Irreversible investment and industry equilibrium (*)

We establish the equivalence of competitive industry equilibrium with a central planner's decision problem under uncertainty, when investment is irreversible. The existence of industry equilibrium is derived, and it is shown that myopic behavior on the part of small agents is harmless, in the sense that it leads to the same decisions as full rational expectations do. Our model is set in continuous time and allows for very general forms of randomness. The methods are based on the probabilistic approach to singular stochastic control theory and its connections with optimal stopping problems.