A stationary mean-field equilibrium model of irreversible investment in a two-regime economy

Arbeitspapier

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.

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• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 679

Classification and Topics

• Classification: Wirtschaft ; Optimization Techniques; Programming Models; Dynamic Analysis ; Existence and Stability Conditions of Equilibrium ; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games ; Intertemporal Firm Choice: Investment, Capacity, and Financing ; Market Structure, Pricing, and Design: Perfect Competition ; Business Fluctuations; Cycles ; Production, Pricing, and Market Structure; Size Distribution of Firms ; Firm Organization and Market Structure
• Subject: mean-field stationary equilibrium ; irreversible investment ; regime-switching ; market concentration ; value of economic stability

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Aïd, René ; Basei, Matteo ; Ferrari, Giorgio
• Event: Veröffentlichung
• (who): Bielefeld University, Center for Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2023

Further information

• Handle: http://hdl.handle.net/10419/278469
• URN: urn:nbn:de:0070-pub-29787967