Overdemand and Underdemand in Economies with Indivisible Goods and Unit Demands

We study an economy where a collection of indivisible goods are sold to a set of buyers who want to buy at most one good.We characterize the set of Walrasian equilibrium price vectors in such an economy using sets of overdemanded and underdemanded goods.Further, we give characterizations for the minimum and the maximum Walrasian equilibrium price vectors of this economy.As a consequence of these characterizations, we can say if overdemanded sets of goods and underdemanded sets of goods exist at a price vector given its position in the price vector space with respect to the minimum and the maximum Walrasian equilibrium price vectors.We also analyze what happens with the Walrasian equilibrium price vectors if one of the buyers or one of the goods is removed from the economy.