Question 1. A firm needs to hire an employee to complete a project. The project may be successful or not depending on how hard the employee works. Suppose there are two effort levels the employee can choose from, high effort (e = eh) and low effort (e = el), if she chooses eh the project is successful with probability 0.8, while if she chooses e the project is successful with prob- ability 0.4. A successful project yields revenue of x = 2500 for the firm and an unsuccessful project yields x = 0. The employer cannot observe the employee's effort choice, but can only observe whether the project is successful or not. Therefore, the employer can only base the wage w on the success of the project, i.e. w = w(2). The firm (employer) is risk neutral, with profit equal to x W(x), and since the success of the project is random, the expected profit of the firm is E[x W(x)]. The employee is risk averse with utility equal to Vw(2) c(e), and again since the success of the project is random, the expected utility of the employee is E[Vw(x)]-c(e). Exerting high effort is costly, in particular, suppose c(eh) = 16 and c(el) = 0. (1) If the wage is w(x) = x, i.e. the employer pays the employee all the revenue the project brings along, what effort level would the employee choose? (2) Suppose the employee has no outside opportunity, so that her reservation utility is 0. What is the optimal incentive contract the firm will provide? (3) Suppose the employee has an outside offer that guarantees her a reservation utility of 20, what is the optimal incentive contract the firm will provide