Search, Information, and Prices

Consider a market with identical firms offering a homogeneous good. For any given ex ante distribution of the price count (the number of firms from which a consumer obtains a quote), we derive a tight upper bound on the equilibrium distribution of sales prices. The bound holds across all models of firms’ common-prior higher-order beliefs about the price count, including the extreme cases of full information and no information. One implication of our results is that a small ex ante probability that the price count is equal to one can lead to a large increase in the expected price. The bound also applies in a large class of models where the price count distribution is endogenously determined.