Reference no: EM13921232
You are a sales manager at the XYZ Corporation. You want to hire a new sales representa- tive. You plan to make an offer to Sally Gomez. You can pay Sally a fixed salary of $20,000 per year or a 10 percent sales commission plus a (a fixed component in the compensation formula). She has a competing offer at another company for $20,000. You anticipate you can hire her if you meet the $20,000 fixed salary offer.
Sally's sales will be either high or low depending on whether she gets a corporate ac- count. If she gets the account, sales will be $100,000. If she does not, sales will be $10,000. The probability of getting the account is .7. This probability is beyond Sally's control.
Sally's utility function can be represented by u (compensation) = (compensation)1/2 (1)
She seeks to maximize expected utility. Expected utilities under the two plans are Fixed salary: u = (20,000)1/2 (2) 10 percent plan: u = .7(a + 10,000)1/2 + .3(a + $1,000)1/2 (3)
a. Sketch the graph of the function u (x) = (x)1/2.
b. Is Sally's utility function convex or concave? Is she risk-loving or risk-averse?
c. What a makes Sally indifferent between the two plans?
d. As the sales manager, which plan do you select? Give an explanation that shows why this plan is optimal.
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