Policy function calculation from value function iterations

Algorithm:

(1) Set a grid consisting of k and k’ columnwise and rowwise respectively.

(2) Calculate utility for consumption as U using the grid matrix above.

(3) Starting from a certain v, update v1=U+beta*v’ so as to maximize v1.

(4) Repeat (3) by setting v=v1 for many times or until some criterion is met.

(5) Find the final corresponding value of k as k’ according to the maximum value.

To generalize the process and set U, we set c=fc(k,k’) and u=fu(c).

Today we consider the basic AK model and its Bellman equation:

where and

where u(x)=ln(x) as .

We set

that is the same AK model as before

and

that is CRRA utility function in general.

Behaviors of policy functions of k according to in CRRA utility function

When n=300 or more in normal version of GAUSS, they are smoothed out.

If we need more coverage from near origin, set a greater number to kpc.