Euler Equation

We consider the following maximization problem with depreciation

subject to

where we assume

for any

The Bellman equation with expectation is

The resulting Euler equation as in 0630 is

where is the derivative of F with respect to K.

In terms of K’s, that is

Thus

On the other hand, FOC w.r.t. L is

Given this,

evaluated at Q’s and A’s.