Discrete convexity and equilibria in economies with indivisible goods and money

We consider a variant of the standard Arrow{Debreu model which contains a number of indivisible goods and one perfectly divisible good (numeraire or money). The objective of this paper is to clarify a general mathematical mechanism which guarantees the existence of an equilibrium in such a model. It is shown that the crucial condition for the existence of an equilibrium is that the sets of supply and demand of indivisible goods should belong to a class of \discrete convexity." The class of generalized polymatroids provides one of the most interesting classes of discrete convexity. JEL classi cation D50