Optimal pricing and investment for resources with alternative uses and capacity limits

Airport runways, radio spectrum, and hospital beds are resources with capacity limits used to provide multiple services with specific capacity requirements in separate markets, which contribute to recover capacity investment costs. A welfare-maximizing and (possibly) budget-constrained firm, whose operating costs significantly increase as total capacity use presses against capacity, chooses prices and capacity. When the equilibrium capacity is reached, second-best Ramsey prices must be adjusted, and mark-ups on marginal costs may be higher for services with higher demand elasticities, if they intensively use capacity. Moreover, for a given output vector, the firm invests more than in first best. Instead, the equilibrium capacity may be first best when there is excess capacity to reduce operating costs and thus improve welfare. Our model can be used as a benchmark to evaluate the efficiency of market mechanisms for resource allocation and pricing, or when market mechanisms are not adopted.