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

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We solve an N ∈ 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 ∈ 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.

Original languageEnglish
Pages (from-to)396-414
Number of pages19
JournalJournal of Macroeconomics
Volume30
Issue number1
DOIs
Publication statusPublished - 2008 Mar 1

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Endogenous growth
Externalities
Competitive equilibrium
Optimization problem
Balanced growth path
Differential games
Nash equilibrium
Differential equations
Capital stock

Keywords

  • Nash-equilibrium
  • Open-loop strategies
  • Ordinary differential equation
  • Value function approach

ASJC Scopus subject areas

  • Economics and Econometrics

Cite this

The open-loop solution of the Uzawa-Lucas model of endogenous growth with N agents. / Bethmann, Dirk.

In: Journal of Macroeconomics, Vol. 30, No. 1, 01.03.2008, p. 396-414.

Research output: Contribution to journalArticle

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