The unification of Ronald W. Shephard's duality theory

Ronald W. Shephard developed four fundamental duality theorems. They relate the following four pairs of representations of the technology: cost function-input distance function, revenue function-output distance function, indirect cost function-indirect input distance function, and indirect revenue function-indirect output distance function. In this paper we show that all eight of these representations are equivalent. The implication of this equivalence is that there are twenty-four duality theorems and four inverse relationships involving Shephard's eight representations of technology.