Euler Equation

We consider the following maximization problem

subject 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

when

The Bellman equation with expectation is

The resulting Euler equation as in 0627 is

In terms of K’s, that is

Thus

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