Mexico - Agricultural prices and subsidies : a case study (Vol. 1 of 2)

DISCUSSION DRAFT The views and interpretations in this document are those of the authors and should not be attributed to the World Bank, to its affiliated organizations, or to any individual acting in their behalf. AGP- 4 L: Li C> '''usL'Ri MEXICO: AGRICULTURAL PRICES AND SUBSIDIES A CASE STUDY (Volume I) AGREP Division Working Paper No. 4 Prepared by: Yakir Plessner (consultant) Economics & Policy Division Agriculture & Rural Development Department May 1977   Acknowledgement I should like to gratefully acknowledge the substantial degree of cooperation and assistance accorded me by Roger D. Norton and members of his division at the Development Research Center of IBRD.   CONTENTS Page I. INTRODUCTION 1 - 2 II. SHADOW PRICES AND DRC MEASURES 1. A Basic Property 3 - 4 2. Biased DRC's 4 - S III. AN OUTLINE OF CHAC 1. The Programming Model 6 - 8 2. The Dual Problem and Shadow Prices 8 - 9 IV. DESCRIPTION OF EXPERIMENTS 1. Types of Subsidies 10 - 11 2. The Experiments. 11 3. The Basic Data 12 - 14 V. RESULTS 1. Output 15 - 19 2. Use of Resources 20 - 22 3. Prices and Income 23 - 27 4. Exports--Volume, Prices and Value 27 - 31 S. Domestic Resource Costs (DRC's) 31 - 34 REFERENCES 35 ANNEX 1: ON SHADOW PRICES 36 - 38 ANNEX IJ: COMPUTATION OF DRC's 39 ANNEX III: DISTRICT LEVEL RESULTS 40 - 46   I. INTRODUCTION The main purpose of this case study is to demonstrate the usefulness of mathematical programming models in the evaluation of various kinds of public intervention in the economy. Under consideration are the policies of the Mexican government in respect of subsidies to agricultural inputs and outputs and foreign exchange rates. The analysis is based on the application of a linear programming model, a short description of which is provided herein, to the Mexican agricultural sector, exclusive of livestock products and orchards. The model is used initially to compute a competitive equilibrium, free-of-intervention solution. Various subsidies and a devlauation of the peso are then introduced gradually and a new solution is computed each time, so that the impact of the new policy features can be examined. In each case a comprehensive description of the changes is given and their economic significance analyzed. In order to concentrate attention on the attributes of the methodology employed in this study, no detailed background material is provided. Furthermore, this would seem to be a superfluous undertaking in any event, since ample such material is available elsewhere, most of it in IBRD reports [1], [2], [3]. Quite extensive background material and a detailed description of the programming model-/ are to be found in Duloy and Norton [4], [6] and Bassoco and Rendon [5].2/ The main objective of the case studies of which the present is one, is stated as the assessment of the impact of public intervention on production in general, and on agricultural output in particular. Quantitavely, the main tool of analysis is the computation of DRC's and related measures, which in / The programming model was dubbed CJIAC and will be henceforth referred to as such. 2/ The enumeration of references is logical rather than alphabetical.  2- turn provide an ordering criterion. The latter provides for a ranking of the various production activities by comparative advantage, degree of protection, etc. The use of a linear programming model affords one the opportunity to shed additional light on these measures. Basically, it turns out that if programming results are available, measures like DRC's have no useful information to add. In fact, programming results help to highlight the limitations of such measures and the pitfalls that might trap a researcher if he is unaware of these limitations. Understanding the problems associated with measures such as DRC entails familiarity with some simple, but very important properties of linear programming models. After discussing these in some detail, they will serve to examine the impact of subsidies and taxes on DRC's. This will be followed by a brief description of the essential features of CHAC. The application of CHAC, the experiments conducted, the results and conclusions therefrom will then be discussed in considerable detail.  -3- II. SHADOW PRICES AND DRC MEASURES 1. A Basic Property Consider a linear programming model in which the objective is the maximization of profits of the economic unit under consideration (firm, sector, etc.). Consider further a factor of production whose supply to the unit is perfectly elastic up to a certain quantity and perfectly inelastic thereafter, which is the usual way one introduces "limiting" factors. Water resources in a specific region constitute a typical example, and a very prominent one in Mexico. Assume that the farmer pays c pesos per 1000 cubic meters of water, and this is the price at which supply is perfectly elastic. There are now two possibilities as regards the optimal solution: either the available water is exhausted, or it is not. The first is the simpler case, since it involves a positive shadow price for water, say of w pesos per 1000 c.m. (cubic meters). These pesos are pesos of profits, so that the shadow price w is the worth of water to the economic entity over and above the price charged. Suppose now that the price paid by the farmer is changed by s pesos. If the change is upwards, i.e. the farmer has to pay c+s pesos per 1000 c.m., then as long as s<w the optimal production plan does not change and the shadow price of water simply declines by s, other shadow prices being unaffected. If, on the other hand, the change constitutes a reduction in price, so that the farmer pays c-s pesos per lO00 c.m., then as long as c-s>O, the optimal production plan is again invariant to changes in s, the shadow price of water increases by s and other shadow prices are unaffected, as before.1' What characterizes the two cases considered is that the total value of water under optimal allocation, given by w+c