A firm's output depends on which state of the world will result. In the good state, the firm output will be 300; the bad state it will be 100. The probability of the good state depends on how hard the firm's manager works. If she works really hard, this probability is p sub H=2/3 while if she shirks this probability is p sub L=1/2. The manager wages depend on the firm output. She gets w^G when output is good and w^B when output is bad. The manager receives utility from her wages, and her utility function is w^1/2 , but incurs a cost depending on how hard she works (in other words, the manger's utility is w^1/2-cost). This cost is 6 when she works hard and 2 when she shirks. The manager is currently working for another firm and her utility in this job is 4.

a. Write the manager's expected utility if she works hard

b. Write the manager's expected utility if she shirks.

c. Write the firm's expected profits if the manager works hard

d. Write the firm's expected profits if she shirks. Assume the manager can be observed while working, so that the firm can force her to work at the contractually specified level.

e. Find the optimal (for the firm) w^G and w^B such that the manager works hard.

f. Find the optimal (for the firm) w^G and w^B such that the manager shirks.

g. Given the wages you just found, does the firm prefer the manager to work hard? Explain Now assume that the manager cannot be observed while working. In this case, the firm cannot specify how hard she works in the contract.

h. Write down the constraint w^G and w^B must satisfy if the manager is to work hard voluntarily. Can a contract such that w^G=w^B satisfy this constraint? firm's output depends on which state of the world will result. In the good state, the firm output will be?