Existence of Competitive Equilibrium in an Optimal Growth Model with Elastic Labor Supply and Smoothness of the Policy Function

Goenka, Aditya and Nguyen, Manh-Hung (2009) Existence of Competitive Equilibrium in an Optimal Growth Model with Elastic Labor Supply and Smoothness of the Policy Function. TSE Working Paper, n. 09-064

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Official URL: http://tse-fr.eu/pub/22185

Abstract

We prove the existence of competitive equilibrium and the moothness of policy function in an optimal growth model with elastic labor supply by using a simple method. Our approach is based on the result of existence of Lagrange multipliers and their representation as a summable sequence due to Le Van and Saglam [2004] to define the sequence of prices and wages. The proof of existence of equilibrium we give is more simple than in Le Van and Vailakis [2004] and requires less stringent assumptions (neither Inada conditions for the utility function and the production function nor constant return to scale for the production function nor strict concavity). We also prove the differentiability of the policy function at a stationary optimal stock where the derivative of the policy function equals the smaller characteristic root in absolute value associated with Euler equation. Conditions for differentiability of the policy function have so far been assumed in the literature.

Item Type: Monograph (Working Paper)
Language: English
Date: 20 July 2009
Uncontrolled Keywords: Lagrange multipliers, competitive equilibrium, elastic labor supply
JEL codes: C61 - Optimization Techniques; Programming Models; Dynamic Analysis
D51 - Exchange and Production Economies
E13 - Neoclassical
O41 - One, Two, and Multisector Growth Models
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 18 Jan 2012 06:00
Last Modified: 07 Mar 2018 13:22
OAI ID: oai:tse-fr.eu:22185
URI: http://publications.ut-capitole.fr/id/eprint/3225

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