. Innovation consists of the introduction of new process of production. The effects of tech- nological change on production can be analyzed by identifying a time period in which a major innovation has been introduced. Thus, innovation may be treated as a condition of the production structure, and may be accommodated in the model by introducing new activities and new constraints pertaining to the new technology. The rate at which innovation takes place determines the ultimate effects of technological change on production. This rate is termed diffusion or the rate of adoption. It can be incorporated in the model by means of adoption patterns which show how innovations are adopted by farmers over time. Aggregation Bias and Farm Size Considerations One of the major problems with regional aggregate models is aggregation bias, which appears wherever aggregate relationships are modeled without explicit reference to individual decision-making 67 units. Several approaches have been suggested to deal with this problem. The most accurate method would be to model individual farm firms as units of analysis, and then derive the aggregate estimates. This procedure would result in a bias-free estimate However, it is not usually feasible due to limited availability of resources to carry out the study. Therefore, the practical pro- cedure is stratification of individual decision-making units into homogenous groups, according to some characteristic such as region, farm size, resource combination, etc. Aggregation bias exists when the sum of the solutions for each of the individual firms in the set does not equal the estimate obtained by determining the optimal solution to the entire set directly. Methodological aspects of aggregation concern the con- ditions of similarity among individual firms permitting estimation of the aggregate response without bias. This problem has been analyzed by various authors. Day10 establishes sufficient con- ditions for exact aggregation based on the requirement of "propor- tional heterogeneity." The conditions are: a) all firms must have identical matrices of input-output coefficients; b) the vector of net returns of every firm must be proportional to the corresponding aggregate vector, and c) the vector of resource constraints of every firm has to be proportional to the corresponding vector for the aggregate. 10R.H. Day, "On Aggregating Linear Programming Models of Pro- duction," Journal of Farm Economics 45(4): 797-813. 68 Subsequently, Miller11 has argued that Day's conditions are too restrictive, and states less binding requirements for exact ag- gregation as f0110WS= a) all firms must have identical input-output matrices, and b) all firms must have qualitatively homogeneous out- put vectors, which means that all firms must have identical sets of activities in the optimum solution. The question of less binding requirements is further analyzed by Paris and Rausser.12 They argue that "obviously, suf- ficient conditions are of interest because they may indicate an easy test for LP aggregation; but on the other hand, they are of greater interest if they realistically admit the existence of empirical cases which satisfy the specified requirements." In their judgment, "it is not possible to find empirical cases which fit Doy's sufficient conditions." They demonstrate that it is possible to formulate more general and less binding sufficient conditions for exact aggregation which are also empirically meaningful. Aggregation problems arise from the fact that firms are different in respect to structural and behavioral aspects which will cause individual firms to respond differently to changes in economic conditions. Many differences among firms are due to the physical environment such as soil, topography, climate, etc. These factors are important determinants of production, but even in a homogeneous 11T. A. Miller, "Sufficient Conditions for Exact Aggregation in Linear Programming Models," _gricu1tural Economics Research 18 (April 1966): 52-57. 121. Paris and G. C. Rausser, "Sufficient Conditions for Aggrega- tion of Linear Programming Models," American Journal of Agricultural Economics 55(4): 659-666. 69 environment differences in response will exist due to differences in relative factor endowments. The importance of farm size arises from differences in re- sponse to factors such as economies of size, risk and uncertainty, technological change, and market response. Differences in farm size can explain differences in the decision-making process regarding these factors. Larger farms can make use of larger size machinery and benefit from operation of economies of scale. Depending on the size of the operational unit, different approaches can be used to deal with situations involving risk and uncertainty. Differences in size will bring about differences in the rate of adoption and ad- justment to technology change, due to differences in management and access to the market. Market response is dependent on the partic- ipation in factor and product markets which is a function of the degree of commercialization of the farm firm. Differences in size cause farms to respond differently to changing market conditions due to differences in the degree of participation in the market. These considerations are important for this study. As it is shown in Table 111.4, the distribution of farm size in Rio Grande do Sul is wide and rather skewed. This results in significant dif- ferences in relative factor endowments which in turn give rise to differences in response to economic factors. This justifies the explicit treatment given in this study to different farm size groups. General Description of Model Structure The primary objective of this study is to analyze the effects on production, income, and employment by changing some basic farm 70 level technology. The analytical instruments used to achieve this objective are various concepts of economic analysis and production theory incorporated in a dynamic model of production and resource allocation. The model is developed for one region with stratifica- tion in two farm size groups. The allocation problem is solved through a sequenceirflinear programming models, with the solution for one year recursively linked to previous years. The programming technique is known as Recursive Linear Programming. The model is developed with a great deal of flexibility, allowing for changes in its structure which represent changes in technology of production. The model to be developed has a special characteristic which allows for model coefficients to vary over time. Most of the ob- jective function coefficients, constraints elements, and input-output coefficients should be time variant, and shall represent changes and adjustments in the conditions under which the production decisions are made. In this study those coefficients that change as a function of technological advance, are of particular interest. Or, to put it another way, this study examines those coefficients whose changes would reflect meaningful changes in the technology opportunities open to farm firm operators. One important characteristic of the model is its flexibility which allows it to serve as a component of a larger sector model. It is basically a decision-making component based on an optimization criterion and a set of resource and behavioral constraints. Most of the relationships considered exogenous in this model could be 71 modeled as separate components and then linked together with this model without major difficulties.13 Most regional models of this nature involve a large number of relationships, allowing for the analysis of a large number of results. The basic economic problem involved is that of efficient allocation with simultaneous determination of optimum production levels of various commodities and the resource requirements to carry out such production. A model of this nature is designed to be used for three major purposes: a) explanation and basic projection of the regional structure of production, given a series of assumptions in respect to resource endowment, technology, and prices; b) pro- jection of impacts of exogenous variables and key model parameters, and c) projection of impacts of alternative agricultural policies on the regional economy. The modeling of farm level decision-making is a central feature of this study. It takes into account a number of char- acteristics of regional production. These are: a) the simultaneous aspects of decisions at the farm level; b) the multi-dimensional features of farm activities; c) the interdependencies between firm and household decisions; d) the interdependence of activities com- peting for a given set of inputs; e) the competition among farms for 13 The modelling approach of this study is similar to that de- veloped by de Haen for the Korean Agricultural Sector Study, where resource allocation using Recursive Linear Programming is a component of a large systems model. See Hartwig de Haen, "The Resource Allocation and Production Component of the Korean Agricultural Sector Model," in G.E. Rossmiller, ed., A Systems Approach to Agricultural Sector Development Decision-Making: Building and Institutionalizing an Investigative Capaciry, Agricultural Sector Analysis and Simulation Projects, Michigan State University, 1977 (Forthcoming). 72 the use of regional resources, and f) a wide range of technology choices available for farm operators. The basic structure of the model, including exogenous vari- ables and model output variables, is shown in Figure IV-l. Essentially, the model consists of three components: yield com- ponent, resource allocation component, and production and accounting component. The yield component is basically designed to compute crop yields based on fertilizer response functions. Yield rates are determined as a function of nitrogen application. The fertilizer application rate is determined based on the equimarginal principle of equating the marginal value product of the factor to the price of the factor. The allocation component consists of a one-periodic linear programming model allocating given resources to production, an interval feedback relating previous actions to current decisions, and an external feedback establishing the interactions of the com- ponent with exogenous variables. In the production and accounting component, production levels for crops and livestock activities are computed given land allocation and yield projections. Other results such as resource requirements, income, resource productivities, and input ratios are also computed. Results are obtained by commodity, farm size, and regional aggregates. The structure of the linear programming problem to be solved for each time period is block diagonal with one block for each farm size and additional regional constraints (Figure IV.2). The coupling 73 32320.6 .05 858?. wozmm Sac. cozmficmzoofi oEooE mm: :65 cozoanocn. .822 05 B 250.“. 53:0 use. 59: #.>_ 23mm. 33909.: .9563“. new mum 5:095:00 3 A, 2986:. mocmEcotoo 332.0. .86; $25 2685 . 8500 65992 893 362324 cozoanoi u.oom . moo? Simon. oczcaooo< moors no.0 _ €45 0cm 5:822 5:335 _ oocaomom . U L ego; 86 _ H e a «5:05.... 825 3:8on Sac. 522.3 new 8:85 «4:22:80 .mco_>mcom 9:26“. @5390 $2638 8:92:80 5920-235 74 2511:) + 2%) 11(t) A§j1t1 35(t) A§j(t) BL(t) R§j(t) R§j(t) 31(t) Figure IV-2: Farm Size Disaggregation for a Periodic Linear Programming Model constraints account for interdependencies among farm size groups competing for regional resources such as supply of machinery and supply of wage labor. A number of crucial assumptions underly the structure of the model: 1. Farmers maximize expected net returns defined as expected gross revenue minus expected variable costs. 2. The objective function for the region is the sum of the objective function for the two farm size groups. 3. Farms in each size group are assumed to meet necessary con- ditions for aggregation. 4. All farms are assumed to have the same degree of information and knowledge about prices and technology choices. 5. The structure of the model is the same for each farm size, i.e., same activities and same constraints. 6. Some yield rates and some input-output coefficients are dif- ferent between farm sizes, reflecting differences in manage- ment and resource combination. 7. The structure of activities is assumed to remain the same over time. 75 Alternative Approach for Modelipg Resource Allocation In this study resource allocation is modeled using Recursive Linear Programing. Clearly, the resource allocation problem can also be modeled with the use of production functions. After produc- tion functions are estimated for each product, a programming algorithm can be developed to simultaneously solve the set of equa- tions to determine optimum production and resource use levels which satisfy certain optimization criteria. This approach was used by Watt,14 when he modeled a production component for Michigan's agri- culture using Cobb-Douglas production functions in a recursive simultaneous solution programming algorithm. If the resource allocation component is to be modeled by a Cobb-Douglas programming algorithm, the problem can be formulated in terms of a set of simultaneous equations in which a solution is generated for the level of activities and input use, similar to an activity analysis framework. Production functions for each com- modity in each farm size group in the region are defined as follows: b n ij Y.(t) = A.(t) n X.. (t) (2) 1 1 ._ 13 J-1 where Y1 = expected output of 1th commodity xij = jth input requirement for production of ith commodity 14 David L. Watt, "Michigan's Agricdltural Production," Un- published Ph.D. dissertation, Michigan State University, 1976. 76 A1 and bij = parameters i = index conmodity j = index input The maximization of an objective function can be incorporated together with the specification of resource and behavioral constraints. In Watt's formulation the assumptions of input supply and expected com- modity demand functions, and the behavioral assumpution that input price is equated to its value of marginal product, maximize an implicit objective function defined as total revenue minus variable costs. Basically, it seems that the same type of analysis can be carried out using either Recursive Linear or Cobb-Douglas Programming. Choice between the two approaches in this study was made based on the possibilities of incorporating technological change in the model. The production function format requires a rather high level of aggregation of outputs and inputs. Considerably more detail can be explicitly examined in the recursive programming framework which can deal with many outputs and allow for a much more specific treat- ment of the inputs and their combinations. Changes in the parameters of the production function rep- resents changes in technology. However, considerable difficulty was encountered in the attempt to connect these changes to specific and meaningful changes that could be understood in terms of variety improvements, fertilizer application, and mechanization. A further difficulty has to do with the nature of the production function. With the assumption of constant returns to scale, the sum of the 77 elasticity coefficients has to be equal to one. If changes are introduced in one coefficient, adjustment has to be made in the others to maintain the assumption. When the coefficients change, other results, such as marginal value products, also change. With- out a well-established relationship among the coefficients, only purely arbitrary changes can be analyzed. CHAPTER V MATHEMATICAL STRUCTURE OF THE MODEL This chapter presents a complete description of the model 1 An overview of the model structure was developed in this study. given in Chapter IV. Here the structural equations of the model are presented. The model is composed of three components. These com- ponents are: yield, resource allocation, and production and account- ing. The chapter is divided into three major sections describing the three components of the model, and two additional sections which discuss price projections and data requirements of the model. Yield Component One variable needed in other components of the model is yield per hectare for the crops considered. Crop yields are determined with the use of fertilizer response functions. Livestock yields are assumed constant throughout the period of model run. Crop yields are a function of a number of factors: crop variety, fertilizer application, irrigation, weather, etc. The large number of factors affecting yields and the interaction effects that can occur among them makes the task of modeling rather difficult. ¥ 1The computer program of the model is given in Appendix C. 78 79 Among the various factors influencing yield, fertilizer may be considered the most important mainly because of its interaction effects with variety and also the degree of control that can be main- tained over such a factor. If data is available though, adjustments can be introduced to take into account the effect of other factors. To generate the yield rates of different crops endogenously in the model this study uses fertilizer response functions. For situations where biological technologies are crucial, it is important to introduce yield-nutrient response data in order to be able to evaluate optimum nutrient levels and the relationships among variety, fertilizer and yield. The basic data needed are experimental data on the response of yields to nutrient. Large variation in yield is usually due to variation in the doses of a major element. The present case considers nitrogen as the basic element determining yields. The fertilizer response func- tions used in this model are of the non-linear quadratic form, so that the yield rates are given by YLDj(t) = YBASEj + ALPHAj - FERTj(t) + BETAj . FERT§(t) (1) where YLD = yield rate for crops determined from the response function (kg/ha) FERT = amount of nitrogen applied for given levels of phosphorous and potassium (kg/ha) YBASE, ALPHA, BETA = parameters of the response function 5 = indexes crops (j = l,...,4) 80 The amount of fertilizer applied is a decision variable and depends on a number of factors such as capital availability, be- havior of farmers in respect to improved cultural practices, and prices of products and inputs. Here optimum application rates are determined on the basis of the economizing principle of equating the marginal value product of an input to its price. Following this principle the optimum fertilizer application rate is given by FERTj(t) = {PFER(t)/PYCj(t) - ALPHAjl/Z ° BETAj (2) where PFER expected price of fertilizer (Cr$/kg) PYC expected price of product (Cr$/kg) To account for the effects of mechanization and differences in farm size, the yield rates are further adjusted for incremental yield increase on mechanized areas and on larger farms. Mechaniza- tion can increase yields due to better land preparation and cultiva- tion. Furthermore, large farms can achieve higher yield rates due to better management techniques. Thus, the final yield rate is ob- tained as YLDAijk(t) = YLDj(t) ° (1 + SYLDijk) - (1 + RYLDijk) (3) where YLDA = adjusted yield rate (kg/ha) SYLD = proportion of yield increase due to farm size (dimensionless) RYLD = proportion of yield increase due to mechanization (dimensionless) 81 indexes farm size (1 = 1,2) do 11 (.1. II indexes crops (j = 1,...,4) x 11 indexes mechanization (k = 1,2) In Equation 3, yield for each crop is adjusted according to farm size and the condition of mechanization. The model includes four crops: rice, corn, wheat and soybean. Farm size is stratified into two groups: "small" representing farms of area equal or less than 100 hectares, and "large" representing farms of area greater than 100 hectares. For each crop in each size group, two levels of mechanization, traditional and modern, are considered. The former level uses draft animals, and modern uses tractors and combines. Besides the four basic crop activities, rice, corn, wheat and soybean, the linear programming model of the resource allocation component includes soybean following wheat as an activity distinct from independent soybean. Since fertilizer response functions are only defined for the four basic crops, yield rates for soybean follow- ing wheat are determined by applying a discount factor to the yield of soybean. Usually fertilizer is not applied to soybeans when it is cultivated in double cropping with wheat. Yield can drop by as much as 30 percent due to lack of fertilizer application and delay in planting time which occurs because wheat is not harvested until passing the optimum period for planting soybeans. Thus, the yield rate for soybean following wheat is determined as YLDASNik(t) = YLDASik(t) - (1 - YLDDIS) (4) where 82 YLDASW = yield rate for soybean following wheat (kg/ha) YLDAS = adjusted yield fbr soybean independent of wheat (kg/ha) YLDDIS = yield discount factor (dimensionless) Resource Allocation Component This component models farmers' decision-making processes with respect to allocation and production using Recursive Linear Programming. This section describes the structure of the component only in a general way. Specific details of the model are presented in Appendix A. The section is divided into three major subsections. The first subsection presents the programming problem in its mathematical form giving a general idea of the process and relationships involved. The second describes the structure of a linear programming model for a given time t, and the third presents the linkages between different planning periods. Mathematical Programmipngodel: A recursive programming model can be defined as an infinite sequence of mathematical programming problems in which the input-out- put coefficients, the constraint elements and the objective function coefficients for one period of time depend on the solution of pre- ceding programs in the sequence, with certain lag lengths, and on a vector of exogenously projected variables. A recursive linear programming problem consists in finding the maximum n*(t) of the objective functions II*(t) = next? (t) Y(t)] t = 1,2,...,T (5) X(t) 83 subject to linear constraints Alt) rm 5611:) and nonnegativity conditions Y(t) _>_ 0 where H*(t) = optimal value of the objectjye function in period t under the optimal plan X*(t). 7(t) = n-dimensional vector of objective function co- efficients for period t. X(t) = n-dimensional vector of the levels of activities for period t. A(t) = m X n matrix of input-output coefficients for period t. p(t) = m-dimensional vector of constraints for period t. * = indicates optimal solution. A unique characteristic of a recursive linear programming model is a set of dynamic feedback functions which relate decisions for a period t to previous decisions and to exogenous variables.2 These feedbacks hold for the objective function coefficients for the elements of the constraint vector and for the elements of the input- output matrix and are defined by Equations 6, 7 and 8, respectively: 2See Hartwig de Haen, "The Resource Allocation and Production Component of the Korean Agricultural Sector Model," in G.E. Rossmiller, ed., A Systems_Approach to Agricultural Sector Development Decision- Making; Building and Institutionalizing an Investigative Capacity, AgriculturaT'Sector Analysis and Simulation Prejects, Michigan State University, 1977 (forthcoming). 84 zlt) = 217*(t-1).....1*(t-p). F*(t-1).....F*(t-p). Vlt)l (6) 5(t) = blB'(0).'i*(t-1).....Y(t-p). F*(t-1).....‘F*(t-p). V(t)1 (7) Alt) = AEY*(t-1)....;7r(t-p), F*(t-l).....F*(t-p). Vlt)1 (8) where 7*(t) = vector of optimal dual values (shadow prices of constraints). V(t) vector of exogenous variables. p maximum length of a lag. To solve the model, it is necessary to obtain initial con- ditions for period t = O for all endogenous variables and time- varying coefficients and the time profile of the exogenous variables. The linear programming problem is solved once in each period. Clearly, this model is appropriate for incorporation in a systems simulation model because it has all the features of a recursive system which is convenient for use in a computer programming frame- work. Structure of a Periodic Linear Programming Model: The linear programing model for each time period t is block diagonal with one block for each farm size and a set of coupling constraints which hold for all farm sizes simultaneously. Since the structure of the model is the same for all farm sizes, complicated notation can be avoided by describing only one model for one farm size group. The structure of a linear programming model includes three sets of relationships: a) The objective function; b) The activities, 85 'and c) The constraints. This subsection describes each of these elements composing the periodic linear programming model. Objective Function: The objective function represents a decision criteria which is the basis for choices among alternatives available and subject to a whole range of constraints faced by the economic unit. The optimizing principle underlying the objectives and goals of the farming operation should be the basic indication for setting the objective function, since it represents what farmers are attempting to optimize. However, this is an area of much discussion and no definite principle is agreed upon, as knowledge about behavior and expectations of farm operators is very limited. It is true, how- ever, that in order to be able to solve the programming problem an explicit formulation of an optimizing criteria is needed. The most commonly used specification of the objective func- tion in programming models is the maximization of short run profits or the maximization of short-run returns to fixed resources. In this study it is assumed that farmers maximize expected short-run profits defined as expected gross revenue minus expected variable costs, that is, it is assumed that farmers maximize expected short- run returns to fixed resources. Included as fixed factors are land, family labor, and power capacities. The model also includes the following: (1) to meet requirements for home or subsistence con- sumption; (2) to avoid unbearable risk by taking decisions based on a safety-first principle; and (3) to maximize expected profits. In a recursive linear programming framework the subsistence consumption 86 requirement criteria can be handled either by specifying consumption activities explicitly in the model or by defining feedback function which forces the retention of some proportion of production for home or subsistence consumption. The introduction of flexibility and adoption constraints takes care of safety and cautiousness be- havior. Typically, the objective function is defined in mathematical form as the maximization of expected yearly gross revenue minus variable costs (Equation 9). Gross revenue per hectare is expected yield times expected prices for all income producing activities. Variable costs per hectare include the cost of all inputs that are not drawn from the original resource availability and also those costs that are not charged in the model through a system of pur- chasing activities and appropriate transfer rows. The objective function can be expressed as follows: m n Max n(t) = Max[j:1 wil Pij(t) - Yjw(t) m n d - 3:1 WE] 1.__>i1a1.‘].w(t) . Pxi(t) . Yjw(t)] (9) where n = profit or net return. Yjw = output j produced by method w. Pij = price of output j produced by method w. = price of ith input. 87 X.. (t) a.. (t) = 1 w , the unit requirement of 1th input to produce 1jw Yjw t output j by method w, at a given time t. xijw = total amount of 1th input used to produce output j by method w. The activities considered in the model will be described in the next subsection. In order to reduce the size of the model, in- come producing activities are used to produce and to sell the output. Therefore, the objective function values for these activities are defined as gross returns minus variable costs per hectare. Family labor is regarded as a fixed resource for the farm, and its cost is not priced through the objective function. Activities: A linear programming model can be constructed based on data from individual farm units or based on regional aggregate data. If it is constructed in an individual farm basis, aggregation can be achieved by weighting farm results by the number of farms in each category. Disregarding data requirements and time and cost of analysis, the ideal situation is to model individual farms mainly to reduce aggregation bias which can be significant in terms of model predictive power. This study uses a combination of these two approaches. Farm data is used with disaggregation in farm size groups and regional constraints are introduced for those resources which are competed for by all groups. Since the basic unit of the model is the farm, the activities programed must be based on the nature of the farming operation and 88 its interdependencies with the physical and economic environment. The basis is the situation in the Southern Region of Brazil. As it is true in any other developing country, a farm in Brazil is typically a multiproduct firm with a decision-making process highly dependent on the firm-household interactions. Production, consumption and in- vestment for the farm firm and for the family are interacting activities carried out simultaneously. Thus, the model should in- clude these activities and the relationships among them. Besides the characteristics of farming operations in a region, the activities and constraint structure of a linear programming model should be based on two additional considerations. The availability of data to implement the model, and the objectives for which the model is built. In many cases basic experimental or field survey data for estimating model parameters and relationships are not available for some of the elements to be included in the model. This, of course, precludes their modeling. Moreover, the model should be constructed with the necessary features which allows one to reach the objectives of the study. Based on the above considerations, five sets of activities are included in the model. They are: a) Production of various annual crops; b) Production of natural and cultivated pasture; c) Production of beef; d) Investment in draft animal and farm ma- chinery, and e) Seasonal labor hiring. Each of these groups of activities are discussed in detail below. 1. Production of field crops: The four major crops of the region studied are included in the model. They are: rice, corn, 89 wheat and soybean. Each crop is considered as an activity. Since double cropping of wheat and soybeans is a common practice in the region two distinct soybean activities are considered, namely, soy- beans following wheat and soybean independent of wheat. In the basic model each activity is disaggregated by two types of technology. Traditional, using animal power, and modern, using mechanical power. The objective function coefficients for these activities are posi- tive and are defined as gross returns minus variable costs. In- cluded as operating costs are fertilizer, seed, transportation, vari- able machinery costs, and other inputs such as insecticides. Let this set of activities be denoted by P , g = 1,...,10. 9 2. Production of natural and cultivated pasture: Pasture, an intermediate product for beef production, is considered in the model as natural and cultivated. Most beef production in the area studied uses natural pasture and only a small part uses cultivated pasture. Natural pastures which are of poor quality have low pro- duction capacity. A higher productive system based on improved pasture is available, and could be used as a means of improving the competitive position of beef production relative to other activities. Like the crop activities, cultivated pasture is also con- sidered with two levels of technology, traditional and modern. The objective function values for these activities are negative and in- clude the value of the variable inputs used. For natural pasture only repairs and maintenance costs are included. In addition to these costs, fertilizer, seed, and variable machinery costs are considered for cultivated pasture. Let this set of activities be denoted by Fh’ h = 1,2,3. 90 3. Production of beef: Agricultural transformation in the area has been characterized by expansion of livestock activities to new frontiers and substitution of crop or intensive livestock acti- vities for extensive livestock operations in those established areas. Beef production activities are considered in the model in order to capture the changes in enterprise pattern and best represent the opportunities open to farmers in operating and organizing their farms. The model includes beef production by two methods or tech- nologies. One uses natural pasture and the other uses cultivated pasture. The objective function coefficients are gross returns minus variable costs. Included as variable costs are bone meal, salt, and veterinary costs. This set of activities is designated by B , m = 1,2. m 4. Investment activities: Investment in draft animal, tractor and combine is considered in the model as three distinct activities. They represent the possibilities of replacement and addi- tion to farm animal power and machinery capacities. The investment cost of these activities are composed of depreciation and interest costs on capital. This set of activities is denoted by In, n = 1,2,3. 5. Seasonal labor hiring activities: The two major sources of labor for the farm are family labor and hired labor. Family labor is considered as a fixed resource for the farm and the possibility of using more than what is available on the farm is introduced by hiring activities. Due to seasonality in the use of labor, three periods of the year are considered. These are: Period 1, from July through October; Period 2, from November through February; 91 Period 3, from March through June. One activity is defined for each period. The cost of hiring is the market wage rate. Let Hp, p = 1,2,3 designate this set of activities. In summary, if the set of all farm activities is denoted by R, then: R = {P1,...,P]0, F], F B],B I ..,I3, H .,H ..., 3, 2, 1,. 1,.. 3}. An activity j in set Pg, for example, can be denoted by j 6 P9. The level of an activity j can be designated by X. = {lej 6 P9}, and j e R can be written to refer to an activity J without specifying the set or the sets to which it belongs. Constraints: Decisions at the farm level are made subject to a set of financial, physical, and behavioral constraints. Within a region, different farm size groups compete for regional resources. Given the disaggregation scheme used in the resource allocation component being described here, it is necessary that the constraint structure includes: (a) constraints on farm resources for each of the two farm size groups, and (b) regionalconstraints which hold for all farm size groups simultaneously. These two sets of constraints hold for one periodic static model of firm-household decisions. The dynamic properties of the model are introduced by a set of decision feedback functions which generate restraints in a recursive manner to account for the impacts of past actions on the elements of current decisions. 92 The inclusion of overlapping regional constraints carries the crucial assumption of resource mobility between different farm size groups. Market imperfections may exist and can preclude the mobility of certain resources. This has to be observed when de- ciding on the types of overlapping constraints to be included in the model. The constraints of the model include: a) Land constraints by season; b) Labor constraints by season; c) Machinery and animal power constraints; d) Balance equations; e) Behavioral constraints, and f) Regional constraints. The first five sets of constraints are the same for each of the farm size groups. The last set include the overlapping constraints. Before a description of each of the constraint sets is pre- sented, some notation is developed to facilitate further reference. Denote the complete constraint set by B. This set is then parti- tioned in subsets representing major constraint groups, such that B = {89, Bh’ Bm, Bn’ Bp’ Br} where B , g = 1,2,3: a group of constraints on available land by 9 season. Bh’ h = 1,2,3: a group of constraints on available labor by season. 8 , m = 1,2,3: a group of constraints on available machinery and draft animal power capacities. B , n = 1,...,4: a group of balance equations. B . p = 1,...,14: a group of behavioral constraints con- sisting of upper and lower flexibility bounds. 93 The right hand side elements of the inequalities are denoted by bi' A particular constraint in set 89, for example, can be h referred by bi’ i e B . The level of the jt activity, at time t, 9 is designated by Xj(t), and the input-output coefficients are de- noted by aij' Now a description of the constraint structure of the model is presented with reference to each constraint group separately. 1. Land Constraints: Available land can be allocated to crop and pasture activities. Equation 10 assures that the amount of land allocated to different production activities do not exceed the total amount available at time t. 2 a~ NO + 2 a.. mu _<_b.(t); i e B (10) jeP 1J J jeF 13 j 1 g g h where P9 = set of crop production activities Fh = set of pasture production activities W 11 set of land constraints. The model includes three land constraints: a) Summer land; b) Winter land, and c) Irrigated land. Rice is the only crop that uses irrigated land. 2. Labor Constraints: Due to the nature of farming opera- tions, labor use is characterized by peak seasons. This makes it necessary to define labor constraints by seasons (Equation 11), which involves the use of family labor and any hired labor for each period. 94 z a..X.(t) + z a..X.(t) + z a. . 13 J . 1:] J . '| Jepg JEFh 368m P :_bi(t); i e Bh (11) where = set of crop production activities h = set of pasture production activities p F B = set of beef production activities H m p = set of labor hiring activities 8b = set of labor constraints Three constraints on human labor are considered, one for each of the following periods: Period 1, July-October; Period 2, November- February, and Period 3, March-June. Equation 11 assures that the amount of labor used by the crop, pasturing, and beef activities do not exceed the amount available on the farm plus the amount that is hired for each period at time t. 3. Machinery and Animal Power Constraints: Equation 12 de- fines machinery and animal power capacities. The total availability on the farm can be augmented by investment activities. 2 aijxj(t) + .2 ai.Xj(t) - z ai.Xj(t) 5_bi(t); i 6 8m (12) jePg Jth 3 351m 3 where P9 = set of crop production activities Fh = set of pasture production activities Im = set of investment activities 8 = set of machinery and animal power constraints. 95 Three power sources are included in the model. They are: tractor capacity, combine capacity, and draft animal capacity. Equa- tion 12 assures that, for a given time t, the amount used is less than or equal to the amount available plus the increases in capacity for any of the power sources. 4. Balance Equations: These equations are used to transfer resources from one activity to another and to account for intermediate- final output relationships. Intermediate outputs are produced by some activities and used by others. Balance equations allow the model to determine endogenously the proportions of the different inter- mediate outputs used by different activities, assuring that the amounts required to not exceed the amounts available. The same holds for a resource transfer between activities. Two groups of balance equations are included in the model. The first group consists of two equations which account for the rela- tionships between pasturing activities and beef production activities. All pasture produced has to be used for beef production. Equation 13 and Equation 14 define the relationship for natural pasture and cul- tivated pasture, respectively. ‘a1o,11x11(t) 1 a1o,14x14(t) = 0 ('3) where X 1] natural pasture activity X14 beef production activity using natural pasture 'all,12x12(t) ‘ a11,13x13(t) * a11,15x15(t) = 0 (‘4) 96 where X12 - cultivated pasture activity using traditional tech- nology X13 - cultivated pasture activity using modern technology X15 = beef production activity using cultivated pasture. Another group of balance equations, consiSting of two equa- tions, accounts for the double cropping relationships between wheat and soybeans. Equation 15 and Equation 16 assure that the area planted with soybeans following wheat does not exceed the area planted with wheat, for two types of technology, respectively: -a]2’5X5(t) + a12,7X7(t) §_O (15) where X5 = wheat production activity using traditional tech- nology X7 = soybean following wheat using traditional technology 'a13,6x6(t) + 313,8x8(t) 5_O (16) where X N 6 wheat production activity using modern technology >< ll 8 soybean following wheat using modern technology. 5. Behavioral Constraints: The behavioral conStraints in- cluded in the model consist of upper and lower flexibility con- straints. Limiting year to year changes in production patterns, they are assumed to account implicitly for farmers' response to risk and uncertainty related to expansion of production activities. These constraints are defined as: 97 (1 - £4) - X3(t - 1) :. Xj(t) :_(l + 3;) - X§(t - I); i e Bp (17) 315R where Xj(t) = jth activity level for time t X3(t-l) = optimal level for activity j at time t-l B} = estimated maximum expansion rate , 81 = estimated maximum contraction rate R = set of activities with upper and lower bounds Bp = set of behavioral constraints 6. Regional Constraints: The constraints described above apply to each of the farm size groups. Besides those groups, the model includes four overlapping constraints. One constraint is re- lated to the regional supply of tractors; the other three are related to the regional supply of wage labor during the three periods considered. The general form of these constraints is given by Equation 18. 2 2 2 z a.. x. (t) + 2 z a.. X. (t) 5_b.(t); i e B (18) s=1 jeI '35 35 s=1 jeH '35 35 ' r m P where Im = set of investment activities Hp = set of labor hiring activities Br = set of regional constraints 5 = indexes farm size groups Summary of the Model The structure of the yearly linear programming model is summarized in Table V.l. A complete description of the components of the model is presented in Appendix A. 98 Pmn Loam.— S 3 no u 2 2 one: u nu. h o < < O O O LOHUMLP m. . m. an co 3&8 n w sun 5 3 O. .3 . 2 2 9.383 um “N. o . o . o p. . I? x e_. o o o < < mecca mu nu.u a :22 a 2 2 533m a.. o o ..< .5 .3 been: uMm H m J. n o: teem s o a 8.533 a e _eere< .e.e ..e e e e . ten 8 u o < o < < oe:oeeu m.1 no .839; ..M on m eo:toe m. . n a: a: a. H HJ o .:< ..< ..< N eo:eoa m ea _ eo:eoe no eooem:ee: m. H 2 .2 W . o o o < < Luv—:3 E .8555 PNN.....mPN m~N.....c_.N m.._.N.¢pF m..N.....:N CPL.....—N Amzev m:.....:: m:.....:~ ~m.:m met.....o o:o.....:a muwm newcwx pcosumo>cH :owuoauoco covuuavoco cowuuauoco mucwogumcou 23: 23m .253 econ 95.53 no.5 .352 £3332 22858 53332 3.533. .23 5 3523.28 can 3.5332 mo .3253 ”..> opoec 99 Dynamic Feedback Mechanisms and Exogenous Variables: Equations 6, 7 and 8 above indicate the general nature of the dynamic feedback mechanisms that relate the allocation decision prob- lem for period t to previous decisions and to exogenous variables. The main problem now is to define explicitly dynamic feedback func- tions which relate the values of the objective function coefficients, constraints elements, and input-output coefficients to preceding solutions of the resource allocation problem, to variables being computed in other components of the simulation model and to exo- genously projected variables. These dynamic feedback operators and linkages account for the dynamic properties of the adjustment and growth process simulated by the model. The functions defined below will be general formulations of the relationships involved. A specific formulation is presented in Appendix A. Objective Function Coefficients: The definition of the objective function coefficient depends on the type of activity. These coefficients are generally function of yield, product prices, input prices, and input quantities which are either exogenous to the model or projected by other components. The specification of feedback operations for these coefficients should be based on some sort of expectation model which represent farmers' anticipation of future events. This study assumes a simple expectation model for the co- efficients of the objective function. The expected coefficient for year t is equal to the coefficient of the previous year. The coefficients for crop production activities are given by the 100 difference between gross returns and variable costs lagged by one year. For pasture activities, they are just the negative of vari- able costs lagged by one year. For beef production activities, they are the one year lag of gross returns minus variable costs. The coefficients for machinery investment activities are investment costs which include depreciation and interest on capital. The model assumes a straight line depreciation defined as the dif- ference between acquisition price and salvage value divided by the number of years of life of a machine. Interest applied to the average value of the machine is defined as acquisition price plus salvage value divided by 2. Thus, the objective function coeffi- cients, Zj, are given by Paj(t) - st(t) + Paj(t): st(t) Zj(t + 1) = N. 2 * Int(t) (19) J where j 6 Im = set of investment activities Paj = acquisition price of jth investment st = salvage value of jth investment Int = interest rate Nj = number of years of life of jth investment For labor hiring activities, the objective function co- efficients are simply wage rate lagged by one year. This concludes the specification of how the objective function coefficients are gen- erated. Further details are given in Appendix A. Crop yields are projected by the yield component. Price considerations will be dis- cussed in a separate section below. 101 Constraint Elements: The elements of the constraint vector or the right-hand side of the inequalities are the farm resources. They are generated for each period through a series of recursive feedback functions. Flexibility constraints are also included as right-hand side elements. Farm resources include land for crop and livestock production, labor and power capacities. The projection of the availabilities of these resources is made exogenously. Only the transference of capacities from one period to the other is endogenously made. In a general form, this transference of capacities can be defined by a first-order linear difference equation with endogenous and exogenous infbrmation as fellows: b(t)=A(t-l)HX*(t-l)+Gb(t-l)+V(t) (20) where 6(t) = m-dimensional vector of capacities and numerical values of behavioral constraints A(t-1) = m x n matrix of input-output coefficients for the preceding period X*(t-l) = n-dimensional vector of optimal activity levels for the preceding period H = n x n diagonal transfomration matrix that transfer investment made in period t-l G = m x m diagonal transformation matrix that transfer all or parts of the capacities of period t-l 7(t) vector of exogenous variables. Equation 20 represents the general process of generating the right-hand side elements. The specific procedure used for each of the elements is explained below. 102 Land capacity: Besides the problem of projecting aggregate land resources it is also necessary to project land distribution among farm size groups over time. Clearly, land structure is an important factor determining production response and adjustments in the agricultural sector. As the land structure changes over time, a transference of farms is made from one categoryto another which implies a transference of resources. When land is transferred among groups it carries a certain amount of other resources such as labor and capital. Data on agricultural land, number of farms and land distribu- tion are available from the Census which is taken every ten years. These data shows that the supply of land has increased substantially mainly‘due to incorporation of new land. Number of farms and area in each group has increased for the past four decades in absolute numbers. However, while the absolute area in each size has increased through time, in relative terms, the area in the "small" group has increased at an increasing rate, and the area in the "large" group has increased at a decreasing rate.3 In this study, this trend of land supply and distribution is assumed to continue over the projection period for which the model is applied. It is alSo assumed that land available for agri- cultural use will continue to increase toward an upper bound capacity of land that can be used for cultivation and pasturing 3The definition of farm size groups used in this study is as follows: "small" group includes farms with 100 hectares or less; "large" group includes farms with area over 100 hectares. 103 activites. Furthermore, the share of each group in the total will continue according to past trends. The procedure used to implement these assumptions involves: a) projection of total land available; b) projection of the distribu- tion of land between the two farm size groups, and c) projection of the number of farms. Total land available is projected using an exponential ad- justment model in which the amount of land that can be allocated to farm production each year increases toward an upper bound capacity determined on the basis of the total area available in the region (Equation 21). It is assumed that this model well represents the process of land incorporation into production. It also assures that projected land available does not exceed the total capacity in the region. TLAND(t) = TLAND(t-1) + DT/DEL - (TLCP - TLAND(t-1)) (21) where TLAND = total land available at time t (ha) TLCP = upper bound on land capacity (ha) 01 = time increment in simulation run DEL = average lag (years). The total land available (TLAND) is split between the two farm size groups according to a projected percentage of participation of each group. This proportion is projected using an exponential function adjusted to the historical percentages of land in each group (Equation 22). 104 BCC1(t) = A1 ° EXP (A2 ° T) (22) where BCCl = proportion of total land in one group Al and A2 = parameters of the function EXP exponential function T time variable After estimating the proportion of land in one group, the total amount of land can be split between the two groups as follows: ASMALL(t) = BCC1(t) - TLAND(t) (23) and ALARGE(t) = (1 - BCC1(t)) ° TLAND(t) (24) where ASMALL = area available for the "small" group (ha) ALARGE area available for the "large“ group (ha) The number of farms in each size group was projected using, as a first approach, an exponential growth function. Some attempt was made to use a probabilistic model based on the Markov Chain Process,4 but the nature of the data did not allow reasonable estimates through this proCedure. 4For the use of Markov Chains to project number of farms by classes see, for example, Ronald D. Krenz, "Projection of Farm Numbers for North Dakota with Markov Chains," Agricultural Economics Research 16(3): 77-83; Gerald W. Dean et al., “Supply Functions for Cotton in Imperial Valley, California," Agricultural Economics Re- search 15(1): 1-14, and Rex F. Daly et al., “Farm Numbers and Sizes in the Future," in A.G. Ball and E.O. Heady eds., Size, Structure, and Future of Farms (Ames: Iowa State University Press, 1972). 105 Thus, the number of farms in each group is given by SNFS(t) = 81 - EXP (Cl - T) (25) and LNFL(t) = 82 - EXP (C2 - T) (26) The total number of farms is then TNF(t) = SNFS(t) + SNFL(t) (27) where SNFS = number of farms in the small group SNFL = number of farms in the large group TNF = total number of farms T = time variable The difficulty in maintaining consistency between the number of farms and the area in each category is a major short- coming in using an exponential growth function to project farm numbers. Using this procedure, projection is simply an extrapola- tion of past trends into the future. However, in the present case this may be a reasonable assumption to make, given the time horizon considered in the study and the indications that past trends of increasing farm numbers and decreasing average farm size will continue for at least a decade.. The total land available in each size group can be allocated either to summer or winter crops. This allocation is taken care of in the set up of the linear programming model. Another land 106 restriction included in the model is irrigated land which is used only for rice, and is considered as a subset of total land. Irrigated land capacity is projected assuming a constant rate of increase which accounts for land developments (Equation 28). AIRG(t) = (1 + BC1) - AIRG(t - 1) (28) where AIRG = irrigated land available for rice production (ha) 801 = rate of change (dimensionless) Labor capacity: The seasonal capacity for a given time t depends on the capacity for time t-l, on the growth rate of farm population, and on the number of hours a person works per period. Labor force is projected assuming a decreasing rate for increases in farm population (Equation 29). ACFPOP(t) = (1 + BT1(t)) - ACFPOP(t-1) (29) where ACFPOP projected active agricultural family labor force (man-equivalent) BTl annual growth rate of farm population (dimension- less) The annual growth rate of farm population (8T1) is assumed to decrease from 0.8 percent to 0.4 percent during the period 1970-1985. The total number of family labor hours available during th the i season, at time t, is given by active labor force times the number of hours a person works per period (Equation 30). where 107 TFLHi(t) = BCC2(t) - ACFP0P1(t); i e B (30) h TFLH total family labor available (hours) BCCZ working time equivalent (hours/man-equivalent/ period) Bh set of labor constraints The coefficient BCC2 in Equation 30 is time variant; its increase is assumed to account for learning effects which increase the efficiency of labor use. The model assumes that the working time equivalent increases continually until it reaches a maximum at the end of the simulation time horizon (Equation 31). where BCC2(t) = BCC2(t-1) + DT/DEL - (BBAR — BCC2(t-1)) (31) BCCZ = workin time equivalent (hours/man-equivalent/ period BBAR = upper bound on working time equivalent (hours/ man-equivalent/period). Machinery and Animal Power Capacity: The number of hours available by draft animal and machinery at time t, is the capacity available at time t-l, less depreciation on a straight line basis, plus investments made at time t-l (Equation 32). POCAPi(t) = (1 where BCDi) - POCAPi(t-1) + BCHi - INVP¥(t-1); i e Bm (32) h capacity available of it power source (hours) POCAPi investment in ith power source (unit) INVPi 108 BCD1 = depreciation rate (dimensionless) BCHi = working capacity (hours/unit/period) Bm = set of power constraints Flexibilityégonstraints: The general nature of flexibility constraints is shown in Equation l7 above. Basically, these con- straints establish feedback linkages through which production patterns become a function of the previous year's optimal level of the decision variables. This model includes flexibility constraints consisting of upper and lower bounds on crop and pasture areas. The hectarage bounds for year t are defined as follows: Upper bounds: xjm 1 (1 + 8,.) - xgu -1) (33) Lower bounds: xjm .>_ (1 - 2,) . xg -2 ll 1j tractor requirement per hectare with new process W (hours/ha) > I 1 - tractor requirement per hectare with modern process M J (hours/ha) WTA proportion of modern process in the new process (dimensionless) A. ll tractor capactity constraint and, for draft animal as W _ . T Afim - (l - will) Aijm . (6) 139 where > -2 ll 1. draft animal requirement with new process W J (hours/ha) > ll 1 draft animal requirement with traditional process 3 T (hours/ha) draft animal capacity constraint ‘0 ll Basically, Equations 4, 5 and 6 define a combination of processes. In order to increase the level of mechanization, it is necessary only to increase the proportions WTL and WTA. In fact, these parameters are time variant, with changes determined by an innovation pattern similar to the one used for yield. Modernization takes place over time according to an innovation pattern which gives the proportion of land using the higher technology level for a given time t. ' A given increase in WTL and WTA applies to a certain pro- portion of land. These proportions are determined as follows: NTL(t) = WTL(t - 1) + PRMOL(t) ' WTLCH (7) WTA(t) = WTA(t - 1) + PRMOL(t) - WTACH ' (8) where PRMOL = prOportion of land using new technology (dimensionless) WTLCH = rate of increase in WTL (dimensionless) WTACH = rate of increase in WTA (dimensionless). Tractor mechanization substitutes for labor and draft animal. Three alternatives related to the level of mechanization are analyzed: a) a 25 percent proportion of modernization (WTL = 0.25, WTA = 0.25); b) a 50 percent proportion of modernization 140 (WTL = 0.50, WTA = 0.50), and c) a 75 percent proportion of modern- ization (WTL = 0.75, WTA = 0.75). The model run alternatives made are summarized in Table VI.l. They include three alternatives in respect to yield, given a 50 per- cent proportion of combination of modern and traditional processes, and three alternatives in respect to mechanization, given base yield levels. Table VI.l: Summary of Alternative Techonology Runs Run No. Alternative Description 1 IA. YLDCH = 0 (i) Base yield levels WTL = WTA = 0.50 (ii) 50 percent mechanized process 2 _IB. YLDCH = 0.30 (i) 30 percent increase in yields WTL = WTA = 0.50 (ii) 50 percent mechanized process 3 IC. YLDCH = 0.50 (i) 50 percent increase in yields WTL = WTA = 0.50 (ii) 50 percent mechanized process 4 IIA. YLDCH = O (i) Base yield levels WTL = WTA = 0.25 (ii) 25 percent mechanized process 5 118. YLDCH = 0 (i) Base yield levels . WTL = WTA = 0.50 (ii) 50 percent mechanized process 6 110. YLDCH = 0 (i) Base yield levels WTL = WTA = 0.75 (ii) 75 percent mechanized process 141 Simulated Model Results This section presents the simulated impacts of alternative varietal and mechanical technologies on: a) Land use and cropping patterns; b) Production; c) Employment and input utilization, and d) Income and factor productivities. The results are for the year of l980 with anintertemporal comparison with l970. Thus, the focus is on the results for the eleventh year of each run with comparison with the base year. All the performance variables are given by farm size group and for the regional total. Each farm size group is to be inter- preted as an aggregate of farms in that group. Net farm income in small farms, for example, means the aggregate income for all farms in the group. The results are not in a per farm basis; they are for the aggregate of farms in each group. To find average figures per farm the result has to be divided by the number of farms in the re- spective group. The results for varietal technology alternatives are presented first. They are followed by the results concerning mecha- nization. The Impacts of Varietal Technology The results presented here refer to alternatives IA, 18, and IC described in Table VI.l. Alternative IA refers to base yield lev- els, alternative 18 assumes a“30 percent increase in yields, and al- ternative IC assumes a 50 percent increase in yields. All three al- ternatives assume a 50 percent level of process combination, which means that traditional and modern processes were combined in a 50 percent basis. 142 Land Use and Cropping Patterns: The optimal solution for land allocation by size and crops is given by the linear programming model of the resource allocation com~ ponent. The simulated impacts of alternative yield assumptions on crop and pasture areas, as given by the optimal solutions, are shown in Table V1.2. Under alternative IA, i.e., base yields, the area cultivated with rice increases by about 72.5 percent over that of the base year for both farm size groups and for the region. The introduction of - higher yield varieties would have no impact on area cultivated with rice, since the increases over the base year for alternatives IB and IC are the same as for alternative IA. Corn area decreases by 14.6 percent in small farms, 40.0 per- cent in large farms, and 21.2 percent in the total, under alternative IA. The increase in yields would have impact on the area cultivated with corn in small farms and in the region, but not in large farms. Under alternative 18 the corn area in small farms shows a lower de- crease in relation to alternative IA, while under alternative IC it shows an increase of 8.6 percent over that of the base year. In ab- solute terms corn area in small farms would increase from 1,137 to 1,194 thousand hectares with a 30 percent increase in yield, and from 1,137 to 1,446 thousand hectares with a 50 percent increase in yield. This means yield impacts of 5.0 percent and 27.2 percent, respectively. For large farms no change is observed. Model results indicate that yield increases would have signi- ficant impacts on wheat area in large farms and in the total. Under 143 Table V1.2: Optimal Land Use and Cropping Patterns for 1980 Under Different Yield Alternatives and a 50 Percent Mechani- zation Level. *Base AlternatTVe Yie1d7Assumptions Year ATternative"TA—"TATternative IB Alternative IC (1970) AFea 771 Area I_T§4 ’Area 135 Rice -S 135 233 72.6 233 72.6 233 72.6 L 315 543 72.4 543 72.4 543 72.4 T 450 776 72.4 776 72.4 776 72.4 Corn -5 1332 1137 -14.6 1194 -10.4 1446 8.6 L 467 280 .-40.0 280 -40.0 280 -40.0 T 1799 1417 ’-21.2 1474 -18.1 1726 - 4.1 Wheat -S 279 1274 356.6 1274 356.6 1276 357.3 L 722 388 -46.3 964 33.5 963 33.4 T 1001 1662 66.0 2238 123.6 2239 123.7 Soybeans-S 304_ 2025 566.1 2025 566.1 2024 565.8 L 274 274 -26.7 538 :43.8 567 51.6 T 678 2299 239.1 2563 278.0 2591 282.1 Cult. -5 159 ‘ 1219 '666.7 1162 630.8 910 472.3 Pasture L . 387 _ 232 -40.0 232 -40.0 232 -40.0 T ' 546 1451 165.7 1394 155.3 1142 , 109.1 Natural -S{ 3806 1890 450.3 1890 ‘ -50.2 1890 -50.3 I Pasture L‘ 9927 9551 - 3.8 8712 -12.2 8683 1 -12.5 T 13733 11441 -16.7 10602 -22.8 10573 -23.0 Note: 1) S = Small Farms; L = Large Farms; T = Regional Total 2) Area in 1,000 hectares 3) %A means percent change from respective base year (1970) values. 144 all alternatives, the area in small farms shows an increase of about 357 percent from the base year level. Thus no change is observed with increase in yield. Under alternative IA, the area of wheat in large farms decreases by 46.3 percent in relation to the base year. However, going from alternative IA to 18 or IC would cause an increase of about 33.5 percent. The aggregate area cultivated with wheat increases by 66.0, 123.6, and 123.7 percent under alternative IA, IB, and IC, re- spectively. The changes for soybeans are similar to those for whaet. There is a substantial increase of about 566 percent for small farms under all three alternatives during the period. For large farms, alternative IA shows a decrease of 26.7 percent, while alternative 18 and IC show an increase of 43.8 and 51.6 percent, respectively. For the region, soybean area would increase from 2,299 thousand hectares under alter- native IA, to 2,563 thousand hectares under alternative IB, and to 2,591 thousand hectares under alternative IC. The increase in crop yields would cause the shift of land from pasture to crops as indicated by the percentage growth rates during the period. Cultivated pasture decreases in small farms and in the region under alternatives IB and IC in relation to alternative IA. Under the same conditions natural pasture decreases for large farms and for the region. For all alternatives absolute decrease in the area with natural pasture occurs indicating the tendency for crops and intensive livestock production to substitute for natural pasture. In surrmary, model results indicate that the introduction of technological change in the form of high-yielding crop varieties would 145 have some impacts on cropping patterns for the region and in each farm size group. Wheat and soybean would experience large increases in large farms, while no change would be observed in small farms. Corn would increase in small farms. Increases in crop areas appears to come mainly from natural pasture areas. Production: Changes in the quantity produced are caused by changes in yield rates and land allocation. The optimal production levels sim- ulated by the model-for 1970 and 1980 under different yield alter- natives are shown in Table V1.3. The data show the combined effect of yield increase and changes in land allocation. Clearly, in the case of rice differences in production are caused by yield increases only since there was no change on land allocation (Table VI.2). Rice production increases under all alternatives in about the same propor- tions as the respective increases in yield. Corn production decreases for both farm size groups and for the region under alternatives IA and 18. Under alternative IC, it increases for small farms. Changes in corn production reflect changes in area observed for this crop. For the region, yield increase under alternative IC more than offsets the decrease in area cultivated, giv- ing an increase in production of about 11 percent during the period. Wheat and soybean production follow the same pattern observed for cultivated area. Production decreases for large farms under alter- native IA, but increases in all other situations. Increases in pro- duction under alternative 18 and IC are due in part to yield increases 146 but are due mainly to changes in cropping patterns which bring more land into wheat and soybean production. Beef production in small farms changes from 237 thousand tons in 1970 to 310 thousand tons in 1980, under alternative IA, represent- ing an increase of 30.7 percent during the period. When crop yields are higher, the growth rate dr0ps to 26.6 percent and 8.7 percent for alternatives IB and IC, respectively. For large farms, beef produc- tion decreases under all situations. For the region, beef production under alternative IA varies from 848 thousand tons in 1970 to 877 thousand tons in 1980. Clearly, under the conditions of the model, technological change in the form of high yield varieties would raise the profitability of crops relative to beef thus causing substitution of crops for beef in production. Employment and Input Utilization: The generation of employment is a major concern of development policy formulation in developing countries. When the industrial sec-V tor has a limited capability of expansion to absorb unemployed labor, the creation of employment is dependent on the possibilities of expan- sion in the agricultural sector. Labor use and the rate of employment growth is directly related to the form of technological change that takes place. A priori technological change in the form of biological innovations is supposed to have a positive impact on employment due to increases in production which require more labor. The trends in employment and input utilization are basically guided by the changes in the cropping patterns described above. The yearly demand for inputs shows an increasing trend under all 147 Table V1.3: Optimal Production Levels for 1970 and 1980 Under Different Yield Alternatives and a 50 Percent Mechanization Level AlternatiVe’Yield’Assumptions AlternatTVe 1A AlternatiVe IB [ Alternative IC 1970 1980' 71970 7T980 ‘1970 1980 Rice -S 469 809 494 1018 510 1177 L 1149 1981 1210 2494 1250 2884 T 1618 2790 1704 3512 1760 4061 Corn -5 1907 1694 1941 1928 1963 2472 L 669 416 680 452 688 478 T 2576 2110 2621 2380 2651 2950 Wheat -S 298 1377 313 1704 322 1955 L 810 440 850 1352 877 1550 T 1108 1817 1163 3056 1199 3505 Soybeans-S 373 2651 394 3332 407 3847 L 462 343 487 892 504 1073 T 835 2994 881 4224 911 4920 Beef -5 237 310 237 300 237 258 L 611 567 611 526 611 518 T 848 877 848 826 848 776 Note: 1) S = Small Farms; L = Large Farms; T = Regional Total 2) Production in 1,000 tons. 148 alternatives (Table V1.4) that directly reflect area and production increases. 1 b The total labor employment in the region under alternative IA increases by 25.1 percent or at the rate of about 2.5 percent per year during the period. With the introduction of tehcnological change, labor employment would raise by 38.7 percent and 40.3 percent under alternatives IB and IC, respectively. The net impact of yield increase on employment can be measured by comparing the three alter- natives. Going from alternative IA to IB, total labor employment increases from 2,039 million hours to 2;260 million hours, correspond- ing to 10.8 percent increase. Similarly, there is a 12.1 percent net increase for alternative IC relative to alternative IA. Thus, the marginalimpact of alternative IC over 18 is fairly small compared to the marginal impact of alternative 18 over IA. In respect to farm size groups, employment on small farms increases by about 90.0 per- cent during the period under all three alternatives. Thus, no major yield impact on employment would be observed. For large farms, em- ployment decreases during the period for all alternatives, showing the tendency of larger farms to adjust to technological choices based on labor-saving modern farm power. However, when the three alternatives are compared, there is evidence that yield increases would have a' greater impact on employment in large farms. The impact of alterna- tive 18 over IA is of the order of 43.5 perCent. For alternative IC over IA it is 44.8 percent. Thus, some scope for expanding employment exists, especially on large farms, through technological change based on high-yielding crop varieties. 149 Table V1.4: Optimal Input Use for 1980 Under Different Yield - Alternatives and a 50 percent Mechanization Level Base Alternative—Yield Assumptions -‘_ Input Year Alternative IA Alternative 18 Alternative IC (1970), Amount %A Amount 22 Amount %6 Labor -S 812156 1543252 .90.0 1547658 90.6 1587083 93.0 L 817381 496139 -39.3 712184 -12.9 718355 -12.1 T r629537 2039391 25.1' 2259842 38.7 2285438 40.3 Tractor -S 3872 15255 294.0 15268 294.3 15328 295.9 L 3644 4368 19.9 6432 76.3 ' 6472 77.6 T 7426 19623 164.3 21691 192.1 21800 193.6 Draft -5 118143 202492 71.4 204300 72.9 212272 79.7 Animal' L 106209 62567 -41.1 94523 -11.0 95432 -10.1 ‘T 224352 265059 18.1 298823 33.2 307704 37.1 Fertilizer S 126315 274701 117. 5 278399 120.4 294736 133. 3 L 93769 74415 -20.6 116038 27.7 116038 27.7 1 220084 349116 58.6 394437 79.2 410774 86.6 Note: 1) 5': Small farms; L = Large farms; 1 = Regional total 2) %A means percent change from respective base year (1970) values. 3) Labor in 1,000 hours; Tractor in 1,000 hours; Draft animal in 1,000; Fertilizer in tons. 150 Model results indicate large increases in the projected amount of tractor hours used. Under alternative 1A, the regional total would increase by 2.6 times, compared to a 2.9 times for alternatives IB and IC. For small farms, the results show a 3.9 fold increase over the period for all alternatives. For large farms, the increases would be only of the order of 1.2 times, under alternative IA, and 1.8 times under alternatives IB and IC. The impact of yield increase on tractor use is much higher for large farms than for small farms. For the re- gion, alternative 18 would employ 10.5 percent more tractor services than alternative IA, and alternative IC would employ 11.1 percent more than alternative IA. I The projected use of draft animal services shows an increase of 18.1 percent for the region under alternative IA, 33.2 percent un- der alternative 18, and 37.1 percent under alternative IC. For the regional total the impact of yield increase indicates a 12.7 percent increase for alternative 18 and 16.1 percent increase for alternative IC. In respect to farm size groups, the results show increasing use on small farms and decreasing use on large farms during the period for all alternatives. Under alternative IA, the model projects an increase in the demand for fertilizer in the region of 58.6 percent over that of the base year. This increase is the result of a 117.5 percent increase in the demand by small farms and a decrease of 20.6 percent in the demand by large farms. The impacts of yield increase can be seen by comparing the projected results for the three alternatives. This com- parison shows for example, that under alternative 18 the demand for 151 fertilizer in the region is 13.0 percent higher than alternative IA, (and that under alternative 1C the demand is 17.7 percent higher than alternative IA. In conclusion, the model projections of employment and input demand show substantial increases during the period considered and significant differences among the alternatives mainly due to changes in the patterns of land use. In general, small farms use from 50 to 70 percent of the total amount of each input due to a more intensive use of land in this group. Yield increases of 50 percent (alternative 1C) Show only marginal differences in respect to yield increases of 30 percent (alternative 18). Income and Factor Productivities: The net returns to fixed factors and factor productivities projected for 1980 under the three alternatives considered are shown in Table V1.5. Net farm income or net returns is defined as gross revenue minus variable costs. It is given by the optimum value of the objective function of the linear programming model. Land productivity is net return per hectare of total utilized land which includes crop land and pasture land. Labor productivity is defined as net returns per hour of total labor employed. Concerning net returns by farm size, an observation should be made in reference to optimization of the objective function and the disaggregation procedure used. The definition of net returns to each group separately is not indicative of individual optimization. The model maximizes the aggregate objective function which is the sum of the individual objective functions. However, maximization of the 152 Table V1.5: Net Farm Income and Factor Productivities for 1980 ‘ Under Different Yield Alternatives and a 50 Percent Mechanization Level. Base Alternative Yield‘AEsumptlons Item Year Alternative IA 'ATternative 18 Alternative IC (1970) T' Value VElue ‘TTiK Value 7753— Income S 455365 4662092 5404314 15.9 5941825 27.5 L 31747] 2048463 2596690 26.8 2935995 43.3 T 772842 6710555 8001004 19.2 8877820 32.3 Land S 75.71 599.38 694.80 15.9 793.90 27.5 Productivity L 26.04 181.80 230.46 26.8 260.57 43.3 T 42.45 352.34 420.09 19.2 466.13 32.3 Labor 5 0.56 3.02 3.49 15.6 4.79 25.5 Productivity L 0.3 4.13 3.65 -ll.6 4.09 - 1.0 T 0.4 3.29 3.54 7.6 3.88 17.9 Note: 1) S = Small farms; L = Large farms; T = Regional total 2) %A means percent change from respective values of Alter- native IA. 3) Income in 1,000 Cruzeiros; Land Productivity in Cruzeiros per hectare; Labor Productivity in Cruzeiros per hour. 153 regional objective function does not necessarily imply maximization of each one separately. The separation of net returns by size group is based on the optimal values of the activities obtained after the re- gional objective function is maximized. Table V1.5 includes the values for the base year and for 1980 under each alternative. Given the price relationships assumed in the model, net regional farm income increases by 8.7 times during the period, under alternative IA. Under the same alternative, it increases by 10.2 times for small farms and by 6.5 times for large farms. Basi- cally, the higher rate of growth for small farms is due to intensifi- cation hithe use of land and faster expansion of crop land in this group during this period. According to model results, the introduction of high yield varieties would have significant impacts on net regional income. Un- der alternative 18 net returns would be 15.9, 26.8, and 19.2 percent higher for small farms, large farms, and for the region, respectively. For alternative IC, net returns would be about 1.7 times higher than alternative 18. Large farms would experience a higher increase in net returns than small farms. Average net land productivity measured as the ratio of total net returns to total land use is a decreasing function of farm size in all cases. Under model conditions, land productivity in alternative IA increases by 8.0 times in small farms, 7.0 times in large farms and 8.3 times for the region from the base year values. The differential impacts Of yield increase on land productivity are higher for large farms due to the faster rate of transition to crop farming on larger 154 farms and their increased use of commercial inputs under alternatives IB and IC. Labor productivity measured as the ratio of net returns to total labor employed is higher in large farms than in small farms. Comparing alternatives IA, 18, and IC the introduction of varietal technology can be seen to have different impacts on labor productiv- ity according to farm size. For small farms, average labor productiv: ity would be 15.6 percent higher under alternative 18 compared to al- ternative 1A. Similarly, alternative IC would show a 25.5 percent in- crease in labor productivity compared to alternative IA. For large farms, labor productivity decreases by 11.6 percent and 1.0 percent for alternatives IB and 1C, respectively, in regard to alternative IA. This result is due to an increase in labor employment which is more than proportional to the increase in net returns in large farms. To summarize, model results show that net farm income and factor productivities would be enhanced with increases in crop yields. Large farms would tend to experience greater impacts relative to small farms. The Impacts of Mechanical Technology This section presents the results for alternatives IIA, 118, and 11C described in Table V1.1. The objective is to show the impacts of changing labor, draft animal, and tractor requirements for produc- tion activities such that the effects of an increased level of mecha- nization on production and resource allocation can be analyzed. As described earlier, each alternative refers to a certain combination of traditional and modern production processes. In alternative IIA 155 the resulting process is a combination of 0.25 modern and 0.75 tradi- tional; for alternative 118 the combination is in a 50 percent basis and alternative IIC has a 0.25 proportion of traditional and 0.75 of modern. All three alternatives are analyzed maintaining yields at base levels, i.e., the yield levels determined by the original ferti- lizer response functions. Land Use and Cropping Patterns: Model results for crop and pasture areas under the different mechanization alternatives are shown in Table V1.6. Rice area in- creases by 72.6, 14.3, and 31.8 percent during the period for small farms, large farms, and the region, respectively, under alternative IIA. With a higher level of mechanization (alternative 118 or IIC), rice area would remain the same in small farms, increase by 51 per- cent in large farms, and increase by 31 percent in the region, rela- tive to alternative IIA. Area cultivated with corn would decrease by approximately the same proportions under all three alternatives for both farm size groups and the region. Thus, under model conditions of prices and behavioral constraints, no major effect would be observed on corn area with changes in the pattern of mechanization. Area of wheat, under alternative 11A, would increase by 410 percent in small farms, decrease by 65 percent in large farms, and in- crease by 67 percent in the region over that of the base year. If al- ternative 118 is introduced, the increase in area on small farms would fall to 357 percent, and the decrease on large farms would be46 per- cent. Under alternative IIC, the area on small farms remains the same 156 Table V1.6: Optimal Land Use and Cropping Patterns for 1980 Under ' Different Mechanization Alternatives and Base Yield Levels. Crops 125:7' Alteriati$2iii"iitefiaiiiii‘tiflr-%i136nat?oestic (1970) 'Area "'TZZT*" Area‘ "':%ZT‘ ' Area ‘ ‘TTEETTT Rice -S 135 233 72.6 233 72.6 233 72.6, L 315 360 14.3 543 72.4 543 72.4 T 450 593 31.8 776 72.4 776 72.4 Corn -5 1332 1110 -16.7 1137 -14.6 1137 -14.6 L 467 280 -4o.o 28o -4o.o 280 -4o.o T 1799 1390 -22.7 1417 -21.2 1417 -21.2 Wheat -S 279 1423 410.0 1274 356.6 1274 356.6 L 722 1252 -65.1 388 -46.3 1260 74.5 T 1001 1675 67.3 1662 66.0 2534 153.1 Soybeans-S 304 1923 532.6 2025 566.1 2025 566.1 L 374 170 -54.5 274 -26.7 722 93.1 T 678 2093 208.7 2299 239.1 2747 305.2 Cult. -S 159 655 311.9 1219 666.7 1219 666.7 Pasture L 387 232 -40.1 232 -40.1 232 -40.1 T 546 887 .62.4’ 1451 165.7 1451 165.7 Natura1 -S 3806 2434 -36.1 1890 -50.3 1890 -50.3 Pasture L 9927 9974 0.5 9551 - 3.8 8231 -17.1 T 13733 12408 - 9.6 11441 -16.7 10121 ’26.3 Note: 1) S = Small farms; L = Large farms; T = Regional total 2) Area in 1,000 hectares. 3) %A means percent change from respective base year (1970) values. 157 as in 118, but would increase on large farms by 74.5 percent and in the region by 153 percent over the base year values. Thus, higher levels of mechanization tend to increase the area of wheat, with large farms experiencing larger proportion of the increases. Projected area of soybeans follow basically the same pattern as that of wheat. For the aggregate it is 9.8 percent higher under alternative 118 than IIA, and 31.3 percent higher for alternative IIC relative to IIA. These increases would result from 5.3 and 61.2 per- cent increase in the area in small and large farms, respectively, un- der alternative IIB relative to IIA, and 5.3 and 324.7 percent under alternative IIC relative to IIA. Similar to wheat, the major propor- tion of the increases in soybeans goes to large farms. Increased levels of mechanization would raise the area of cul- tivated area of wheat and soybeans reflect the decreases in the area with natural pasture. In the aggregate the area decreases by 9.6 per- cent under alternative IIA, 16.7 percent under alternative 118, and 26.3 percent under alternative IIC from that of the base year. Production: Quantity produced of the various products projected by the model is shown in Table V1.7. Production impacts for the different mechanization alternatives result from changes in land use and crop- ping patterns determined by the optimal allocation of land among dif- ferent farm activities. Rice production in the region is projected as 31.2, 72.5 and 72.5 percent higher than the base year, under 158 Table V1.7: Optimal Production Levels for 1980 Under Different Mechanization Alternatives and Base Yield Levels. Base ,, ATternative—Mechanization Assumptions Products Year Alternative IIA Alternative IIB AlternatiVéIIC (1970) Quantity %A Quantity %A Quantity %A Rica, -5 468906 808644 72.5 808644 72.5 808644 72.5 L 1148820 1314349 14.4 1981176 72.5 1981176 72.5 T 1617726 2122993 31.2 2789820 72.5 2789820 72.5 Corn -5 1906840 1653443 -13.3 1693528 -11.2 1693528 -11.2 L 668632 416595 -37.7 416595 -37.7 416595 -37.7 T 2575472 2070038 -19.6 2110123 -18.1 2110123 -18.l Wheat -S 298022 1536978 415.7 1376617 361.9 1376617 361.9 L 810452 285632 -64.8 439900 -45.7 1428928 76.3 1 1109474 1822610 64.4 1816517 63.9 2805545 153.1 Soybeans-S 373306 2486421 566.1 2651179 610.2 2651179 610.2 L 461632 207154 -55.1 342584 -25.8 955850 107.1 T 834938 2693575 222.6 2993763 258.6 3607029 332.0 Beef -5 237305 242998 2.4 310123 30.7 310123 30.7 L 610711 590377 - 3.3 567091 - 7.1 494445 -19.0 T 848016 833375 - 1.7 877214 3.4 804568 - 5.1 Note: 1) S = Small farms; L = Large farms; T = Regional total 2) Quantity in tons. 3) %A means percent change from respective base year (1970) values. 159 alternatives IIA, 118, and IIC, respectively. Corn production would decrease for both sizes and the region by about the same proportions under all alternatives. ' According to model results quantities produced of wheat and soybeans are projected to increase significantly. This increase is due to large amounts of land being transferred into production of these two crops. For wheat, increasing the level of mechanization causes a decrease of production in small farms and very significant increases in large farms. For soybeans, production increases in both sizes for higher levels of mechanization. Beefproduction on large farms would be greatly affected by increased mechanization. It would decrease by 7.1 and 19.0 percent under alternatives 118 and IIC, respectively, compared to a decrease of only 3.3 percent under alternative IIA. 0n small farms it would be 27.6 percent higher for alternative 118 or IIC than for alternative IIA. Basically, according to model projections, increased mechani- zation would tend to shift resources away from corn and beef produc- tion in favor of rice and mostly wheat and soybeans. Employment and Input Utilization: Resource demands necessary to meet production levels under the various alternatives are shown in Table V1.8. The total amount that given input is used is a function of total amounts of land to which the input is applied and the unit requirements of the input per unit of land. Table V1.8 gives the demands for the inputs under conditions of changing unit requirements per hectare. For a given alternative, 160 Table V1.8: Optimal Input Use for 1970 and 1980 Under Different Mechanization Alternatives and Base Yield Levels. - ATternativeTMechanization Assumptions Input Alternative IIA Alterna ive 118 Alternative IIC 71970’ 1980 1970 71980 1970 1980 Labor -5 862954 1980722 812156 1543252 761358 934166 L 869546 518095 817381 496139 765215 511610- T 1732500 2498817 1629537 2039391 1526573 1445776 Tractor —S 3151 7222 3782 15255 4412 22481 L 3037 1746 3644 4368 4252 11174 T 6188 8968 7426 19623 8664 33655 Draft -S 126582 278711 118143 202492 109704 115710 Animal L 113795 65543 106209 62567 98622 64398 T 240377 344254 224352 265059 208326 180108 Fertilizer 5 126315 262131 126315 274701 126315 274701 L 93769 57774 93769 74415 93769 138291, T 220084 319905 220084 349116 220084 412992 Note: 1) S = Small farms; L = Large farms; 1 = Regional total 2) Labor in 1,000 hours; Tractor in 1,000 hours; Draft Animal in 1,000 hours; Fertilizer in tons. 161 the input-output coefficients of labor, tractor, and draft animal change over time in such a way as to increase the level of mechaniza- tion through substitution of tractor services for labor and draft ani- mal services. The initial mechanization level at the beginning of the period increases from alternative IIA to IIC. Labor employment grows at the rates of 13.0 and 4.4 percent per year for small farms and the region, respectively, under alterna- tive IIA. For large farms employment would decrease at the annual rate of 4.0 percent, under the same alternative. Under alternative 118, employment would grow at the annual rates of 9.0, -3.9, and 2.5 percent for small farms, large farms, and the region, respectively. If alternative IIC is introduced, employment would increase by only 2.3 percent on small farms, it would still decrease by 3.3 percent on large farms, and decrease by 0.5 percent in the region. Thus, the rate of growth of employment decreases from alternative IIA to IIC for small farms, increases slowly for large farms, and decreases for the region. This indicates that the substitution effects of tractor for labor on small farms are greater than on large farms and would come about at a faster rate. Under alternative IIA, tractor use on small farms would in- crease at the annual rate of 13.0 percent, while on large farms it would decrease by 4.3 percent per year. In the aggregate it would increase by 44.9 percent or at the rate of 4.5 percent over that of the base year. Under the other alternatives these rates increase considerably. For small farms the average annual rates of growth would be 30.3 and 41.0 percent for alternative 118 and IIC, 162 respectively. For large farms they would be positive 2.0 and 16.3 percent, and for the region 16.4 and 28.8 percent for alternative 118 and IIC, respectively. Draft animal use presents a similar picture as that of labor. As we move from alternative IIA to IIC, the average growth rate of use decreases for small farms, increases for large farms and decreases for the region. Under alternative IIA draft animal use would increase at the rate of 12.0 percent on small farms, decrease by 4.2 percent per year on large farms, and increase by 4.3 percent in the region. On the other hand, under alternative IIC, draft animal use would increase on small farms by only 0.5 percent per year, it would de- crease by 3.5 percent instead of 4.5 percent on large farms, and would decrease by 1.4 percent per year in the region. The regional demand for fertilizer increases by 45.4, 58.6, and 87.6 percent over that of the base year for alternatives IIA, 118, and IIC, respectively. The demand under alternative 118 is 9.1 per- cent higher than that of alternative IIA for 1980. Likewise, the demand under alternative IIC is 29.1 percent higher than that of al- ternative IIA, at the end of the projection period. Thus, model re- sults indicate that the demand for fertilizer would increase with in- troduction of higher levels of mechanization. Income and Factor Productivities: The introduction of technological change in the form of mech- anical technology has some potential for increasing net returns to fixed factors in farming through more efficient combination of re- sources (Table V1.9). Net regional farm income would be 14.7 percent 163 Table V1.9: Net Farm Income and Factor Productivities for 1980 Under Different Mechanization Alternatives and Base Yield Levels. Alternative’Mechanizatien Assumptions Item 1ternative1171 Alternative IIB ATternative IIC value Value %A Value %A Income -5 4325008 4662092 7.8 4595719 6.3 L 1525467 2048463 34.3 3131011 105.3 T 5850467 6710555 14.7 7726730 32.1 Land -S 556.04 599.38 7.8 590.84 6.3 Productivity L 135.39 181.80 34.3 277.88 105.3 T 307.18 352.34 14.7 405.69 32.1 Labor S 2.18 3.02 38.5 4.92 125.7 Productivity L 2.94 4.13 40.5 6.12 108.2 T 2.34 3.29 40.1 5.34 128.2 Note: 1) S = Small farms; L = Large farms; T = Regional total 2) %A means percent change from respective values of Alter- native IIA. 3) Income in 1,000 Cruzeiros; Land Productivity in Cruzeiros per hectare; Labor Productivity in Cruzeiros per hour. 164 higher under alternative 118 and 32.1 percent higher under alternative IIC, relative to alternative IIA. Large farms would take a larger proportion of the increase in net regional farm income. Net returns of large farms would increase by 34.3 and 105.3 percent with alterna- tives 118 and IIC, respectively, relative to alternative IIA. For small farms the increases would be only of the order of 7.8 and 6.3 percent. Land productivity changes in exactly the same proportions as net returns, indicating that total utilized area increases more pro- portionally than net returns. Net returns per hectare are higher for small farms, even though the gap decreases from lower to higher levels of mechanization. It is 4.1, 3.3, and 2.1 times higher in small farms than in large farms, for alternatives IIA, 118 and IIC, respectively. The index of labor productivity is about 1.3 times higher for large farms than small farms under all situations. The aggregate in- dex for the region increases from Cr$2.34 per hour under alternative IIA to Cr$3.29 per hour under alternative 118 and to Cr$5.34 per hour under alternative IIC. This corresponds to a 40.1 percent increase from alternative 11A to 118, and,a 128.2 percent increase from alter- native IIA to IIC. Model Evaluation The main purpose of this section is to present an evaluation of the model. This is done by two procedures. The first procedure eval- uates the extent to which model results would change if prices were maintained constant at initial nominal values instead of using prices projected by the expectation models. The objective is to test if price 165 changes would have any significant effect in determining model results. If price changes affect the results, the impacts of technology cannot be distinguished from the effects of price. The second procedure eval- uates the ability of the model to track events over a given historical period. This is done by comparing the estimated model results on area and production with observed data for the period 1970-76. The purpose is to test the "goodness of fit" of the model, i.e., to evaluate how the model "explains" actual data. Area and production of the four field crops are shown in Table VI.lO for two sets of price assumptions. Under constant prices, the commodity prices are maintained constant at initial nominal values. The results under varying prices are the same as those presented ear- lier in this chapter with prices projected on the basis of the expec- tation models. Table VI.lO presents the results for Alternative IA. The other alternatives are not shown because the results presented basically the same pattern under all alternatives. Crop area is about the same for both price assumptions. The only differences observed are for wheat from 1976 to 1980 and for soybeans from 1978 to 1980. This shows that resource allocation is rather stable in respect to the price assumption. Thus, the price changes introduced by the expectation models had no effect on deter- mining model results. The impacts of technology analyzed earlier in this chapter were not influenced by price changes. Production levels with constant prices are different from those with varying prices in all cases. The reason for this is that changes in prices affect the fertilizer application rate which in turn affects 166 comm mpom o_o_ omom oppm m_om oonm sumo coop mmom Room oom_ oppm ommm mmmm ommm ommm onop moo, one, mmwp o~m_ comm “New momm oomm onop omp_ mm_F oPFP mopp oNoN “cum onom meow «noF moo omo Nnop moo, mmum ooow «mop «mop mnop moo moo oopp oopp mumm mumu opop _ opop ouo— . "Amoco ooo.Pv copuuzooeo oomm Poom moo” moou “Pop “pop ohm men ooop mPoF momp oomp omop onmp omm_ mom mo“ onop oopp oopp m~_F oomp omnp ommp omo omo muo— Nom moo ooop moo. sump nmop mum mum okop omn om“ me puo ooo_ ooop opm o_m «no, omo ono Foo_ pooF oomp om“. omo ome omop "Ammgmuum; ooo.pv mmg< mmuwgo mauve; meowea mmowea mauve; mmo_ea mauve; mmowga ocpxgm> pompmcoo ocvxgm> pcmpmcoo ocwxgm> acmpmcoo ocwxgm> pcmumcoo me> mommaxom poms: :Loo wwwmli .oooplomop .wpmcewup< .mcowuq53mm< women mo mymm 03» Love: mpm>mo cowuuoooga com mme< _wswpoo uo_.H> open» 167 yields. With different yields production levels change. Price changes affect the allocation of fertilizer becahse it is determined as a di- rect function of prices. The allocation of other variable resources should not be affected since it is determined as a function of the in- put requirements per unit of land. Model performance can be evaluated in several ways. Probably the most common procedure is the comparison of estimated model results with historical data observed during a certain period. This procedure shows the ability of the model to track actual data. It is used here with data on area and production for the period 1970-1976. Actual and estimated data on area and production are presented in Table V1.11. The tracking ability of the model is summarized by the Average Proportional Error (APE). The APE is calculated as fol- lows: APE = -:-.- g Elf-At t=l t where APE = average proportional error Et = the estimated value at time t At = the actual value at time t n number of years in the series Analysis of the APE provides a rough indication of the accuracy of the model results. It gives the percentage of error of the model in estimating actual data. In general, model tracking as shown in Table VI.ll is not very satisfactory. The model overestimates area and production of rice and corn. For wheat and soybeans model results are lower than the actual 168 Table V1.11: Actual and Estimated Area and Production Levels, 1970-1976. *Rice Corn Wheat ISpyBeans Year Esti- Esti— Esti- Estis Actual mated Actual mated Actual mated Actual mated Area (1,000 hectares): 1970 431 450 1737 1799 1500 1001 871 678 1971 412 482 1722 1843 N.A. 987 1133 705 1972 434 516 1717 1890 N.A. 971 1460 750 1973 416 551 1507 1943 1373 981 2218 814 1974 436 579 1525 1927 1565 1009 2770 902 1975 470 608 1524 1831 1899 1188 3113 1018 1976 520 638 1580 1739 2016 1398 3296 1166 APE* 0.2251 0.1517 0.3309 0.5303 Production (1,000 tons): 1970 N.A. 1618 2387 2575 1500 1108 977 835 1971 N.A. 1732 2371 2633 N.A. 1080 1393 878 1972 N.A. 1852 2235 2698 N.A. 1069 2173 939 1973 1434 1977 2101 2770 1536 1077 2872 1023 1974 1550 2075 2236 2747 1690 1103 3870 ‘ 1137 1975 1700 2178 2367 2609 1234 1299 4688 1285 1976 1850 2286 2443 2477 1814 1529 5107 1473 APE* 0.3086 , 0.1514 0.2234 0.5529 *APE = Average Proportional Error 169 throughout the series. A positive feature of the model is its ability to estimate the turning point in the area of wheat. This area decreas~ es from 1970 to 1973 and then increases thereafter. The average proportional error indicates that the estimates for corn are the most accurate, while the estimates for soybeans pre- sented larger errors. The average error for corn is about 15 percent; for soybeans the error is over 50 percent. Clearly, the most signifi- cant projection problems of the model are related to soybeans. The model is not able to estimate the rapid increases in soybean area and soybean production observed during the past years. There are basically two sources of errors of model estimates. These are model specification and quality of the data used in the mod- el. Specification error could have occurred in various areas of model development. The most critical area is the Specification of the linear programming model of the resource allocation component. Improvements of this model in terms of better specification of resource constraints should increase model accuracy. The quality of the data used in the model is also an important source of model error. The model uses var- ious sources of data to estimate a number of parameters, rates of change, and initial conditions. These estimates are crucial in deter- mining model results. Improvements in the data base should contribute a great deal to increase model performance. In summary, the empirical results presented in Chapter VI show that introduction of alternative technologies in the form of high-yield varieties and mechanization would have impacts on production and re— source allocation in the Southern Brazilian agriculture. In general, 170 it would tend to change cropping patterns with significant shifts of resources into wheat and soybean production. Varietal technology pre- sents a great potential for increasing labor employment in the region. Both types of technology have significant effects on increasing net farm income. Large farms tend to experience higher increases in in- come than small farms. This indicates that technological change would tend to increase the income gap between the two groups. Model evalua- tion show that the price changes introduced by the expectation models had no effect on the results. Unfortunately, model performance eval- uated in terms of its ability to track actual data was not satisfac- tory. Improvements of model specification and data base would enhance model performance. CHAPTER VII SUMMARY AND CONCLUSIONS The purpose of this chapter, which is divided into three parts, is to present the summary and conclusions of the study. The first part gives an overview of the study with focus on the problem, objec- tives, and methodology. The second part presents the summary of I findings, conclusions and implications for develOpment and technology policy. Finally, the third and last section presents some limitations of the study and recommendations for further research. Summary of Problem, Objectives and Methodology_ Basically, this study deals with the problem of how research programs can be directed to affect technological change to increase productivity of scarce resources and increase total production of major commodities. Historically, the major source of output growth in the agricultural sector of the region studied has been the expansion of the frontier with incorporation of new land, labor and associated capi- tal. Given the exhaustion of possibilities for further extensive expan- sion of output, increases in production will have to rely more on pro- ductivity growth in the agricultural sector. The potential contribution of technological change to develop- ment has been recognized for some time. Yet, it will remain as an important economic problem to study its impacts and adjustment in the 171 172 agricultural sector characterized by a complex structure of economic variables and interrelationships among producers, consumers, and other economic units. Technological change is, for the most part, generated by research activities carried on by the public sector. The effects of introducing new technologies can be characterized by impacts on the cost structure or the product mix of individual firms, shifts in indus- try demand curves for factors of production, shifts in product supply curves, and impacts on the growth and distribution of total and per capita income. The primary objective of this study has been to examine the potential impacts of technological change in production patterns, employment and resource utilization, income and resource productivi- ties for the agricultural sector of the state of Rio Grande do Sul, Brazil. More specifically, the analysis is concerned with the impacts of varietal and mechanical technologies. Varietal technology, in the form of high-yield cr0p varieties with higher capacity to respond to fertilizer application, is analyzed by means of a number of alternative assumptions in respect to yield per hectare for annual crops.' Mecha- nized technology is analyzed on the basis of the effects of changes in labor, draft animal, and tractor input requirements for production ac- tivities. High-yield varieties are supposed to facilitate substitution of fertilizer for land, thus changing resource proportion and resulting in substantial increases in output. {Tractor services are assumed to substitute for labor and draft animal, permitting more efficient combi- nation of factors and resulting in higher returns to farm resources. 173 The instrument of analysis used to reach the objectives of the study is a regional, dynamic, microeconomic model of farmers' decisions with respect to resource allocation and production. The major objec- tive of the model is to simulate the year-to-year allocation of land and other farm and regional resources on the basis of their opportunity cost in alternative uses and on the basis of relative enterprise prof- itability. Furthermore, the model is used to simulate the impacts of changes in structural parameters related to yield levels and response to fertilizer, labor, draft animal and tractor input-output require- ments, under the condition of prespecified product and input prices relationships and initial conditions with respect to resource levels. The model provides a time profile of optimal land use and cropping patterns, production, farm income, and derived demand for farm inputs for the region and by farm size groups. The model isapplied to the whole area of the state of Rio Grande do Sul in Brazil.‘ This state is one of the most important pro- ducers of agricultural productsirlthe South Region and also in the country. Because of its mild and temperate climate, and adequate soil conditions, its agriculture has been largely complementary to that of the rest of Brazil. It has provided large proportions of the country's production of rice, corn, and beef, and has been the most important wheat and soybean producer in the country. Because of the wide distri- bution of land in the state, the model includes disaggregation of farm size in two groups: "Small Farms" including farms of size ranging from 0 to 100 hectares, and a group of "Large Farms“ of size greater than 100 hectares. The disaggregation by farm size serves to: a) capture 174 distributional effects of technology change, b) analyze the inter- dependence of different farm size groups competing for regional resources, and c) partially account for aggregation bias. The model developed in this study is composed of three major components: yield component, resource allocation component, and pro- duction and accounting component. The yield component is designed to estimate crop yields based on yield-nutrient response functions. Yield rates for crops are determined by means of quadratic production func- tions estimated from experimental data on yield per hectare and nitro- gen application.1 The fertilizer application rate is determined on the basis of the equimarginal principle of equating the marginal value pro- duct of the factor to the price of the factor. Yield rates are further adjusted to account for the effects of mechanization and differences in farm size. The resource allocation component consists of a Recursive Linear Programming model which allocates land and other farm resources to alternative farm enterprises based on the opportunity cost principle and on relative profitabilities. In the production and accounting component, production levels for crops and livestock activities are computed given land allocation and yield projections. Other results such as resource requirements, income, resource productivities and input ratios are also computed. 1The response functions for rice, corn, and wheat are taken from Peter T. Knight, Brazilian Agricultural Technology and Trade - A Study of Five Commodities (New York: Praeger Publishers, Inc., 1971). DUE‘UD the'lack of experimental data, the response function for soybeans is graphically estimated through a scatter diagram of yield and nutrient application. 175 Results are obtained by commodity, farm size and regional aggregates. Recursive Linear Programming was used as the basic approach to represent resource allocation decisions in the region. It is assumed that farmers would select a land utilization pattern which would maxi- mize the expected net returns, subject to a range of physical and behavioral constraints. The input-output matrix of the linear program- ming model is block diagonal with one block for each farm size and additional regional constraints which hold for all farm sizes simulta- neously. The linear programming model is solved iteratively for each year giving optimal enterprise combinations over time by farm size. The decision rule to be satisfied is the optimization of the regional objective function defined as expected gross returns minus variable costs. The activities considered in the model are: a) Production of various annual crops; b) Production of natural and cultivated pasture; c) Production of beef; d) Investment in tractor, combine and draft animal, and e) Labor hiring by season. Crops included are: rice, corn, wheat and soybeans. Two distinct activities for soybeans are considered, namely, soybean following wheat and soybean independent of wheat. The constraints of the model include: a) Land constraints by season; b) Labor constraints by season; c) Tractor, combine, and draft animal power capacities; d) Balance equations; e) Behavioral constraints in the form of maximum and minimum hectarage for land using activities, and f) Regional constraints on tractor and wage labor supply. 176 Summary of Findings, Conclusions and Implications for Development and Technologerolicy This section presents a summary of the results and the major conclusions of the study. At this point model results cannot be taken as conclusive for policy recommendation since further model testing and refinement are required in addition to improvements and checks in the data used in the model. Conclusions and implications derived from model application are subject to the limitation of the data and the appropriateness of model assumptions and specification. Model results indicate that in response to technological change farmers can change, to a certain extent, their land utilization, pro- duction, imput demand, and income patterns over time. The impacts on area allocated to the various crops are the primary effects of changing technological coefficients in the model. Impacts on other variables are in essence determined as a consequence of changes in land alloca- tion decisions among alternative enterprises. According to model results the introduction of technological change in the form of high-yielding varieties would have significant impacts on the area cultivated with wheat and soybeans, only minor effects on the area of corn, and no changes would be observed on the area cultivated with rice. Area of corn would increase from 5.0 to 27.0 percent in small farms and no change would occur in large farms. An increase in yields of 30 percent would increase area of wheat in large farms by about 148 percent. Area of soybeans would increase by 96 and 107 percent in large farms if yields were 30 and 50 percent higher, respectively. Increases in crop areas come about mainly at the expense of natural pasture areas. Changing technical coefficients 177 for labor, draft animal and tractor use, so as to increase the level of mechanization, would have only marginal effects on the area of rice and corn. However, higher levels of mechanization would tend to increase the area cultivated with wheat and soybean, with large farms experiencing larger proportions of the increases. For the region, soybeans experience increases in area up to 30 percent. Projected production levels show the effects of changes in yield rates and changes in cropping patterns that would be observed under the different technology alternatives. The model projects sub- stantial increases in production of all crops during the 1970 - 1980 period, under all yield alternatives. Higher-yield varieties tend to have higher and more uniformily distributed impacts over all crops than mechanization (Table VII.1). In both cases wheat and soybeans experience the highest increases in production. Improved crop varie- ties and increased mechanization tend to raise the profitability of wheat and soybeans in greater proportions relative to other products. Furthermore, most of the increases in wheat and soybean production go to large farms. The implications of this are that large farms tend to benefit more than small farms from improved technology. The impacts on income due to increases in the amount produced of a given commodity will depend on the price elasticity of demand for the product. If prices do not change as a consequence of increased production, income will increase for the producers of the given com- modity. If prices change with changes in supply, the impacts on income will be positive if demand is elastic and vice-versa. Not much can be said about income effects for producers of individual commodities 178 Table VII.1: Sample of Output Results Comparing the Impacts of Varietal and Mechanical Technologies in 1980. It Farm Source of Technological Change em Size Varietal* Mechanical** Rice Production Small 45.5 0.0 Large 45.6 50.7 Corn Production Small 45.9 2.4 Large 14.9 0.0 Wheat Production Small 42.0 -lO.4 Large 252.3 400.3 Soybean Production Small 45.1 6.6 Large 212.8 361.4 Beef Production Small -l6.8 27.6 Large - 8.6 ~16.3 Labor Employment Small 2.8 -52.8 Large 44.8 - 1.3 Net Farm Income Small 27.5 6.3 Large 43.3 105.3 Land Productivity Small 27.5 6.3 Large 43.3 105.3 Labor Productivity Small 25.5 125.7 Large - 1.0 108.2 *Values are percent changes for Alternative IC in respect to Alternative IA. **Values are percent changes for Alternative IIC in respect to Alternative IIA. 179 without knowledge of price elasticity of demand. For example, decrease in beef production will tend to lower income of beef producers if price elasticity of demand for beef is elastic. The most important single factor influencing a developing coun- try's ability to absorb a growing labor force into productive employ- ment is the type of strategy pursued for developing its agricultural sector. Technology is a major factor to be considered in the develop- ment strategy. The choice of technology is an important element deter- mining the employment effects of development. The projected annual rate of employment growth during the period of analysis ranged from 2.5 to 4.0 percent under the different yield alternatives. Improvement in yields of 30 and 50 percent would raise total labor employment by 10.8 and 12.1 percent, respectively. Almost all increases in total employment would reSult from higher labor use in large farms (Table VII.1). The impacts of labor displacement by mechanical technology are higher on small farms than on large farms. Moving from lower to higher levels of mechanization the rate of growth of employment decreases for small farms, increases slowly for large farms, and decreases for the region. Substitution of tractor for labor and trac- tor for draft animal is explicity formulated in the model. If the rate of growth of employment decreases for small farms while it increases for large farms, the substitution effects are greater for small farms than for large farms. This implies that it is easier to substitute tractors for labor in small farms than in large farms. This is mainly because small farms are abundant in labor. The majority of labor used on small farms is family labor. Most increases in employment on large 180 farms come from hired labor. This indicates that policies which would have impacts on increasing consolidation of land would have additional impacts on increasing rural employment when these policies are combined with biological innovation programs. One phenomenon that Occurs coincidentally with the moderniza- tion of traditional agriculture is a change in consumption of farm inputs, particularly purchased inputs. For instance, the demand for fertilizer in the region is projected at 349,116 tons for 1980 under the condition of base yield levels. This is an increase of 56.8 per- cent over that of the base year. This demand would be 13.0 and 17.7 percent higher, under the alternatives of 30 and 50 percent increases in yields, respectively., The introduction of higher levels of mechan- ization would raise the regional demand for fertilizer by as much as 29 percent, Thus, technological change would have significant impacts on changing the structure of farm demand for a manufactured input. This increased demand may be an incentive for development of the domes- tic fertilizer industry, which in turn would represent savings in foreign exchange used to import fertilizer. In general, the group of small farms used over 50 percent of the total amount of inputs. This is due to a more intensive use of land in this group. Large farms have more extensive natural pasture area than small farms. A large proportioncflicultivated area is found on small farms. Since crop production requires the use of larger amounts of inputs than beef production, more input is used on small farms. Improvements in technology tend to affect more the pattern of employment and input utilization in large farms because they will have 181 greater potential to expand use of the various inputs. If input supply is limited there will be shifts of resources from one group of farms to another, with large farms buying up large proportion of the resources. Some analysts have suggested that the distribution of benefits from the new technologies parallels existing resource endowments. Basically, new varieties can be adopted regardless of the size of a given farm, everything else being equal. Even though large and small operators tend to use the new technology, large farms may benefit more because they control a greater proportion of the resources. Indication of the distribution of benefits from use of new technologies is given ’by the rate of growth of net farm income. Net returns to resources in farming can be improved significantly with improvements in crop yields. Net regional farm income raises by 19.2 and 32.3 percent for the two alternative yield assumptions compared to the situation of base yield levels. For small farms, net returns are higher by 20 percent, and for large farms they increase by over 30 percent under alternative yield assumptions. Projected net farm income shows significant dif- ferences among the different mechanization alternatives analyzed. Net regional farm income increases by 14.7 and 32.1 percent for a 50 per- cent and a 75 percent mechanization alternative, respectively, compared to a 25 percent alternative. The increases for large farms would be significantly higher than those for small farms. For the above situa- tions, the corresponding increases for small farms would be 7.8 and 6.3 percent, while for large farms they would be 34.3 and 105.3 percent (Table VII.1). 182 Income of large farms increases more than that of small farms for varietal and mechanical technology. However,a great difference exists when mechanical technology is introduced. Model results indi- cate that technological change in the form of mechanization tend to enhance income of large farms in much greater proportion than that of small farms. The implications for income distribution are clearly a tendency for the income gap between farm size groups to increase over time. The introduction of higher levels of varietal and mechanical technology would result in a higher projected growth rate of net output in large farms compared to the rate of growth in small farms. Conse- quently, the share of large farms in both total and net regional out- 'put would increase at the expense of small farms. Thus, large farms would tend to buy off resources and increase farm size even faster, since they would be better off by experiencing higher increases in income. Changes in land and labor productivities show the relative factor scarcities and different technology choices among farm size groups. Land productivity is higher for small farms while labor pro- ductivity is higher for large farms. For both types of technology, land productivity increases by higher percentages in large farms (Table VII.1). Mechanical technology induces substantial increases in labor productivity in both farm sizes. Differences in factor productivity among farm sizes are possibly due to differences in the technology employed. Labor productivity, for instance, is higher in large farms which use less labor per unit of land and in turn will have lower vari- able costs than small farms. Thus, the choice of technology will af- fect resource productivity. 183 From the point of view of the decision-maker responsible for the allocation of funds to alternative research programs it is of interest to know which investment would give the highest pay-off. However, the concept of returns to investments has to be based on a set of criteria. In this study only varietal and mechanical technology are analyzed. The results of Table VII.1 show that there are trade- offs among criteria. The objectives of investment in research may be increased production, employment or income distribution. In order for the model to supply useful information for policy making, interaction with public decision-makers is necessary to determine their interests and the several direction of policy variables. Thus, model applica- tion can be very useful when used in interaction with decision-makers. The model can be used to analyze a whole range of situations in respect to biological and mechanical technology. Model results will indicate major direction of changes and also will provide estimates of the im- pacts and adjustment which will potentially occur with the introduction of alternative technologies. This study suggests that in order to develOp technology policy the interrelationships among farm size groups and crops should be taken into account. Improvements in technology for a given crop will in- crease its comparative advantage relative to others. With limited sup- ply of land, increases in area cultivated with one crop is only possi- ble at the expense of others. The introduction of technology change which affects cropping patterns should consider the consequences of changes in area of one crop due to changes in area of another crop. 184 Comparing the results for the various crops, the model projects large proportions of increase in area and production of wheat and soy- beans, under conditions of alternative technologies. Thus, given the same improvements in technology for all crops, it appears that wheat and soybeans would tend to benefit more in comparison to other crops. This indicates that to maintain basically the same competitive rela- tionship, greater emphasis should be given to increase productivity of the other crops. 1 The results of this study suggest that the type of technolo- gical change to be implemented in a region would have impacts on land use and cropping patterns, production, employment and input utiliza- tion, and income. Furthermore, the choice of technology to be gener- ated and disseminated by research institutions should consider the adjustments and impacts that such technology improvements wOuld have on the relative competitive position of the various farm enterprises and on the income accruing to the different producing groups. Limitations and Suggestions for Further Research The analytical framework used in this study is found to be feasible for analyzing the impacts of technological change with consid- eration of a large number of interrelationships among farm enterprises, farm size groups, and different regions. Due to the time dimension of the model, it can account for the dynamic properties of the adjustment and growth process under conditions of changes in technology. However, at the present stage the model still has several weaknesses which are the subject to further research. Several aspects of the model can be improved and extended. The most important areas for further research are: 185 l. Improvements of the Data Base -- The model makes use of farm level data and also secondary data collected by census statistics. Improvements of data collection and consistency checks on secondary data should receive greater attention of government agencies responsi- ble for such tasks. The basic difficulty with the primary data is its limited availability by farm size groups. Input-output coefficients, production costs and returns should be available by farm size to allow for taking into account in the model the basic differences among farm sizes with respect to production decisions and choice of technologies. Especially in the case where the model would include several classes, basic data by size group would be essential for model performance. 2. Resource Tranference Between Farm Size Groups -- Further research should concentrate on ways of dealing with the dynamics of farm size groups. Land structure changes over time. Transference of land from one group to another will carry other resources such as labor and capital. The model should allow for the changes in structure including some mechanism to account for resource transference among groups. Also, related to land structure is the problem of projecting number of farms per farm size group in such a way as to maintain con- sistency between number of farms and area in each group. 3. Include More Than One Region and More Than Two Farm Sizes -- Dissaggregation in farm size groups has been found to be a very useful way of generating information. It provides a basis for analyzing the effects of scale and different factor proportions on resource alloca- tion, and choices of technology. Besides accounting to some extent for aggregation bias, this procedure allows also the modeling of inter- actions among farm size groups competing for regional resources. 186 Analysis of model results indicates that the disaggregation into farm size groups should include a larger number of classes. Even though the stratification in two groups proved useful, it did not al- low for very conclusive findings with respect to the process of re— source allocation under conditions of changing resource endowments. Choice of technology is a function of resources scarcities in the farm. Only with consideration of a wider range of sizes could the effects of size and its relationships to technology choice be identified. Extension of the model should also include more than one region. Inclusion of more than one region would be useful to study inter-regional competition, and the effects of technology change on different regions. 4. Link to Other Sector Models -- Due to the flexibility of the model and its computer program, it can be used as a separate model or in interaction with a larger sector model. Its basic function would be to serve as a decision-making c0mponent used to determine endoge- nously in the larger model allocation of land and other farm resources to production, based on the opportunity cost of the resources in alter- native uses, and based on the relative profitability of the various farm enterprises. Further modeling effort could include other compo— nents of the agricultural sector and models of other sectors of the economy. The model developed in this study can be used as a component representing farmers' decisions with respect to resource allocation and production in a larger model. 5. Model Improvements -- Some basic improvements of the model would include: a) Incorporate financial activities and constraints; 187 b) Include other activities which also use farm resources; c) Incor- porate other regional constraints such as fertilizer, fuel and credit; d) Include more detailed classification of labor by season, and e) In- clude farm machinery capacities by season. The model seems to over- emphasize the role of flexibility constraints. These constraints are used to represent farmers' ability to change activity levels from year to year. Clearly, the estimation of flexibility coefficients is cru- cial for model behavior. However, their role should not override the role of other elements in the model. The improvements in model speci- fication mentioned above would reduce the importance of flexbility constraints in projecting production patterns and would also improve model performance. 6. Risk and Uncertainty -- The model only deals implicitly with risk and uncertainty by means of flexibility constraints. An explicit approach would prove useful to represent farmers behavior under conditions of risk and uncertainty which characterizes the nature ofthe decision process. I 7. Price Expectation Models -- One area of severe limitations in this study is that of product and input prices projections. Improve~ ments of price expectation models or the modeling of demand and supply through a marketing component, thus making price expectations endoge- nous in the model, is considered an important area for future research related to this study. 8. Diffusion of Innovation -- In order to account for the temporal aspects of technology change, a more detailed treatment of the process of diffusion and adoption of new technologies would be an important improvement of the model. 188 9. Income Distribution -- The introduction of new technology would have effects on the income among regions and farm size groups. To study these impacts more than one region should be included with disaggregation in several farm size classes. More important, however, is a detailed treatment of the various sources of income at the firm- household level by farm size. This would require the inclusion of specific income earning activities in the programming model to account for the di-ferent alternatives open to farmers. 10. New Commodities -- The basic structure of the model is assumed constant over time. The same set of activities is maintained constant which means that there is no possibility of introducing new products. This may be a most realistic assumption for the region studied which has a more or less well established cropping pattern. 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In addition there is a set of overlapping equations to account for constraints which hold for all farm size groups simultaneously. The definition of the variables in the recursive linear pro- granming model is as follows: ActivityVector1 Xi(t): Production of rice using draft animal power (ha) x;(t): Production of rice using mechanical power (ha) x;(t): Production of corn using draft animal power (ha) XZ(t): Production of corn using mechanical power (ha); x;(t): Production of wheat using draft animal power (ha) xg(t): Production of wheat using mechanical power (ha) 1For each activity 1 = 1,2, designates farm size groups. 194 195 x;(t): Production of soybeans, following wheat (double cropping), using draft animal power (ha) Xg(t): Production of soybeans, following wheat (double cropping), using mechanical power (ha) x;(t): Production of soybeans, independent of wheat, using draft animal power (ha) ‘ Xflb(t): Production of soybeans, independent of wheat, using mechanical power (ha) x:](t): Production of range natural pasture (ha) x:2(t): Production of Cultivated pasture using draft animal power (ha) x:3(t): Production of cultivated pasture using mechanical power (ha) x:4(t): Production of beef using natural pasture (cow unit) st(t): Production of beef using cultivated pasture (cow unit) x:6(t): Investment in tractors (unit) xf7(t): Investment in combines (unit) x:8(t): Investment in draft animals (unit) Xf9(t): Hiring labor during July-October (hours) Xé%(t): Hiring labor during November-February (hours) x;](t): Hiring labor during March-June (hours) Constraint Vector2 Y}(t): Summer land capacity (ha) Y;(t): Winter land capacity (ha) 2For the constraint vector i = 1,2, designates farm size group con- straints and r designates regional constraints. 196 Y;(t): Irrigated land capacity (ha) Y1(t): Labor capacity in Period 1 (hours) Y;(t): Labor capacity in Period 2 (hours) Y;(t): Labor capacity in Period 3 (hours) Y;(t): Tractor capacity (hours) Y;(t): Combine capacity (hours) Y;(t): Draft animal capacity (hours) Y:b(t): Balance equation transferring total hectares of natural pasture to beef production (ha) Y:](t): Balance equation transferring total hectares of cultivated pasture to beef production (ha) Yf2(t): Balance equation for wheat/soybeans crop rotation using draft animal power (ha) Y:é(t): Balance equation for wheat/soybeans crop rotation using mechanical power (ha) Y:4(t), Y:5(t): Flexbility constraints for rice, upper and lower bounds, respectively (ha) Yflfi(t), Yf7(t): Flexibility constraints for corn, upper and lower bounds, respectively (ha) Y:8(t), Y:9(t): Flexibility constraints for wheat, upper and lower bounds, respectively (ha) Y;0(t), Yg](t): Flexibility constraints for soybeans, independent of wheat, upper and lower bounds, reSpectively (ha) Y;2(t), Yg3(t): Flexibility constraints for natural pasture, upper and lower bounds, respectively (ha) Yg4(t), Y;5(t): Flexibility constraints for soybeans, following wheat, upper and lower bounds, respectively (ha) 197 Y;6(t), Y;}(t): Flexibility constraints for cultivated pasture, upper and lower bounds, respectively (ha) Y¥(t): Regional tractor supply (unit) Y£(t): Regional availability of wage labor, period 1 (hours) Y;(t): Regional availability of wage labor, Period 2 (hours) YZ(t): Regional availability of wage labor, Period 3 (hours) The linear programming model is solved for each year. From one run to another the elements of the base model change as a result of previous solutions of the problem and as a function of projections made exogenously or through other components. The following section describes the mechanisms used for changing the elements of the linear programming model. Qynamic Feedback Mechanisms The iterative nature of the model requires a number of dynamic feedback operators to generate changes in the elements of the model over time. Following is a description of how the objective function coefficients, the constraint vector elements and the input-output coefficients are generated. Objective Function Coefficients: All of the objective function coefficients are time variant. The definition of the coefficient varies with the type of activity in the model. Crop Production Activities: For these activities the objective function coefficients, Zj(t),...,Z:B(t), are defined as one year lag of gross returns minus variable costs and are given by 198 i . + = . . + . . o + . o . ZJ(t l) YLDJ(t) (1 SYLDJj) (l RYLDJ) PYCJ(t) - [PFERT(t) - FERTj(t) + PSEEDj(t) - SEEDj + PTRPI . TRPIj(t) + pTRpp . TRPPj(t) + OINPj + VMCj + CINPj] . (l + 0.5 RINT) where YLD = expected yield (kg/ha) SYLD = yield differential factor due to size (proportion) RYLD = yield differential factor due to mechanization (propor- tion) PYC = average expected producer price (CrS/kg) FERT = fertilizer input (kg/ha) PFERT = average expected fertilizer price (CrS/kg) SEED = seed input (kg/ha) PSEED = average expected price of seed (CrS/kg) TRPI = amount of input transported (kg) PTRPI = input transportation cost (CrS/kg) TRPP = amount of product transported (kg) .PTRPP = product transportation cost (CrS/kg) OINP = expenditure on other inputs (CrS/ha) VMC = variable machinery costs (Cr$/ha) CINP = capital input costs (CrS/ha) } RINT = interest rate (proportion) Pasture Activities: These activities produce intermediary input used for beef production. Their objective function coefficients, 2:](t), 2:2(t), 2:3(t), are negative and contain only the variable costs lagged by one year. 199 i . + =-LRm.+ ‘1' o .+ .0 . ZJ(t 1) J CINPJ PFERT(t) FERTJ PSEEDJ SSEDJ + PTRPI . TRPI + VMCj]. (1 + 0.5 RINT) where RMC = repairs and maintenance costs of fences (CrS/ha) Beef Production Activities: The objective function coef- ficients for the beef production activities, 2:4(t), 2:5(t), are the one year lag of gross returns minus variable costs. i . + = . . . + . - . + . . . - ZJ(t 1) [PROPSJ YFATSJ PROPCJ YFATCJ PROPCCJ YFATCCJ] - PYB(t) - [PBOM - BOM + PSALT - SALT + VETCJJ - - (l + 0.5 RINT) where PROPS = proportion of fat steers output per cow unit (dimensionless) YFATS = yield of meat per fat steer (kg/head) PROPC = proportion of fat cow output per cow unit (dimensionless) YFATC = yield of meat per fat cow (kg/head) PROPCC = proportion of cullcow output per cow unit (dimensionless) YFATCC = yield of meat per cull cow (kg/head) PYB = average expected price of beef (CrS/kg) BOM = bone meal input (kg/cow unit) PBOM = price of bone meal (CrS/kg) SALT = salt input (kg/cow unit) PSALT = price of salt (Cr$/kg) VETC = veterinary costs (Cr$/cow unit) 200 Investment Activities: The investment costs of these activi- ties, Z{%(t), 2:7(t), Zf8(t), are composed of depreciation and interest charges on capital computed as follows: 1' - - . Zj(t+l) - [(PAQj(t) PSLj(t))/NLIFj + (PAQj(t) + PSLj(T)) 0.5 RINT] where PAQ = acquisition price (CrS/unit) PSL = salvage value (CrS/unit) NLIF = number of years of life of the investment (years) Labor HiringrActivities: For these activities the objective function coefficients, 2:5(t), Z£0(t), 2;](t), are simply the expected wage rate, WAGE, lagged by one year. Z}(t+l) = - WAGE(t) This completes the specification of how the objective function coefficients are generated. In the equations above variables without a time subscript are constant over time. Crop yields are determined usingfertilizer response functions. Prices are projected using simple expectation models. For a specific activity the amount of an input nay be zero, when the activity does not use that input. Constraint Vector Elements: Projection of resource capacities are exogenous to the model. The computation of the elements of the constraint vector is described by the following equations: Summer and Winter Land: Y}(t) = BCCij(t) - TLAND(t); i = 1,2 where 201 th th v} = amount of j type of land available in 1 size (ha) BCCij = proportion of jth type of land in ith size (dimensionless) TLANO = total land available (ha) The variable TLAND is determined as follows: TLAND(t) = TLAND(t-l) + DT/DEL - (TLCP - TLAND(t-1)) where TLCP = upper bound on total land capacity (ha) DT = time increment DEL = average lag (years) Irrigated Land: Y;(t) = Y;(t-l) . (1 + 8C2],i) where Y; = amount of irrigated land available in size i (ha) 8C2],i = annual rate of change (dimensionless) Labor Cgpacity: Y;(t) = BCCj(t) . ACFPOP(t); j = 4,5,6 ACFPOP(t) = ACFPOP(t-1) - (1 + BT1) BCCj(t) = BCCJ(t-1) + DT/DEL - (BBAR - BCCj(t-1)) where Y} = labor capacity in period j for size i (hours) . ACFPOP = projected active agricultural family labor force (man-equivalent) BTl = annual rate of growth of labor force (dimensionless) BCC = working time equivalent (hours/man-equivalent/period) BBAR = upper bound on working time equivalent (hours/man- equivalent/period) 202 Tractor Capacity: Y;(t) = Y;(t-l) - (l - BC1) + 8C2 - x:6(t-l) where Y; = tractor capacity for size 1 (hours) BCl = depreciation rate (dimensionleSs) 8C2 = working capacity of tractor (hours/unit) Xi% = investment 1n tractors (unit) I Combine Capacity: Y;(t) = Y;(t-l) - (l - 8C3) + BC4 - xf7(t-l) where Y; = combine capacity for size i (hours) 8C3 = depreciation rate (dimensionless) 8C4 = working capacity of combine (hours/unit) xf7 = investment in combines (unit) Draft Animal Capacity: i "' i o _- o i .- Y9(t) - Y9(t-1) (l BC5) + BC6 X18(t l) where. < do 11 9 draft animal capacity for size i (hours) 8C5 depreciation rate (dimensionless) BC6 working capacity 0f animal (hours/unit) XYB = investment in draft animals (unit) Balance Egpations: 1 _ 1. — i _ I O Yi3(t) ‘ 203 Flexibility Constraints: i _ i Yj(t) - Xj(t-l) - (l + BCj) where Y} = upper and lower bounds on cr0p and pasture hectarage (ha) X} = optimum level of the activityirlthe previous period (ha) BC = flexibility coefficients (dimensionless) Regional Sppply of Tractors: v;‘(t) = Y;(t+l) . (l + 816) where Y: = regional availability of tractors (unit) 8T6 = annual growth rate of tractor supply (dimensionless) Regional Availability of Wage Labor: Yg(t) = BCCj(t) - ACWPOP(t); j = 2,3,4 ACWPOP(t) = ACWPOP(t-l)'- (1 + BT2) where Y; = regional wage labor availability in period j (hours) ACWPOP = projected active agricultural wage labor force (man-equivalent) 812 = annual rate of growth of labor force (dimensionless) BCC = as defined above. Input-Output Coefficients: Some of the input-output coefficients are constant over the whole projection period. Others vary through time and are exogenously changed for each year reflecting changes in production processes. The changes are related to requirements of labor, draft animal and tractor hours for the various production activities. Since the definition of 204 these changes are simple and rather Specific their description is given in the first part of Chapter VI, when presenting the procedures used for model application in analyzing the inpacts of alternative produc- tion technologies. Data used to implement the model are contained in the computer program given in Appendix C. The definition of the variables and coef- ficients in the program is the same as in Appendix A. APPENDIX B A SAMPLE OF THE YEARLY OUTPUT RESULTS OF THE MODEL 205 -197Io 10 - _ _1. RE§OURGE ALLocAiIou. cowsvnaxwts. ALTERNATIVE YAQLE SNADOI PRICE SLACK --—-_._- VALUE USED Yves- !£”§-__. NC. SHALL FAQHSISOICOHAO —v AAARRRRRRAAAAAAAAAAAAAAA AA NHHHHHHHHHHHHHHHHHHHHHHHM NH ccccccccccccccccccccccccccc .039030990373505000906090 0.. 20300335500 h 095501.67 06050 ..OOOOOOOOOOOOOOO000.00.... 008880523905090839070 0‘ n. 6 7 3 2 O o 1. 5 o z 1. o 1 o o o o o . ““pp 9.RRPAA“‘A‘A .“AAA‘.“ "NHNHHHNHHHHNHHHNHHNHHHHHHH "HHHHHHHHHNHHHHNHHHHHHHH“in" TTTTTTVTTTTYTTTYTTTYTYTTTYT 92965256b00010502060106thO6 0.0.00.0.000000000000000000 007938535000505020503010009 533.45993 “29.65.53 1. 1.22336 2 z 9 I. 511212 772Q26 2‘7 5 ‘AARRRRRR‘A ‘:A“A‘AA“A‘A “NHHHHHNHHHM MHHHMHHHMHHHHHHHHMHHHHHHHHH TTTTTTTTTTTTTTTTTTTTTTTTTTT 065679567000109209339210363 OOOOIOOOIOCOOOOOO0.0.0.0... 25581:... 131500055527 8703 633369 013553510 #353 w7ls70.-.03157 7316.00.35 21 36212159 1 56 20.03 .0 o 1 31. 3.99 2 6 1 1 33333333333333-33333333333- 000...... 0.0-0.....OafioO. 3533533335‘353553355053 ooPTTDO TT TT 000123PPA$SRO NNSSTTSS NNN AACAATH AAAAHHAA AAADODCC Po TT..:..PDNHPP LLL: ii. i HH. ....NNAAP. D PPPRET‘ILYVCCD R.CC.YYTT""LL Q9 0 CJNAUCOIIOCHHOOAACOUU ....:C.d .KQTIA N CC.SG hcsbfl ”SSH Nrusabc N TIC...O.LR. n.NRBGSAHTLLLLXIMNKM‘N‘NXNIN U... ‘AAARO: AAAAAIAIAIAEAlAzAX SMILLLV 333.3331 n i‘u I Q! filiflifl 121.8561 596.123... 557 I 90123.... .07.. 311.051.5111 1 Aw‘ZQLflLa £9.2«t [APFE FA’HSO ’15CHA’ AAARD‘RQRDAAAAAAAAAAAAAAAAAA HHNHHHHHHNHHNHHHHHHHHHHHHHH I’llIII/IIIIIIIIIIIIIIIII/l (0.333.390 9.05.330 CO 0.0.2.305... Q. Q: RGPCFRRF‘PPRD.FEFF¢R§PQ DER gcccccccccccccccccccccccc “(59990066300100.3108 020-00306 02980800006.u060080107000733 .00000.......OOOOOOOOOOOOOO 05°....O.ZQOODOO5O3OZOOOHOJ $3 5 2 5 2 o .1 1 3 u "2 IAAOQRRQRAAAAAAAAAAAAAAAAAA HHHHHHNHHHHHNNHHHHNHHHHHHHH NHNHHN“HNNNHNHHHHHNHHHHNHHH TTTTTTTTTTTTTTTTTTTTTTTTTTT rg§z1goaagoouzos.;35. U20 ‘A‘RRRRRR“I“‘ HHHHHHHHHHHHHHH HM." To HHHHHHHHHHHM TTTTTTTTTTTT 10.0.0005 1.700....051133 Q “195555 31‘99990? 632‘“?72290 33 051. “AV.“ “ 3-333333333-33-33333333333 .OOOOOOOO GOO-00......O... 333533533533333533353‘33 I O’clolcc moo 123PPASSD. 0 TT 7.! NSSTTSS AAAAHHAA TTE.PPNNPP ll. ...tNoIAAJQ PPPREITLYYCC.» n .cEYYTTYV LL PR. 9 CNNAUCCIIOCHHOOAACOUU ...C..:U. o. n ..o 'leAhNCSS.’ .rccu HQ.SM¢.N.\:\.CC HTIOPOCS 119x533.»‘TLLLL‘N‘V'NXN‘N‘N‘N JIRGAA: OF autuon‘A.AouIIuvAadv.4-Ioao£x §.VY.LLLV P215525?! 1 Q I i Q a?! i n. ‘ Ni a. “35.123555? 90 00.9.3hse 7 2‘ 33333333333.» a... L b .5 b... ‘0 30.23 A. b 5555:. REGIONAL COWSTPAINTS 3333 O O O O ‘1‘“. K. 67‘. ‘o—H.C.‘o - :204L 206 _19700 10 2. RESOURCE ALLOCATION. ACTIVITIES. ALTERNATIVE TABLE mesa» coEFiSEIE¥$ °'Ii382 NAME N00 SNALL FAQHSlO-1CONAD T001000! 11111 AAAAAAAAAAAAANNNNNFRR HHHHHHHHRHHHHUUUUUHHH III/II/IIIIIIIIIIIIII 2338398T13030109319$1 PRPPFFEFPRCCFRCFRKRFF CCCCCCCCCCCCCCCCCCCCC 00.309000000003035999 00000003000000C009066 000 00 0000000 000000000 0 0 0 0 0 0 0 009 o u c 0 0 0 0 O 0 839 0 0 0 0 0 0 .071 U 0 O 0 0 0 3. o 0 0 0 O 0 0 o o O 0 I 0 0. 0 0 0 0 0 0 0 0 0 O O 0 0 0 0 0 0 0 0 0 I 0 O 0 0 0 0 0 0 0 0 0 O C O O 0 0 O O O 0 0 C 0 O 0 0 0 .... (.2 .2... 0. ...,... 2 0.. 0.0. 0.002.192. RRPRRP REPERRPO‘RPP RRRP. CCCP. cc CCCCCCCCCCC CE 0 70 no. 50 60 4990 5770031999 0 .00 90 50 60 .670 691800559 000 00 00 00000000000000 0 90 50 90 30 360 “33006 c o o 0 [0 5. 0.0 7.0 7 .0 0.17605 050 020101 0.11.17. 0 0 0 0 O 0 3° 0 u 0 0 0 0 c o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O O O C 0 .ITT 111 NNN ‘PPIP‘Aflfi‘PA‘UUUUURRR HHNHHHHHHHHHHCC "H" CH1 HHNHHHHHNHHHHHHRONHJ‘H TVTTTTTTTTTTTTTTCATTT 0023.80020659808J 000000000000000000000 asgaaguuoeodZSdcoso 3 7 3 7r. 52?. u 3 2 20 151 1 3 1 Toes.) H 023 DOOOQKKO‘ ‘R..I . TPTH HHAAAIANCiCcLLL TTHHECS PP TCD ......NNA"IBA.U Fr. .12.... CCQREEYVVYTLLELTIiikfl 1130 1 F3DUOAUJ....;VN N 11 a..... x .H 030.550.334.3v1f. 44 0 1233561 491912365.» 7 I. 901 111111111122 LJRGE FAQ‘S! DldGNA) TTTTT 11111 A‘AA‘AAAPAIAINNNNNRD P _ HHHHNHHHHHHRHUUUUUHNH. lll/IIIIIIIIIIIIIIIII T’SST099‘933333503333. .- PPRRRRD RFPPRED kkPFFR. CCCCCCCCCCCCCCCCCCCCC 0 00 000 10. a. 000 nag-.0030 0 .00 00 00 00 000 33300.05... .00 00 00 00 00 000000000 0 0 0.0.0. 0. 00.3 0 0 0 0 0 0 0° 0 0 0 0 0 0 .07 0 0 0 0 0 0 3. 0 0 0 0 0 0 .- _ 0 0 0 O 0 0 _ 0 0 0 0 0 0 0 0 0 0 0 0 _ 0 0 0 0 0 0 O 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 0 0 0.0.0.0100 0.0.0.30 300.00.30.00 .0 RRO RRRRRRRRD. P P. RRRQRRP CCCCCCCCCCCCCCCCCCCCC. O o. o. a. 6. 99. .d'7001999. 080002030360“38006.... 0 b0 .00 10 30 9 o 0 517.650. 050 030101 0 .1107. 0 O 0 I 0 O 3. O O O C O O o o . 0 O O O 0 O O O O O O O a O 0 0 O O 0 cl 0 C O I O O 0 .IOIT 5 7.0.01 2 . "NH 7 ‘23‘2‘2‘1‘2‘PUUUUURPR HHHHHNHHHHHHHCC M. "NH c I HHHHHHHHNHHHHNHRONHHH TTTTTTTTTTTTTTTTCATTT I oaégnh1gzo.005é 00 0000000000000000000005 0590203607. ”0308“,?) R 6 2 9 62 .5 “1 2°. “2 c 3 “ 7 29 393 770.. 9 3 5.09 To 0g~ H. ~ 2 0‘ .N .063 .30. T m. ...” 10:55 "1.23 U23) 0 flODDSROAPR.r—I VOW, 7111133....711 0 T719501. 0.1.5.0712... OTWTTNNLSSAUAHTAidolAR H- HH‘JAAANP. :‘UFLLL-TR:_3 #90 ...-co ...»... ADS VB..1//.1.......U FF .... ...... ..TNC ...v‘. ....YT'VvlLl-o: ..10'03 3.3 o 040101..— .Ud #fi»1...1..30nUU .. ..NNNIII. a.. a: ‘-\.:.-\..\.Va ..0 031.501.1010” 4 d. (S vznun a P O ”E 2380.67 A. 0 9123.056? 0. O 22.0232223333333336 N'U‘ri'p. Cr 55 T1 NJ‘ C 60 b .E ..--..--- p F 207 ocno¢no o~n~u okhOhho annouoc omnuu ouccnhn commas» oONNu ooohnon zom .a~:.ouu .mwnu .-d«¢a« .~n¢a«. .-«« .nm-- .-a.o~ .ooad .mccns~ pamx: .-.msm~ .“n;« .mnnaosu .unoooo ..n;u .mnaso: .a.cooon ..nca .ao-nm~ zaou .o-sao. .domn ..cwoao ..uoqa.. ..aan ..moaan .onwooe .:s:n .~.oan« you. 3...... ---.fim. ..2 ‘ 4%... mm: . a..." ‘ s. 3- -----mm.-...-um-- - - ----4 . w o p p z a . an m o u ‘ 3m x a . u w 4 ¢ 2 w n ..sau .« u>~p ..uu. .4 ago.» . -- “mnwmuu ’, .. .ummmwmu 1 amm w - .mco‘:». zoupmouoma no “3mm, 4. or omw mmh ouonm: emu mahmqu JQmDhaz 3? m: . oaNo .«mnmo .szo uxapmca om»«>.»4:u oynm: .zo». zonhusnoua mums a... ou.a no.9 “amouma .m .o .a «mug ONNqurwuz.zoz a .99“ mo.acw ao.aou hzumuua .mo«;»cc own. Nu .a~;.e- «wu‘ cu~u..¢zumz .41. zo»».-z<:oux ..~nnnsnu .«««»~¢a .s«~onon maahmqm dqu=h¢z ..u«o¢m .wamson .~wmom« uzapmqu cu q»~ 42g .M~w*mm .«wcnmn .omsnan zqum om . ~ « .nmw~ s .ooocs~ S 1: .mmnoos .mn so: . .ou-mna amen unmwwmmn ”wmwuwwd ”~wwmmw~ “MW“ “or“ .nam~e~ou .so.~a«~« .mummuuo . «mac ou~uauw= 4.~m» .42. mm: OZCJ 4.»om1 -1 mzamm-mumm4 ' m:¢.u admrm ‘ ‘ . xmwm' - -- . ‘ -.-o« .« m’HM¢z¢u»4« .mwmamua paupao‘m=m~¢.. .» ‘q- ~40.» TOle EXPEN o It“ CRSI VILUENQGTgTHEfi (TH CR?) 1970. VALUE (TH CRII' S E E D 19 QUANTIYY I7H K5! R--- E (7H CR3! W ‘ ‘ ‘ Mu s. UYILIZATION of AGRXCULTUDIL xupurs. ILTERNATIVE '51 CUAN (7H KGI 7337333: SIZE SHALL FAQHSIJ-IJIHII LARGE FAIHSI >IIIHAI TIBLE ZCHB II‘O‘NOII‘I O ~Do¢wfl~ b o o O C O O . Nkmnr: u N054: N WON: OI WG-0“ HI JJIJod 8 (I I I . INBHMND n Orww~av n o o o o 0 I I nuance: h k N II CONN v-III I ”’0‘“ ”I J oI ¢I I I-I 00. can 00050 ooocNchneu I I OI ooh Ham decH whacJMQQQI I I bl Ork- v-I. {Iona Och-0.0.00 I «won Uh'd o vma IANMHD Mcusau I _; Imocl a no NMMIM cuOuraI I It” I) 3 can: umuwdl I II N N ”80‘ Cd I who to OII v-I NOWNVd h I4I o o o o o 0 9| U‘NU‘U‘U‘ In II IIIII 0‘0:th :I C WNo-IO 0‘ oauuvn Q I I J o I I our ' I I . I. I 3 I I I I ?I I l I 0.0 00" 0000*“ ooocddU‘MII I U I Ohm '65 ”Man MdMNka-I I M30 D II ‘I ma ID". € 0000 O‘dnooooool owns” 91 ‘ on LI was mc~ 3 «a NJON nnNou o o o o o 0 GI I I On” MC 0 o JWN NC‘IA- II “Lyn In 8 MI .0 vI Id: ra~: In: I 1'3-33m I 0 9| 0 VII M ¢~~ 0Q Means I d «I d oI c I FWMDNN. (I In OI“ J: O vI I I I I I I " I u 3 u 03mg: OII H I I ”NOW Ix II .- I I o o o o o o I ‘ (III I QHNNnO o 2 I II 0.0 0.5 ooc$J~ Coodnuhflnk uwu=N¢> an 8 «I IDHGI 9cm: kumon runwkuwnsdcl DOOQIB II III QI “VI-Q O N OQU U‘UI'. on. 0 col 25::uw~ .3" hi kI Irwus c: c v“: hmmom rhflkn" mm vI J I N000 o o NIP ON 0")”6‘4 N C .1: o N NINA 80‘ ..I o vI 690 v4 1 0 fl I ‘ In 1’ I I: (III I O I I 0 I I I 8010700 6‘ Z I «*an 0‘ H I I o o o o a CI I II U 3804: 3 MI 0 g I C as ooaumn '0 z 0 ¢ ¢ Nfifioh o (I h D- I OI’ON ’3 I I O a .00. m mm N I- I :- qu 01 «row-mm N :I h «to u- ‘\uw¢m ‘9‘ ma- Iu< ha oflo'\“~1naq OI- VII-(YI- O: “‘0' O'JJI > I 0 «014‘: 10 nutv 0| 0 z a In y. p- a ‘I' L z I 4 am ah- or O vzm- (IHZI II x xx xv w mun pt >km H" w . II a: x 4 :wwo» N'Q>h «m I W I In: 'u n ‘r I34 PFNEQ. t: byw15?vu D I 11% IHh macaw OMIH’M OII r- _II o I I-I P" #10 u- I.) Ulh’oanUO’ I In (I 0 I Iv unr- n m \r z'Dvr-o- 1.3-n I a bI I rII h~.J ‘\ cr4_KD r“; hcaumrugo ch OI I I m 0:100 Int-torn 2 '1 I- I I I mt 0mm I) Ottd fHIanfiluILu. I L—m o I I I Iu‘so-o «ctr 'IYHsaJ n r fin”! On I wzth JI I 2 ch Q 22\ qtcoazo I Uu m>4 <1 I I ,3qu .13 1 In cuur kfldtrQHQI-I— I I0' ZI I ¢ u ZzI uuzmu OI NI uhh c O uhbbh who uWHme H I .J I Out; I. H ouuuu m MOW UL: I OI IT I 044 a...» 61:44.: CINJLGOFUQ’ In I «I I «1.1.: Hunt 40’). n. l II"UQ‘I JQDIL‘M. 3 I I- I I)“ JI-ODI- 02>44QZQ¢ I APPENDIX C COMPUTER PROGRAM GOO GOO O 00 ZCHB PPOGPAN RGSPLPIOU'PUY.YNDUY,TAPE6:cn'PuV, YIP :. ~1vou7I cannon ILPAC/ 3:54.623‘ VI‘II. ?(u?). ONI’ lcfigl. IXISI % :étrggé .OUIIBI. SILLoI. (10; I. we. N95. NR°. cannon ICNIRLCI cf: 35L. O'L? xvr. uva. vrAr. vrAcn. IALI.Lucur.LLi~ 'IwLP I086. VLocu.uTL.u A.w§Lcu.u¥ACH INITIALIZATION ' 1V9 : 6 CALL CMTRL CALL INA CALL IPV SINULAIICN THPOUGH VINE on so tvg- .NYR YEAP = :A or LI~EAP PROGPAHHING MODEL CALL LPPU C‘LLDET53HINE PRICES. VIELDS. Etc. 50 OUTPUT FPO? H006; CALL ACC’G (Y. n=8.AC .Nte.A.OEJ.NP.NC.z.IY°I cAL PDT Tout an INUE EN 0 SUBROUTINEfiACCTG IY;NPP;X.NCB.A.OBJ9"R.NC¢Z.IYRI ACCOUNVING RCUTINE - PERFORHANCE CQI'ERIA cannon IBINPCI anné PEOH. SAL? PSALT ISTCIZI. PPOPCtzI. Q are rCIZI . “91°§(2)I éPAICIzI.' IPA ccczI. vrArs¢2I . Avnv connou chnpc/ ALPHAISIo AVPv0téI. BETAISI CINPISI¥ CINPPIZI. réPYISI. crara, PF. . Plro. P (SI PFPPTP PoIISI, oruPISI. PsarnIPI Psseofi ¢?RPI(§). P1Q°.P, PTPPPIe : :1c« 3. s sotéI. a seePPs vnc¢12 zI. VHCP. Ps.c:F(5I. YBASEISI. s PVCHIAI YLDDIS cannon ISVSVC/ ACPPCPIEI AcuPon va. ¢YCIPI QINYo % PVchzI. §VLots.zI. rLuNo. ILCI. uACr VLocsI connou IACCVARI A=CSI6.2I APSIzI.TUAsx2I.APCIsI.AQ.YUA I A~CQ.EC 5555355535 .JJIiJJniJlliJJAZQJAZJJIKJJlfidJIfl!JIi!JI1¢Jl?IIA§II s E I .... I V I '- o c 1 I: L 11112 A 77991 N O. O 9 O 1 o 8.656.“ 1 11111 1| 1‘111 1 D 00.... A 0‘ 1'1”, '1 LLLLL TYYTT or HHHHH 0 g o o o o 1 o o o 0 0 J2 S 11111 1 T 11111 9 0 N 19 E 1 .9. O. ‘1 I J -1, 1 ‘ c 9 1’ :11) 13 O 1 1 86111 J1 . F 1 9 9 0 O Q 9 1 1 F K ‘ 55.7.0“ 77 ‘1 m m A‘fl“ A‘ "VI c o L on o a 1 O o O a 0 Z. O o. S 80880 a O 2.10.0.3). 0000000“ .380 LLLLL I.“ L 11 T R 10800802 TRCN TTTTT. 11" 1 9 1 ad "9 o . ‘NNO HHHHH 9H“ H o: N 003:333333 CovJ Z 1 1 I I 11 8 I11 33...... a... N 8|. Mu 88811111, [.389 it), uh J 1 ‘ J1- 1 IJ 2222:2421 pre 11C n3 o 13 93 L 111111118 U FN 8&111 T JJ1 .l 011 F. 03.4 v o o o o o 91 DJJNP. 9911' c 1'. F 2'. 8895591671 556.” 56.» b.» A 77 A 99 I 1229 ITO 11111 F 011 P 011 00111111111 001.CN AAAAA T 0AA O 0AA ODAAAAAAAAA DOAKE a... \U c o 1 z 6 5 8 C E C C 8 8 23‘ {$031 ”A! ‘2 .lTTilQOflFXkIYTéLUOnfiu E...e.:1LLFFeE.E-:Ir¢1 555$... .C.CCSSSSQ RD D 98886 JP EPFPBGGGG c c a 9 N ‘ 0 s O 9! ll N R c. . 1 E 1 c Y D I z 0 F 1 0 an F F or. o E . 1 1 o E 0 P4, I c '6 g ' 8H8 I 1 8 00c 3 0 961A 1 3 G Y 11'- O .... l. 9 9V 9. D‘ Y 1" H1 ‘ Y P 0 Ice 0 E I A YT L18 V 1 V 1 OTC.) 1 v! o “Qua; a In P: 1 O O 0 Fa H 3C.» 08 o l. I LLTC K a F Y. .... OHA s C no! '3 I I 1 E ULBB B I H OCT 0 K 1’ 'I LU" O I O 1 B l. 9’. 9 1 Z O 1 o CHAR- I ‘1 T TC 6 9 11 8 OLD 1 1 P6,, 7.51.4.1 1 chtI. .3 CIVDB 0| ER. 1 O at. a 11 T T I v o.(( E u c 1 cc 5 P L I L 1ccc B H R c F. ‘183 c T F g E c N C 1 .. I a a N c 8 1' 1 0! I I 8 I1!” 9.. .... 18 1241?. U a“ N N 1 O V O O 8 O O 0’ 1122 R n H 7.1 1111 B H H 1 Chvcc U 0 O 0' C86 5 c c 08 886D. 12 1 o 2 ccc c c m 909015.. 11112222?- YTYTTVYYY :EééecEEE 503935555-35 PaBBPPBEB “91! O (DT/DELD‘CSBAE-8001ho1’l 501’ “91’ 82611.1) 2155 23‘5112’33‘9012356‘5 1 11 11 YTYYILLYILLYYIYTIIT NNNNO ... 9. ND. : c NNQNNDD NM tribal...“ JJCGJJCCGCCGGCC . H 1 C o o. u l H as. O Y H C 9 L F T I H C... 9 VG A DJ" vl One H 311 9 Yo? L MPH T L9 H OH” 1 0 91C H E VTL C 2 IoT D I "H L L 119 V ‘ 3Uh 9 1 thl G T 59" n I Dvl’ D N U I 1 1CT 9 LUH 1 S rLo L R P.” I ..r '18 1 T 910 1 E VAL R L ” rIY V- O 2 Q 3‘ I N. 1 h P L 20. C 9 0590 L 1 1:71 E 0 N 929‘ O N O C ”11...... 06 I T I 513 '63 n N U13 1 088 1 0 N SILT. I :1 N C C 0 1A0 8 PT? P H NOHRR JILUU B H IAQAALL HOTD ! n "EnrfFErvUrN S C LFFYYDDDTLRE 12 0. o 1 066 C m 2315112236239012365670901239567098123$567899123b5670 1111111111222222222233333333336hh666huh CSCCCCC AllIILLRIIYIAIAI‘IRI‘hlfiAlfilllllllfillltllfillfllllAlAA NNNNoFQDoPINNNflNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN IIIIGJJLGL711!!!IIIIIIIIIIIIIIIIIIII1111111111111!!! n was» $.‘Ng. "as: use. 0 9 1 P 3 1 1 E 5 V 63 1 1a Q: 1 9 X1 T t 1 X F 1 .1 E o E! JC 1 '6 Q.“ 5 ENG 1 T 90C 0 1 N 9‘1“ II! 2 E '- 110 .U H "D H 72L 9 E L961 7 L ."H11 1 F. 9C2.) c VTL 9| 7 1.1,! X N "1“,- ... A 11 9.1..“ T- '1 3UIFC.1 s LI'I10I O N F. 9" YU \l 0 ”0| 1 o la C UL.1 5 CAST \I C E. LUN Z '87 H 9L9~|C1 T n. 9H 03 NF TCCC. vl 5 1L051 1X .t Ta»L1Y.C— L 2 CIYAPNT 1 L I I A C N I L I I oon.0000000000.0000000000000000...coo I A T o o W N N P X190 a8883accusatillssssatx88888388888838: I C L T11 1 I l ’3 8 I 1,111,1111111‘!”1,111,111-11111111’1 F k N N NIJ 111112222233335hh5555566657777RGBRQ9Q U N 1 o T. o 0 90R.J 1911011111111911111111111110111111111 R H H H11 0 123“5123“5126712672259569225.5238512° B H H .H I 11 11 111 111 122 122 U 0 O 0001 111111111111111111111111111111111111 S C C 2CDDA IIAAA‘AI‘AAI‘IDA‘AAALAflAAA‘flAAAAAAAAA 12 1 r0. 1 CCC C 216 901233567C90123“567390123~567090123‘56739.123,5390123‘5667. L5:55955‘:55566666666777777777788638I98889999 9 111111199 _ 0 655555655 AIAAMIAAAAAAIIAAAAll!I11111111ll1111AllililfilleIIIIIIIIII NNNNHNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNDNDRD990RD MN I 7.7.9 .17.? .117. .111111.17111111111117.111116716COGGCC IT. - J , 1 Q .l 3 3 J J R v v N I 1 1 l 1 1 J 2 R C o 1 1 T I I X X 1 E E 1 8 T T T X 0 o O 8 1 .... 8 8 so 01- J T 333577720 305 3 O .1 u! 00.0000.00000000000000.0000.“001000000088J R38 E 8988 111111111111111111113332333121212111111RCO RCC T RPCC . . o a .- . e c 9N3 NNN I TNNNN z8:828:88:3888888888888888888888888888899C 999 C 90600 11K 111 I 11J1J 3’11,,13,133,131,33333133,,3133’33,,’,,8 3 I 8 3 O L 8 = '3 In: QJJJO111112222233133Lhbb‘55566783990011111 1J3 P IJIJIU 11111111111111111111111111111111112222 O P. U 1 1NN 099'0V00099001000900!9!!!!9'99999’!’OQV‘LOR O‘DN o 923kCIR- 112111232312167121676565“56175690L657665:.R 66o 99T9TTU‘ 2 2.2 122 122 122 5 1 5 5 5 N 2 X XNTD 111111111 111111111111111111111111111111 001 0.01 GOERJEOFN ‘flfiflnfitflflflaflfllu‘fl‘fi‘filAAA‘AA‘AA‘AAAAA‘AAFCA c0“ OPTOTCRI 0 9 2 LG . 5 5 9 99 2365237390123§567090123 1111111112222 939599983398‘9 NNNNNNNNNNNNMNN IIIIIIIIIIIIII! 86: Inc ms 9 053 05° 03° 33° 01,. 012 J 2 O O z o 0 m 1 o o 1 o c O O I 5 b“... C fur-r.- 9 3° 1 o o o ’ ’ , ' C C 0 0.0.4 an...) 3 1L". 1“6 2 O31 031 O o O o o S ‘- 0 0 O 'l 1 c 3.5—.... N c, a fl..l.c E C6 9 03° 1 a: 0 1 O o o c b 9 9 9 O 9 9 Y. 91 035 000 F ’9! 955 0.55 F 28 fwd-.0 rZUad E 0' a o o o o o O 1 2.. 2.. 999 C 2 9 ... 666 ‘8 7 Q‘Qc-J 8 CS 9 00° 1.. 1 o o 0 K. 9 O U V 9 I 9 9’ o 15 flogbzcahz 9‘ 17131710 5 A ICE 0 0 db 0 N B O o o o o 0 BE 9 9 9 I D a 853 'l 9 7 use: _ C 29 9 000 _ E A, 1 o o o _ J 6 9 O O O O O O O o 1 0303 033.". _ P .1?! .UQ.s ......LQ 008 . F ‘8 oo11cas11 . nu O O o“ o 0 06 u s z. o .2. o .N B E B I .N I I Y 1 R C T R . E F N I ‘ s c ‘ Q I 0 9 9 O O 0v I 9| 9 TIOBAZHXLLC; . 1 E I 5 100013035 T u N No 0131 0131M. B I N 08 o o o o o 1 V K T 0 C T c H N ‘ o H T T L O a A 8 C O O 1 123h5676 123 CCC CC CC #56739012365 222222333313 33998393 .133 NNNNNNNNNNNN IIIIZTYIITII O OI £35 etc on; O O o C ' Q 555 300 no 0 o o I O a a 9 O Q a 665 o .1100 6 co 0 o o I I O I 5 3 z 2 0 z O o 1 1 O O O o 1 : 655 7 o J 030 9 0 no 0 1 C \l o o 6 O 1 9 8 NI 5 7 = I O 0 I C.) 9 0 2° .1! D 0 J I1 9 9 I a. 2’ C s N c C C. O 0‘ a a 1n. 1 N 13. 1 I “ A T TT T D | fin A N 0 F0 0 E 556 C C C C 217 9.36523023651123610136508053607.3922564236.9019355670901233“ 59013335567801236567890 111111 1122222222223 1.1333111133656656 “LC-52.5555 666 66666: 67? 9 7777 7775 NNNNCCCCCCC CC NNNNNN NNNNNNNNNNNNN N NNN. NNNNNNNNNNNNNNNNNN NNN NNNNNNNNNNNNNNNNNN 00000 PPD D o 9 OCCDVV00000000000000000000000003000000000000OOOOOOOCOOOC CCCOO0AA000000000000000000 P. P ... C NNNNN NNIIIISSILLCP PuCCCICCCCPJC CCPaCCPJIPaCCCTOLIIn :CCPCCCPJCCCCCCWCCI ITCCQ‘IPJPaCCnIP n PJCCC. .C c CCCC NNNNTT751T1750coYYor... NNNNNNDNNNNNN NNNNNNDNRNNNDFOCINNNNNNNNNNNNNN "NP. POONNNDONNNNNNNNNNNNNNNNNN T1173. PD. CCFCCCCGSSGJJIIIIIIGT.11117.717¢TIICIGIIIGCf 57111171911171.1110 5067.17.66 7711111117.!1TTITV .1 0 0 Z O a! O 9 III I II II 9 9 OIIII II I D ’1 0n.- 0 5 a 0 0809 0%.. “I. 7 v 0 1:5 005 3 00 933303111 22 1 TON-6" H 050 N no 0700000". .0 0 2|! 1’00 6. C 601 2 5 To, 0 O ‘2 C5? ES E 01 o 1 3 3 Cl. (...CA G D .... I? r .0 r A 7 0 0C To P Y NW 0 n T R . . 7 N 3 PA (.7717 1 A 777 ...! 77 970777007 . 07 9 r P913... To .... no) 0 C0 N 9.... a. chain”. a“ u LA. 7 9' N 5!: 3 o v. 1.50 v.0 0 00 303513111 2?. 1 .l 7.0(Cl‘109 $00 90 7. no 07000090 . oo o 2 7 Co 0H9... HTC 9 N00 P... T 5 5050 o o s I.) p 1;... CCL F C o o A 1 2 2 p... 62 off 0 OT A 7. R Z G T‘ Tare. C AC E 7 T p: T I A CC C. P‘s PY 7 V6 C 7. A N N VT 1. o r P D0 8H N 7. F. A 9 A AH 97. ON 90C 0090 L! H E H 79 797097999 0 6.99 II 0 or M. C33 0 T A 9A r 11. o 7.2 N R C 05 .V 00151 A“ N 2&9 on. L TYCr F.HPP 30L Y T 661 70 U E 00 50010111 A 1“.“ 66 Z L H7019C TVT NC“ I 09:3 97 P T In 0. 00.0000 CC I... F... o A .7 Pv P. LO L v 5506 91 F. S 3 0505 o 0 SI 7. 36 5’0. 9 thV a) O QMH N o F o T A 0 1 2 z T T .5 P2 1:.1 P II PC 0 F P. N 5 58 P In 1500 0 9 DZ YTL D. 0 A A ..r. 02 F. ve..B( D! 0 o I T S N 0 C C1 F T3 VP. 9 97333.10 5 NH ... A In) c. ... 7. Z LnJDYP’:1.SH( 10 900! I N T 7. 09370790799. No B. 07! 9! 0 AF VFY... : CDTCC 10A 9... o T1CA A 1 309.... oOGEG oh“ C Fl N56 0 g 0 . SD A V0 (7 1.005 LTLI‘I 9265 029.: V. s 00 0259A0111 I 7. A11 00 6 Ar 7... (LA Y..— 6 ON .... 060 UZCB 1 0 on. 01 o o o o g T O III/II IL 0 o o 00 o 7 o 0 F0 070. 151.07. 7 20 0“ I 02.17 T. R N0 9.370 o o 7.0 215 o o o o 5 s 00 .T H) o P 9H ‘1 0 UL 7.1 0 IC 0 QC 1. 0 A1 3 3 52 117.000 .00 P 5‘. t. C7.” 9 TV 7 1,. 0L 0T. L o a. s U F 7.1 o O 0297 QE 0 6 0 n.(9.: I v... 7.)!)YLHH S 7. 069 9 VIC I 5 I07. A38 6T 0 P. C S or.((co(.:.sp3 ...Lo R T ..6 ZR 7. L E 0. C o S C N "1......IT75 (TC! .0 9H E R L oN 10 7. 0. A5 T SC I r 0 N L O ATHTFOUHFPD... Tr. T E907 97.93? C“ 10012907999779 I a..-A 000779 90.1 0 .voIIII 00 IA! 7. NOAP v r 9 c CIFLG 9L0 E F97 o 1 ABE/7 0090 0 0010.1 oh“ I 0 905698 0 o 0 OX 7. «9:..th o o 97.7 T 0: Fl... Fv r VLF YATIL H 3335 v 1.. .../TIP, 7. N 30 03.0131111I BI3 .789051090 I OE T 32290.91 5.; 87? 1 n or YAFPD Spy-AD N017 A F 0:.1T:.3G.J N ASA CE 7 o o. 07 o o o 0 Ct 01 32.20 0 0075/ I o O I 7. F o o o o o o 00 ON 0 N 0 9‘ OJZthgNZHJSCARCD 0 51305 0 O 053k 1317...! A350 5 5 c A». 0 C 1 1 0..“ E 0 N I A 2 029 o A or.0 o «I or» o S... 3 3 0 O 070...»). 0.: I1 0 0T3 N I A 0.. C 0 I I II F P S N7LH RC 0991....0 T 2 0:...- o N A.“ 0?. T1A1 0 D. 7 2 E N C C C CC I. R 17 C YSIN1E F W II9 0A IAIIIIII o o 1 N D. o C F N PI 1 P 9 VV R T .../II I P 7. A ZIII III 1D..I CI IE IIIIIIE F L N N NS T N 7 LI FI DSLII D I NII PPI HA C C I I NIT] L L N IIF A A 7. 1 1T N A EA EA P0 0 7. LP 7. I IIPPDI IEHCPCCSCCS IT T S A A C BTII 01 T .. n r. S C ... HHASTFD HH70LFv.. 000 90 PDQ...PD CC... DDPTTTH. L7CSF..T 7. 7. Y D VS 5.: 0 A T I I II I S APTAINNECCLOAC7OLLL PNSC IRQEFQCCNOGFOOOAAAO NALTEIDN T TCP EBP:,OLEGQC n. 7. N P.Lc..sDIITYF.._LT LD.EEYY 075.." OTT...STHHLAAE3.QQFFFB OSQEVL..1 7. 7.7 VFFVVVASGAELD N N N NN N 0 AARYACCADDIYOTEFIDS 903V PPD SPPVOHpHFAvPDYYYP BPSJNYT.» N NPAPPDANDDAHCd. K 1 0 0 00 0 C P C P. Y T F Y C . C 8 7. N 7. I I H S C H N I." N AAA AA AA A A A AA AAA AAAAAAAA AA AAAAAAA AAAA AA AAAAAA AA A A 0 N N NH N TTT TT TT T T T TT TTT TTTTTTTT TT TTTTTTT TTTT T T TTTTTT TT T TO L n o no 0 AAA AA AA A A A AA AAA AAAAAAAA AA AAAAAAA AAAA A A AAAAAA AA A A" 8 C C CC C 000 0.0 00 0 0 0 00 000 00000000 00 0000000 0000 0 0 000000 00 0 0E 1?. 123“; 12 12 . 1 12‘. CCC CE CCCCCC C CC CCCCCC CCC COO 2123 BLOCK DQTI INTXT TFXT FOR OUTPUT ° COHHDH ITxTc/ Ttxvct7.56). YEYT017 “2!. TQYYsl‘.3) DIMENSION DTxTn(r,2T.31. DTXTCI7 21 51 FOUIVLLEHCE (TEXIH DTxTca. «TEXTé.DTxTc1 DATA «(nTxTATI.J.1‘.I=1.71.121,101 I % AHSHAH, Auto L. AHAAD . AH H H. AHA , AHcoeI. AHHINT. AHT° L. bHAND . AHTH H. AHA . AHCD'I. 3 “HIRDID “HG. LD “VANO D “H7“ H9 ‘HA , LHCQ'ID H bHLA‘O. AH? F0. AND 1 , bNTH H. AND , LHCD'I. 5 ENLARO. «HR FF. 6H" 2 . «HTH H, “H? , ‘HCP‘I. 6 AHLnno. hHR FF. AHD 3 . AHTH H. AHD . AHCOOI. 7 AHTpAc. AHTDR . AHcAp.. AHTH H. AH? . AHCR I. a AHnoHa. bHINE , AHcAP.. AHTH H. AH° . AHCGPI 9 EHOFT . AHAHIH. AH CAP. AH'H H. AHq , ggcogl, 0 MN IA! LHOAST. AHfH H. LHA . hHC°SIA DATA ((DTxTQ(z.1.1¥. =1 7).J=11.203 I % AL . HCUL . AH HPKST. AHT H AHA . AHcpo/, quAL . AHSDVH. AH 790. AHTH H. AHA . LHCP'I. 3 AHTAL . AHSDVH. AH HOD. AHTH H. AHA . AHcch. “ BHW‘X . “HQICED “H 0 “HT” "9 “HA 9 “Hebe/v 5 “”4!" ' ‘OHQICP, “H g “H!“ H. “HA 9 ‘Hcc‘lg 9 AHHAV . AHCDOH. AH . AH'H H. AHA . AHcgfl. AHHIH . AchPN. AH . AHTH H. AHA . AHce L B BH‘TAX ’ “Hi":‘g “Ht 9 “HT" H. “HA ' “HCQ;’Q 9 AHHIH . AHHHEA. AHT . AHTH H. AHA . LHC3*/. ‘ HHA kHSOTB. AHEAN H AHA . AHcQTI. DATA «(nTxTR¢I.J.11.I=1 TT.J=21.271 I AHH: . AHsnva. AHEXH . . AHA . AHcpxI. AHHA! . AHHAT , AHDASY. AHTH H. AHA , LHcctI, AHHIH . AHHAT . AHPAST. AHTH H. AHA . LHC°’/g AHHAX . Arsovl. HHHFT . AHTH H. AHA . LHCDfI. “HNIN : “HSOVIQ “HRH? 9 “HT" H, “H“ 9 “NCO: I: AchL AHDAST. AHTH H. AHA . AHco DATA (IOTXTRU 1.35.1: -1.71.J=1,AT I HSU HT=AD A. De . . AHUHIT. uHCR‘I. :HAAfiE: “H Lkg: “Hop 9 :HTfiC "p ‘0": , “NCOQ’O :H‘AGE. “H LA". “”09 o “"7“ H, “HQ ' ‘HCC'=’. “W “H LAB, “H0: 9 “PT” My “HQ ’ LHCQ'SIO DATA 11¥TxTc¢I.J.1). .1:1.7).J:1:%0L I H COOVGmtuNM rMNH VwmtuNM tcn. . H. . AHA . AHcvgl. tdaICE, l.“ "CD, “H 9 “HT" "9 “NA ‘ “Hgsl , “H003N: “H T90: “H p hth H. AHA . AH =‘I. hHCOSN. AH Hon. AH . AH’H H. AHA . -H R‘ AHHH=A. AH? 19, AHo , AHYH H. LHA . AHCD'I. IoH'de’A, “HT PO. :H? 9 “H7" H9 EH8 . LHCR’I LHEOVI, “HHHT . =0 9 “H?“ H. ‘0": . LHCD’]. AHSDYB. AH=AH :HTao . AHTH H. AHA . AHcc'I. AHSOYB AHTH H AHA . AHCRQI. DATA ((DTxTDTI 1.13.1: 1 cia.4a1 .213 I AHHATU. AHSAL . AHPKST. AH H H. AHA . LHCR319 5 “HPUL g JANUMST. ‘0" TD 9 “HT" H. “HA 9 5"C°.II uHéUL . «HPAct. AH PC . AHTH H. AHA . AHCCTI. “ “HIECF. ‘0“ "AT, ‘H F‘s. ‘HTH c, 5”" ' ‘H'fcg’, 5 BHBFEF. ‘0" CUL. :59. “HT". Cg BHU g ”(39.9/9 6 AHIHV . AHTGAC. AHTCC . hP°¢C . LHUVIT. AHrt'I. 7 BHINV . AHcoHe. AHXHr . AHDDH . AHunxT. AHcvtI. n “HINv . “HQFT , “HQKI‘T, ““5"! Q BHU'JI , th:‘/. q AHHIPE. AH LAB. AHDR 1. AHTH H. AHQ . AHcatI. 0 hHHI’E. AH LAB. AHOC z. AHTH H. AHD . AHc9'I. A HIRE. “H LAB. LHOR 3. bHTH H. HM! ' hHCRS/o DATA: TFXTB I 1 H§Ha AL. AH FA. AH°~$(. AH3-1a. AHDHAT. 2 AHLADG. AH, FA. LHfirfil, 8% >13. AHJHAT. 3 hHQEGI. BHONAL. 5H CCN. LHST°A9 “HINTS! «4444 “XXX“ 44444444444444444444444444444444444444~4444444dddd 4444 \oocooooov \OOOOOCOOC \oodooo \OOOOOOCO. HHMHHHNHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHAHHHH zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzxzzzz q144«fiddqfidddddqqddddflidfld«daddqqddqqaqqdddqfiqqdqq xxxxKxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxfixxxxxxxxxxxxxx noonnmmrrcrrt:crruuuuuuuuum-----nupnnpuppn outan»eoo~outu~nooowoutunnaoawouru~»000flouruuw0001~mcu~ \oooooocoo HHHHHHHHHHHHHHHH 4444444444444444 V i VMNOOM’J‘ QWWJI WONG“! PWMOV 219 23‘523‘2'090123‘567.9012:‘56,090123“;s'agu‘zs“56’.9.123‘367°9.‘23 BLOCK DATA IMY cccc 'YVIIIRVY NNNDQPPNN IITLGLLII TNV CONTAIN? THE INITIlL VJLUES OF Y(1979’ AND TITYPF! COMMON ILPAC/ ccc 1 Z TMP(63T O IFIXCZS). TOL(5D9 E‘62'6°,! EQR(“!. COMMON ILPSC/ 11111111112222222222333333333356hhb55bb§55555555596666 1N1 INY THY INY NY NV III/II,III/l”””/”””/”/”"I””’//”””’IIIIII” OOOOOQOOQ .0....OoOoO-O...OOJOOOOOO OO....‘.0.0.0.0.00 HHHHHHH“HHHHHHHHFHHHHHHHHHHHHHHHHHHHHHHHHHHNHHHHHHHHHHHH 11111111111111111111111111111111111111111111115111111.1111 9000900099.!9090'9’!90090909990!OOODO'OO'O'OIO!OOOO90"! 000000000000000000000000000000000000000.0000000000000000 553030033J02312937.57‘ “39.1%11010039113035335736R. 61:03296; 81.05663 h 1.39—3.00. “F ”Hutu 1* “cc“ so “1.7K...“ 190170.03.“ 9520... 0092673: 9553000900 96915201450049.0585 “020,330,0683388333999629 57075250.".30536730 31387 97.522937551717115“ 8586 1.576129193939153 a 119:0212185 110 93777139 ‘.2C..4~17~21V31 :43 2 1 9.2 szzgqg 5619999...‘ 55 :50... BO .11 32 3.4 5551—25 28 9 55....“ 11.. 11 3.73823 1 O 56‘ b [I’ll/lI’ll/I’ll’l/I/I/I/l/[III/IIII/IIIIIII/IIII’III/l’ ”,”’, ”,",,"’,’,’,’””l"”’)”’”-’”’,,,-,”’,,’,’ 123.: 567 R 931235567M90123..»56789C173. h c. 67890123 5 567! 90123556 111111111123222222223333?T3333hhabhthhhh§555555 “‘((““““‘(‘(‘(‘(‘(l\“(‘((“‘(‘(“‘(‘(“““(‘(““‘ TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTYTTTTTTTTTTTTYTTTTTT '.'."."".....,.""."’.'."'.""""....".""".. ’,’)’-",,,"""T””\l\l"AII,‘0’,,,,\l"’|l””’-”””””’ 1.235567 891-121. k: 5.9 “91.123 a Q & 7.4.0 31);? 4 R 578991.23h557 591.123hc..6 11111111113222222222?333333333hh55hhhbhk5555555 t“"“ "(‘(“(‘(“(“‘(‘(“(““‘ ‘(““‘(“("“‘(‘((‘( YY'YYYYV YY'VYYYVVYYVVVYVYYYYYYYVYYYYYYYYYYYVYYVYVYYYYYYY AAAAAAAAAAAAAAAAAAAAQAARAAAAAAAAAAAAAAAAAAAARAAAHAAAAAAA TTTTTTTTYTTTTTTTTTTTTTTTT?TTTTTTTTTTTTTTTTTTTTTVTTTTTTTT AAAEABAAAAAAAAADAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAnAAADAAAA DCDPDODDDDDCODCCDDOPPDHOnDCDDCDCDPPDCCDDDOCDDDDDDDDDDDDD Ad 56' 6 666 TNY {NV NY INT 220 23556iS‘SNC‘At-Ctofizzcafltvbzsgogb5:“3126703123390123k 567890123 356756 . 1111111122522§336hhbk §3g55112222222222333331 35¢. 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