Consumer Search and Product Line Length: The Role of the Consumer-Product Fit 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 either shorter or longer product lines, and higher or lower prices and profits depending on the distribution of product valuations across consumers, even if there is no market expansion effect (i.e., if all consumers buy). We derive a general condition on the distribution (related to its hazard rate) under which lower search costs lead to longer product lines even when the market expansion effect is absent, thus highlighting the critical role of the value distribution in determining firms' optimal strategies in competitive markets. 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 exhibit an inverted-U-shaped relationship. Incorporating the market expansion effect, firms have an additional incentive to expand product lines when search costs decrease, and the relationship between search costs and equilibrium product line length may reverse direction.