A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy
Aïd R, Basei M, Ferrari G (2023) Center for Mathematical Economics Working Papers; 679.
Bielefeld: Center for Mathematical Economics.
Diskussionspapier
| Veröffentlicht | Englisch
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Autor*in
Aïd, René;
Basei, Matteo;
Ferrari, GiorgioUniBi
Abstract / Bemerkung
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.
**OR/MS subject classification:** Dynamic programming/optimal control: Markov; Games/group decisions: Stochastic; Inventory/production: Stochastic models.
**MSC2020 subject classification:** 49N80, 49L20, 91A15, 91A16.
**OR/MS subject classification:** Dynamic programming/optimal control: Markov; Games/group decisions: Stochastic; Inventory/production: Stochastic models.
**MSC2020 subject classification:** 49N80, 49L20, 91A15, 91A16.
Stichworte
mean-field stationary equilibrium;
irreversible investment;
regime-switching;
market concentration;
value of economic stability
Erscheinungsjahr
2023
Serientitel
Center for Mathematical Economics Working Papers
Band
679
Seite(n)
33
Urheberrecht / Lizenzen
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2978796
Zitieren
Aïd R, Basei M, Ferrari G. A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy. Center for Mathematical Economics Working Papers. Vol 679. Bielefeld: Center for Mathematical Economics; 2023.
Aïd, R., Basei, M., & Ferrari, G. (2023). A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy (Center for Mathematical Economics Working Papers, 679). Bielefeld: Center for Mathematical Economics.
Aïd, René, Basei, Matteo, and Ferrari, Giorgio. 2023. A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy. Vol. 679. Center for Mathematical Economics Working Papers. Bielefeld: Center for Mathematical Economics.
Aïd, R., Basei, M., and Ferrari, G. (2023). A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy. Center for Mathematical Economics Working Papers, 679, Bielefeld: Center for Mathematical Economics.
Aïd, R., Basei, M., & Ferrari, G., 2023. A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy, Center for Mathematical Economics Working Papers, no.679, Bielefeld: Center for Mathematical Economics.
R. Aïd, M. Basei, and G. Ferrari, A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy, Center for Mathematical Economics Working Papers, vol. 679, Bielefeld: Center for Mathematical Economics, 2023.
Aïd, R., Basei, M., Ferrari, G.: A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy. Center for Mathematical Economics Working Papers, 679. Center for Mathematical Economics, Bielefeld (2023).
Aïd, René, Basei, Matteo, and Ferrari, Giorgio. A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy. Bielefeld: Center for Mathematical Economics, 2023. Center for Mathematical Economics Working Papers. 679.
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