A system of inequalities arising in mathematical economics and connected with the Monge-Kantorovich problem

In this article, we study a class of functions defined by a system of linear inequalities which arises naturally in at least four different economic issues: redistribution, spatial economics, theory of incentives and utility theory. The main tool used to study solutions of those inequalities is the duality theory for the Monge-Kantorovich problem with a given marginal difference.