A bettor with utility function U(x) = ln(x), where x is total wealth, has a choice between the following two alternatives:
A. Win $ 10,000 with probability 0.2 Win $1000 with probability 0.8
B. Win $3000 with probability 0.9 Lose $2000 with probability 0.1
a. If the bettor currently has $2500, should he choose A or B?
b. Repeat a, assuming the bettor has $5000.
c. Repeat a, assuming the bettor has $10,000.
d. Do you think that this pattern of choices between A and B is reasonable? Why or why not?
Source: D. E. Bell (1988) "One-Switch Utility Functions and a Measure of Risk." Management Science, 34, 1416-1424.