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The open-loop solution of the Uzawa-Lucas model of endogenous growth with N agents

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  • Bethmann, Dirk

Abstract

We solve an player general-sum differential game. The optimization problem considered here is based on the Uzawa-Lucas model of endogenous growth. Agents have logarithmic preferences and own two capital stocks. Since the number of players is an arbitrary fixed number , the model's solution is more general than the idealized concepts of the social planer's solution with one player or the competitive equilibrium with infinitely many players. We show that the symmetric Nash equilibrium is completely described by the solution to a single ordinary differential equation. The numerical results imply that the influence of the externality along the balanced growth path decreases rapidly as the number of players increases. Off the steady state, the externality is of great importance, even for a large number of players.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Macroeconomics.

Volume (Year): 30 (2008)
Issue (Month): 1 (March)
Pages: 396-414

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Handle: RePEc:eee:jmacro:v:30:y:2008:i:1:p:396-414

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Web page: http://www.elsevier.com/locate/inca/622617

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  1. Mulligan, Casey B & Sala-i-Martin, Xavier, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, MIT Press, vol. 108(3), pages 739-73, August.
  2. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
  3. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  4. Caballe, Jordi & Santos, Manuel S, 1993. "On Endogenous Growth with Physical and Human Capital," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1042-67, December.
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Cited by:
  1. Dirk Bethmann, 2007. "Homogeneity, Saddle Path Stability, and Logarithmic Preferences in Economic Models," Discussion Paper Series 0702, Institute of Economic Research, Korea University.
  2. Dirk Bethmann & Markus Reiß, 2012. "Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations," Journal of Economics, Springer, vol. 107(2), pages 101-128, October.

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