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 $1,000 with probability 0.8

B. Win $3,000 with probability 0.9

Lose $2,000 with probability 0.1

1. If the bettor currently has $2,000, should he choose A or B

2. Repeat (1), assuming the bettor has $5,000

3. Repeat (1), assuming the bettor has $10,000

4. Do you think that this pattern of choices between A and B is reasonable? Why or why not?