Existence of a competitive equilibrium when all goods are indivisible

We study a production economy where all consumption goods are indivisible at the individual level but perfectly divisible at the overall economy level. In order to facilitate the exchange, we introduce a perfectly divisible parameter that does not enter into consumer preferences (fiat money). When consumption goods are indivisible, a Walras equilibrium does not necessarily exist. Hence, we introduce a new concept of competitive equilibrium for the economy (called rationing equilibrium), and the proof of its existence is the main result of this work. Unlike the standard Arrow-Debreu model, fiat money will have a strictly positive price at the rationing equilibrium. In our set up a rationing equilibrium is a Walras equilibrium, provided the Lesbegues measure of agents with identical initial holdings of fiat money is zero