On the regularity of smooth production economies with externalities: Competitive equilibrium à la Nash
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26 janvier 2017
- handle: 10670/1.a2wyru
- hal: hal-01438970
- doi: 10.1007/s00199-016-1029-5
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info:eu-repo/semantics/altIdentifier/doi/10.1007/s00199-016-1029-5
Mots-clés
private ownership economies competitive equilibrium à la Nash regular economies externalities C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C62 - Existence and Stability Conditions of Equilibrium D - Microeconomics/D.D5 - General Equilibrium and Disequilibrium/D.D5.D51 - Exchange and Production Economies D - Microeconomics/D.D6 - Welfare Economics/D.D6.D62 - ExternalitiesSujets proches
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Elena L. del Mercato et al., « On the regularity of smooth production economies with externalities: Competitive equilibrium à la Nash », HAL-SHS : économie et finance, ID : 10.1007/s00199-016-1029-5
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Résumé
We consider a general equilibrium model of a private ownership economy with consumption and production externalities. The choices of all agents (households and firms) may affect utility functions and production technologies. The allocation of a competitive equilibrium is a Nash equilibrium. We provide an example showing that, under standard assumptions, competitive equilibria are indeterminate in an open set of the household’s endowments. Next, we consider a new version of this model, with firms’ endowments in the spirit of Geanakoplos et al. (J Math Econ 19:113–151, 1990). In our model, firms’ endowments impact the technologies of the other firms. We then prove that, generically in the space of endowments of households and firms, each economy has a finite number of competitive equilibria and each competitive equilibrium is locally a differentiable map of the fundamental parameters.