Applications of Duality Theory

Although a comprehensive framework for most of the theoretical foundations of duality has been available to economists since the seminal work by Shephard in 1953, empirical applications of duality have become popular mainly during the last ten years. The first empirical study which I am aware of that exploited duality theory is the one by Nerlove in 1963 which estimated a CobbDouglas cost function as an indirect way of measuring the parameters of the production function of electric utilities. The development of the concept of flexible functional forms and its applications in the derivation of plausible functional forms for dual cost and profit functions in the early seventies [Diewert 1971; Christensen, Jorgensen and Lau] was an important step which led to the proliferation of empirical applications of duality. Several of these studies have concerned the agricultural sector. Of these, the study by Binswanger [1974a and 1974b] using U.S.A. data appears to be one of the earliest. A reason for the increasing popularity of the use of duality in applied economic analysis is that it allows greater flexibility in the specification of factor demand and output supply response equations and permits a very close relationship between economic theory and practice. If a transformation function dependent on factor quantities, a vector of output levels and the production technology is specified then empirical factor demand equations can be derived from the first order conditions of cost minimization. If profit maximization is