Managerial Economics & Organizational Architecture 6th Edition by James Brickley , Clifford Smith ,Jerold Zimmerman

Exercise 8

ANALYZING MANAGERIAL DECISIONS: Structuring Salesforce Compensation
Assume that a salesperson, Edwynn Phillips, has the following annual compensation package:

This compensation plan induces Ed to exert a given level of effort in selling. Given this effort level, expected sales are $30,000 per year.
Below are 10 years' worth of data for Ed's sales and the average sales for other employees in the company (Ed's own sales are excluded in calculating this average). The expected value of average sales is also $30,000. However, in any given year, average sales might rise or fall, depending on general economic conditions, and so on. Some of these same conditions affect Ed's sales. Ed has no impact on the average sales for other employees.

Calculate Ed's average pay and standard deviation under the alternative plan:

Note: We adjust the intercept of the pay plan by $6,000 to reflect Ed's average loss imposed on the employee by subtracting 0.2 (average sales) from the compensation. This adjustment keeps the expected pay the same as before. Also, the sample mean of average sales over a 10-year period need not equal the expected value of $30,000.