## [solution]: A bettor with utility function U(x) = ln(x), where x is total

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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.

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