Questions 9 and 12 A firm hires risk neutral employees who produce an output Q(e,x) = e + x that depends on the employees' effort level, e, and an unobservable random factor, x, with E(x) = 0. As a result, the firm has introduced a pay-for-performance contract. Accordingly, an employee's pay is w = a + BQ(e,x): w is the total wage paid to an employee, a is the fixed part of the wage and B is an incentive parameter based on the quantity produced. Employees have an outside option or reservation utility U. = 2, incur a cost of effort Ce) = e/2, and choose their effort level to maximize their expected wage net of the cost of effort. The firm or employer maximizes its 2 expected profit, which is equal to the difference between expected revenues E[pQ(e,x)], where p is the price at which the output produced by employees can be sold, and the expected wage Ela + BQ(e,x)] 9) Determine the effort level that would be chosen by an employee as a function of the intensity of incentive parameter B, i.e., determine e employee 10) Determine the effort level that would be chosen by the employer as a function of the output price p, i.e., determine e employer, knowing that the employees' participation constraint must be satisfied. 11) Suppose p = 2. Determine the value that should take so that the employees' objective is aligned with the employer's objective. 12) Continuing with p = 2, determine the value that a should take so that the employees' participation constraint is satisfied. Questions 9 and 12 A firm hires risk neutral employees who produce an output Q(e,x) = e + x that depends on the employees' effort level, e, and an unobservable random factor, x, with E(x) = 0. As a result, the firm has introduced a pay-for-performance contract. Accordingly, an employee's pay is w = a + BQ(e,x): w is the total wage paid to an employee, a is the fixed part of the wage and B is an incentive parameter based on the quantity produced. Employees have an outside option or reservation utility U. = 2, incur a cost of effort Ce) = e/2, and choose their effort level to maximize their expected wage net of the cost of effort. The firm or employer maximizes its 2 expected profit, which is equal to the difference between expected revenues E[pQ(e,x)], where p is the price at which the output produced by employees can be sold, and the expected wage Ela + BQ(e,x)] 9) Determine the effort level that would be chosen by an employee as a function of the intensity of incentive parameter B, i.e., determine e employee 10) Determine the effort level that would be chosen by the employer as a function of the output price p, i.e., determine e employer, knowing that the employees' participation constraint must be satisfied. 11) Suppose p = 2. Determine the value that should take so that the employees' objective is aligned with the employer's objective. 12) Continuing with p = 2, determine the value that a should take so that the employees' participation constraint is satisfied
