A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy

We study firms size distribution in a mean-field model of Cournot competition in a commodity market, where price follows an inverse power demand function. Firms face irreversible investment decisions and constant depreciation of production capacity. Output is affected by Gaussian productivity shocks, whose volatility and the price function can shift due to rare macroeconomic events modeled by a two-state Markov chain. Firms aim to maximize expected discounted profits, net of investment and operating costs, based on the long-run stationary price. We establish existence and uniqueness of a stationary mean-field equilibrium and characterize it through a barrier-type investment strategy with endogenous thresholds for each economic regime. A quasi-closed form for the stationary distribution of firms’ states is provided. The model generates Pareto-distributed firm sizes, consistent with empirical industry data. It also shows that downturns raise market concentration and that firm performance depends on depreciation rates and the persistence of economic fluctuations.