Suppose that Betsy’s utility function is given by the equation U=Y0.3 where Y is measured in thousands of dollars. Betsy’s current job pays her $20,000 per year and she can earn this amount next year with certainty. Betsy is offered a different job but in this new job, Betsy has a 50%

chance of earning $36,000 and a 50% chance of earning only $15,000.

a) Should Betsy take the new job?
b) Does your answer change if Betsy’s utility function is U=Y0.9? Why?
c) Does your answer change if Betsy’s utility function is U = Y1.25? Why?

My answer:

A)

0.5(36,000) + 0.5(15,000)
=$25,000

B)

0.5(36,000)^0.3 + 0.5(15,000)^0.3
= 20.58

0.5(36,000)^0.9 + 0.5(15,000)^0.9
=9,013.70

C)

0.5(36,000)^1.25 + 0.5(15,000)^1.25
= 330,942.01

I feel that the numbers seem wrong?? Please help!

To determine whether Betsy should take the new job, we need to compare the expected utility of the current job with the expected utility of the new job for each given utility function.

a) For Betsy's utility function U = Y^0.3:
- Current job: U(c) = (20,000)^0.3 = 21,544.35
- New job: U(n) = 0.5(36,000)^0.3 + 0.5(15,000)^0.3 ≈ 21,494.80

Comparing the expected utility of the current job (U(c) = 21,544.35) with that of the new job (U(n) ≈ 21,494.80), there is only a slight difference. Therefore, Betsy may not have a strong incentive to take the new job.

b) For Betsy's utility function U = Y^0.9:
- New job: U(n) = 0.5(36,000)^0.9 + 0.5(15,000)^0.9 ≈ 22,323.33

Comparing the expected utility of the current job (U(c) = 21,544.35) with that of the new job (U(n) ≈ 22,323.33), there is a noticeable increase in expected utility for the new job. Thus, Betsy may have a stronger incentive to take the new job under this utility function.

c) For Betsy's utility function U = Y^1.25:
- New job: U(n) = 0.5(36,000)^1.25 + 0.5(15,000)^1.25 ≈ 23,953.73

Comparing the expected utility of the current job (U(c) = 21,544.35) with that of the new job (U(n) ≈ 23,953.73), there is a further increase in expected utility for the new job. Therefore, Betsy may have an even stronger incentive to take the new job under this utility function.

Your calculations for expected utility seem to be incorrect. Make sure you apply the power (exponent) to each individual outcome before summing them up. Also, verify the calculations with a calculator or spreadsheet to ensure accuracy.