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The open-loop solution of the Uzawa-Lucas Model of Endogenous Growth with N agents

Dirk Bethmann

No 2004,42, Papers from Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE)

Abstract: We solve an N 2 N 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 N 2 N, 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.

Keywords: Value Function Approach; Nash-Equilibrium; Open-loop Strategies; Ordinary Differential Equation (search for similar items in EconPapers)
JEL-codes: C61 O41 C72 (search for similar items in EconPapers)
Date: 2004
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Journal Article: The open-loop solution of the Uzawa-Lucas model of endogenous growth with N agents (2008) Downloads
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