Question

An individual has utility function U(x)=x1/4U(x)=x1/4 for salary, and is considering new job offer which pays $80,000 with a bonus. The bonus will be $0, $10,000, $20,000, $30,000, $40,000, $50,000, or $60,000, each with equal probability. What is the certainty equivalent of this job offer?

Answer 1

108,280.22

Step-by-step explanation:

Certainty equivalent is solved by taking the inverse utility function from the expected utility of a random wealth variable

U(x) = x^1/4

U^-1(x) = x^4

U^-1(x) === x^4

CE(x) = x^4

Salary Bonus Total income U(x)= x^(1/4) P(x) U(x)*P(x)

80000 0 80000 16.82 1/7 2.4

80000 10000 90000 17.32 1/7 2.47

80000 20000 100000 17.78 1/7 2.54

80000 30000 110000 18.21 1/7 2.6

80000 40000 120000 18.61 1/7 2.66

80000 50000 130000 18.99 1/7 2.71

80000 60000 140000 19.34 1/7 2.76

Sum 18.14

CE(x) = 18.14^4

CE(x) = 108280.22

So therefore, the certainty equivalent of this job offer is 108,280.22