Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment

Summary. We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics.

Authors and Affiliations

1. CNRS, CERMSEM, Université de Paris 1, MSE, 106-112 Bd de l' Hopital, 75647 Paris, FRANCE (e-mail: levan@univ-paris1.fr) , , , , , , FR

   Cuong Le Van

2. IRES, Université Catholique de Louvain, Place Montesquieu, 3, 1348 Louvain-la-Neuve, BELGIUM (e-mail: vailakis@ires.ucl.ac.be) , , , , , , BE

   Yiannis Vailakis

Received: September 13, 2001; revised version: December 9, 2002

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ID="*" We are grateful to Tapan Mitra for pointing out errors as well as making very valuable suggestions. Thanks are due to Raouf Boucekkine and Jorge Duran for additional helpful discussions. We also thank an anonymous referee for his/her helpful comments. The second author acknowledges the financial support of the Belgian Ministry of Scientific Research (Grant ARC 99/04-235 “Growth and incentive design”) and of the Belgian Federal Goverment (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”).

Correspondence to: C. Le Van

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