On the regularity of smooth production economies with externalities: Competitive equilibrium à la Nash

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2015.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2015.44R - ISSN : 1955-611X. Version originale Mai 2015, révisée en Décembre 2016, acceptée le 15 Décembre 2016 par Economic Theory.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. We introduce the model with firms' endowments, in the spirit of Geanakoplos, Magill, Quinzii and Drèze (1990). In our model, firms' endowments impact the technologies and the marginal productivities of the other firms. We then prove that these economies are generically regular in the space of endowments of households and firms