3. [40 Points] Suppose you are the owner of a company that is undertaking a new project. You have to hire a manager to supervise it. The success of the project is uncertain, but good supervision by the manager can increase the probability of success. The value of a successful project is 500 units. The project is still worth 100 units even if it is not successful in achieving all the projected goals. The probability of success in case of high effort by the manager is 0.8 (accordingly, the probability of not being successful is 0.2); and the probability of success in case of low effort by the manager is 0.2 (accordingly, the probability of not being successful is 0.8). The cost (disutility) of high effort to the manager is equivalent to 40 units and that of low effort is equivalent to 10 units. The manager has an alternative employment opportunity that would give him a net payoff of 20 units (net of cost of effort). As the owner of the company, you are to come up with the best incentive scheme to offer to this manager. The managers payoff is given by the payment he receives minus the cost (disutility) of effort. Your payoff is given by your expected profits (that is, expected value of the project minus the wage paid to the manager). Suppose you can choose between a fixed-wage scheme and a wage-plus-bonus scheme. (Consider the wage-plus-bonus scheme we discussed in class; i.e. the manager is paid a low wage if the project fails, i.e. yields the low value, and a high wage if the project succeeds, i.e. yields the high value. To make sense of the numbers, you can think of a unit as $1,000, but for simplicity work with the unit numbers as defined in the question rather than converting them to dollar amounts.).

a. [10 Points] Fixed Wage

i. What would be the fixed-wage offered under the fixed-wage scheme?

ii. Would you be able to elicit high effort from your manager, i.e. would the manager choose high or low effort in equilibrium?

iii. What would be the expected payoffs to you and the manager under this scheme?

b. [25 Points] Wage-plus-bonus mechanism

i. What would be the levels of low wage and high wage you would offer in a wage-plus-bonus scheme? (Consider the low wage as the base wage and the high wage as the (base wage + bonus).)

ii. Would you be able to elicit high effort from your manager, i.e. would the manager choose high or low effort in equilibrium?

iii. What would be the expected payoffs to you and the manager under this scheme?

c. [5 Points] In what way is the role played by the bonus component of the wage-plus-bonus scheme similar to the role played by the co-payments and deductibles that are paid in addition to the insurance premium for insurance coverage?