i hope you would be able to assist me with this question on Principal Agent Problem, thank you!

4. The following problem has you work through a special case of the model discussed in lecture. The common income utility function is u(a:) = lnw, so overall preferences are represented Eln(as) e, where e is the effort level and so is income. Output can assume only two values, R1 > R0. As before, entrepreneurs must hire exactly 71 workers each. a. Set up the case of no insurance for entrepreneurs and verify that in equilibrium the \"rich hire the poor\" (i.e. show that at wealth level ('1 at which an individual is indifferent between the two occupations, we must have Vd) > mo) ). b. Do the same for the secondbest case. You should be able to solve eXplicitly for the two income levels yl and yo. How does yl yo vary with wealth? Verify by direct calculation that V)