Duality principles in the theory of cost and production

Abstract

The theory of production, as typically described by Samuelson [2, (IV, 57–89)], is primarily concerned with the optimum allocation of factors of production that minimizes the total cost for each output, and with the nature of the cost curves derived from production processes under neoclassical hypotheses. However, it is customary in econometric studies of production structure to specify the form of production functions, up to a certain parametric class (such as Cobb-Douglas or Constant Elasticities of Substitution), and then estimate the parameters, through the cost curves which are usually derived by minimization of total cost. It is of some interest to see if production functions are uniquely determined by curves of minimum total cost and to characterize the class of total cost curves which are derived from production functions with neoclassical properties. This dual determination of production functions from cost curves has been established by Shephard, and in the present note we are interested in extending some of his results as well as formulating explicitly the conditions for cost curves that are derived from neoclassical production processes by a minimization of total cost.