The Law of One Price for Heterogeneous Goods

The law of one price fails to hold in the presence of heterogeneity. Employing Shapley and Shubik's (1971) model for markets in which buyers have heterogeneous valuations for indivisible goods, we recover a connection between prices in a competitive equilibrium. This connection becomes tighter and holds for a larger percent of markets as market size increases. As in the case of homogeneous goods, this approximate law of one price implies uneven surplus distribution even in slightly unbalanced markets. In the second part of the talk I will explain how these results continue to hold when goods have different qualities and for buyers with varying willingness to pay for quality. I will also try to explain what happens when valuations are drawn from an unbounded distribution.