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

  • Goenka, Aditya
  • Nguyen, Manh-Hung

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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  1. Kazuo Nishimura & Tapan Mitra, 2004. "Intertemporal Complementarity and Optimality: A Study of a Two-Dimensional Dynamical System," Econometric Society 2004 Far Eastern Meetings 543, Econometric Society.
  2. Cuong Le Van & Manh-Hung Nguyen & Yiannis Vailakis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00101237, HAL.
  3. Le Van, Cuong & Cagri Saglam, H., 2004. "Optimal growth models and the Lagrange multiplier," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 393-410, June.
  4. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September.
  5. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Economic Theory, Springer, vol. 22(4), pages 743-771, November.
  6. Aliprantis, Charalambos D. & Border, Kim C. & Burkinshaw, Owen, 1997. "New Proof Of The Existence Of Equilibrium In A Single-Sector Growth Model," Macroeconomic Dynamics, Cambridge University Press, vol. 1(04), pages 669-679, December.
  7. Dana Rose-anne & Le Van Cuong, 1987. "Optimal growth and pareto-optimality," CEPREMAP Working Papers (Couverture Orange) 8723, CEPREMAP.
  8. repec:hal:journl:halshs-00101237 is not listed on IDEAS
  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. Jeremy Greenwood & Gregory W. Huffman, 1993. "On the existence of nonoptimal equilibria in dynamic stochastic economies," Research Paper 9330, Federal Reserve Bank of Dallas.
  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.
  14. 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.
  15. 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.
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