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 800 units. The project is still worth 200 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 0.7 (accordingly, the probability of not being successful is 0.3); and the probability of success in case of low effort by the manager is 0.3 (accordingly, the probability of not being successful is 0.7). The cost (disutility) of high effort to the manager is equivalent to 20 units and that of low effort is equivalent to 4 units. The manager has an alternative employment opportunity that would offer him a fixed wage of 10 units.

As the owner of the company, you are to come up with the best incentive scheme to offer to this manager. The manager's payoff is given by the payment he receives minus the cost (disutility) of effort. Your payoff isgiven 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.)

1. [10 points]What would be the fixed wage you would offer under a fixed-wage scheme? What would be the expected payoffs to you and the manager under this scheme?
2. [15 points]What would be the levels of low wage (paid when the project fails) and high wage (paid when the project succeeds) you would offer in a wage-plus-bonus scheme? What would be the expected payoffs to you and the manager under this scheme?