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, while large non-anticipated 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 establish a relation between economic instability and market concentration and we show how macroeconomic instability can harm firms' profitability more than productivity fluctuations.
Optimal Entry to an Irreversible Investment Plan with Non Convex Costs
最近在De Angelis，Ferrari和Moriarty（2015）[SIAM J. Control Optim. 53（3）]。这个问题可以被认为是一个不可逆的投资与成本功能，这是非凸的控制变量。在本文中，我们研究的最佳进入这个投资计划。最优进入策略可以有一个不规则的边界所产生的非凸性，与扭结的形状。
School of Management and Economics, ESOMAS, University of Turin（都灵大学管理经济学院）；Collegio Carlo Alberto（卡洛阿尔贝托学院）；Department of Modeling and Engineering Risk and Complexity, Scuola Superiore Meridionale（南方高等学院建模与工程风险与复杂性系）；CREST, ENSAE, Institute Polytechinique de Paris（巴黎理工学院ENSAE CREST研究中心）
