Función de transformación y funciones de producción

Abstract

A mathematical formula is derived in order to discuss the concavity-convexity of the transformation curve in a sample two goods-two factors model, using the parameters of the underlying production functions representing returns to scale and elasticities of substitution. Several cases are considered. For instance, two production functions with the same factor intensity generate a lineal transformation function if the returns to scale are constant; concave if such returns are increasing; convex, if they are decreasing; and with two zones, one concave and the other one convex if one production function has increasing returns to scale and the other one decreasing returns; in such a case the inflexion point appears where the allocation of factors is proportional to the relation of the departures from constant returns to scale. The formula is also applied to consider other cases.