R. Preston McAfee

Pricing Damaged Goods

Companies with market power occasionally engage in intentional quality reduction of a portion of their output as a means of offering two qualities of goods for the purpose of price discrimination, even absent a cost saving. This paper provides an exact characterization in terms of marginal revenues of when such a strategy is profitable, which, remarkably, does not depend on the distribution of customer valuations, but only on the value of the damaged product relative to the undamaged product. In particular, when the damaged product provides a constant proportion of the value of the full product, selling a damaged good is unprofitable. One quality reduction produces higher profits than another if the former has higher marginal revenue than the latter.

Continuing Wars of Attrition

This paper presents a new model of the war of attrition, based on a geographical or territorial dispute. Both sides try to extend their boundaries, and the level of effort at each time is endogenous. There are two kinds of stationary equilibria, one with fighting to completion, the other with a cessation of hostilities. As a player gets closer to losing, that players probability of winning battles falls, social welfare rises, and the levels of effort of both players rise. A draw or standoff is possible. The theory is applied to a variety of conflicts, including wars and attempts at market domination.