WIAS Preprint No. 917, (2004)

A simple method to study the transitional dynamics in endogenous growth models


  • Bethmann, Dirk
  • Reiß, Markus

2010 Mathematics Subject Classification

  • 91B62 49L20 91B66


  • transitional dynamics, dynamic programming, Uzawa-Lucas model, human capital allocation, dimension reduction


We introduce a simple method of analyzing the transitional dynamics of the Uzawa-Lucas endogenous growth model with human capital externalities. We use the value function approach to solve both the social planner's optimization problem in the centralized economy and the representative agent's optimization problem in the decentralized economy. The complexity of the Hamilton-Jacobi-Bellman equations is significantly reduced to an initial value problem for one ordinary differential equation. This approach allows us to find the optimal controls for the non-concave Hamiltonian in the centralized case and to identify the symmetric Nash equilibrium of the agents' optimal strategies in the decentralized case. For a wide range of the degree of the human capital externality we calculate the global transitional dynamics towards the balanced growth path. The U-shaped course of output growth rates is explained in detail. JEL Classifications: C61, O41, C72

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