Aggregation and optimization with state-dependent pricing

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.