Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth
AbstractIn 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.
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Bibliographic InfoPaper provided by DEGIT, Dynamics, Economic Growth, and International Trade in its series DEGIT Conference Papers with number c009_014.
Length: 18 pages
Date of creation: Jun 2004
Date of revision:
Value Function Approach; Nash-Equilibrium; Open-loop Strategies; Ordinary Differential Equation.;
Other versions of this item:
- ReiÃŸ, Markus & Bethmann, Dirk, 2003. "Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth," SFB 373 Discussion Papers 2003,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- 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, Technological Change, and Growth - - Economic Growth and Aggregate Productivity
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