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

Duality and existence for a class of mass transportation problems and economic applicationsGuillaume Carlier

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

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- 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 Transformand using its basic properties. The cost functions we consider satisfy a generalization of the so-calledSpence-Mirrlees conditionwhich is well-known by economists in dimension 1. We therefore end this article by a somehow unexpected application to theeconomic theory of incentives.

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