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

TL;DR

This paper develops a continuous-time equilibrium model for irreversible capacity investment with stochastic demand and heterogeneous producers, providing explicit solutions and a free-boundary characterization.

Contribution

It introduces a mean-field equilibrium framework with a closed-form solution for the investment decision boundary under stochastic demand.

Findings

Explicit solution to the Hamilton-Jacobi-Bellman equation.

Closed-form characterization of the investment-waiting boundary.

Model captures heterogeneity and stochastic demand effects.

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.