Multidimensional Product Design

Abstract

In selection markets, where the cost of serving consumers is heterogeneous and noncontractible, non-price product features allow a firm to sort profitable from unprofitable consumers. An example of this “sorting by quality” is the use of downpayments to dissuade borrowers unlikely to repay. We study a model in which consumers have multidimensional types and a firm offers a single product of endogenous quality, as in Spence (1975). These two ingredients generate a novel sorting incentive in a firm’s first-order condition for quality, which is a simple ratio. The denominator is marginal consumer surplus, a measure of market power. The numerator is the covariance, among marginal consumers, between marginal willingness to pay for quality and cost to the firm. We provide conditions under which this term is signed, and contrast the sorting incentives of a profit maximizer and a social planner. We then use this characterization to quantify the importance of sorting empirically in subprime auto lending, analytically sign its impact in a model of add-on pricing, and calibrate optimal competition policy in health insurance markets.