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. We consider a mean-field model of firms competing à la Cournot on a commodity market, where the commodity price is given in terms of a power inverse demand function of the industry-aggregate production. Investment is irreversible and production capacity depreciates at a constant rate. Production is subject to Gaussian productivity shocks, whereas large nonanticipated macroeconomic events driven by a two-state continuous-time Markov chain can change the volatility of the shocks, as well as the price function. Firms wish to maximize expected discounted revenues of production, net of investment, and operational costs. Investment decisions are based on the long-run stationary price of the commodity. We prove existence, uniqueness, and characterization of the stationary mean-field equilibrium of the model. The equilibrium investment strategy is of barrier type, and it is triggered by a couple of endogenously determined investment thresholds, one per state of the economy. We provide a quasi-closed form expression of the stationary density of the state, and we show that our model can produce Pareto distribution of firms' size. This is a feature that is consistent both with observations at the aggregate level of industries and at the level of a particular industry. We provide evidence that persistent periods of economic downturn increase market concentration. We demonstrate that firms with slowly depreciating production capacities fare better in a stable, average economy, whereas firms with quickly depreciating assets can benefit from sequences of boom and bust. Funding: This work was supported by the Agence Nationale de la Recherche.