Search, Information, and Prices

Consider a market with many identical i¬ rms oi¬€ering a homogeneous good. A consumer obtains price quotes from a subset of i¬ rms and buys from the i¬ rm oi¬€ering the lowest price. The “price count†is the number of i¬ rms from which the consumer obtains a quote. For any given ex ante distribution of the price count, we obtain a tight upper bound (under i¬ rst-order stochastic dominance) on the equilibrium distribution of sale prices. The bound holds across all models of i¬ rms’ common-prior higher-order beliefs about the price count, including the extreme cases of complete information ( i¬ rms know the price count exactly) and no information ( i¬ rms 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.