Existence of Equilibrium in Economies with Indivisible Commodities and Savings

We consider a two-period exchange economy without uncertainty. Every commodity can be consumed only in integer amounts and there exists one financial (nominal) asset whose trading unit is divisible. Holding the asset does not directly affect agents' preferences. We prove the existence of an equilibrium if there exists a continuum of agents and if the distribution of agents' initial holdings of the divisible asset is dispersed in the sense that the set of agents who initially have the same amount of the asset is negligible relative to the size of the entire economy. Since agents cannot run out of their wealths because of the indivisibilities, our equilibrium concept permits the presence of some commodities in excess supply. This causes the inefficiency of equilibrium allocation. Also, our economy exhibits the real indeterminacy of equilibrium allocation. Equilibrium allocations depend on the price level of the second-date commodities.