Martina Genser sells copiers for Xerox. Her sales are a function of her effort e and can be expressed in the following manner:
Sales = 100e + µ,
where µ, is a random error term with expected value of zero. Martina's personal cost of ex- erting effort is
C(e) = e2
She is paid a straight salary plus a commission:
Compensation = $1,000 + 0.10 sales Her personal objective is to maximize
U = E (Compensation) - C(e)
the difference between the expected value of her compensation and her cost of effort.
a. Find Martina's optimal effort level.
b. Now assume that Xerox compensates Martina based on her sales relative to the average sales for salespeople in the company. Assume that Martina's sales are not included in the calculation of this average and that she cannot affect the average sales through her effort. The expected value of average sales is 500. Her compensation is now
Compensation = $1,000 + 0.10(sales - average sales) Calculate Martina's optimal effort level under this compensation plan.
c. Including average sales in the contract affects expected compensation. What adjustment must be made in the salary to keep expected compensation the same as before?
d. Does including average sales in the compensation contract affect the variance of Martina's compensation? Assume that her sales and average sales are positively correlated. Give a brief verbal explanation to support your answer.