This paper studies the price-setting behavior of a monopoly facing two capacity constraints: one on the number of its consumers, and the other on the amount of products it can sell. The characterization of the firm’s optimal pricing and optimal customer mix as a function of its two capacities reveals a rich structure. In contrast to the results under one-dimensional capacity constraints with constant marginal cost of production, a firm may optimally respond to an exogenous reduction in one of its capacities by decreasing one of its prices. Moreover, neglecting the existence of the second capacity constraint can reverse some policy interventions’ effects on consumer welfare. In particular, easing a regulatory restriction on one of the constraints may harm the average consumer.