Journal of Economics

, Volume 107, Issue 2, pp 101–128 | Cite as

Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations

  • Dirk BethmannEmail author
  • Markus Reiß


We introduce a simple method for computing value functions. The method is demonstrated by solving for transitional dynamics in the Uzawa and Lucas endogenous growth model. 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 equilibrium in the decentralized case.


Transitional dynamics Value function approach Symmetric equilibrium Initial value problem U-shaped growth rates 

JEL Classification

C61 O41 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Otto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.Institut für MathematikHumboldt Universität zu BerlinBerlinGermany

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