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J ‘Ofl'*~ - l;£i::§£§£ilr .. 141mm W“ \ Univafim { \ u ‘ _—-— THESIS O I This is to certify that the thesis entitled A LAND BASE GOAL PROGRAMMING APPLICATION TO NATIONAL AGRICULTURAL SECTOR OBJECTIVES IN A DEVELOPING COUNTRY presented by James Glenn Robb has been accepted towards fulfillment of the requirements for M.S. Agricultural Economics degree in Q4 K .523“ [/qu Major professor 9 Date -/ 7 E25 / / 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES ” RETURNING’MAJERIALS: PIace in book drop to remove this checkout from your record. FINES wiII be charged if book is returned after the date stamped beiow. V2 3"“ —- /?”0— 9’6 x7 0.. A LAND BASE GOAL PROGRAMMING APPLICATION TO NATIONAL AGRICULTURAL SECTOR OBJECTIVES IN A DEVELOPING COUNTRY By James Glenn Robb A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1983 ABSTRACT A LAND BASE GOAL PROGRAMMING APPLICATION TO NATIONAL AGRICULTURAL SECTOR OBJECTIVES IN A DEVELOPING COUNTRY By James Glenn Robb Quantifying trade-offs and complementarities between objectives is seen as an important input into decision making. The purpose of this study was to investigate the multiple agri- cultural sector objectives of Costa Rica and demonstrate a land base programming model. The sector objective functions under study were maximizing export earnings, maximizing labor employ- ment, minimizing costs of production and self-sufficiency in the basic grains. Secondary data sources were used to develop the set of coefficients used in the model. Six agricultural regions and fifteen cropping activities were included in the analysis. The goal programming model optimizes by using soft con- straints with targets, then minimizes weighted deviations between them. This approach is analogous to minimizing disutility (weighted underachievement). For objective functions stated in terms of maximize or minimize targets were generated by using standard linear programming on each function independently. For self-sufficiency in the basic grains 1985 demand projections were used as targets. Trade-offs between objective functions were developed by analysis of various weightings and sensitivity analy- sis resulting in representative solutions depicting points on the efficient set. End points of the trade-off set are original goal programming targets. Major trade—offs were apparent between regional crop- ping activities compared to the base year, between relative weightings of objective functions, and between short and medium- run planning horizons. ACKNOWLEDGMENTS For their assistance, I wish to thank the members of my guidance committee: Carl Eicher, Stephen Harsh and Peter Schmidt. I also gratefully acknowledge the guidance provided by my assistantship supervisor James Johnson. Special thanks are due to Weldon Lodwick who provided countless hours of com- puter assistance and Mark Cochran who provided data gathering and insight. Thanks to Sue Perkins for her typing and patience. This thesis is dedicated to Dad, Mom, Tom and Charles. ii TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES Chapter 1. Introduction Problem Setting Objectives of Study Organization of Thesis Conceptual Base and Approaches to Multiple Ob- jective Analysis Terminology Conceptual Base Traditional Approaches Multiple Objective Optimization Linear Multiobjective Programming Approaches An Overview of Costa Rican Agricultural Sector Objectives The Agricultural Sector Sector Objectives National Sector Planning Land Base Regional Model Introduction Comparative Advantage Regional Specification of the Model Data Base Implications of Regions and Data Model Structure, Coefficients, Assumptions and Limitations Introduction Model Structure Model Assumptions, Limitations and Usefulness Results of Analysis Introduction Short-Run Results Medium-Run Model Results Conflicts Between Time Horizons iii Page vii mbHH Partial Opportunity Costs of Sector Objec- tives Some Implications: Magnitude of Change for Basic Grains, Self-Sufficiency and Labor Em— ployment 7. Summary and Conclusions Review of Problem and Objectives ‘Review of Analytical Model Summary of Results Additional Useful Research APPENDIX A: Example of GP Model Output: Medium Run ‘ Weights 100, 100, 10, 1000 (Model V) BIBLIOGRAPHY iv Page 108 108 112 112 113 114 117 119 133 LIST OF TABLES TABLE Page 3.1 Number of Poor Farms, Non-Poor Farms and Percent of Farms Which are Poor by Farm Size 32 3.2 Projection of Possible Labor Force 36 3.3 1975/76 Imports of Basic Grains and Imports as a Percent of Total Consumption 37 3.4 Demand for Basic Grains: Actual 1975, Pro- jected 1985 and Percent Increase Required 38 4.4 1973 National Crop Production From Central Bank, Census of Aggregate (Crop Specific As- sociation) Data 51 5.1 Codes Used by Crops 62 5.2 Codes Used by Region 62 5.3 Objective Function and Goal Constraint Right- Hand-Sides for Short-Run and Long-Run Models 62 5.4 Current Cultivable Area by Region in Hectares 65 5.5 National Requirements in Metric Tons 66 5.6 Labor Employment (LABORi j) Per Hectare For Regions by Crop 69 5.7 Information on Exports and Internal Consump- tion for Coffee 70 5.8 Information on Exports and Internal Consump— tion for Bananas 70 5.9 Information on Exports and Internal Consump- tion for Sugar-Cane 71 5.10 Information on Exports and Internal Consump- tion for Cocoa , 71 5.11 Information on Exports and Internal Consump- tion for Cocoa 72 TABLE Page 5.12 Adjusted Annual Yields Per Hectare Reflect» ing Double Cropped Production 72 5.13 Crop Yields Per Hectare by Region in Metric Tons 73 5.14 Crop Costs of Production by Region in Colones 74 6.1 National and Regional Values of Objective Functions for Short-Run Models 90 6.2 Medium-Run Natural Results as Percent of Short-Run 101 6.3 Medium-Run 102 6.4 Short-Run Opportunity Cost of Non-Perfect Competition Formulation 109 6.5 Medium-Run Opportunity Cost of Non-Perfect Competition Formulation 109 vi LIST OF FIGURES FIGURE Page 2.1 Two Objective Function Depiction of Ef- ficient Frontier and Specified Preference ‘ Function 15 2.2 NISE Estimation Technique 20 4.1 Absolute Advantage in Each Region 45 4.2 Comparative Advantage 45 4.3 Linear Production Possibility 46 4.4 Agricultural Regions of Costa Rica 48 5.1 Depiction of Model 61 6.1 Agricultural Regions of Costa Rica 81 6.2 Short-Run: Maximize Labor (Model I) Produc- tion Patterns 83 6.3 Short-Run: Maximize Export Earnings (Model II) Production Patterns 84 6.4 Short—Run: Minimize Cost (Model III) Pro- duction Patterns 85 6.5 Short-Run: Equal Weights (Model IV) Produc- tion Patterns 86 6.6 Short-Run: Weights 100, 100, 10, 1000 (Model V) Production Patterns 87 6.7 National Short—Run Results: Value Path Dis- Play 89 6.8 Medium Run: Maximize Labor (Model I) Produc- tion Patterns 95 6.9 Medium Run: Maximize Export Earnings (Model II) Production Patterns 96 6.10 Medium Run: Minimize Cost (Model III) Pro- duction Patterns 97 vii FIGURE 6.11 6.12 Medium Run: tion Patterns Medium Run: Equal Weights (Model IV) Produc- Weights 100, 100, 10, 1000 (Model V) Production Patterns viii Page 98 99 Chapter 1 INTRODUCTION Problem Setting Decision making takes place in an environment of limited resources given a specified planning horizon. From an economic perspective decision making is an activity that is directed towards maximizing utility (minimizing disutility). Utility has many com- ponents. At the national level utility may include income, security, equity and other specific components. These components of utility may often be conflicting. Resolving these conflicts of trade-offs is a major element of decision making. One of the criticisms of traditional decision theory and analytical tools is that a single economic criterion objective function like maximization of profits does not reflect the multiple components of utility maximization and associated trade-offs. In multiobjective analysis the specific objectives of utility maximization are quantified in their own units of measure; it is not necessary to collapse units like hours of labor, gg§£_of production, yields, etc. into a single objective function. Sfeir and Bromley (1977, p.179) state:. ”One of the first steps in improving decision making in developing countries is to introduce explicitly the objective function of the policy makers into our conceptual framework. This is not so difficult as might seem at first blush. Countries have targets, and countries have priorities; this represents a multidimensional objective function." Public specification of weights on objectives is seldom done be- cause it implies who will benefit most. The focus here is not on determining the decision or policy makers (government's) weighting (value) structure but to quantify the decision space representing the trade-offs between objectives. This can be done by using stated agricultural sector economic objectives and optimizing different value structures to estimate the trade-off surface between weighted objectives, thus, a priori utility is not determined but implicit utility is one point on the trade-off surface. Another method, would be to interactively let the decision makers change objective weightings looking for a solution. As Zeleney states (1974, p.170) "Priority weights should be a result of the analysis rather than its input.” At the national planning level analyzing trade-offs is seen as an input into the decision making process. Jan De Veer (1971) says that planning is always aimed at the future and in- volves three elements: formulation of objectives, analysis of possibilities, and determination of a program of action. Trade-offs between objectives is part of analyzing possibilities which may feed back into the formulation of objectives stage. This study will focus on the usefulness of multiobjec- tive planning in an agricultural resource utilization context with the particular focus on Costa Rica. For Costa Rica implications of objective functions like export earnings, labor employment, cost of production, and self-sufficiency need to be analyzed. The spatial location and regional implications of crop production on sector objectives is one component in analyzing conflicts and "bottle necks". Exports provide money for purchasing products of foreign countries and by taxing them the government generates revenues. Agriculture is a sector increasingly relied on to pro- vide employment. Costs of production are important as they reflect efficiency of production, the country's ability to compete in ex- port markets, and the country's ability to meet food demands at the lowest cost to consumers. Being self-sufficient is a major concern (objective) in Costa Rica. Currently this self-sufficiency objective is a function of the basic grain food crops; corn, beans, and rice. Time horizon is an important component of analysis. Long run steady states are an important type of analysis but often do not fit into a national decision makers planning horizon while short and medium run analysis apply better to their political en- vironment. Constraints are greater in the short than in mediUm time frame and this has implications for the cropping pattern and the achievement of the national objectives. Planning trade-offs may occur if short-run planning precludes longer term possibilities. Quantifying these trade-offs in a static sense allows decision makers to compare potential contribution to multiple objective functions between planning horizons. In the short-run tree crop (coffee, banana, etc.) production cannot be increased due to establishment or production lag. Conflicts thus can result between time periods in the spatial production pattern that maximized utility. Objectives of Study Maximizing export earnings, maximizing labor employ- ment, minimizing cost of production, and being self-sufficient in the basic grains are agricultural sector economic objectives in Costa Rica. The purpose of this study is to investigate these objectives and their associated trade—offs. More specifically, the objectives of these research were: 1. Study mathematical programming optimization tech- niques that could be used to quantify conflicts and trade-offs between agricultural planning ob- jectives through the use of a demonstration land base model for the stated agricultural sector ob- jectives in Costa Rica. 2. Analyze the implications and direction of change in crop production patterns between the regions for Costa Rica in both a short and medium term planning horizon. 3. Compare model results of the above-specified model to the traditionally used land base linear program- ming model with a single objective function specified to minimize production costs. Organization of Thesis This thesis is organized in the following manner. Chapter 2 presents the conceptual base and optimization approaches to multiple objective function analysis. Chapter 3 is an overview of the Costa Rican agricultural sector and stated objectives for the sector. The land base approach is modelling and an analysis of secondary data sources available for Costa Rica is presented in Chapter 4. Chapter 5 specifies the multiobjective programming model used including its structure, coefficients, assumptions, and limitations. The results of the multiobjective model are given in Chapter 6. In Chapter 7 the study is summarized and conclusions on the apparent advantages of the multiobjective approach compared to traditional linear programming are presented. Chapter 2 CONCEPTUAL BASE AND APPROACHES TO MULTIPLE OBJECTIVE ANALYSIS In this chapter a conceptual base for the multiple ob- jective approach to analysis is presented and a methodology devel- oped. The first section presents terminology followed by sections on: a conceptual view and reason for using a multiple objective format; overview of economic approaches; and, the multiple objec- tive model used in this study. Terminology Based on Keeney and Raiffa (1976), an "objective” in— dicates a direction of preference and an attribute is the units in which the objective is quantified. A "goal" is a specific target that differs from an objective in that it is either achieved or not. "Values" give rise to the ranking or relative importance of objectives and goals. They define preference functions and also the approved or disapproved means of attaining goals. For example, an objective may be to maximize employment with more employment as the direction of preference. This objective could be quantified by the attribute of hours. A goal for this objective might be the employment of 1000 people or 2 million hours.1 1(40 hours per week) (50 weeks) (1000 people). -6- Objective functions which are objectives or goals can be conflicting or complementary with respect to a given set of resources. For example, trying to achieve objectives like ”maxi- mize employment" and "minimize cost of production" simultaneously in the agricultural sector would at some point become conflicting, it is required labor to be employed beyond the amount necessary to meet demands for production, but would be complementary within a range as labor is required for production. It is often possible to simultaneously move toward two objectives but at some point furthering one objective can often only be accomplished through diminishing the other objective. Such an occurrence implies "trade-offs". If all objective functions could be maximized simultaneously utility would be maximized. Conceptual Base Conceptually, objectives and goals are viewed as having a hierarchical structure because they are specified at various authoritative levels. Many of the direct goals and objectives of policy are not themselves ends, but are only means in a complex means-ends chain. Specification of attributes is often difficult because high level goals like "to become developed” must be further defined at lower levels in terms of attributes like employment, costs, etc. At the national level often both objectives, like maximize employment, and goals, like metric tons of grain produc- tion, are specified. When analyzing any decision problem objectives must be clearly identified and attributes must be defined that measure attainment and movement toward goals. Irrelevance of results to the planning situation is a reason often given for the scant use of mathematical model results (see Jan De Veer (1971), Quade (1975), Johnson (1977)). This may be due to the assumptions built into the model and/or lack of appropriate data in both quan- tity and quality. Not having incorporated the multiple nature of objective functions also can lead to a lack of acceptance by decision makers. In designing agricultural sector plans no one objective is appropriate. At the national level agriculture not only pro- duces food for consumption but also provides employment, supplies foreign exchange, and interacts with many economic and political objectives. The trade-offs between objectives and the concept of objectives being multiple in nature is often acknowledged but seldom emphasized. The purpose of analyzing objectives and their trade-offs is to clarify the decision space or opportunity set for policy makers. Hitch states, "first it is impossible to define appropriate objectives without knowing a great deal about the feasibility and cost of achieving them. And this knowledge must be derived from the analysis."2 Nature of Objectives Objective functions are part of a dynamic process and constantly are being revised whether explictly stated or not. 2Cited by Quade (1975, p.87). Objective functions change as decision makers perceptions of the problems change and as the structure of society changes. Also, the relative weightings of objectives change over time. Presum- able the overall weighting of agricultural sector objectives changes as a society becomes more industrialized and urban. How objectives are weighted at any particular level of aggregation depends on the values held by those making decisions which can be influenced by information availability and politics. As the distribution of power to make and influence policy changes the relative weightings of multiple objective functions will change. Stated Objectives Political decision makers often state policy in very broad terms. Policy is often stated in terms of very broad ob- jectives rather than in specific targets. The more specifically stated objectives are defined the more apparent it becomes what groups in society will benefit. Specific goals, if not achieved, provide fuel for opposition and delineation of priorities can, especially with economic issues, be politically very naive. From an economic perspective fairly broad objectives, like maximize employment and minimize cost, can be approached by optimization and specific targets can be approached in terms of level of attain- ment or achievement. Multiple Decision Makers National level planning is characterized by multiple decision makers which differs from micro optimization based on a -10- single decision maker's objective function. In any political system that is not perfectly totalitarian,conf1ict resolution is an important component of policy formulation. Combining mul- tiple objectives with multiple decision makers seems to imply quantification of trade-offs. A Role of Information The role of information focused on here is as an input in the decision—making process. By supplying decision-makers with some insight into the economic trade-offs between delineated ob- jective functions they may better be able to evaluate their ex- plicit and undisclosed preference orderings. Assuming this is better information than they possessed before analysis, they should be able to better understand the interactions of multiple objectives. In a policy context this type of analytical approach may lead to more informed conflict. Traditional Approaches Traditional approaches to economic analysis either as- sume away multiple objective behavior or use a utility function approach. Assuming away multiple objective behavior is done by specifying a single criterion for analysis, like maximization of profit or minimization of cost, as opposed to utility analysis which is a single function which may contain numerous criterion reflecting multiple objectives. Single Criterion Analysis Economic analysis is often based on a single, easily quantifiable, objective function which implicitly approximates -11- the real world. The classical approach to spacial programming models in agriculture (Heady, 1976) is to form the problem with an objective function that minimized the cost of agricultural production subject to exogenous demands. When modeling com- parative advantage in agriculture, analysts using a minimization of cost objective function assume that marginality conditions of the perfectly competitive market structure apply. Such an assump- tion fails to take into account the multiple objective nature of farm level management (Wheeler and Russel, 1977; Chandler and Boehlje, 1971; Dobbins and Mapp, 1979). When analyzing national agricultural sector objectives the undimensionality of this ob- jective function results in incomplete analysis, although cost minimization may be an important component. Using a single ob- jective function model fails to approach the very important issues of multiple and conflicting objective functions. Utility Function Analysis Utility function approaches are based on applying the theoretical economic concept of utility maximization. Theoretically economics handles multiple objectives in the premaximization process that defines the utility function. Johnson (1977, p.34) defines the normative nature of these preconditions for maximization and notes that a high proportion of the decision making problem is embodied in establishing an interpersonally valid common denom- inator (CD). The CD is used to collapse goals and objectives into a single function by attaching values. The CD must be inter- personally valid if, as in most public sector problems, decisions -12- will hurt some in order to benefit others. To get an analytical solution once a utility function is defined requires second order conditions and a decision rule. This requires quantification of the decision makers preferences and some measure of preference attainment (Lee, 1972). Campbell and Nichols (1977) argue for specifying objectives as well as priorities before analyzing alternatives by scaling utility. A common practice is to "price out", that is scale down to a standard level all the non-monitary attributes into a single monitary attribute function. A comparison of alternatives is then made only in terms of "adjusted" levels of the monitary attribute function. The requisite assumptions necessary for such an approach to be valid are strong (Keeney and Raiffa, 1976). As Roy (1971) points out, many difficulties deve- lopin.extracting real preferences of the decision makers which often results in an arbitrary representation of preference in a very crude form. This problem is compounded when working at the national level with multiple decision makers and interest groups. The preference or utility function derived then becomes the objective function which is maximized resulting in a deter- minate solution like single criterion analysis. Although theoreti- cally very satisfying in an efficiency context, two problems with this type of utility approach are: 1) a priori quantification of preferences 2) economic rationality of quantified preferences. First, national decision makers often may not be able to define a single set of national preferences to which all decision makers -13- can agree; furthermore, they may not want to be very explicit in revealing preferences. Second, if preferences are extracted, can they be economically rational if information on trade-offs is not available? To make a rational weighting of the objectives that make up utility requires knowledge about the opportunity costs or set involved. In a mathematical programming context authors questioning the utility approach include Roy (1971), Lee (1972), Zeleney (1974), Bartlett et. al. (1976). Many others have questioned the utility approach on both theoretical and application grounds. Summary Cohon (1978, p.315) states traditional single-objective methods ”proceed to a so-called "optimal" solution that is best in terms of a single measure of value. Decision makers are given the choice of accepting or rejecting this single solution without learning anything about how the solution compares with other feasible solutions. Since in a public decision-making context, a single objective can be defined only by making important and perhaps con- troversial value judgements, the analyst is forced by single-objec- tive approaches to usurp a large part of the decision makers re- sponsibilities." Combining the problems of extracting utility functions in the public sector with the assumed role of public decision makers as those responsible to make value judgements in a world of multiple and conflicting objective functions leads one to multi- objective analysis and ranges of efficient solutions (opportunity sets). -14- Multiple Objective Optimization Optimization of multiple objective functions can be viewed as a vector maximization problem. Efficient solutions result when all objectives are maximized or minimized, as appro- priate. For example, labor use is maximized and cost of produc- tion is minimized. The problem is conceptualized as maximizing a vector of objective functions, F(x): III (Xfl f2 (X) f3 (X) F(x) = ft (X) t J. Subject to: Functional relationships (matrix of m rows and n columns) II I—‘ N LA) 8 fl) :3 Q.- Ai(x) O, i Xj 0, j = l, 2, 3 ... n, assuming convexity. This solution defines the "efficient frontier" or optimal set of possible solutions in objective function space. FIGURE 2.1 is a representation of the two objective function case. The ob- jectives are f1(x) and f2(x). Point A represents the result of solving for only f1(x), point B the results of solving for only f2(x), and point C the optimal solution given a specified preference -15- FIGURE 2.1 TWO OBJECTIVE FUNCTION DEPICTION OF EFFICIENT FRONTIER AND SPECIFIED PREFERENCE FUNCTION. Sspecified preference function f1(x) ‘Pefficient frontier V f2(x) Note: This figure depicts two maximization-type functions. -16- function. In this example, the curve defining the efficient function does not intersect either the fl(x) or f2(x) axes. This demonstrates the case where interaction between objectives (fl(x) and f2(x)) permits at least some of each objective to come into solution. The efficient frontier is the portion of the figure between A and B which is the competitive range between the two objectives. Complementarity occurs, as depicted, where one or both objective functions can be improved without a negative im- pact with respect to the other objective. As depicted (FIGURE 2.1), it is easy to visualize trade- offs between two objectives. But, further consideration brings out some limitations of this depiction. The two objective func- tions (fl(x) and f2(x)) generally are not independent. To more completely see the implications of trade-offs we need to look be- hind the curve to the activities in solution at given points that generate the set. Activities in solution vary continuously (since the objective space varies continuously) resulting in an infinite number of resource allocations occurring -- one for each point on the efficient set. Conceptually each objective function is defined by an axis in the first quadrant. Multiple objective analysis is then a partial analysis if 923 related objective function of an interest group, present or future, is not included. Brill (1979) states, "the best planning solution may lie in the inferior region.” The inferior region is that area below (toward the origin) the effi- cient frontier for two maximization-type functions. In the more -17- realistic three objective function problem point D (FIGURE 2.1) may be a selected optimal solution, not point C. Optimization models assume the objective function is completely specified and that decision makers are optimizers. Hence, decision makers choices could logically be off the effi- cient frontier because any analytical model is based on simplifica- tion of the "real world". One way to partly look at the robust- ners of a model with respect, solutions off the efficient frontier, is with sensitivity analysis of efficient sets which has been done in a farm management decision setting by Schurle and Erven (1979). Efficient Frontiers The efficient vector making up the efficient frontier has been given different names in the literature including the pareto set (Ecker, 1975), non-inferior set (Cohon, 1978), efficient set (Saygideger, Vocke and Heady, 1977) and non-dominated set (Lee, 1974). The vector maximization problem is the problem of finding all solu- tions which are efficient. The main property of the frontier is that for all solutions outside the set (which by definition can only be interior of the efficiency surface given the optimization structure where all objectives are to be maximized) we can find an efficient solution where individual objective functions are un- changed or improved and at least one strictly improved (Zeleney, 1974). Efficient frontiers in operations research have been conceptualized by many especially in connection with activity analy- sis of production and allocation, (Koopmans, 1951) and non-dominated set in portfolio selection (Markowitz, 1959). Charnes and Cooper -13- (1961) presented the first multiobjective algorithm and have con- tinued analytical development (Charnes and Cooper, 1977). The utility approach attempts to a_priori define the shape of the decision-makers preference function. By optimizing the preference function, the traditional approach gives a one point determination solution. Meisel (1977) says, "The classical (here utility) approach results in a lighter computational burden and a greater burden on the decision-maker, requiring him to use his intuition to estimate the impacts of the trade-offs he is making." Raiffa3 also makes the point: "Personally, I feel that this quest for a "scientific" and "mathematically objective” rule is all wrong!...; we should limit formal analysis to the charac- terization and determination of the efficient set and let unaided, intuitive judgement take over from there." Parametric Estimation The standard approach to defining efficient frontiers or sets for linear multiobjective programming problems is to use parametric techniques once an initial extreme point (optimum) is found (Ecker, 1975; Lee, 1972). With large matrices it becomes difficult to enumerate all efficient extreme points due to the number of adjacent vertexes that must be analyzed. Parametric techniques are used on the objective function when analyzing mul— tiple objective problems defining the ranges over which coeffi- cients hold constant, by analysis of vectors in the basis. Then 3Raiffa, Howard: "Decision Analysis", Addison-Wesley, 1970, pp. 155—156. Cited by Zeleney, (1974). -19- changing the coefficients to their limit within the range they hold constant and iteratively analyzing the new basis that comes into solution. Following the ”100 percent rule" (Bradley, S.P., A.C. Hax, and T.L. Magnanti, 1977)4 more than one coefficient in the objective function can be changed without changing the basis n if the sum of relative changes is less than or equal to one 2 5.1; i=1 i = 1, 2, ..., n coefficients). When more than three objective functions are involved, a set of solutions that estimate the full efficient set must be developed as graphic depiction is not possi- ble. The larger the number of objectives being analyzed the more difficult it is to define the whole efficient frontier exactly. Non-Inferior Set Estimation (NISE) This technique, developed by Cohon (1978), estimates the efficient set by iteratively defining points on the efficient set for the two objective function problem. The technique first optimizes each objective function without consideration of the other (points A & B FIGURE 2.2-a). The lines AC and BC define upper bounds to the graphic solution set. The maximum possible error for the two points A and B is the perpendicular to AB, DC. When another point is estimated (E), as in FIGURE 2.2-b, the maximum possible error is FG plus HT. The amount of possible error given by the sum of perpendiculars is iteratively compared to a predetermined acceptable error. Esti- mation stops when the possible error is less than the acceptable P.112. -20- FIGURE 2.2 NISE ESTIMATION TECHNIQUE u> r: ‘/ V error. This estimation technique follows the convexity assumptions of mathematical programming. (kfimufissalgorithm becomes greatly more complicated for more than two dimensional problems and has not yet been applied to the higher dimensions. Trade-Offs: Two Step Process The efficient set, as described above, defines the func- tional space of trade-offs between objective functions. When the whole space is generated the decision makers utility is implicitly defined by the choice (C in FIGURE 2.1) that is made after evaluat- ing the set. The efficient frontier explicitly defines the trade- offs given the assumptions of the analytical model developed. But, -21- except for very simple models, the whole surface is not feasible to generate; therefore, various point solutions are selected from the surface. The class of decision problem considered here is con- tinuous which means decision makers are working with an efficient set with infinite possible priority structures, although some priority structures may give the same optimum solutions. Two aspects of this problem (Meisel, 1973) are: (l) obtaining a set of efficient solutions which are meaningfully distinct which de- scribe the efficiency surface; and (2) representation of the trade- offs implicit in that set. These two aspects of the problem lead to a two step process. First, is an algorithm to find solutions on the efficient set which is developed in the following section on linear multiobjective programming., Second, is the depiction of implicit trade-offs which results from changing resource alloca- tions under various preference functions. Linear Multiobjective Programming Approaches Three approaches to linear multiple objective programming are discussed in this section. These are the weighted linear mul- tiple objective approach, the goal programming approach, and the goal programming approach formulated for Costa Rica. The latter approach is basically a synthesis of the first two. All approaches rely on the Simplex algorithm. All ap- proaches are developed from the standard linear programming (LP) model. The LP optimizes a single objective function subject to a -22- number of constraints. A standard formulation of basic LP is as follows: n Maximize: F(x) = 2 c. x. j: J J n Subject to: .E aij xJ = b1 1 = l, 2, 3, , m j—l xj Z 0 j = 1, 2, 3, ..., n Weighted Linear Multiple Objectives Approach In the linear case multiple objectives have been analyzed by simply weighting objectives formulated as constraints and maxi- mizing the sum of weights as the objective function (Chandler and Boehlje, 1971). This approach is often proposed as interactive with decision-makers but, easily extends to estimating the effi- ciency frontier by reformulating the objective function with a number of weights (Saygridegen, Vocke and Heady - for two objec- tives). Zeleney (1974) has rigorously specified conditions for optimizing Z objective functions from the classic Kuhn-Tucker condi- tions using scaler (weights) on objectives. The weights (Wi) must satisfy wi = 1 and ij 1 0. The Z dimensional feasible area must be a non-empty polyhedron which prescribes the standard convexity condition on constraints and the objective function assuring that a single point solution (x*) is on the efficient frontier. The problem assumes all objectives are specified in terms of optimization so the solution for x* on the efficient surface is: Maximize: f(x*) = j IIM'J 0 >4 £2 -23- n Subject to: .E aijxj bi 1 = l, 2, 3, ..., m j—l xj Z 0 j = l, 2, 3, , n SW. = 1 J . 0 WJ Z An alternate formulation of this same basic approach have been presented (Cohon and Marks, 1975) which optimizes one of the constraints (making it the objective function) and formulat- ing other objectives as constraints weighed relative to the objec- tive function numerary. Goal Programming Approach Two goal programming models have appeared over time in the literature. The first method was originally proposed by Charnes and Cooper (1961). They proposed a model and approach for dealing with certain linear programming problems in which conflicting ”goals of management" were included as constraints. Since it might well be impossible to satisfy exactly all such goals, the attempt is to minimize the sum of absolute values of the deviation from such goals (Ignizio, 1978). Orne et. a1. (1975) refers to this as minimizing unattainability. Wheeler and Russel (1977) use this approach in a farm management study and describe the goal constraints as equality constraints with the addition of two special variables. Dobbins and Mapp (1979) refer to this approach as a ”Substitution Goal Structure” formulation. The special variables (ur, Vr) are "reverse slack" (Haverly, 1977) or "soft constraint" (Dekluyver, -24- 1979) variables allowing the equality constraint to be violated at a cost which is specified in the objective function. Let: r = number of activities ai. = per unit contribution of the jth activity J toward goal r r — goal target for the r goal The rth goal is then: n X = ar. x + ur - vr = Gr i=1 3 where: _ - th ur — under ach1evement of r goal _ . th vr — over ach1evement of r goal ur - vr = 0 ie. both u and v cannot be non-zero for the same constraint. The objective function is to minimize weighed deviations between goals: M1n1mize: z (wiui + wivi) where: 1 = 1, 2, 3, ..., r. The second approach is what is most often referred to as goal programming in the recent literature (Bartlett et. al., 1976) and is based on preemptive (Ijiri, 1965) or priority depend- ent (Dauer & Kruegen, 1977) goal constraints. Goals are treated according to their perceived importance which can be done by attach- ing preemptive priority weights to the goal to be met first, (P1), and frozen before moving to the next priority goal, (P2), and so on. Dobbins and Mapp (1979) refer to this approach as a "Ranked Goal Structure" formulation and identify it as representing a lexographic -25- utility function. Lexographic utility theory requires specifica- tion of "satisfactory" levels of dominant goals (1 through n-l), then, the decision maker is assumed to maximize (or minimize) the least important goal (n), subject to "satisfactory" levels of the dominate goals (Lin, Dean and Moore, 1974). The problem is the same as above except the objective function becomes preemptive: M1n1mlze (Piwiui + Piwivi) where 1 = l, 2, 3, ..., n and Pi >> Pi + 1) such that Pi is frozen as an equality once met. Often this linear problem cannot be solved by the simplex method but requires a modified algorithm because there are not enough large preemptive numbers (Pi) for lots of goal constraints. In effect, the algorithm must be made so that optimizations occur in stages. Once the goal associated With P1 is achieved, it is changed from a goal constraint to a strict equality constraint. Then optimization continues for P2 subject to a frozen Pl constraint. The reverse slacks in this case, when multiplied by weight (Wi)’ form ranges around the targets (Gr). For example, if we only want to allow negative deviations from targets, a zero weight is attached to ur and a positive weight to vr. As there may be a number of goals in the same priority level, the relative importance with P1 can be established by weights on ur and VI. The second goal programming model presented has n levels of priorities and the first model has just one priority level which, in terms of model two, means we are just working within P1. In both -26- goal programming models the goal vector does not have to be in the feasible set; however, if all goal functions can be over- achieved the method yields an inferior solution (Haimes et. al., 1975 p.24). Formulation of Study: Goal Programming Both the described methods will work well for the linear multiobjective problem where all objectives are to be optimized, that is, each objective must be stated in terms of either maxi- mization or minimization. If each objective is not in optimiza- tion terms, but in terms of satisfying a goal, a goal programming framework is advantageous because it reduces the relevant full efficient set to a smaller subset when a target is achieved. For example, if the national target is for 100,000 mt. of corn pro- duced we need not be concerned with this dimension of the objec— tive space beyond the target. A goal programming model incorporat- ing both optimization and satisficing objective functions used in this study. The terminology of different programming frameworks is not standardized; in fact, current conceptual viewpoints on goal programming ranges from those who view goal programming as an extension of linear programming (Lee 1972; Bartlett et. al., 1976) to those (Ignizio, 1978) who view goal programming as a general framework from which single objective function problems, such as the linear case LP,are the special cases. This study uses a single tableau land-base goal program- ming model. Three stages are used in the formulation of this model for analysis of trade-offs: -27- (1) Linear optimization of goals defined in terms of maximization and minimization. (2) Formulation of the goal programming model. (3) Formulation for sensitivity analysis. When objective functions are formulated by decision makers in terms of optimization an approach to generating trade- offs is to first optimize each function individually. This generates corner points to the trade-off surface. These solutions are put in as targets in a goal programming formulation, weights on reverse slacks, are generated and the deviation between targets minimized. This has been proposed as an interactive model (Benayoun et. al., 1971; Roy, 1971). The approach used here differs because all objectives are not specified in optimization format and the model is not interactive but develops a partial trade-off set. Step 1 Right-hand-sides (RHS) for objective functions, stated in terms of optimization, must be generated for the GP model. This can be visualized as optimizing an LP for each of these functions or as optimizing the GP model with a weight of l on the objective being considered and zeroes on all other objectives. Given the specification of the model optimization of a single objective func- tion defines a corner point in RP (space defined by n objectives) on the trade-off frontier. Step 2 Specify the GP model allowing only negative deviations from the targets developed in Step 1. Add in objective functions -23- specified in terms of goals allowing only negative deviations. Allowing only negative deviations greatly simplifies the model. For objectives defined in terms of optimization Step 1 assures that no larger RHS can be generated by solving the GP model. For objective functions defined in terms of goals we are only concerned with satisfying RHS so there is no need to penalize overachievement. Step 3 Performing sensitivity analysis on the goal programming objective function by using parametric techniques can delineate the trade-offs. This is basically the approach used here. One of the disadvantages of the GP procedure is inter- preting shadow prices which are in terms of goal satisfaction (thus reflecting the effect of marginal relaxation on total goal achievement). However, Wheeler and Russel (1977) resolve, to some extent, the difficulty of not being able to put an economic value on material resources by re-constructing a particular efficient solution in LP form with a monitary based objective function and other objective functions as constraints. Economic Interpretation of Analytic Framework The GP approach outlined above corresponds to minimizing disutility. Utility is maximized if all targets (generated by individual objective function optimizations) are achieved simul- lnaneously. This would be the case if there were no trade-offs bertween objectives, i.e., objectives are independent. In the nor- HEi]. case of trade-offs minimizing disutility is minimizing the sum -29- of deviations between weighted multiple objective functions. The programming model generates an efficient set of representative points by using a series of linear tangents to possible utility functions (implicit common denominators). A linear tangent to a utility function is the slope of the function at a point which is analogous to the ratio of weights used in the GP objective function. Parametric or estimation techniques are then used to change the implicit common denominator thus developing an oppor- tunity or efficient set. Extensions of Analytic Framework In this chapter the discussion has been limited to linear mathematical programming as an approach to multiple objective trade-off analysis. The standard assumptions of LP still apply to GP, as formulated above, including divisibility and linearity; however, the assumption of optimization is overcome by incorporating targets. Basic LP model adjustments, like separable programming and integer programming, fit equally well into the GP model format as LP. Conceptually goal programming has been extended to mul- tiple planning levels by Salih (1975) for goal conflicts. Sfeir- Younes and Bromley (1977) have conceptually extended goal program- ming to hierarchies of objectives for project evaluation in deve- lOping countries. The focus of most multiobjective strategies it to inter- actively work with the decision makers to systematically reduce -30- the feasible solution to a single optimum. Haimes, et. a1. (1975, 1974), developed the surrogate worth trade-off method which has been used by Lindsay, et. al. (1977), and Goicoechea, et. a1. (1976) for a nonlinear programming problem. Interactively working with decision makers was not pos- sible in this thesis. Chapter 3 AN OVERVIEW OF COSTA RICAN AGRICULTURAL SECTOR OBJECTIVES The Agricultural Sector The agricultural sector has traditionally been, and continues to be, the most important sector of the Costa Rican economy. In 1975 it accounted for about 20 percent of Gross Domestic Product, 65 percent of total export earnings, and 35 percent of total employment (USAID, 1977).1 Agricultural exports are very important to the Costa Rican economy. Coffee and bananas are the major exports followed by sugar and beef. Coffee, sugar, and bananas collectively ac- counted for 57% of total exports in 1975. Coffee was surpassed in 1975 as the major export earning crop by bananas. The total population of Costa Rica, given by the 1973 Census, was approximately 2 million. About 1 million people live in rural areas. About 225,000 people, according to USAID, are classified as "poor" farmers using the USAID poverty definition of less than $150 income per year in 1969 prices. Generally, farmers Classified as "poor" are tied to small farms and do not produce 1Refers to United States Agency for International Deve- loPment . -31- -32- the high value, labor-intensive crops, especially coffee. Small farmers producing coffee are generally not poor. The rural poor, by farm size, are identified (TABLE 3). It is important to note that the number and distribution of poor farmers is not highly sensitive to the definition used (USAID, 1977). Most small farmers who are not poor produce coffee or have substantial off farm employment often coffee harvesting. Farm size definitions, used alone, does not explain farm poverty in Costa Rica. Coffee is grown by small and medium size farmers and is highly labor intensive, coffee production provides substantial employment for non-farmers. Bananas and sugar are generally grown as plantation crops and beef production is characterized as extensive. TABLE 3.1 NUMBER OF POOR FARMS, NON-POOR FARMS AND PERCENT OF FARMS WHICH ARE POOR BY FARM SIZE FARM SIZE NO. OF POOR FARMS NO. OF NON-POOR PERCENT OF (under 1100 FARMS FARMS WHICH Colones/capita) ARE POOR 0-1 Ha. 9,018 4,275 67.8 1-2 Ha. 4,336 2,498 63.5 2-5 Ha. 6,550 5,551 54.1 5-10 Ha. 3,896 4,364 47.2 10-20 Ha. 4,079 4,607 47.0 Over 20 Ha. 0 20,045 g.0 Landless 2,870 l 320 6 .5 Total —§3o,73 27727375 m. ‘1 Note: 1100 colones equals $110. Source: Adapted from 1973 Census as cited by USAID (1977). -33- Virtually all farms in Costa Rica are market oriented. The national average home consumption of any crop on poor farms does not exceed 6.4% of the total value of production for any farm size category (TABLE 3.1) (USAID, 1977, p.11). The highest home consumption is for beans and corn. Both commodities are major staples in the Costa Rican diet. The agricultural sector has been characterized as being over institutionalized, meaning that numerous public agencies, quazi-public associations, and autonomous boards act with little coordination. One of the serious considerations of this study is that no basic data set at the national level has been developed. This has resulted in conflicting agricultural sector statistics. Also, there is no standard regionalization used in developing the statistics. Sector Objectives2 Costa Rica's national agricultural objectives, like those of many countries, define one level of objectives within a whole pyramid of political-economic objectives. The overall societal objective is to become developed. One of the sectors feeding into this objective is agriculture. The agricultural sector has a set of objectives. This analysis is strictly concerned with the subset of multiple economic objectives related to agriculture. This is 2This section relies heavily on the agricultural sector objectives for the current planning period as documented in: OFICINA De Planificacion, Sectorial Agropecuaria Costa Rica, Plan Annual Operativo Del Sector Publico Agropecuario Para 1977, San Jose, Costa Rica, Junio de 1977. -34- a simplification as there are many interrelationships between objectives of different sectors. Agriculture provides important markets for non-farm products, is a major recipient of social overhead capital investments, is a major employer of human re- sources, and makes substantial contribution to the tax base. The contribution agriculture makes to the total economic is sub- stantial and has been looked upon as having increased importance by the government. In general terms the emphasis of the national agricul- tural policy is the improvement of rural society and expansion of agriculture's contribution to national development. The ob- jectives have been further defined, but are still broad, and characterized as: 1) substantial increases in production for exports; 2) increasing rural employment and income; 3) substitu- tion for imports through growth in production of currently im— ported commodities (self-sufficiency); 4) rational use of re- sources; 5) provision of inputs for national industries. Export Crop Objective Costa Rica has chronic balance of payment deficits which have been financed through borrowing. In 1974 the deficit was $260 million. Agricultural exports play a very important role in attempts to reduce this deficit and the need for foreign bor- rowing. The export dollar value of coffee, bananas and sugar in 1975 was $278 million.3 3See TABLE 5.1 to 5.4, Chapter V for details. -35- Fluctuation in export earnings have been mostly the result of prices in international coffee and sugar markets. Increasing beef exports has been part of a diversification policy. Export crops are not only important as earners of foreign exchange, but as a source of government tax revenues. Generally speaking, exports are relatively easy to effectively tax in developing countries as compared to taxing, wealth or income. Maximizing agricultural export earnings captures much of the economic essence of the Costa Rican government's interest in agricultural exports but may not adequately reflect attempts to diversify agricultural production as a hedge against price fluctuations of exported commodities. Employment and Income Objective Increasing rural income oppOrtunities through employ- ment generation is a priority issue in Costa Rica. The age struc- ture of the population indicates that the size of the labor force will continue to increase quite rapidly. Projections based on a study by the Instituto de Estudios Sociales en Poblacion are pre- sented (TABLE 3.2). The general consensus on employment is summarized by USAID (1977, p.63). Underemployment appears to be a serious problem in the agricultural sector. In recent years most new jobs have come from industry which has produced 50% more jobs than the 1973-1978 development plan target while agriculture has provided 50% less than the target. It appears doubtful that in- dustry can continue to provide employment at its past rate of -36- TABLE 3.2 PROJECTION OF POSSIBLE LABOR FORCE 1973 1976 1980 1990 POPULATION (000) 1,872 2,009 2,225 2,822 LABOR FORCE (000) 385 658 750 991 NEW JOBS NEEDED/YEAR* 24,000 24,550 21,460 *Computed on a straight line basis holding unemployment at 6.2% from 1976 to 1990. SOURCE: M. Bogan and C. Raabe, Proyecciones Regionales de la Poblacion de Costa Rica. Universidad Nacional de Costa Rica, Heredia, September, 1976. Cited by USAID, An Assessment of The Agricultural Sector in Costa Rica (1977). growth. This will require a higher rate of employment in agricul- ture if overall employment goals are to be achieved. Two important keys to generating more employment in the agricultural sector are: l) more intensive crop production, which is closely related to government pricing and land tenure policies, and 2) increasing production of labor intensive crops, which is currently closely tied to the export crops, especially coffee. The export crop and employment objective appear complementary as ex- port crops are among the crops with the highest labor demands; how- ever; demand for labor is seasonal as most labor goes into coffee harvest during November through January. USAID (1977), using their definition of poor, estimate that coffee harvest currently pro- vides equivalent to 100,000 person-years of employment. Coefficients -37- of labor requirements by crops for the agricultural region of Costa Rica have been developed for this analysis and are presented in Chapter V (TABLE 5.6). Simplifying this objective into a function of maximizing employment has the limitation of not reflecting the seasonal labor demand for several crops. This simplification ignores the ques- tion of possible year-round employment through the specification of alternative crop rotations in each major agricultural area of Costa Rica. Self-Sufficienpy One objective that is never left off any list for Costa Rica is substitution for agricultural imports through increased domestic production. The intent is to become self-sufficient in the basic grains, corn, beans, rice and sorghum. Corn, beans and rice are the staples of the average diet. Although the demand for these commodities has grown rapidly production has lagged. Imports of the basic grains and percent of consumption imported for the crop year 1975-1976 are shown (TABLE 3.3). TABLE 3.3 1975/76 IMPORTS OF BASIC GRAINS AND IMPORTS AS A PERCENT OF TOTAL CONSUMPTION CROP 1975/76*IMPORTS IMPORTS AS A (in Kg) % OF TOTAL CONSUMPTION Beans 13.9 million 46 Corn 6.2 million 6 Rice -25.0 million (export) —- §9rghum -2.3 million (i.e. exports) -- SOURCE: Adapted from USAID (1977). -38- Beans and corn are generally grown by small farmers. Rice is produced under dryland conditions on both large and small farms. Sorghum is used almost exclusively as animal feed and was not a significant crop in the 1973 Census.4 The 1985 demand estimates for the basic grains, the actual production for 1974, and the percent increases required to meet demands are shown (TABLE 3.4). TABLE 3.4 DEMAND FOR BASIC GRAINS: ACTUAL 1975, PROJECTED 1985 AND PERCENT INCREASE REQUIRED Actual 1974 Project 1985 % Increase Required metric tons metric tons Beans 31,580 43,900 39 Corn 147,181 212,900 45 Rice 69,682 104,026* 37 Adapted from M.J. Lord - "Market Trends and Prospects of Agri- cultural Commodities" IDB/IBRD/AID. Agricultural Sector Survey- Draft, Oct. 1976. Cited by USAID (1977). *Rice - 1985 Demand is the 1973 production as shown by the Census. Rational Use of National Resources Within a framework of national objectives agriculture is one of the competitors for the use of natural resources such as land and water. Two broad elements are considered factors of this objective: environmental rationality and economic rationality. Balancing these two factors is part of the political process involving 4In the analysis done here sorghum is not included as the livestock sector was not modeled and data were not available. -39- critical trade-offs, but are beyond the scope of the analysis. Reference will be made to two environmental concerns with critical economic implications that will be referred to in later sections. First is the threat of coffee rust invading Costa Rica from Nicaragua. The government has discouraged the introduction of coffee production in northern areas of the Costa Rica to effec- tively create a buffer zone. Second, deforestation in Costa Rica has destroyed watersheds. This is especially prominant in the northern reaches of Costa Rica. In these areas land has been shifted from tropical forest to pasture for extensive livestock production. Though these two major environmental concerns are not reflected in the analytical economic model developed, they are considered in the analyses of model results. For example, validity of model results would be tempered if more coffee pro- duction in the northern reaches of Costa Rica were a model result. Economic rationality is defined as the most efficient use of resources given the situation including, farm size, costs of production, and technology levels within a market framework. By efficiently using resources agricultural production takes place where it is most profitable and, assuming perfect competition, the result is the lowest cost to consumers. The concept relied on is comparative advantage which defines, in a relative sense, spatially 'where production should occur. Traditionally this is evaluated by formulating the objective function as minimization of cost. Economic Delineation of Objectives The objectives described in the previous sections are verfiy interdependent. For example, export crops and high employment -40- crops are often the same but the more area planted to these the less area available for basic grains. To study the interrelation- ships and trade-offs between Costa Rica's multiple objectives the following are used: 1) Maximize export earnings 2) Maximize employment 3) Satisfy 1985 domestic demand for basic grains 4) Minimize cost of agricultural production. National Sector Planning Institutions The Ministry of Planning and Ministry of Agriculture (MAG) are the lead Costa Rican agencies responsible for agriculture and rural development planning, although, numerous public and quazi-public agencies, committees and organizations have programs and areas of influence. The National Agricultural Council (CAN)5 is a group of ministers and officials set up to coordinate agri- cultural and rural programs. CAN does not include about 19 autonomous organization like the banks (quazi-public) and crop authorities (banana council, coffee council, etc.) that oversee production. CAN is chaired by the Minister of Agriculture and members include: The Minister of Planning; the Minister of Economy, Industry, and Commerce; the Minister of the President; the Executive President of the National Grain Production Council; the President of the Central Bank; and the President of the Institute of Lands 5Spanish acronyms. -41- and Colonization. CAN has the function of setting the direction, general policies, and objectives for the agricultural sector. A technical support unit established for CAN was the Agricultural Sector Planning Office (OPSA).6 OPSA works closely with CAN to implement and refine objectives and general direction policy statements into programs, projects and specific targets. Planning Horizons and Regions Intermediate length planning horizons are focused on by OPSA. Four year plans are developed based on broad CAN objec- tives, policies and programs, then specific goals such as commodity production targets are set. Currently Costa Rica is operating under an OPSA agricultural development plan for 1973-1982. Two major agricultural planning regionalizations have been extensively used for the country. One was developed by MAG for extension purposes and the other one by the National Planning Office for sector planning purposes. The latter has been adopted by OPSA. This analysis uses a slightly modified MAG regionaliza- tion as it specifically defines agricultural regions and the Census also used it (details Chapter IV). 6Spanish acronyms. Chapter 4 A LAND BASE REGIONAL MODEL Introduction A land base comparative advantage model and a discus- sion of the associated data base are presented in this Chapter. The economic concept underlying land based linear programming models is comparative advantage. Equations and model structure are presented in the next chapter. Comparative Advantage Theoretically comparative advantage is not a static concept though it is often formulated as such in analytical models which are based on natural advantages which affect crop- ping systems and yields, like climate and soils, and costs of production. Land base models are programming models that use geographic land units as the building blocks for model specifica- tion. Land base LP models formulated at the national level are often referred to as Heady models (Heady and Nicol, 1976) and regional models are illustrated by River Basin Studies (Hostet- tler, 1970; Putman et. al., 1977). Comparative advantage is a broad concept based on analyzing relative efficiency to allocate production. This is done by minimizing the cost of production -42- -43- and usually transportation, given exogenous demands. In practice, comparative advantage is affected by more than just physical condi- tions. Barlow (1972, p.261) says, "comparative advantage is meas- ured by the economic ability of an area to compete with other areas in the production of particular good or services. Certain comparative advantages may stem from natural endowment. Others may involve favorable combinations of production inputs, favorable location and transportation costs, favorable institutional arrange- ments, or desired amenity features.” Thus, comparative advantage can be associated with natural resource conditions or can be created by institutions and policy, or can be from a mix of natural resource and institution and policy conditions. For agricultural production purposes the natural re- source endowment includes factors such as climate, soils, and water which influence yield. Favorable production combinations include the availability of capital and labor which often out— weigh natural advantages associated with a region. Transporta- tion considerations can be extremely important and opening up areas of natural advantage with transportation networks can greatly influence comparative advantage. Institutional advantages are created advantages, of any administrative or political-level ac- tion, including direct or indirect public subsidies. For example, factor input price influences comparative advantage. Amenity fac- tors such as cultural practices or values can also contribute to the comparative advantage of a region. -44- General Graphical Depiction A simplified discussion of interregional location of production and comparative advantage is developed for two regions and two products Y1 and Y2. Assuming, that the regions trade, and zero transportation costs, each region has the same product price ratio. By also assuming factors of production are not mobile between regions the location of production can be depicted by the relative shapes of production opportunity (possibility) curves. A regional production possibility curve shows how much production could occur if just Yl of Y2 were produced and all combinations of Y1 and Y2 that could be produced in a region given a set of inputs. A case of absolute advantage for one product in each region is depicted (FIGURE 4.1). Production in Region 2 is the amount Y22 of product Y2 and Y12 of product Y1 (FIGURE 4.1). Specialization in production for Region 1 is depicted (FIGURE 4.1). Comparative advantage shows that while on region may have an absolute advantage in both products specialization still occurs based on relative advantages (FIGURE 4.2). Production in Region 2 is the amount Y22 of Y2 and Y12 of Y1 (FIGURE 4.2). Specialization for Region 1 is likewise depicted. The result of specialization due to comparative advan- tage is that overall production is increased and this increased production provides increased satisfaction to each region given that the price ratio is a valid measure of value. No specializa- tion occurs if production possibility curves are identical. -45- FIGURE 4.1 ABSOLUTE ADVANTAGE FIGURE 4.2 COMPARATIVE ADVANTAGE IN EACH REGION 1 i I 1 xRegion 2 price ratio t ., -----.-.- ------ 1 \YRegion l i i 1 - Y, 22 Y21 2 However, this is highly unlikely under situations with a number of different regions and different products. It is important to note that complete regional specialization does not occur due to increasing rates of production substitution (production pos- sibility curves are concave to origin). The Linear Case Many elementary discussions of comparative advantage suppose that the marginal rate of substitution between products within a region is constant. This implies linear production pos- sibility curves. Most mathematical programming models, including the multiobjective model used here, assume linearity. The end product of optimization using a linear production possibility curve is complete regional specialization in production. That is price ratio, except the unlikely case where the slope exactly -46- corresponds to the production possibility curve, results in a corner solution i.e., producing either Y1 or Y2 (FIGURE 4.3). Complete regional specialization in agricultural production seldom exists. Linearity assumes products compete for resources at constant rates ruling out any supplementary or complementary nature existing between products.1 The real world is much more like the non-linear case than linear. However, when solving complex optimization problems, linearity greatly facilitates solu- tion. To achieve greater correspondence between the non-linear conditions that exist in the real world and the optimization tech- niques non-linear curves are segmented into a number of linear parts or the optimization models are constrained by other linear factors so complete regional specialization does not take place. In the model structure employed in this study regional constraints are employed to eliminate complete regional specialization. FIGURE 4.3 LINEAR PRODUCTION POSSIBILITY AK -production possibility curve 0 F Y2 If: (1) MRS (marginal rate of substitution) < 0: products are complementary. (2) MRS = 0: products are substitutes. (3) MRS > 0: products are competitive. -47- Objective Opportunity The model developed in this study determines comparative advantage within a framework of multiple objectives or dimensions of performance. This might be called an objective opportunity perspective rather than comparative advantage based on opportunity possibilities. Comparative advantage, as defined in a traditional LP model, is just one of the agricultural sector objectives being analyzed here. By incorporating other sector objectives the op- portunity cost of minimizing the cost of production can be defined in terms of export earnings, labor employment, and self-sufficiency. Regional Specification of the Model Costa Rica is approximately 100 kilometers wide and 500 kilometers long with a total of approximately 51,260 square kilometers. The central north-south mountain chain separates the country into two areas. The Central and Pacific area comprises about four-fifths of the country and is characterized by rugged mountains separated by relatively large scattered flat plains. The Atlantic area, which lies on the eastern edge of the country, is relatively flat. The Ministry of Agriculture further divides the country into seven agricultural zones which have been reduced to six for this analysis (FIGURE 4.4). These regions are: Region 1 - Central Region — Pacifico Norte - Pacifico Central Region - Zona Norte 2 3 Region 4 - Pacifico Sur Region 5 6 Region - Atlantico -43- FIGURE 4.4 AGRICULTURAL REGIONS OF COSTA RICA NICARAGUA \m "a PACIFCO mm? film “My .- (REGICN 2) PACIFICDY-J (REGICN 3):;:-/ (if? 2 3% xi 3 AX“: B 3 7 “% WWNM {PM iFun ,;(mmum4 Scale Approx. 1:1,078,000 (In KM) 0. 3.0 6.5 $30 ADAPTED FROM: DIRECCION GENERAL DE ESTADISTICA Y CENSOS, CENSO AGROPECURAIO 1973 REGIONES AGRICOLAS. SAN JOSE, COSTA RICA - JUNIO DE 1975. -49- The boundaries of these agricultural regions follow the political boundaries of cantones. Agricultural regions are delineated on physical and macro-ecological characteristics. Central Region This region produces most of the nation's coffee, sugar cane, corn, beans, and vegetables. The topography is a rough transitional zone with elevation ranging from 600 to 1,600 meters leading to the central mesa with elevations ranging from 1,700 to 3,000 meters. There is a small coastal area included in this region. Pacifico Norte This is a relatively level, dry tropical region with elevations ranging from 0 to 500 meters. The area has a long dry season limiting most nonirrigated production to one crop per year. Crops produced are sorghum, corn, beans and rice (especially where irrigation water is available). Pacifico Central Much of this area is humid tropical forest. The most common crops are sugar cane, beans, rice and corn. Elevations range from 0 to 500 meters. Pacifico Sur This region is characterized as relatively level, humid tropics with elevations of O to 500 meters. The major crop is bananas with some coffee, beans, and corn, also grown. -50- Zona Norte This region is rugged with elevations between 600 to 7,000 meters. There is relatively little agricultural production. Some bean, corn, and sugar cane, cultivation exists. Atlantico This region produces most of Costa Rica's bananas and cocoa. The zone is humid tropical and relatively level with eleva- tions reaching 500 meters. Data Base Sources of Data The analytical model was developed from secondary Costa Rican data. Sources include: the 1973 Census; the Central Bank (BC); the National Production Council (GNP); the crop specific associations for bananas, sugar and coffee; and the Ministry of Agriculture (MAG). Data used and developed from these sources are discussed in subsequent sections. Crop Production Data on production by canton for each crop are reported only in the 1973 Census. No time series data are available except at the national level. The time series national production data sources are from the Central Bank and from aggregating crop specific associations data (Aggregate). There are large differences in production levels reported for each crop depending on the source referenced. However, production trends for each particular crop tend to have the same direction of change over time among sources. -51- Production levels for major crops are compared for 1973 (TABLE 4.4). The discrepencies between estimates of total production among secondary data sources are easily observed, i.e., beans. TABLE 4.4 1973 NATIONAL CROP PRODUCTION FROM CENTRAL BANK, CENSUS OF AGGREGATE (CROP SPECIFIC ASSOCIATION) DATA Crop Central Bank Census Aggregate corn 65476 53491 64444 rice 81641 104026 97131 beans 10030 11445 5222 coffee 480530 394325 453891 sugar cane 2341295 2571505 2246111 bananas 1289401 12571505 1198064 plantain 66863 119511 82811 cocoa 5617.6 4823.5 4535.8 tobacco 2522 1586 1605 potatoes 23238 20626 20628 yucca 9959 13818 13810 minor crops 31940 35491 31940 Crop Areas The Census is the only source depicting where all crops are grown in Costa Rica. The CNP has areas for the large regions they report data by, but only for the basic grains. Data employed in this study are cross-sectional data given by the census. Con- versions from crop area to actual physical area cultivated were made by subtracting second plantings from total crop plantings. Yields Estimates of crop yields by region can be made if an eclectic approach is taken. Implicit yields can be calculated -52- from various sources. The main source is the 1973 Census. MAG cost of production studies have yields for the farms studied between 1972 and 1977; these studies cover many basic crops, but not all regions of the country. Apparently the Ministry of Agri- culture Surveys are only very loosely tied to any "representative" farm concepts. The CNP reports regionalized yields on the basic grains for 1973 and 1975; additionally, this source provides the only data on sorgo (grain sorghum) which has recently become a significant crop. Coffee yields by region for 1975-1976 were available from the Oficene de Cafe (Coffee Institute). Obtaining yield coefficients from these sources poses some problems as tech- nology levels are difficult to define. Some of the MAG Cost of Production Studies have well defined technology levels. However, most data are no more detailed than implicit yields. Costs of Production The cost of production data set relies on BC data that cover the major crops in most regions. These data were developed for agricultural loan purposes. MAG budget data were used as a supplement and not relied heavily on because these data are not based on analysis of representative farms. Coffee costs were supplemented by the Coffee Institutes regional coefficients. Neither the BC or MAG budgets were consistently done over time so costs were put together by source for important inputs. Labor was analyzed in two components, human and mechanical. Materials were grouped as, seed, fertilizer, and herbicides/ pesticides. Costs were updated to 1976 by the FAO consumer price -53- index for Costa Rica. Costs were associated with regions as much as possible. Where costs couldn't be regionalized it was by coincidence fortunate that the national-level costs actually represented crops currently grown in a certain region, i.e., bananas in the region. No data source adequately specified establishment costs for any crop. This type of information is especially necessary for perennial crops (coffee, bananas, and cocoa). Only variable costs were used in the model under the assumption variable costs are included and will be higher in areas where land has to be cleared or otherwise modified to produce new plantings of peren- nial crops. £2221; Obtaining labor coefficients from the secondary data sources proved to be difficult. Both Central Bank and MAG Cost of Production studies often don't list physical units but only labor costs. By reviewing the data sources by crop, especially BC budgets for 1973 to 1976, a set of labor coefficients was developed. Most labor coefficients were assigned to agricultural regions based on yields with the underlying assumption that har- vest labor is proportional to yields. Reviewing that regional data that was available, the assumption that labor use is tied to yield levels appeared to hold. Exports Data on national exports were available from the Central Bank and FAQ. The Central Bank data were used because these data -54- provided both exports and the amount internally consumed so ratios could be developed for national production coefficients. The export crops are coffee, bananas, sugar cane, and cocoa. Data Calculations and Problems Commodities Excluded Information derived from these data sources excludes livestock activities, cotton, and sorghum due to lack of data. Cotton and sorghum have become important in Costa Rica since 1973. Intercropping One of the major problems with the published data sources available was determining the amount of the intercropped land. Information on intercropped land applies only to corn and beans and is very limited. Apparently census enumerators collected data on hypothetical areas that would have been planted in each crop if no intercropping had taken place. Yield ratios were ap- plied to the implicit single crop yields (solo) derived from the census data. This ratio was also used to determine costs of pro- duction since no production costs were available for intercropped corn and beans. The relationship used was: 70%_of the associated solo coefficients for both intercropped beans and corn. For example, intercropped corn yields were specified at 70% of the implicit census yields for solo planted corn. This ratio derived from experiment station studies based on standard inputs and practices (Regional Office of Central America and Panama, USAID -55- Mimio, 1978). It was further assumed that intercropping only allows one planting per year, i.e., no multiple cropping. Multiple Cropping Multiple cropping refers to the number of harvests (plantings) a farmer gets off a particular piece of land in a calendar year. No reliable sources are available that specify the amount of multiple cropping occurring in Costa Rica. There- fore, it was assumed that the census data category "second plant- ing" reflected the amount of multiple cropping practiced. Un- fortunately the 1973 Census period was a droughty year in some areas. Drought would probably reduce the practice of multiple cropping. General references suggest that not much multiple cropping occurs in Costa Rica. Standard Units A problem with some of the data sources is that units of measurement are not specified or are underspecified. The units were inferred by comparing data sources that had units. Products measures that would be influenced by processing and moisture con- tent were difficult problems to handle. Coffee presented a major problem as different sources reported production at different stages of processing. Pasture and Idle Land Qualitatively pasture is difficult to specify, therefore, it becomes a catch-all category. Census reporting of pasture -56- includes conditions that range from improved irrigated pasture to land with essentially no animal carrying capacity. Large amounts of idle land were reported in the 1973 census. Again, this was probably a function of the weather condi- tions during 1973. A Test of Data Sources and Set Used Test A test2 was conducted comparing three basic data sets to study the sensitivity of coefficients in a L.P. model with a minimization of cost objective function. The three data sets on yields, land area, and production used from the BC, Census, and an aggregate of other sources including the crop association boards. Two sets of production costs_were developed. One was developed from the BC and the other from MAG data. The test data sets generally provided the same directions of change in comparative advantage and regional production patterns; however, the magnitudes in the directional changes differed by data set. The analysis of the data set combinations and sensitiv- ity analyses showed the model to be highly responsive to the pro- duction cost estimates. Data Set Used A best set of data was gleaned from all available sources for the model developed here. Major aspects of the set were developed from: 2The work was done by Mark J. Cochran and the author during 1977-78 as part of the CRIES Project and detailed in a pro- gress reports. -57- (1) Census data on yields, areas, and crop production for flexibility restraints. (2) Costs of production and labor coefficients from the Central Bank. (3) Yields and Production Costs for coffee were from the Coffee Institute data. (4) For agricultural exports and export earnings Central Bank data was used. Implications of Regions and Data The level of aggregation implied in the regions used is closely tied to the quality of the data set obtained through reasoned-interpretation from the available secondary data sources. The desired level of aggregation depends on the purpose of the investigation. What is desired is conditioned by the data avail- able. Agriculture in Costa Rica is heterogeneous within the re- gions analyzed due to institutional factors such as farm size and natural factors, especially soil and climate. Costa Rica is in one of the least homogeneous areas of the Western Hemesphere. The number of distinct vegetative types in an area is a good indicator of physical homogeneity (heterogeneity). Costa Rica ranks third behind the Amazon area of Brazil and Malaysia in the 3 number of distinct vegetative types per hectare. This would sug- gest disaggregating of the data beyond the production regions 3Personal communication from A.A. Atchley, Agronomist, SEA, USDA. -53- used would be desirable. Unfortunately, this would be an in- appropriate use of data interpreted from the sources previously cited. Market demand regions are not included in this analy- sis. Most LP spatial agricultural production models use large market regions made up of smaller more homogeneous production re- gions. Costa Rica is a small country so it may appear that na- tional demands are adequate. But, a characteristic of the country is rugged topography making transportation of food difficult. No data on market demand regions are available. Chapter 5 MODEL STRUCTURE, COEFFICIENTS, ASSUMPTIONS AND LIMITATIONS Introduction This chapter presents the single tableau goal program- ming model used to develop regional production patterns for agri- culture that optimize various sector objective functions. Two planning horizons were used; a relatively short-run estimate and a medium run 1985 solution. The model, run for both planning horizons, uses 1973 as the base year. Different flexibility con- straints were used to depict static trade-off associated with the two planning horizons. Sections make up the chapter. The first section on model structure describes the general goal programming formulation including, goal constraints, objective function, national produc- tion constraints, flexibility constraints, and coefficients. The second section discusses model assumptions, limitations and use- fulness. Model Structure The model is termed "land base" meaning activities are all tied to land availability by region. All activities come into -59- -60- solution on a per hectare basis (Xij is the amount of land in crop i in region j). Characteristics such as farm size are not included in the model except implicitly through impacts on re- gional yields, costs, and type of crop produced. The model requires the following input data (FIGURE 5.1): (1) Land available for agriculture in each region. (2) Yields per hectare for crops by region. (3) Costs of production per hectare for crops by region. (4) Labor requirements per hectare for each crop in each region. (5) Export crop earnings per hectare in each region. (6) Regional requirements and national demands. The sources of information and quality of the data set was presented in the preceeding chapter, mathematical structure and model coefficients are discussed in the following subsections. The crop and regional codes are given (TABLES 5.1 and 5.2, respec- tively). Goal Constraints Each goal constraint is associated with one of the mul- tiple objectives being analyzed. The attempt is to achieve the right-hand-side targets for these constraints allowing deviations in one direction only for each constraint. The right-hand-sides for the goal constraints are pre- sented (TABLE 5.3). These were derived by optimizing an LP for -61- FIGURE 5.1 DEPICTION OF MODEL column row One column for each crop by region Right-hand Side costs specified by region _%l Cost ost7hectare’by re- gion iinimum Cost export earnings .I export Earnings/hectare’by Maximum by region earnings region Earnings labor coefficients Tlabfir Labor requirements] Maximum by region hectares by region Labor . self Yield7hectares of 1985 Demands yields by region raL sufficiency basic grain by reg1on crop one row fOr each crop Nat1onal .-ezeéessiee-.--S!ieléa£beese:e§2-- Demands 1 2 Regional 3 Production Requirements 4 5 6 resource one row for each Total _-$lae§2 ..... . ..... E28199 .......... Hectares Available 1 by Region 2 3 4 5 6 -62- TABLE 5.1 CODES USED BY CROPS TABLE 5.2 CODES USED BY REGION Code Crop Code Region 21 Corn 1 Central 1 22 Rice 2 Pacifico Norte 2 23 Beans 3 Pacifico Central 3 24 Coffee 4 Pacifico Sur 4 25 Sugar Cane .5 Zona Norte 5 26 Bananas 6 Atlantico 6 27 Plantain 28 Cocoa 29 Tobacco 30 Potatoes 31 Yucca 32 Interplanted 33 Minor Crops 7O Pasture 99 Idle Cropland TABLE 5.3 OBJECTIVE FUNCTION AND GOAL CONSTRAINT RIGHT-HAND-SIDES FOR SHORT-RUN AND LONG-RUN MODELS Objective Function Maximum Labor Employment (in 10,000 of hours) Maximum Export Earnings (in 10,000 of dollars) Minimum Cost of Production (in 10,000 of colones) Self Sufficiency (in metric tons) Corn Beans Rice Goal Constraints Right-Hand-Sides Short-Run 28998. 32118. 210656. 212900. 104026. 43900. Lees—Rue 34057. 40368. 206008. 212900. 104026. 43900. -53- Export Earnings, Employment and Cost individually. Added con- straints are necessary for Export Earnings because all crops do not produce export earnings. All non-export crops were given upper bounds of .1 percent over regional requirements (1973 pro- duction). Otherwise, since they have zeroes in the objective function, the labor, cost and basic grain production are much above the regional and national requirements which are greater than or equal to (1) constraints. Labor Employment Following is the mathematical statement for the labor employment in agricultural production goal constraint (Right-Hand- Sides, see TABLE 5.3; LABORij, see TABLE 5.6): § : XijLABORij + U2 = Maximum Employment defined for each crop in each region so i = 21, 22, 23, ..., 33 crops j = 1, 2, ... 6 regions Export Earnings Following is the mathematical statement for the agricul- tural export earnings goal constraint (Right-Hand-Sides, see TABLE 5.3; EXPEARNij, see TABLE 5.11): g i XijEXPEARNij + Ui = Max1mum Earn1ngs defined for each export crop by region so i 24, 25, 26, 28 export crops 1, 2 ... 6 regions Cost of Production Following is the mathematical statement for the cost of agricultural production goal constraint (Right-Hand-Sides, see -64- TABLE 5.2; COSTij, see TABLE 5.14): g i XijCOSTij + Y1 = Minimum Cost defined for each crop in each region so i = 21, 22, 23, ... 33 crops ' = l, 2, ... 6 regions Self-Sufficiency Following are the mathematical statements for the self- sufficiency in basic grains goal constraints (Right-Hand-Sides, see TABLE 5.2; Yields, see TABLE 5.13): 1985 Demand : g 21,j ch + U3 R1ce: g X22,j YRj + U4 = 1985 Demand Beans:§ X23,j YBj + U5 = 1985 Demand YC = Yield Corn YR = Yield Rice YB = Yield Beans j = l, 2, ... 6 regions Objective Function An objective function in a mathematical programming con- text is a statement of what the model is attempting to accomplish. The model uses simple weighing factors to develop a partial set of trade-offs. Following is the statement of the objective function: Minimize Z = W1(U1) + W2(U2) + W3(N1) + W4(U3 + U4 + US) where W's are weights (not preemptive) Regional Land Constraints The regional areas used in the model as right-hand-sides for cultivable area are shown (TABLE 5.4). Cultivable area is the -65- sum of currently (1973) cultivated area and idle cropland. TABLE 5.4 CURRENT CULTIVABLE AREA BY REGION IN HECTARES Current Crop Land Use Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 Idle Cropland 9,033.0 30,706.0 12,238.0 44,747.0 15,497.0 12,545.0 Cultivated 100,774.8 51,556.3 34,288.6 65,154.3 33,472.3 51,723.3 Total Cultivable 109,807.8 82,262.3 46,526.6 109,921.3 48,969.3 64,268.3 The equation for each regional land constraints is: X Xi 5; Total Cultivable Area in each Region (TABLE 5.4) i i = 21, 22, ..., 33, 70, 99 This forces the cultivated area in solution to be less than or equal to that available in each region. National Production Constraints National production constraints are used to force the model to produce at least (1) national demands (requirements). The demands (requirements) by crops are listed (TABLE 5.5). The equation is: E Z Xinij 1 National Requirements (TABLE 5.5) j i Yij is the yield associated with crop i in region j (see TABLE 5.13). -66- Note: In the model, minor crops and pasture are set as equalities and flexibility restraints in the short run model may force other crops to be equalities. TABLE 5.5 NATIONAL REQUIREMENTS IN METRIC TONS Crop Requirements Corn 53,49l.0 Rice 104,026.0 Beans 11,445.0 Coffee 394,325.0 Sugar Cane 2,571,505.0 Bananas l,251,580.0 Plantains 119,511.0 Cocoa 4,825.5 Tobacco 1,586.0 Potatoes 20,626.0 Yucca 13,818.0 Minor Crops 35,491.0* Pasture 1,558,056.0* *These are not demands in quantitative terms but just hectares planted with a yield of 1; they are forced solution to remove land for these crops. Flexibility Restraints Usability of this model rests on the flexibility re- straints which are constraints that attempt to make the model more behavioral. Many methods can be used to estimate these constraints. Estimation is usually based on time series data but these procedures cannot be applied to this analysis since time series data are not available except at the national level. —67- The constraints used here are on regional production forcing the regional production of each crop between specified upper and lower bounds. If upper bounding is not done with flexibility constraints, unrealistic results often occur. An example is what happened in the single objective formulation that maximized export earnings. Per hectare bananas are the most pro- fitable export crop in all regions of the country. The model, without bounds, essentially puts all idle land into bananas in all regions. This result is unrealistic from a national resource perspective because the agricultural regions are not homogeneous and regions that produce relatively little bananas get covered by banana production. From an economic perspective, shifts in agri- cultural production are incremental due to fixed factors of pro- duction, social and institutional constraints, imperfect mobility of resources, and risk preferences of farmers. Lower bound flexi- bility constraints are necessary to prevent unlogical regional specialization in production. The lower bounds are 295 analogous to regional demands. Meister and Nichol (1975) use a lower bound on regional production of 2 percent per year and submit that upper bounds are less restrictive. Two sets of flexibility restraints were deve- loped here to reflect both short (5 years) and medium (12 years) team analysis. For the short run model these constraints, based on the 1973 census, are: 90% of 1973 §_ 5 yr. solution f_ 140% of 1973 ~68- To reflect lag in production of tree crops and the high cost of establishment the short run model does not allow them to change: 100% of 1973 §_ 5 yr. solution 5_ 100% of 1973 For the long run formulation the following applies to all crops: 75% of 1973 §_ 12 yrs. 5_ 140% of 1973 The upper bounds do not change because of the increased number of crops allowed into solution. Weise (1978) states: ”The positive view of these flexibi- lity constraints is that they impose a reasonable and recognizable reality on an otherwise unrealistic abstract model. The negative view is that these are arbitrarily selected fudge factors that prevent the model from achieving a least cost solution." The net effect of these constraints is to control the magnitude of pro- duction in any region but not the direction of change in crop lo- cation between regions. Coefficients Coefficients in the goal programming matrix are specified for each of the six agricultural regions on a per hectare basis. Labor Employment Regional labor coefficients are given (TABLE 5.9). These are based on Central Bank data supplemented by Ministry of Agri- culture studies. Export Earnings Per hectare export earnings coefficients by region (TABLE 5.11) are developed from the information on exports and internal -69.. consumption (TABLES 5.7 to 5.10). This coefficient is in terms of dollars and is calculated as follows: (Yield) (l-Percent Consumed Internally) (Price) The yields used are those described subsequently (TABLE 5.13). Prices are F.O.B. New York City and USA, and these prices do not include transaction costs. The coffee price used was the average of prices presented (TABLE 5.7). The 1976 banana price was used (TABLE 5.8). Average prices were used for sugar cane and cocoa (TABLES 5.9 and 5.10). Percent internal consumption is from averaging the national figures (TABLES 5.7 through 5.10). TABLE 5.6 LABOR EMPLOYMENT (LABORij) PER HECTARE FOR REGIONS BY CROP Labor In Hours Per Hectare Crop Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 Corn 512 471 416 416 250 613 Rice 424 250 436 303 208 188 Beans 517 455 349 430 463 286 Coffee 1555 681 606 1330 1399 575 Sugar Cane 667 700 700 373 640 208 Bananas 573 624 956 1868 1493 1561 Plantains 364 435 950 605 256 458 Cocoa 733 120 538 553 389 344 Tobacco 809 1600 1177 Potatoes 1279 361 359 283 499 Yucca 369 217 383 210 413 310 Interplanted (Corn/Beans) 720 648 536 634 499 629 -70- TABLE 5.7 INFORMATION ON EXPORTS AND INTERNAL CONSUMPTION FOR COFFEE 1972-1973 Dollar value of export Volume of* I973:I974 $90,116,700 $120,277,995 $85,894,213 $141,673,454 1974-1975 1975-1976 export in MT 367,726 466,646 388,943 362,079 Price in Dollars 245 269 388 391 Percent Con- sumed Intern- ally 10 10 ll 15 *Volume in terms of fruta, statistics reported in oro using: La Oficina de Planificacion Sectorial Agropecuaria, San Jose, Costa Rica. SOURCE: "Medias y Equivalencies Utilizadas por la Oficina de Planificacion Sectorial Agropecuaria." (1977). Adapted from Banco Central de Costa Rica, Departamento de Credito de Desarrolo, Seccion de Economia Agropecuaria. "Datos Estadisticas del Sector Agropecuario Informe Trim estral a Junio de 1977." (Auosto 1977). TABLE 5.8 INFORMATION ON EXPORTS AND INTERNAL CONSUMPTION FOR BANANAS 1972 1973 Dollar value of export Volume of export in MT 1,077,854 1,178,511 Price in Dollars 77 77 Percent con- sumed intern- al 1y ** ** I974 1975 1976 $82,830,292 $90,681,985 $98,253,456 $144,061,314 $144,604,127 1,037,553 1,105,118 1,068,502 95 130 135 ** ** ** **Essentia11y all banana production is exported. -71- TABLE 5.9 INFORMATION ON EXPORTS AND INTERNAL CONSUMPTION FOR SUGAR CANE 1972-1973 1973-1974 1974-1975 1975-1976 Dollar value of export $18,320,751 $28,030,291 $47,864,439 $17,265,209 Volume of* export in MT 1,075,465 986,589 761,356 592,722 Price in Dollars 17 28 63 29 Percent con- sumed intern- ally 49 52 60 67 *Statistics reported in terms of processed sugar, converted into cane equivalencies by op.cit. La Oficina de Planificacion Sectorial Agropecuario equivalencies. SOURCE: Op.cit., Banco Central TABLE 5.10 INFORMATION ON EXPORTS AND INTERNAL CONSUMPTION FOR COCOA 1972-1973 1973-1974 I974-1975 1975-1976 Dollar value of export $2,815,460 $5,919,514 $6,287,176 $5,148,286 Volume of export in MT 3,757 5,087 5,309 4,108 Price in Dollars 749 1,164 1,184 1,253 Percent con- sumed intern- ally 19 23 22 27 SOURCE: Op.cit., Banco Central -72- TABLE 5.11 INFORMATION ON EXPORTS AND INTERNAL CONSUMPTION FOR COCOA D6I1ars Crop Region 1' Region 2* Region 3 Region 4 Region 5 Region 6 Coffee 1240.5 543.0 483.3 1061.2 1116.0 458.3 Sugar Cane 990.8 1031.2 1039.7 553.3 950.1 308.7 Bananas 1656.5 1803.6 2744.6 5397.3 4314.6 4511.7 Cocoa 122.5 20.0 90.0 92.5 65.0 47.5 TABLE 5.12 ADJUSTED ANNUAL YIELDS PER HECTARE REFLECTING DOUBLE CROPPED PRODUCTION % of Land Region Crop Double Cropped Yield in MT/ha Entral Arroz 13.5 2.670 Maiz 21.4 1.409 Frijoles 32.0 .872 Papa 44.0 16.189 Pacifico Norte Arroz 17.4 1.578 Maiz 33.2 1.296 Frijoles 113.8 .767 Papa 40.7 4.542 Pacifico Central Arroz 20.2 2.747 Maiz 13.2 1.145 Frijoles 55.1 .588 Papa 28.4 9.850 Pacifico Sur Arroz 23.0 1.923 Maiz 28.4 1.268 Frijoles 70.9 .725 Papa 55.5 3.586 Atlantico Arroz 37.8 1.183 Maiz 50.6 1.688 Frijoles 37.6 .482 Papa --* -—* Zona Norte Arroz 4.0 1.312 Maiz 27.1 1.225 Frijoles 49.4 .781 Papa 32.6 6.231 NOTES: _ --, no production Arroz = Rice Maiz = Corn Frijoles = Beans Papa = Potatoes SOURCE: Adapted from Direccion General de Estadistica y Censos, Censo Agropecuario 1973 Regiones Agricolas. San Jose, Costa Rica - Junio de 1975. -73- Yields Using a land based model required accounting for mul- tiple cropping patterns. In Costa Rica very few annuals are more than double cropped. Yields for multiple cropping are given by region (TABLE 5.10). The amount of land multiple cropped was cal- culated from the Census. Then, yields per hectare per year were calculated. When the analytical model brings into solution a hectare of land the yields reflect production for a full crop year. Yields in metric tons by regions are listed (TABLE 5.13). TABLE 5.13 CROP YIELDS PER HECTARE BY REGION IN METRIC TONS Metric Tons Crop Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 Corn 1.41 1.3 1.15 . 1.27 1.33 1.69 Rice 2.67 1.58 2.75 1.92 1.31 1.18 Beans .87 .77 .59 .73 .78 .48 Coffee 4.98 2.18 1.94 4.26 4.48 1.84 Sugar Cane 67.4 70.15 70.73 37.64 64.63 21.0 Bananas 12.27 13.36 20.33 39.98 31.96 33.42 Plantains 14.21 16.98 21.29 23.64 10.02 17.89 Cocoa .49 .08 .36 .37 .26 .23 Tobacco .88 1.74 1.23 Potatoes 16.19 4.54 9.85 3.59 6.30 Yucca 7.29 4.28 7.56 4.15 8.15 6.11 Interplanted A) Corn 1.03 .95 .84 .93 .97 1.23 B) Beans .64 .56 .43 .53 .57 .35 Costs of Production Annual costs of production on a per hectare basis are presented (TABLE 5.12). These costs only include hired labor, seed, fertilizer, machinery, and herbicides/pesticides. -74- TABLE 5.14 CROP COSTS OF PRODUCTION BY REGION IN COLONES Colones* Crop Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 Corn 35.57 27.31 29.09 30.82 30.89 38.10 Rice 33.90 31.80 40.75 43.14 34.11 45.20 Beans 30.89 23.10 36.29 39.99 34.96 23.20 Coffee 170.80 138.70 137.30 108.00 138.70 138.70 Sugar Cane 51.00 24.10 33.40 25.20 33.40 33.40 Bananas 25.00 25.00 25.00 25.00 25.00 25.00 Plantains 29.50 29.50 29.50 29.50 29.50 29.50 Cocoa 40.00 40.00 40.00 40.00 40.00 40.00 Tobacco 197.60 197.60 197.60 197.60 197.60 197.60 Potatoes 257.33 251.43 229.45 277.88 236.96 Yucca 20.60 20.60 20.60 20.60 20.60 Interplanted (Corn/Bean) 48.52 36.80 47.73 51.70 48.07 51.32 *Adjusted for inflation to 1979. Model Assumptions, Limitations and Usefulness As previously discussed, goal programming techniques are closely akin to linear programming. As Lee (1972) states: "Some limitations are inherent to all quantitative tools, and some are attributable to the particular characteristics of individual tech- niques". Numerous approaches have been developed to circumvent technique limitations. The limitations associated with this particular model for- mulation are presented. Assumptions l) The activities are additive, linear and divisible, i.e.; the total output produced by all activities equals the sum of individual activities and the same 2) 3) 4) 5) 6) -75- is true for inputs; the input/output coefficients exclude any interaction (linear); production is in- finitely divisible. Input prices remain at 1976 levels and quantify of input use does not affect price (perfectly elastic input supply functions). National aggregate production of export crops does not affect export prices (perfectly elastic demand functions). The most critical crop with respect to this assumption is probably banana. The agricultural regions are homogeneous production units. The implications of different technology levels is not approached. These could have substan- tial impacts on agricultural sector objectives. For example, if small farms are relatively labor inten- sive, optimization of a model specified by farm size could result in trade-offs between farm size and certain sector objectives, especially export earnings and minimization of cost. The model is deterministic, that is, uncertainty is ignored. The model is static. The assumptions described above are limiting factors specific to this type of optimization model. In the following section limitations not specific to the specifications of this model and conditions affecting its speci- fication are discussed. -76- Limitations Only a partial analysis of trade-offs between national agricultural sector objectives is conducted as interactions out- side of the sector are not approached. Additionally, the complete agricultural sector was not modeled. A major limitation is the absence of the livestock sec- tor. The model set pasture as an equality constraint which does not allow increasing extensive production or the removal of pas- ture for cropland. This influences the models ability to reflect the Costa Rican attempt to diversify agricultural production, to diversify sources of export earnings, and to shift pasture to basic grain production. Costs Ricas' beef export market, the United States, has been strong in recent years. As Costa Rica is located north of the Food and Mouth disease zone so, it can export to fresh meat markets. Another limitation is the exclusion of cotton and sor— ghum from the model. Cotton is a potential export crop. Sorghum is used exclusively as a cattle feed in Costa Rica. A consideration in Costa Rica has been the deforestation of land to establish new pasture. This has compounded drought problems. The equality constraint on pasture does not allow the return of pasture to forest which might be expected under a mini- mization of production cost objective. A substantial limitation is that the model specification abstracts from institutions and infrastructure. Especially im- portant is the inability to reflect costs of transportation in -77- the cost coefficients and the lack of knowledge about the ability of farmers to adapt different crops. For example, if credit and cash flow are constraints farmers may not be able to establish perennial crops. By abstracting from institutions the model is not dynamically prescriptive for policy or change in institutional structure; rather it is a status quo analysis of trade-offs. The implication is that how to achieve objectives in an administrative sense is not addressed. "How to" is a function of the amount of control the decision-makers can generate through policy tools. As the model is a partial analysis, model results can not be interpreted as generating zero cost resource allocation adjustments through changes in regional crop production that lead to objective function values that are higher than the base (1973). The model does provide insight into regional production potential for different national objectives and the crops and regions where micro analyses may be warranted. Usefulness: Direction of Change It is often suggested that the direction of change be emphasized in analytical models. This point becomes especially important when the regions are fairly large and characterized by heterogeneous agriculture, when only secondary data sources are used and, when data sources are somewhat inconsistent and do not include time series. Besides data and aggregation problems the magnitude of change determined by optimization analytical models is sometimes governed by flexibility restraints. Flexibility -78- restraints do not change the direction of change -- only the mag— nitude. For policy purposes this type of model may be most useful by analyzing the direction of change. But, as long as assumptions and limitations of the approach is understood, trade-offs deter- mined by the model should shed light on the agricultural sector objectives. Chapter 6 RESULTS OF ANALYSIS "Quantification is an aid to thought, not a substitute for it, and so long as users treat it this way, it can be helpful to policy analy- sis," (Campbell and Nichols, p.566). Introduction Selected modeling results depicting trade-offs between the stated national agricultural sector goals for both short-run and medium-run planning horizons are presented in this Chapter. Five modeling results (representative point solutions) will be emphasized. These models were optimized for both short-run and medium-run time frames. The models used were: Model I - maximize labor employment only Model 11 - maximize export earnings only Model III - minimize cost of production only Model IV - equal weights on the above objective func- tions (10 used as base weight) Model V respective weights of 100, 100, 10 and 1000. These models reflect the agricultural sector objectives which are: maximizing labor employment; maximizing export earnings; -79- -80.. minimizing cost of production; and self sufficiency in the basic grain (satisfying demands). The weights can be considered implicit linear utility functions with the attributes of the objectives in the multiple objective framework quantified in the following terms: Labor - in hours Export Earnings - in dollars Cost of Production - in colones Basic Grains - in metric tons For example, weights of 100, 100, 10, and 1000 imply a utility function that values one metric ton of basic grain as worth, 10 times more than 100 hours of employment, 10 times more than 100 dollars in export earnings and 100 times more than changing the cost of production by 10 colones. For reference a map delineating the Agricultural regions of Costa Rica is shown (FIGURE 6.1). Fifteen crops and six regions were included in the models discussed here. Only major regional crops and major production changes will be focused on here, complete details are in mimio form.1 An example of the GP model output is given for medium- run model V (Appendix A). Short-run Results The short-run analysis depicts the case where decision makers heavily discount the future. Possibilities for increasing production are restricted to crops that do not have substantial time lags (4 to 5 years) in Costa Rica are coffee, bananas, and 1See (Robb, 1980). -31- FIGURE 6.1 AGRICULTURAL REGIONS OF COSTA RICA NICARAGUA 'es \ mam PACIFCO WE - (REGIW 2) \.,..AILANTICO 0 (REGION 3Y4) (REGION 1) ”"s PANPMA \ PAC mco ,‘1 (REGION 3')“ \ Scale Approx. 1:1,078,000 (In RM) 0 30 65 130 L j ADAPTED FROM: DIRECCION GENERAL DE ESTADISTICA Y CENSOS CENSO AGROPECURAIO 1973 REGIONES AGRICOLAS. SAN JOSE, COSTA RICA - JUNIO DE 1975. -32- cocoa. Flexibility constraints also allow less regional speciali- zation in the short-run compared to longer term model. Production Patterns Agricultural production patterns that optimize associated models in the short-run are depicted (FIGURES 6.1 to 6.6). Each ”+" or "-" illustrates a change of 500 to 1,499 hectares compared to the 1973 base. Regional Activities in Solution For Model I region 1 is the only region to use all the available idle land with 9,033 more hectares cultivated than the 1973 base. All other regions use more land than the 1973 base. The two most dramatic regional production changes are in region 1 where sugar cane increases and region 2 where bean production increases. In this model no solo bean production occurs in region 1 as all the regional bean requirement is met by intercropping. No other regions have the intercropping activity in solution. Under Model II all regions have idle cropland. Regions 2 and 4 have more idle cropland than the 1973 base. The largest regional change in production occurs in region 1 where sugar cane production increases. No solo bean production occurs in regions 1, 2, 4, and 5. Under Model 111 is the only case where region 1 has more idle land, 3662 hectares, than the 1973 base. Other regions with more idle land than in 1973 are 4, 5, and 6. The largest crop hectarage change in any region is approximately 3,000 hectares so ~—~_.__+-— -7 -33- FIGURE 6 . 2 SHORT-RUN: MAXIMIZE LABOR (MODEL 1) PRODUCTION PATTERNS \ k....‘.\ 21 ++ , 21 ++++ '"\‘22 """ 22 ++++++ ‘- 23 + . 23 ++ 11 \ 5 ++ 3 25 ++ 1 \ I 1 ’21 ++ #:25 ++++++++fi / o {22 ++++ 32 +++ X23 + {;J' ,f{ + Ln ’ ‘nf' \ Q S o " '._r~. .' Soc. 0 \ 21 +++++ ‘3 22 +++++ .3 +++ \ 25 + s. .1 Crop Codes: 21 corn 22 rice 23 beans 25 sugar cane -34- FIGURE 6.3 SHORT-RUN: MAXIMIZE EXPORT EARNINGS (MODEL 11) PRODUCTION PATTERNS \ \t..._ 21 -- '“xu. 21 -— 2 "" ‘s‘ 22 ++ 25 ++ ‘“\ 23 -- 32 +++ i 32 +++++ “2 25 +1.} ( ”he"? s \‘a .4 '. .“no':...' '3 g 'x-S‘ - ----- f 0 .‘M21 __ ...... s 23 -- “s. . ° "f\o"’” ......--; 1 - (”A 3‘25 +++++++++3 ‘ ’ 21 ++ '/32 ++ ,3 E". 22 ' :/-1' .3, i 2 3 _ - ~ ...» i 5 :41}, r/“""'\..' \n’f' ' ‘”*~..21 ...... c- 22 +++ ‘ I 23 ----- t I 25 + 32 +++++++ \. ,J .5 Crop Codes: 21 corn 22 rice 23 beans 25 sugar cane 32 interplanted(corn/bean) -_*—'—-I- —-‘*——- -85- FIGURE 6.4 SHORT-RUN: MINIMIZE COST (MODEL III) PRODUCTION PATTERNS \ x... K 21 +++ ~ \ g1 '- 22 " 23 - . 23 + . -- z 25 ++ \" 25 - .) 32,+++ K gird-e"! q ‘o .41 . V" .3... .3 t *"’ "'1’ C} 21 ++ ‘‘‘‘‘‘ ~ , 23 -- ............. , am?!" I r «11525 -- .5 ‘ , 2 - ;/32 ++ (I g 22 ++ ,r- f 25 + L. if {q{’/' \ ".~ 21 — " ~~ 22 - Crop Codes: 21 corn 22 rice 23 beans 25 sugar cane 32 interplanted1 25 + Crop Codes: 21 corn 22 rice 23 beans 25 sugar cane 32 interplanted(corn/bean) -33- changes are not nearly as dramatic as under other models. This reflects that, in the short-run, regional production patterns of 1973 are fairly consistent with a simple minimization of cost market solution. This is the traditional LP land base model for- mulation. There are many reasons why 1973 production patterns are not reflected exactly including the assumptions of the model and non simple market determinants of production. Under Model IV all regions have more land in solution than the 1973 base, but no region uses all available cropland. No intercropping occurs in this case in any region. Under this model corn production increases on the order of 2,000 and 5,000 metric tons in each region except region 6 which decreases. Under Model V region 1 uses all the idle cropland avail- able in 1973. All other regions have idle land but less than the 1973 base. The national cropping pattern is similar to that under Model IV with the most significant difference in region 1 where approximately 8,000 more hectares of sugar cane over the 1973 base. All regions have intercropping in solution. Values of Objective Functions and Sensitivity Analysis A value-path display for the objective functions at the national level is presented (FIGURE 6.7). Cohon (p.161) attri- buted value path methodology to Schilling. The three basic grains are collapsed into one function (metric tons of basic grains) in the figure. The value of objective functions and the breakdown by region for the short-run model solutions are presented (TABLE 6.1). -39- FIGURE 6.7 NATIONAL SHORT-RUN RESULTS: VALUE PATH DISPLAY Export Labor Cost Of Earnings Employment Production in 10,000 in 10,000 in 10,000 of dollars of hours of colones 0 210,000 ...) ‘ 32,006§;-~.H..H,. \ / §\ \ '3 \ . \\\ 28,000.\ ,'/,4, \ . \ _,, \/*. 220, 000 / b" l"\ ° - 31.000 ' \ '*3 L ,. 27, 000 \ . ' . //// /’ \ 0 N -/ , \\\\ , ‘ , 0 000 :- \‘/ 3 30 000 26 000 236,000 0 Model I Model II M odel III P \ L '. \ /b\ \ g \ o. l/ - \ 1' .r. \ . . . X . \/ » . - , \ /-’° \°. I \\\ \ if \ -. \\ Model IV Basic Grains Production in MT 230,000 /l 220,000 I/‘ (II {I 5'210 000 210 000 \“f ./ \‘\ 190, 000 170,000 Model V Hemsaauaoov -90- .mm .NooH .«mmm .omMH .Hme .mmmH .mquH mzHuomnno co muanmz mHMQOZ ZDMIHmomm mom mZOHHUZDm m>HHomwmo mo mMDH<> H Hmeozv .mw .qum .qmmm .NOHN .quq .mOHN .mmOOH mzH Hmuozv O COmem m conom d GOmem m SOmem N GOHwom H COHwom HmCOHumz mm>Huomnno so munwflmz H.u.c00v H.o mamHuommno Go muanmB ZDmuEDHDmZ m.o mHm Hmwozv .mw .NOON .OMOO .NOHN .OOHO .OOHN .MNOOH mzH Hmwozv O GOHwom O COmem q GOmeM m cowwum N COmeM H GOmem HmcoHumz mo>Huoonno no mustoB A.u.coov m.O mqmee -104- of export earnings is $9,746,000. The range of cost is 48,935,000 colones. The total metric tons of basic grains range from 229,612 metric tons, which is much less than the 1985 demands, to a mini- mum of 168,962 metric tons. For equally weighted objectives (Model IV) the base chosen was 10. The ranges over which weights on objectives hold are: 1) Export Earnings - 5.63 to 10.40 2) Labor Employment - 7.24 to 11.16 3) Cost of Production - 9.71 to 13.82 4) Basic Grains Corn - 7.03 to .2 x 1016 Rice - not in Basis (overachieved) Beans - 2.95 to .39 x 1016 The ranges are larger in the long-run model than the short-run model for corn and beans. All vectors entering the bases are the same as in the short-run presented previously. Conflicts Between Time Horizons Comparative statics are used in this section to analyze apparent conflicts between short-run and medium-run time horizons. Given the models constraints, conflicts will result where land re- sources are the most limiting. Regions with substantial idle land will be able to produce equal to the short-run objective function results for non-perennial crops as well as produce perennial crops. An index showing the magnitude of objective function change between -105- the short-run and medium-run formulations was previously presented (Table 6.2). In the following subsections conflicts within models that result from different planning horizons are presented. In the short-run any increase in export earnings is due to sugar cane which is the only non-perennial exported. Labor in the short-run is closely tied to the basic grains and sugar cane. In the medium-run both more export earnings and employment are generated through perennial export crops so that perennials gener- ally go to the maximums allowed by flexibility restraints. Then basic grains and sugar cane are brought into solution. Time horizon conflicts are a result of the flexibility restraints, crops allowed into solution, and land resource availa— bility by region. The model assumes land resource availability does not change over time. The following discussion focuses on regions where conflicting optimal production results between short and medium-run formulations. Regions where the direction of change from the short-run do not change and the available land resources allow increasing perennial production in the medium-run are not considered regions of time horizons' conflict. Model I: Maximize Labor Under Model I only region 1 has conflicting production between the time horizons analyzed. In the short-run this region produces, more solo corn and beans, more intercropping, and about 9,000 hectares more sugar cane than the 1973 base. In the medium- run this region produces less solo corn and beans, more (but less than the short-run model) interplanted, and about 6,000 hectares ~106- less sugar cane than the 1973 base. In the medium-run this region specializes in coffee production with about 17,000 more hectares than the 1973 base. The medium-run formulation results in: $6,840,000 more in export earnings; 15,290,000 more hours of employment, and in 194,220,000 colones higher cost of production compared to the short-run in region 1. Model II: Maximize Export Earnings Under Model 11 three regions 1, 2, and 3 have conflict- ing production between the two time horizons. In the short-run region 1 specializes in sugar cane production with about 9,000 m9£g_hectares than the 1973 base. In the medium-run this region has the same crops being produced as with maximizing labor (Model I) with specialization in coffee and 9,000 fewer hectares of sugar cane than the base. Other crops (corn, beans, and intercropped) are the same for both time horizons. The difference in objective function values between the two time horizons: $8,250,000 more export earnings; 5,169,000 more hours of labor; and 37,126,000 colones higher cost of production in the medium-run. For region 2 the difference between short-run and the medium-run (medium-run minus short-run) is: +l,000 hectares of corn; -l,000 hectares of rice; -4,000 hectares of beans; and -l,000 hectares of interplanted. The difference in objective function values for the region between the two time horizons is: $540,000 more of export earnings; 1,900,000 more hours of employ- ment; and 18,830,000 colones higher cost of production in the medium-run. -lO7- Under the short-run formulation region 3 produces approximately 2,000 more hectares of solo corn and sugar cane over the 1973 base and 1,000 hectares 1§§§_rice and beans. With the medium-run formulation about 4,000 less hectares of corn, 3,000 less hectarage of rice and solo beans are in solution com- pared to 1973. About 1,000 fewer hectares of sugar cane are in production compared to the short-run and intercropping comes into solution with about 5,000 hectares. The difference between short and medium-run objective function (medium-run minus short-run) region 3 are: export earnings + $750,000, labor hours of employ- ment - 1,740,000 hours: and total cost of production drop by 10,080,000 colones. Model 111: Minimization of Cost Under this model magnitude in cost of production is the only major change between the short and medium-run models. The difference in cost is 4,649,000 colones less in the medium-run. Model IV: Equal Weights Under this model major conflicts betwen time horizons are not generally apparent, although, compared to the 1973 base many more crops have significant hectarage changes. Model V: Weights 100, 100, 10, 1000 Under this model major regional conflicts in crop pro- duction between the time horizons are not apparent. -108- Partial Opportunigy Costs of Sector Objectives As discussed in Chapter 4 the optimal solutions of the land base model do not give zero cost regional resource ad- justments that result in higher utility defined in terms of given objective functions. Therefore, the analysis of opportunity costs is partial. The value of multiobjective analysis over the tradi- tional land base LP is that it reflects better the nature of poli- cy considerations and helps to bring opportunity costs to the forefront. Opportunity costs can be defined between the models presented in terms of any of the objective functions used. In this section the minimization of cost objective function (Model III) is used as the base. This objective function approximately depicts the perfect competition equilibrium solution to regional crop production patterns (given the underlying assumptions of the model). The difference between the minimization of cost model and other models can be interpreted as how much adjustment cost and benefit, in terms of objective function achievement could be derived from not allowing free market solutions not including the costs of inducement. The national relationships for the short-run and medium-run are shown (TABLE 6.4 and 6.5, respectively) in the form of differences (model under study minus model III). Some Implications: Mggnitude of Change For Basic Grains,Self-Sufficiency and Labor Employment Flexibility constraints control the amount of regional specialization allowed in crop production and thus the magnitude ~109- TABLE 6.4 SHORT-RUN OPPORTUNITY COST OF NON-PERFECT COMPETITION FORMULATION Model EXPEARN LABOR COST B GRAINS (in $10,000) (in 10,000 hours) (in 10,000 (in metric colones) tons) I +1,498 +2,696 +25,228 +63,505 II +1,498 +l,030 + 9,468 + 1,689 IV 0 +l,015 + 7,367 +25,974 V +l,390 +2,028 +14,808 +29,993 TABLE 6.5 MEDIUM-RUN OPPORTUNITY COST OF NON-PERFECT COMPETITION FORMULATION Model EXPEARN LABOR COST B GRAINS (in $10,000) (in 10,000 hours) (in 10,000 (in metric colones) tons) I +9,707 +7,749 +63,957 +60,550 II +9,748 +6,l93 +51,243 + 1,689 IV +6,669 +3,325 +ll,4l4 +25,974 V +8,834 +5,263 +28,848 +25,974 of objective function achievement. is emphasized in most macro land base models. limitations, this section discusses the apparent (assuming flexibil— This is why direction of change Realizing these ity constraints are correct) ability to generate substantial new -110- employment in the sector and to satisfy 1985 demands for the basic grains through changes in regional production patterns. Self sufficiency requirements for the basic grains in 1985 were given (TABLE 3.4). The aggregated demands are never approached under any model. The maximum aggregate production is under short-run Model I (maximizing labor) due to the complemen- tarity between labor and basic grains under this formulation. Rice production exceeds demand by 40,343 mt. under Model I (as demands are equal to 1973 production).2 The maximum corn pro— duction is under Model IV and Model V (both short and medium-run) with production 138,013 mt. less than requirements. Bean supply is maximized under Model I (short-run) and under models IV and V (both short and medium-run) but they underproduce demands by 27,887 mt. This seems to imply that changing production patterns will not meet demands. Demands could only be met by substantial annual yield increases per hectare. The projected number of jobs needed per year was given (TABLE 3.2). The average for the 1976, 1980, and 1990 projections is 23,337 jobs per year. The difference between the short-run Model III, which has little change from the 1973 base, and the medium-run maximization of labor employment (Model I) is 38,775 3 jobs [(77,550,000 hours of employment) % (40 hours per week) 2Note: The country traditionally has had exceeded self sufficiency demands for rice; see TABLE 3.3. 3Note that export earnings, costs of production, and basic grains production also increase. -111- (50 weeks)]. The analytical model suggests that jobs can be generated by changing crop production patterns but not enough jobs would be created to keep up with the annual increase in demand for jobs. As in the case of basic grains, increases in annual yields per hectare would apparently be required to generate more jobs.4 4As described in Chapter 4 employment is tied to yields within specific crops. Chapter 7 SUMMARY AND CONCLUSIONS Review of Problem and Objgctives National agricultural sector objectives and goals do not fit well into undimensional objective function optimization techniques. For Costa Rica the agricultural sector objective include non-commensurable functions of: maximization of labor employment; maximization of export earnings; minimization of costs of production; and self sufficiency in the basic grains. The degree of competiveness between these functions defines trade-offs. Defining trade-offs resulting from different region- al crop production activities was the role of this analysis leav- ing decision makers with the burden of making value judgements to determine the ”best" solution. The objectives of this study were to: 1) Study mathe- matical programming optimization techniques that could be used to quantify conflicts (trade-offs) between objectives and then employ a demonstration land base model for the stated agricul- tural sector objectives of Costa Rica; 2) Analyze the implica- tions and direction of change in crop production between regions in both short and medium term planning horizons; 3) Compare the -112- ~113- multiobjective approach to the traditional minimization of pro- duction costs land base linear programming formulation. Review of Analytical Model A single tableau regional goal programming model (GP) was developed for Costa Rica that treats several national agri- cultural sector objectives simultaneously. The GP framework used here is conceptually analogous to minimizing disutility. Maximizing utility is defined by achieving all individual tar- gets on goal functions. This is done by minimizing the devia- tion between weighted objectives given targets. The GP model developed here is an extension of tradi- tional land base LP models which minimize the cost of production given ex0genous demands. Land base models define regional pro- duction activities for each crop in a per hectare basis. The GP model developed for Costa Rica incorporates objectives (eg. maximizing export earnings) and satisfying specific goals (eg. 43900 metric tons of rice). By incorporating satisfying ob- jective functions the size of the trade-off surface can be re- duced to a more applicable set from which point selections can be generated. The GP model is flexible, for example, if decision makers reformulate the maximization of labor objective into a goal of "X" hours only the right-hand side of the goal function needs to be changed. The GP model is a normative efficiency model with the same basic assumptions of a traditional land base LP. The model -114- is not behavioral. The relatively simple model developed for Costa Rica does not prescribe policy but does bring to the fore- front ideas of conflict in formulating objective functions through a partial analyses of potential regional agricultural production adjustments. Summary of Results Selected objective functions on the trade-off surface between objectives were generated to depict trade-offs. The results are regional crop production activities that optimize implicit utility functions. The models analyzed were: Model I - maximize labor employment Model II maximize export earnings Model III - minimize costs of production Model IV - equally weighted objective on, labor employment, export earnings, cost of production, and basic grains self suf- ficiency. Model V - weights of: 100 on labor employment and export earnings; 10 on cost of pro- duction; and 1000 on basic grains self sufficiency. Selected results of this analysis are given below. 1. The short-run minimization of cost model (Model III) results in relatively little change in regional crop production activities compared to the 1973 base. -115- Implying that a short—run market solution to region- al production activities could have determined the base years solution. There are significant short-run trade-offs between national sector objective functions in both activi- ties in solution and levels of goal function achieve- ment. Labor and basic grains production are closely related in the short-run. Conflicts between objective functions are apparent under the medium-run model both in activities in solution and levels of goal function achievement. Labor and export crops are closely related in the medium-run. Region 1 is the major area of conflict between models. Under both time horizons this region ranges from having no idle land (Models I and II) to much more idle land than the 1973 base (Model 111). Crops specialized in vary greatly by the objective func- tion used in this region. Conflicting production between time horizons is greatest in Region 1. Conflicts are not nearly as great in other regions as idle land is more often in solution. The potential to meet self sufficiency and national labor employment demands by changing regional crop production activities appears limited although -ll6- large gains compared to 1973 apparently can be made. More drastic changes in institutions and productivity are implied. An option includes more intensive production of basic grains which could make simultaneous movement toward both self suf- ficiency and labor employment possible. Of the various programming model approaches to incor- porating multiple objectives the GP approach, as used here, is relatively easy to develop and use. The land base cost minimization LP model was a component of the GP model developed for this study. These two formulations are complementary so the costs in terms of time and effort were not much greater for the GP. For example, coefficients for labor employment come out of farm budgets studies necessary for LP. The insight generated appears to be a valuable input into the decision making processes. The philosophy that decision makers are best able to make subjective value judgements in trad- ing off objectives is used in the GP approach used here. The traditional LP generates just a one point deterministic solution that decision makers can either accept or reject and does not give information on trade-offs. Neither the land base LP nor the GP help in defining institutions to achieve national level sector objectives. But, the GP makes more accessible the implications of what could be possible, under current natural resources and technology, and brings to the forefront conflicts between objec- tive functions and the resulting opportunity set. -ll7- Additional Useful Research The Formulated GP Model Data problems limit how much analysis can be performed on the Costa Rican agricultural sector. The secondary data sources available were used to their potential in developing this partial regional analysis. Data by more homogeneous regions would strengthen analysis of production potential under alterna- tive objective functions greatly. This includes specification of present and alternative technologies of production and micro constraints to adoption. The land base model developed here does not consider institutional structure within the sector. Implications of ob— jective functions related to the rural poor and farm size were not included in this study. Finally, to fully effectively evaluate trade-offs the agricultural sector, it can not be partitioned from the broader economy. Analytical Methods Increasing the number of objective functions under study results in dimensionality problems. Constructing efficient sets in more than two dimensions is computationally difficult and requires better estimation methods. One approach would be extension of(kflun1%3(l979) Noninferior Set Estimation Method beyond two dimensions. If it is possible to interact with deci- sion makers Surrogate Worth Trade-off methods could be used (Haimes, et. al. 1975, 1974) to reduce the size of the efficient under study. -118- Better efficient set estimation techniques should also lead to concern about the sensitivity of the whole efficient set being depicted (Schurle and Erven 1979 (a), (b)). APPENDIX A EXAMPLE GP MODEL OUTPUT: MEDIUM RUN WEIGHTS 100, 100, 10, 1000 (MODEL V) -ll9- moHH no.3. 0-.3w3mmm pm. om.¢¢HH so.~ ~m.¢~oH H3.“ om.~o~¢ mumwu HEWMMMHmmMM OUZmc wNHIHZHslI \ oo.o¢mom~ oo.omo¢ L- ¢~.~om 33.nmoo- ¢~.mem ¢~.m~ o~.¢~mH om.-mm~H oo.mommo- oo.-mmom o¢.mo- mm.¢~o- om.m~mm onhUDooma lgwoom wzmrrdeOmm OPZH do ¢¢omhoo¢m muothOOM ----..---- Mmummmw--- cooOOOOMN OOoOOOOmN .oo.omo¢ 00.0moc ~mc¢omm OM0NNH OO.HOH 000NHNH OncmoHH mW2OOO O0.0~O Nwohm O .a H¢omNH oooooH OnoHNoH omoomh wH2¢o~Nm OOomo¢mm ¢N2mmoHo nooHHOmO ooonhH Nboomh 00ow¢o mho¢mmm OCoNh¢¢ \Hr\m - mmqunoo coo-OH do mbwz z- m" oz_rmsm .mesoz oco.nH dc mp-ao z~ m .muzcucu moo-oH ac mpmrn a“ m» nHoOHmomH HOoMOmNH ONoHOHHH Acwsh <1 mrqOmCMu ugh” «I wmahmaa «I waoau GUY—v o3. m¢.mom- o-.~mw a; muhzeuonwtx- Hm. -.m~ mm.¢ . y» «662» ~m.~ Ho.o~Hm o~.mm- :» meHapco mu mm.- sm.omm- mo.¢m 3H cuuamre m“ o¢. om.¢~ m~.~ 03. y» daucu om. mm.~m Ho.¢ . w» 7-4Hr432 . mm. mm.mmm . mm.mm m-.oo- :» marazcm Hm; m~.ao~o- hm.mm- -.O¢~m . ye mzau dawn“ up.“ 7 no.0-mmo- mA.Mmoo om.mm¢> x» wmuuoe Hm. y» mzauu . 3m. ~m.¢¢~ em.om a» wu-a om. 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"van #32? o CUHHZ<4b< ZDHCmm .mo wwmsfiyflyau ugmnow ozmsz m¢.m¢m~ a~.~m~ * hm.¢w~m «x omwzd4amupz~ o¢.~hm ¢~.¢o oo.m~mm~ ~m.nomw~ -.mom~ oo.e~o~ yr duuo> mo.¢omm o¢.~o~ oo.o~oo~ oo.m~oo~ m~.-m~ o~.mc¢~ rh mmcpakca o~.mHm~ mm.m¢~ 90.0mm~ oo.omm~ so.m~¢~ oo.mom~ r» ouocm;» o¢.m~no mm.oom om.¢m~ om.mmm¢ o¢.¢cmm «~.mmm~m oo.momo~ y» «nucu oo.o¢m~ -.o~¢ oo.-mo- m~.-mom~ mm.¢mo~ co.om¢o sh . 2_«»z«4¢ mo.¢mo- oo.mm~m ~m.mmom~ 00.0mm~m~H oo.oowmm- ¢m.mfloom ofi.¢m~om x» maydrcm -.mo~m~ -.~mmm o~.-~m oo.momahm~ oo.~m~oomm odrmo~¢m oo.mc~mm y» wzqu «wc y:x.7H: “mmmwmmfimmmflfl 4u~x «hmou mo 4mo u-xuz~ysz sawoox oszxqaooia Aqua 2m “mm“: memmm wuwmm '-""" ---- "-'I‘ '-"' -' ----.. .owzmdhhd wxw; wgcco TUHII Oh mau>ud «Qua «hmou mo 4qmpzwu ouzqm 034 mnmzwu 4420~qu 240nm «pmou msoM roam qwmo wwwxmrmrtl launor ozmrrdxoema 4%00 740mm «hmcu osxwmxu BIBLIOGRAPHY BIBLIOGRAPHY Barlow, R. Land Resource Economics: The Economics of Real Prop- erty. New Jersey: Prentice-HaIl, Inc., 1972. 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