Euler Equation

We consider the following maximization problem with depreciation

subject to as in 0628.

We continue to suppose Lt=1 all the time for simplicity. In addition, we have

and

where and are error terms with mean zero.

On the background, we assume

for any

The Bellman equation with expectation is

The resulting Euler equation as in 0628 is

In terms of K’s, that is

Thus

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