13.24A bettor with utility function U(x)= ln(x),wherexis total wealth, has a choice between the following two alternatives:

AWin $ 10,000 with probability 0.2 Win $1000 with probability 0.8

BWin $3000 with probability 0.9 Lose

$2000 with probability 0.1

aIf the bettor currently has $2500, should he choose A or B?bRepeat a, assuming the bettor has $5000.cRepeat a, assuming the bettor has $10,000.

dDo 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.