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

  • Bethmann, Dirk

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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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
Contact details of provider: 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. repec:cup:cbooks:9780521637329 is not listed on IDEAS
  3. 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.
  4. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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