Return to problem 15.2. Suppose that Clare can still choose to exert effort, as in the previous problem, but that she can also choose not to exert effort. If she does not exert effort, she has no effort cost, so her utility is just the wage, w; the shop's return is $400 for certain.
a. If shareholders offered to share half of the store's gross profit, what effort would Clare choose? Would she accept such a contract? What if she were only given a quarter share? What would be the lowest share that would get her to exert effort?
b. Suppose instead that shareholders decided to offer her a $100 bonus if the store earns $1,000. Show that this would not get her to work hard. What is the minimum bonus that she would need to be paid? What fixed salary would she need to be paid in addition to get her to accept the contract?