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Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth


  • Dirk Bethmann


In this paper we solve an N N N players differential game with logarithmic objective functions. 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 N N N the model's solution is more realistic than the idealized concepts of the social planer or the competitive equilibrium. We show that the symmetric Nash equilibrium is completely described by the solution to one single ordinary differential equation. The numerical results imply that the influence of the externality along the balanced growth path vanishes rapidly as the number of players increases. Off the steady state the externality is of great importance even for a large number of players.

Suggested Citation

  • Dirk Bethmann, 2004. "Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth," DEGIT Conference Papers c009_014, DEGIT, Dynamics, Economic Growth, and International Trade.
  • Handle: RePEc:deg:conpap:c009_014

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    References listed on IDEAS

    1. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    2. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
    3. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 739-773.
    4. Bond, Eric W. & Wang, Ping & Yip, Chong K., 1996. "A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balanced Growth and Transitional Dynamics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 149-173, January.
    5. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    6. 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 1042-1067, December.
    7. Rubio, Santiago J. & Casino, Begona, 2001. "Competitive versus efficient extraction of a common property resource: The groundwater case," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1117-1137, August.
    8. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May.
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    10. 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, March.
    11. P.M. Hartley & L.C.G. Rogers, 2005. "Two-Sector Stochastic Growth Models ," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 322-351, December.
    12. 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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    Cited by:

    1. Dirk Bethmann, 2005. "Notes on an Endogenous Growth Model with two Capital Stocks II: The Stochastic Case," SFB 649 Discussion Papers SFB649DP2005-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Dirk Bethmann, 2007. "A Closed-form Solution of the Uzawa-Lucas Model of Endogenous Growth," Journal of Economics, Springer, vol. 90(1), pages 87-107, January.

    More about this item


    Value Function Approach; Nash-Equilibrium; Open-loop Strategies; Ordinary Differential Equation.;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity


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