Dualities in the Functional Representations of a Production Technology

Given the production technology of a multiproduct firm, economists usually try to represent this technology by functions, namely the cost function, the revenue function and the input and output distance functions. In doing so the analysis directs the attention to the (dual)matching of quantities and prices. Here, the duality scheme is based on Mahler's inequality and stresses dual aspects of associated functions, whereas the underlying optimization problems are not dual programs. Nevertheless, the discussion of shadow pricing reveals the similarities which exist with respect to some appropriately chosen dual programs.