Euler Equation

We consider the following basic maximization problem:

subject to

where . The corresponding Bellman equation is

where

Euler equation we got in 0620 is

or

It leads to

when . In terms of k’s,

Thus

where we can regard it as recurrence formula from initials of and .

Starting from and , we get and plot them as:

where the relation must hold to get to the steady state.

As we all know, we consider the following trajectories starting from k0

between k’=k and that is policy function of capital.

However, we have to know the policy function of capital to get this graph.