I am an economist with some math background but not strong enough to solve this. I'm trying to solve:
is a linear function of and are constants. and is a compact and continuous subset of . is a concave and differentiable function.
Now, my problem is that the optimal choice of depends on the value of (), which depends on .
I would like to know how to solve for, if possible, a closed-form solution. If it is impossible, what kind of algorithm should I use, and where can I find the essential readings to learn them.
EDIT: Thanks Robert for his great answer. Now I would just like to ask this follow-up question:
Can this method of solving for the maximum be adopted in a dynamic programming version of this problem? Say I want to maximise but the constant now becomes a function of ? is a discount factor.