3. The stockholders of a firm - called the principal - want to hire a manager - called the agent - to run the firm. The performance of the firm depends on the effort made by the manager and random factors. The performance of the firm can be a great success or a failure. A great success brings a profit of $420000, and a failure a profit of $0. If the agent makes no effort (e = 0), the project is a success with probability , and a failure with probability . Profit $ 420 000 No effort (e = 0) If the agent makes a great effort (e = 1), the project is a success with probability - and a failure with probability ? Profit $420000 Great effort (e=1) The manager is risk neutral, so his expected utility equals his expected income minus his disutility of effort. He can get other jobs paying $90000 without requiring any effort. Also, his disutility for exerting a great effort is $100 000. A contract - when the action of the agent cannot be observed - is a pair (x, y), where x is the remuneration if the project fails and y is the remuneration if the project is a success. (a) Show that inducing high effort would require the firm to offer a compensation scheme with negative base salary; that is, if the project fails, the manager pays the firm an amount stipulated in the scheme. (b) How might a negative base salary be implemented in reality? (c) Show that if a negative base salary is not feasible, then the firm does better to settle for the low-pay low-effort situation