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

Answer:

108,280.22

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