Investments in flexible production capacity

Abstract

We examine the technology and capacity choice problem of a multi-output firm facing stochastic demands in a continuous-time framework. The firm can install output-specific capital, or, at greater cost, flexible capital that can be used to produce different outputs. Investment is irreversible. The firm must choose a technology and decide how much capital to install, knowing it can add more later as demand evolves. We formulate the capacity choice problem as a singular stochastic control problem, show that the value of the firm equals the value of its installed capital plus the value of its options to add capacity in the future, and derive an optimal investment rule that maximizes the firm's market value. We also address the analogous problem for a multi-input firm that faces stochastically evolving factor costs, and can install input-specific or flexible capital.