Policy function calculation from Euler equation

We use Euler equation

with depreciation. F’( ) is the first derivative w.r.t. the first element.

On the other hand, FOC w.r.t. labor is

In steady state, we have

or

Thus

　for some Q and A.

We have to find so as to satisfy

Powered by , we have

Thus

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

Algorithm:

(0) Calculate constant labor from

(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.

Behaviors of policy functions of K according to