Profit Maximization and Supermodular Technology

A dataset is a list of observed factor inputs and prices for a technology; profits and production levels are unobserved. We obtain necessary and sufficient conditions for a dataset to be consistent with profit maximization under a monotone and concave revenue based on the notion of cyclic monotonicity. Our result implies that monotonicity and concavity cannot be tested, and that one cannot decide if a firm is competitive based on factor demands. We also introduce a condition, cyclic supermodularity, which is both necessary and sufficient for data to be consistent with a supermodular technology. Cyclic supermodularity provides a test for complementarity of production factors. ∗Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena CA 91125, USA. Email: [email protected] (Chambers) and [email protected] (Echenique). We are very grateful to two anonymous referees for suggestions, comments, and corrections. We also thank Kim Border for his suggestions on an earlier draft. All errors remain our own.