QUESTION 1. Employers have long recognized that healthy employees are more productive, and therefore many employers have begun to financially encourage gym attendance by employees. However, sometimes these payments lead to gym attendance but fairly low effort, since an individual employee's effort at the gym is not easily monitored. Thus, one employer is considering paying employees both for gym attendance and for passing an annual physical fitness test. However, the test is only partly related to one's effort at the gym. The requisite data are: Employee's Gym Effort Level Chance of Success (passing annual test) Employee's Opportunity Cost of effort Low 25% $1,500 High 75% $2,500 For the year, the employer can pay an employee a fixed payment (f) for gym attendance and a bonus (b) paid only if the employee attends the gym and passes the annual test. Employees are risk neutral. 1. What is the optimal combination of a fixed payment and bonus to entice high effort? Show all work. 2. What is the optimal combination of a fixed payment and bonus to entice low effort? Show all work. 3. Suppose that the chance of success for low effort changes from 25% to 50%. What will happen to the optimal bonus and fixe payment to entice high effort? QUESTION 1. Employers have long recognized that healthy employees are more productive, and therefore many employers have begun to financially encourage gym attendance by employees. However, sometimes these payments lead to gym attendance but fairly low effort, since an individual employee's effort at the gym is not easily monitored. Thus, one employer is considering paying employees both for gym attendance and for passing an annual physical fitness test. However, the test is only partly related to one's effort at the gym. The requisite data are: Employee's Gym Effort Level Chance of Success (passing annual test) Employee's Opportunity Cost of effort Low 25% $1,500 High 75% $2,500 For the year, the employer can pay an employee a fixed payment (f) for gym attendance and a bonus (b) paid only if the employee attends the gym and passes the annual test. Employees are risk neutral. 1. What is the optimal combination of a fixed payment and bonus to entice high effort? Show all work. 2. What is the optimal combination of a fixed payment and bonus to entice low effort? Show all work. 3. Suppose that the chance of success for low effort changes from 25% to 50%. What will happen to the optimal bonus and fixe payment to entice high effort