The story of my question is
I have multiple question.
(1) when John doesn’t work in the underground economy at all , t=0, how can I find the optimal value of $l$ and consumption bundle and his utility.
(2) And when john work in the underground economy, t>0, how can write his optimization problem? Can I say that $l=0$ for t>0 by using the equation (1) in the picture? And in this case, when he is not fined, which way I can find his optimal consumption bundle and his expected utility?
(3) finally, I would like to derive an inequality in order to describe for which parameter values John elects to work in the underground economy. And how can I decide whether John is willing to work in the underground economy or not if m and w increase by the same dollar amount ?
Sorry for not posting my answer, because I am not familiar with such a question, my answer is really trivial.