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
as derived yesterday.
Today we start from steady-state level of
capital 
.
Given 
and 
where 
is very small,
we find 
as in
.
Given 
and 
that is got
above, we find 
as in
and so onc up until
to find 
from 
and 
.
If we continue to do this without stopping, k will approach zero.