3. (30 pts. total + Bonus) In the Principal Agent experiment with asymmetric inf

3. (30 pts. total + Bonus) In the Principal Agent experiment with asymmetric information, expected payoffs for the risky project are as follows (where RS equals revenue if successful, RU equals revenue if unsuccessful, w equals wage, b equals bonus, p equals the probability of success, e_H equals the cost of high effort and e_L equals the cost of low effort): Boss (if worker chooses high effort): p*(RS) + (1-p)*(RU) – w – p*b Boss (if worker chooses low effort): RU – w Worker (if worker chooses high effort): w + p*b – e_H Worker (if worker chooses low effort): w – e_L Suppose: RS = 800 RU = 200 p = 0.5 e_H = 100 e_L = 50 a. (15 pts.) What minimum bonus will induce the worker to exert high effort? b. (15 pts.) At the minimum bonus amount, will the bossβs payoff be higher under high effort than under low effort? Show work to get credit. c. (10 pts.) Bonus: What range of bonus amount will both induce high effort from the worker and ensure the boss is better off than under low effort? Show all work to get credit.