Consider the contract problem in Example 10.5. Suppose that when considering whether to take the contract or not, the worker tries to maximize the function U(b) + maxiε[h,l] Vi, where U(b) = b0.88, the value b is the base level of pay in the contract, and Vi is as given in equations 10.12 through 10.17. Consider that if the worker takes no contract, she will receive $0.
a. What is the minimum level of base pay the worker will accept for a contract with a high base pay and penalties for poor performance (so b = rh)? What are the resulting rl, rh?
b. What is the minimum level of base pay the worker will accept for a contract with low base pay and rewards for good performance (so b = rl)? What are the resulting rl, rh?
c. Suppose the firm can sell high-quality pizza for $10 and low-quality pizza for $7. Which contract will the firm offer in order to maximize their profits?