A Search-Theoretic Model of Equilibrium Cycles with Sales

There is a unique stationary equilibrium in the price-posting game played by firms. Depending on parameters, this equilibrium can take one of three possible forms. First the equilibrium can be one in which all firms post a high price. Second, all firms could post a low price. Finally, there can be an asymmetric equilibrium -- some firms post a high price (only the high utility type buys from these firms) while others post a low price (all consumers buy from these firms). These are essentially the equilibria analyzed in the Gaumont, Schindler and Wright (EER 2006) version of the Albrecht and Axell (JPE 1984) model of the labor market. More interestingly, the model also has nonstationary equilibria in which the market alternates between periods in which all firms post high prices and periods in which all firms post low prices. These cycles (high-price periods followed by low-price periods followed by high-price periods, etc.) are self-generating. The mechanism underlying the nonstationary equilibria is the change in the composition of the pool of shoppers, i.e., the relative mix of high and low types. In high-price periods, the fraction of low types in the pool increases; in low-price periods, the composition of the pool moves in the opposite direction. We relate these nonstationary equilibria to theories of sales and to the strand of the macro literature that tries to estimate the frequency of price adjustment, ie, how often does the Calvo fairy visit?