I study the price-setting behavior of a monopoly facing two
kinds of capacity constraints: one on the number of consumers it can
serve, the other on the total amount of products it can sell. Facing
two consumer groups that differ in their price-inelastic demands and
the distribution of their willingness-to-pay, the monopoly's optimal
non-linear pricing strategy consists of offering one or two
price-quantity bundles. The characterization of the firm's optimal
pricing as a function of its two capacities reveals a rich structure
that also gives rise to some surprising results. In particular, I show
that prices are non-monotonic in capacity levels, moreover, there
always exists a range of parameters in which weakening one of the
capacity constraints decreases consumer surplus.