Law of one price and optimal consumption-leisure choice under price dispersion

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 that results in a new equilibrium price and in optimal consumption-leisure choices of all consumers.