A Model of Search with Price Discrimination

We introduce heterogeneity in buyers' size into a model of simultaneous search. Buyers' differences in their willigness to search give rise to price discrimination, even if their valuations for the good are equal. We shed light on three related questions: (i) what is the relationship between prices and buyers' size? (ii) what are the effects of reducing search costs?, and (iii) who benefits and who is hurt by price discrimination? The answers critically depend on the elasticity of the search cost distribution. Interestingly, for normally distributed search costs, (i) there is an inverted U-shape relationship between prices and buyers' size, (ii) when search costs go down, the prices charged to small buyers do not fall as much as those charged to the large ones (and can even go up), and (iii) price discrimination benefits small and large buyers, at the expense of the medium-size buyers.