Question

Sally is considering an investment project that will give her a 75% chance of a wealth of 25 and a 25% chance of a wealth of only 2. Assume that Sally has the utility function U = 250W-2:5W^ 1.25 1. What is the difference in Sally utility at the good and average outcomes U(good) -U (avg:): (a) 2; 448; (b) 1; 399;(c) 247; (d) 1; 169; show steps please

Answer 1

Solution:

At good outcome, that is W = 25, Sally's utility is:

U(25) = 250*25 - 2.5*(25)^1.25

U(25) = 6250 - 139.75 = 6110.25

Average outcome (as per the probabilities assigned) = probability of good outcome*good outcome value + probability of bad outcome*bad outcome value

Average outcome = 0.75*25 + 0.25*2 = 19.25

So, U(19.25) = 250*19.25 - 2.5*(19.25)^1.25

U(19.25) = 4812.5 - 100.8 = 4711.7

So, the required difference

U(good outcome) - U(avg outcome)

= U(25) - U(19.25)

= 6110.25 - 4711.7 = 1,398.55 (nearly)

So, correct option is (B) 1,399