Theoretical Economics 5 (2010), 479–518

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### Dynamic monopoly with relational incentives

*Alexander Wolitzky*

#### Abstract

This paper studies the price-setting problem of a monopoly that in each time period has the option of failing to deliver its good after receiving payment. The monopoly may be induced to deliver the good if consumers expect that the monopoly will not deliver in the future if it does not deliver today. If the good is non-durable and consumers are anonymous, the monopoly's optimal strategy is to set price equal to the static monopoly price each period if the discount factor is high enough, and otherwise to set the lowest price at which it can credibly promise to deliver the good. If the good is durable, we derive an intuitive lower bound on the monopoly's optimal profit for any discount factor and show that it converges to the optimal static monopoly profit as the discount factor converges to one, in contrast to the Coase conjecture. We also show that rationing the good is never optimal for the monopoly if there is an efficient resale market and that the best equilibrium in which the monopoly always delivers involves a strictly decreasing price path that asymptotes to a level weakly above the ratio of the monopoly's marginal cost to the discount factor.

Keywords: Coase conjecture, durable goods, monopoly pricing, non-durable goods, rationing, relational incentives

JEL classification: C70, D42, L12

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