Factor substitution in linear programming: A methodology and an application to cane alcohol pricing policies in Costa Rica.

摘要

The main methodological contribution of this study is the development of a technique to link activity analysis and neoclassical production functions, in the context of constrained optimization models. The technique has two major components. First, a procedure was developed to incorporate the isoquants into a linear programming model. Second, there is an algorithm to generate numerical isoquants that requires only information on the elasticity of factor substitution, the input ratio and input prices observed at a single point on the hypothetical isoquant. Among the types of applied research that this marriage between activity analysis models and the neoclassical production function make possible are: (1) Estimation of neoclassical production function for primary factors, and its inclusion in a model along with activity analysis specifications for intermediate inputs. (2) Modeling of conceptual alternatives on factor substitution, such as differentiation of factor substitution possibilities in agriculture between hillside and flat lands, between fragile and fertile soils, between high potential and low potential areas. This possibility offers a powerful tool to evaluate technical options for sustainable agricultural growth. (3) The effects of factor substitution, or of technological change for that matter, on distribution of costs and benefits of various policy actions can now be assessed.;To empirically test the technique developed in this study, a model of Costa Rican agriculture was built. This is a price-endogenous, market-simulating model that includes farmers' risk aversion behavior. It also includes downward-sloping demand functions. The basic model was modified to incorporate systematic labor-machinery substitution possibilities along CES isoquants. Then, a cane-alcohol pricing scheme was evaluated using the basic model and the enhanced one. Some of the salient results suggest that: (1) There should be an entirely new criterion for designing price support programs if the goal is to increase farmers' incomes. (2) There is a need to complement price support programs with technical assistance programs. (3) The distribution of benefits of price support programs, as between consumers and producers, depends on labor substitution possibilities.