A dynamic competitive equilibrium model of irreversible capacity investment with stochastic demand and heterogeneous producers

Abstract: We formulate a continuous-time competitive equilibrium model of irreversible capacity investment in which a continuum of heterogeneous producers supplies a single non-durable good subject to exogenous stochastic demand. Each producer optimally adjusts both output and capacity over time in response to endogenous price signals, while investment decisions are irreversible. Market clearing holds continuously, with prices evolving endogenously to balance aggregate supply and demand through a constant-elasticity demand function driven by a stochastic base component. The model admits a mean-field interpretation, as each producer's decisions both influence and are influenced by the aggregate behaviour of all others. We show that the equilibrium price process can be expressed as a nonlinear functional of the exogenous base demand, leading to a three-dimensional singular stochastic control problem for each producer. We derive an explicit solution to the associated Hamilton-Jacobi-Bellman equation, including a closed-form characterisation of the free-boundary surface separating investment and waiting regions.