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Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth

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  • Dirk Bethmann

Abstract

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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    1. repec:hum:wpaper:sfb649dp2005-033 is not listed on IDEAS
    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.

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    Keywords

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    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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