Derivative with respect to x - constraint is : b= max(x+y+z ,0)

General DSGE Modeling
1

Hi everyone
I have a question about the derivation with respect to the control variables in the household sector. My question arises in a particular case
One of the constraints is : b= max(x+y+z ,0)
I would be very grateful if anyone can help me
I attach my question
many thanksquestion.pdf (674.9 KB)

2

This problem is not differentiable and therefore generally cannot be solved using first order conditions. Sometimes you may be able to reformulate the problem as one with inequality constraints so that it becomes a Kuhn-Tucker problem. In that case, first order conditions work.