Euler Equation

We consider the same basic maximization problem:

where

as yesterday’s.

Euler equation is

or

and

Given and , from the second relation, we can get .

Then, , , and , from the first relation, we have to find together with .

can be derived from the second relation given and simultaneously.

Instead, we keep as constant in the first relation and we can calculate each

from t=0. That is, we solve

and

from t=0 starting from and . We can do the same thing from steady state

backwards.