A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy
研究企业在商品市场古诺竞争下的规模分布，考虑不可逆投资、产能折旧和高斯生产率冲击，以及由两状态马尔可夫链驱动的宏观经济事件，证明平稳均场均衡的存在唯一性，并得到帕累托分布的企业规模。
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.