Consumer Search and Product Line Length: The Role of the Consumer Distribution

More intense consumer search across firms may lead to both stronger price competition and a better match between customers and products. We show that the net result of these forces may lead to the optimality of either shorter or longer product lines, and higher or lower prices and profits depending on the distribution of the product valuations across consumers, even if lower search costs do not lead to total demand increase. We derive a general condition on the distribution under which lower search costs lead to longer product lines in the absence of the market expansion effect. In particular, when consumer search costs decrease, product lines become longer if the distribution is Exponential or Log-Normal, become shorter if the distribution is Normal, Logistic, or Gumbel-Minimum, and do not change if the distribution is Gumbel-Maximum. With uniformly distributed product values, equilibrium prices and product lines are inverted-U shaped in the search costs. If lower search costs expand the market, firms have an additional incentive to increase product line length when search costs decrease.