Adv. Math. Econ. 5, 1-21 (2003)

Duality and existence for a class of mass transportation problems and economic applications

Guillaume Carlier

Université Bordeaux 1, MAB, UMR CNRS 5466 and Université Bordeaux IV, GRAPE, UMR CNRS 5113, Avenue Léon Duguit, 33608, Pessac, FRANCE

Received: April 15, 2002 Revised: May 20, 2002

JEL classification: C61, C82

Mathematical Subject Classification (2000): 90C08, 90C46, 91B40

Abstract. We establish duality, existence and uniqueness results for a class of mass transportations problems. We extend a technique of W. Gangbo [9] using the Euler Equation of the dual problem. This is done by introducing the h-Fenchel Transform and using its basic properties. The cost functions we consider satisfy a generalization of the so-called Spence-Mirrlees condition which is well-known by economists in dimension 1. We therefore end this article by a somehow unexpected application to the economic theory of incentives.

Key words: mass transportation, duality, general Fenchel transform, economic theory of incentives, Spence-Mirrlees condition