Duality Between Multi-Output Production Correspondences and Cost Functions

The production correspondence associated with a technology maps every input vector into the set of output vectors that may be obtained by means of those inputs. The cost function induced by a production correspondence assigns to every pair consisting of a vector of input prices and an output vector the smallest possible cost that has to be paid for achieving that output vector under those input prices. Our main result characterizes cost functions and establishes a bijection between them and the set of quasi-concave production correspondences. In the framework of this bijection, we characterize co-radiant, as well as positively homogeneous, production correspondences. We also study demand correspondences.