(Moral Hazard) Ben hires Alice to work as a manager in his store. Each month, Alice can either have a high volume of sales, in which case Ben's revenue is $ 20,000, or a low volume of sales, in which case his revenue is only $ 10,000. If Alice works hard (e = 1), the probability that she has many customers is 50%. If she is lazy (e = 0), the probability that he has many customers is 30%. Working hard costs Alice the monetary equivalent of $ 400. Being lazy costs nothing. If Alice does not work for Ben, she could get a monthly wage of $ 1000 with no effort elsewhere. a) Suppose first Ben pays Alice a fixed salary (wage) w. What level of effort would Alice choose? And what wage w* should Ben pay Sally? Explain! b) Now suppose Ben can observe the volume of sales number of customers, and can pay Alice a bonus 6 in addition to her fixed wage w* you computed in a). The bonus would be paid only if she has a high sales value. What is the minimum bonus b* to ensure that Alice works hard? And given that bonus b* , should Ben still hire Alice? Explain! c) Finally, suppose Ben cannot observe the volume of sales and revenue, so bonus payments are now longer feasible. Ben has taken Econ 302, however, and remembers that Alice's moral hazard can still be solved by having her lease the store from him. Under a lease contract, Alice would receive all the revenue (not Ben) and only pay Ben a fixed amount _ of monthly rent. Explain carefully why this contract will solve the moral hazard problem! What is the optimal lease pay I* that Ben should offer Alice