General existence of competitive equilibrium in the growth model with an endogenous labor–leisure choice

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We prove the existence of competitive equilibrium in the canonical optimal growth model with elastic labor supply under general conditions. In this model, strong conditions to rule out corner solutions are often not well justified. We show using a separation argument that there exist Lagrange multipliers that can be viewed as a system of competitive prices. Neither Inada conditions, nor strict concavity, nor homogeneity, nor differentiability are required for existence of a competitive equilibrium. Thus, we cover important specifications used in the macroeconomics literature for which existence of a competitive equilibrium is not well understood. We give examples to illustrate the violation of the conditions used in earlier existence results but where a competitive equilibrium can be shown to exist following the approach in this paper.

Bibliographic note

Funding Information: We would like to thank Professors Atsushi Kajii, M. Ali Khan, Cuong Le Van and two anonymous referees for helpful suggestions and comments. Manh-Hung Nguyen acknowledges support from ANR under grant ANR-17-EURE-0010 (Investissements d'Avenir program). Publisher Copyright: © 2020 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.


Original languageEnglish
Pages (from-to)90-98
Number of pages9
JournalJournal of Mathematical Economics
Early online date16 Sep 2020
Publication statusE-pub ahead of print - 16 Sep 2020


  • Optimal growth, Competitive Equilibrium, Lagrange Multipliers, Endogenous labor, Inada Conditions, Lagrange multipliers, Inada conditions, Competitive equilibrium, Elastic labor supply