We consider the following maximization problem
![]()
subject to ![]()
as in 0629. The Bellman equation with expectation is
![]()
The resulting Euler equation as in 0629 is
![]()
In terms of Kfs, that is

![]()
Thus
![]()
On the other hand, FOC w.r.t. L is
Given this
,
![]()
evaluated at Qfs and Afs.