Law of One Price under Equilibrium Price Dispersion: Arbitrage and Optimization of Search

Abstract

If the demand under price dispersion is formed by consumers with zero search costs and consumers with positive search costs, the law of one price holds at the equilibrium price level, where the lowest willingness to pay between consumers with zero search costs meets the willingness to accept or to sell of consumers with positive search costs. The equilibrium price level is provided by the individual equality of marginal losses in labor income during the search with marginal savings on purchase. Suboptimal decisions of consumers with positive search costs create an opportunity of arbitrage with willingness to pay at the zero costs search level. Arbitrage corrects suboptimal decisions of consumers with positive search costs and sets the stable equilibrium price dispersion with new equilibrium price.

Keywords

• equilibrium price
• consumption-leisure choice
• cost of search
• price dispersion
• willingness to pay
• willingness to accept