A competitive market model for indivisible commodities

A general competitive market model for trading indivisible goods is introduced. There are a group of traders and several indivisible goods. Each trader is initially endowed with several units of each indivisible good and some amount of money. Traders have preferences over the bundle of indivisible goods and the quantity of money they consume. It is shown that the market has a Walrasian equilibrium if and only if an associated linear program problem has an optimal solution with its value equal to the potential market value, and that the equilibrium prices of the goods and the profits of the traders are the optimal solutions of the linear program problem.