Assaulting the Ramsey model (numerically!)

Everything (and then some!) that you would ever want to know about using dynamic programming techniques to solve deterministic and stochastic versions of the Ramsey optimal growth model can be found in this paper.

I wrote up a quick implementation of the most basic version of the value function iteration described in the paper (vanilla value iteration with a good initial guess and cubic spline interpolation).  Below is a graphic I produced of the optimal value and policy functions as well as every 50th iterate (to give a sense of the convergence properties).

The Python code is slowish (takes several minutes to compute the above functions).  Suggestions on ways to speed up the code are definitely welcome!

Back to the grind of marking essays...enjoy!