Computation of the Optimal Policy for the Optimal Growth (Euler Equation)

(Mainly for students attending my class.)

As supplementary matrials on our way to understanding the optimal growth model, I put an R code and related documents on my github repository: kenjisato/intro-macro:

• /r/optimal_growth_euler.R
• /doc/r/optimal_growth_euler.Rmd
  • Compiled PDF

I do this mainly for a pedagogical reason. As a matter of fact, the above mentioned script isn’t practical; it does work if the initial condition is close to the steady state and the initial guesses of optimal consumption are sufficiently accurate but otherwise doesn’t (it’d take very loong time).

The only utility of this excercise is to show how it is difficult to compute the optimal policy!

Human beings (as main agents in our economic system) might have a different decision making strategy such as adaptive learning (when you realize that you aren’t on the right track you will make some adjustments). Incorporating such notion in formal analysis might be an interesting direction but is beyond the scope of the course.

We, in fact, have a more practical method to compute the optimal policy, in which we exploit the technique of dynamic programming. This will be discussed elsewhere.