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

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  • Goenka, Aditya
  • Nguyen, Manh-Hung

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.

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Paper provided by Toulouse School of Economics (TSE) in its series TSE Working Papers with number 09-064.

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Date of creation: 20 Jul 2009
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Handle: RePEc:tse:wpaper:22185

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Keywords: Lagrange multipliers; competitive equilibrium; elastic labor supply;

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  1. LE VAN, Cuong & SAGLAM, Cagri, 2003. "Optimal growth models and the Lagrange multiplier," CORE Discussion Papers 2003083, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. LE VAN, Cuong & VAILAKIS, Yiannis, . "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," CORE Discussion Papers RP -1762, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September.
  4. Dana, Rose-Anne & Van, Cuong Le, 1991. "Optimal growth and Pareto optimality," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 155-180.
  5. S. Rao Aiyagari & Lawrence J. Christiano & Martin Eichenbaum, 1990. "The output, employment, and interest rate effects of government consumption," Working Papers 456, Federal Reserve Bank of Minneapolis.
  6. Cuong Le Van & Manh Hung Nguyen & Yiannis Vailakis, 2005. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Cahiers de la Maison des Sciences Economiques b05096, Université Panthéon-Sorbonne (Paris 1).
  7. Tapan Mitra & Kazuo Nishimura, 2005. "Intertemporal Complementarity And Optimality: A Study Of A Two-Dimensional Dynamical System," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(1), pages 93-131, 02.
  8. Jeremy Greenwood & Gregory W. Huffman, 1993. "On the existence of nonoptimal equilibria in dynamic stochastic economies," Research Paper 9330, Federal Reserve Bank of Dallas.
  9. Cuong Le Van & Yiannis Vailakis, 2004. "Existence of competitive equilibrium in a single-sector growth model with elastic labour," Cahiers de la Maison des Sciences Economiques b04123, Université Panthéon-Sorbonne (Paris 1).
  10. Kazuo Nishimura & Makoto Yano, 2006. "Introduction," The Japanese Economic Review, Japanese Economic Association, vol. 57(4), pages 455-456.
  11. Manjira Datta & Leonard Mirman & Kevin Reffett, . "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Working Papers 2132846, Department of Economics, W. P. Carey School of Business, Arizona State University.
  12. Majumdar, Mukul, 1972. "Some general theorems on efficiency prices with an infinite-dimensional commodity space," Journal of Economic Theory, Elsevier, vol. 5(1), pages 1-13, August.
  13. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
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