Policy function calculation from value function iterations

Today we consider the model with labor and its Bellman equation:

where and

Here, is leisure utility such as

using a common parameter for simplicity.

For the same procedure as before, we set

and

where we find beforehand so as to satisfy

and

at the same time.

Behaviors of policy functions of k according to(0.99,0.7,0.4 from the bottom)