Search, Information, and Prices

Consider a market with many identical firms offering a homogeneous good. A consumer obtains price quotes from a subset of firms and buys from the firm offering the lowest price. The “price count” is the number of firms from which the consumer obtains a quote. For any given ex ante distribution of the price count, we obtain a tight upper bound (under first-order stochastic dominance) on the equilibrium distribution of sale prices. The bound holds across all models of firms' common-prior higher-order beliefs about the price count, including the extreme cases of complete information ( firms know the price count exactly) and no information ( firms only know the ex ante distribution of the price count). A qualitative implication of our results is that even a small ex ante probability that the price count is one can lead to dramatic increases in the expected price. The bound also applies in a wide class of models where the price count distribution is endogenized, including models of simultaneous and sequential consumer search