A job candidate with a salary utility function Uw squareroo

A job candidate with a salary utility function U(w) = squarerootw receives a job offer that pays $90,000 plus a bonus. The bonus will be $0, $70,000, $160,000: or $270,000, each with equal probability. a) What is the expected value of this job offer? b) What is the expected utility of this job offer? c) Is the certainty equivalent of this job offer greater than, less than, or equal to the expected value of the job offer?

Solution

a)

Expected value of Job offer = 90,000 + expected bonus

P

Bonus

P x Bonus

0.25

0

0

0.25

70000

17500

0.25

160000

40000

0.25

270000

67500

125000

Expected value of job offer = 90,000 + 125000

                                                      = 215,000

Part b)

Expected utility = (215000)^0.50

                                = 463.68

Part c)

We can see that the bonus amount is not fixed, therefore, there is some degree of risk associated with the job.

The risk will reduce the certainly equivalent value of this job, therefore, certainly equivalent will be less than expected value of job offer.

P	Bonus	P x Bonus
0.25	0	0
0.25	70000	17500
0.25	160000	40000
0.25	270000	67500
		125000