Policy function calculation from Euler equation

We use Euler equation

as in 0627 and 0708. We assume for simplicity.

We know the form of policy function of K. That is

.

We check if the resulting computation is going to be the same as this form.

In steady state, we have

or

Thus

　　for some Q and A as in 0627.

We have to find so as to satisfy

Thus

starting from and evaluated at some Q’s and A’s.

Algorithm:

(1) Set Euler equation:

　

and

(2) Find K* such that as steady-state level of K.

(3) Calculate given and from and up to t=n and save it.

(4) Change and find the best leading to .

(5) Change and repeat (3) and (4) to recover policy function of K.

The resulting function should be

derived in guess and verify as long as we assume log utility function.