Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth

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.