I. Introduction, 220. — II. A simulation model, 221. — III. Estimation of the model, 223. — IV. Results of the simulation, 228. — V. Tests of the simulation hypotheses, 232. — VI. Summary and conclusions, 238. — Statistical appendix, 240.

International Development

The use of numerical techniques for solving dynamic nonlinear multisectoral models for development planning is analyzed. A four sector model with nonlinear welfare, production, and investment functions is developed and solved using conjugate gradient and neighboring extremal methods. The model draws on recent developments in nonlinear theoretical growth models and linear development planning models. Sensitivity tests on the turnpike properties of the model and on changes in the elasticity of substitution parameters in the production function are discussed. The numerical techniques used have their origins in control theory applications and exploit the dynamic structure of the planning model. THIS PAPER discusses the application of numerical methods to the solution of nonlinear planning models of a type that could be used in the formulation of development programs for less developed countries. The numerical methods were originally developed by control theorists and our chief interest has been in testing their capability to solve moderately sized economic problems. In general, we have been satisfied with the results of these tests, and wish to demonstrate the usefulness of the nonlinear specification with a realistically formulated four sector model. This model is based on ideas drawn from two recent lines of thought about economic growth over time. The first is that of neoclassical theoretical models designed to analyze the characteristics of an economy in asymptotic optimal growth, viz. Samuelson and Solow [24] and Koopmans [19]. The other line is that of finite horizon linear programming planning models, viz. Bruno [4], Eckaus and Parikh [10], and Chakravarty and Lefeber [7]. We have attempted to blend the nonlinear production and welfare functions of the neoclassical models with the disaggregation and emphasis on foreign trade of the linear programs. In future applications this combination should offer growth theorists the possibility of using greater disaggregation than their present closed-form solution methods permit and at the same time give economic planners the opportunity to specify their models with nonlinear functions in both the performance index and the constraints.2

FOOD is macroeconomically important in poor countries, for obvious reasons. Agriculture (mainly staple food production, in most places) may make up half or more of total valueadded, and the average share of consumer expenditure going to food products is likely to be around 50% as well. Among the poor, the food budget share may be as high as three-quarters. Given all dimensions of the food sector (including production, processing, transportation and distribution activities, and consumption), the policy instruments that are supposed to influence its behavior also have noticeable macro repercussions. These have been little traced in the literature, though they can be important for all kinds of planning. In the medium to long run, for example, newly fashionable Basic Needs development strategies will require sustained growth in food intake on the part of the poorest half of the population in many countries. By Engel's Law, rapidly increasing staple food consumption imposes strong constraints on both growth and composition of aggregate demand. In the short run, food supply shortfalls and the threat of rising prices have forced more than one set of ministers to exit from the back door with rioters out front in the street. Corrective measures that they or their successors impose dramatically shift the balance of payments and government deficit positions. This paper is devoted to sketching how a simple macroeconomic model can provide guidance on how to calculate probable impacts of food policy changes in a poor country. We work specifically with Pakistan, and have tried to be as realistic as possible in designing an analytical scheme that can fit the available data, and give policy-relevant information. These requisites lead us to set up the data for accounting consistency in a Social Accounting Matrix (or SAM), discussed in the following section. Section III then outlines the structure of the analytical model built around the SAM, and section IV explains how it works. Several possible food policy interventions in Pakistan are discussed in section V, along with some implied policy conclusions. 1

I. Introduction, 197. — II. The welfare approach, 198. — III. Costs of producing foreign exchange, 207. — IV. Equilibrium and parity exchange rates, 213. — V. Comparisons of the methods and a recommended evaluation rule, 220.

I. Introduction, 197. — II. A formal model, 199. — III. Some extensions of the model, 212. — IV. Conclusion, 215. — Appendix, 216.