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 success or a failure. A success brings in a profit of $450000, and a failure a profit of $0. If the agent makes no effort (e = 0), the project is a success with probability 1 4 , and a failure with probability 3 4 . If the agent makes a good effort (e = 1), the project is a success with probability 1 2 , and a failure with probability 1 2 . The manager is risk neutral, so his expected utility equals his expected income minus his dis-utility of effort. He can get other jobs paying $90000 without requiring any effort. Also, his dis-utility for exerting a good 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 is a success and y is the remuneration if the project is a failure. (a) Show that inducing a good 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) What is the optimal contract if a negative base salary is not feasible?