Camilla wishes to employ Charles to repair her lawn mower. The value of the lawn mower is10if it is working and0if it remains broken. Charles can put in effort into fixing the lawn mower denoted by

e[0,1]whereeis the probability of fixing the lawn mower and the effort costs10e^2.

However, Camilla can only observe whether the lawn mower is fixed and not Charles' effort.

(a) Show that if Camilla can repair the lawn mower herself at an effort cost of10e^2, then the probability of the lawn mower being repaired is 0.5.

2.(b)Why might asking Charles to fix the lawn mower create moral hazard problem?

3.(c)What advice would you give Camilla about the kinds of incentive schemes that might be relevant and the evidence for them being effective?

4.(d)Unless employed by Camilla, Charles expect to be unemployed and so to earn0. Camilla offers to pay Charles a cash bonus for fixing her lawn mower. What is the optimal bonus that Camilla should offer Charles, to be paid, if he successfully repairs her lawn mower? What is the probability that that the lawn mower will be fixed with this bonus payment?

5.(e)Camilla offers Charles the option to sit on the lawn with her if he repairs the lawn mower successfully. Charles gets utility of5from sitting on the lawn with Camilla. Camilla does not mind Charles' company so it costs her nothing to allow him to sit on the lawn. He may also be offered a financial bonus if he repairs the lawn mower. Is the possibility of sitting on the lawn with Camilla an incentive for Charles? Does Camilla's offer to sit on the lawn affect the optimal bonus she chooses for Charles? Does Camilla benefit from offering Charles the option to sit on the lawn with her?

6.(f)Charles receives a phone call from Elizabeth who offers him work that yields a payoff of 2 but means he is no longer available to repair Camilla's lawnmower. Camilla is keen to retain Charles as a lawnmower repairer. Discuss how this affects the bonus Camilla offers Charles for repairing the lawn mower, assuming she offers him the option to sit on the lawn with her? Will this offer of employment by Elizabeth increase the probability that Camilla gets her lawn mower repaired?