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On the equilibrium in a discrete-time Lucas Model with endogenous leisure

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Abstract

In this paper I study a discrete-time version of the Lucas model with the endogenous leisure but without physical capital. Under standard conditions I prove that the optimal human capital sequence is increasing. If the instantaneous utility function and the production function are Cobb-Douglas, I prove that the human capital sequence grow at a constant rate. I finish by studying the existence and the unicity of the equilibrium in the sense of Lucas or Romer.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2006/B06054.pdf
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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b06054.

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Length: 22 pages
Date of creation: Jul 2006
Date of revision:
Handle: RePEc:mse:wpsorb:b06054

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Keywords: Lucas Model; human capital; externalities; optimal growth; equilibrium.;

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  1. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
  2. Lisa Morhaim & Charles-Henri Dimaria & Cuong Le Van, 2002. "The discrete time version of the Romer model," Economic Theory, Springer, vol. 20(1), pages 133-158.
  3. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-32, May.
  4. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  5. LE VAN, Cuong & MORHAIM, Lisa, 2001. "Optimal growth models with bounded or unbounded returns: a unifying approach," CORE Discussion Papers 2001034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Dana, Rose-Anne & Le Van, Cuong, 2003. "Dynamic Programming in Economics," Economics Papers from University Paris Dauphine 123456789/13605, Paris Dauphine University.
  7. Salvador Ortigueira, 1997. "A Dynamic Analysis of an Endogenous Growth Model with Leisure," Working Papers 9705, Centro de Investigacion Economica, ITAM.
  8. Ladron-de-Guevara, Antonio & Ortigueira, Salvador & Santos, Manuel S, 1999. "A Two-Sector Model of Endogenous Growth with Leisure," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 609-31, July.
  9. Ryder, Harl E & Stafford, Frank P & Stephan, Paula E, 1976. "Labor, Leisure and Training over the Life Cycle," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(3), pages 651-74, October.
  10. Brock, William A. & Gale, David, 1969. "Optimal growth under factor augmenting progress," Journal of Economic Theory, Elsevier, vol. 1(3), pages 229-243, October.
  11. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-37, October.
  12. Dana, Rose-Anne & Le Van, Cuong, 2003. "Dynamic Programming in Economics," Economics Papers from University Paris Dauphine 123456789/416, Paris Dauphine University.
  13. GOURDEL, Pascal & NGOC, Liem Hoang & LE VAN, Cuong & MAZAMBA, Tédié, . "Equilibrium and competitive equilibrium in a discrete-time Lucas model," CORE Discussion Papers RP -1742, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
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