Aggregation and Optimization with State-Dependent Pricing

Abstract

The literature on the aggregation of (S, s) policies has ignored the impact of aggregate behavior on the individual's optimization problem. In the case of pricing, the feedback effects are clear. Not only do pricing strategies determine the evolution of the price level, but the evolution of the price level also influences the optimal pricing strategies. In this paper, we provide a consistent treatment of aggregation and optimization. We use this model to analyze three issues in the menu cost pricing literature: the relationship between strategic complementarity and the real effects of money; the relationship between the variance of the money supply and the correlation between money and output; and the relationship between the cost of price adjustment and the size of price adjustment. QUESTIONS CONCERNING THE DYNAMICS of aggregate variables such as prices, employment, investment, and consumption represent the core of business cycle analysis. One striking feature of these variables is the radical difference between properties of these aggregates and the nature of the individual behavior that underlies them. The behavior of a firm's prices, investment and employment, and the behavior of an individual's consumption all involve frictional elements that lead to discrete adjustment at the microeconomic level. Heterogeneity among individuals, however, tends to smooth the behavior of the corresponding aggregates. In recent years, a large body of research has developed to examine the manner in which microeconomic frictions influence aggregate dynamics. One of the centerpieces of this research has been the (S, s) model developed by Arrow, Harris, and Marschak (1951). The key element of this model is the state dependence of individual decisions. Agents act when a state variable crosses some critical threshold which balances the cost and benefits of adjustment. The aggregate implications of this form of microeconomic behavior have been analyzed by Blinder (1981), Caplin (1985), and Mosser (1991) in the context of inventory dynamics; by Caplin and Spulber (1987), Caballero and Engel (1991, 1993), and Caplin and Leahy (1991) in the context of prices; and by Bertola and Caballero (1990), Caballero (1993), and Eberly (1994) in the context of con- sumer durables. One of the most limiting aspects of these models is that they focus exclusively on the impact that microeconomic inertia has on aggregate dynamics. They 1We would like to thank Michael Harrison, loannis Karatzas, John Leahy Sr., Andreu Mas-Colell, a co-editor and four anonymous referees for helpful discussions and comments, and the National Science Foundation and the Sloan Foundation for financial support.

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