An investor with utility function U(x)- In(x), where x is total wealth, has a choice between the following two alternatives:

A: Win $10,000 with a probability of 0.2 or win $1,000 with a probability of 0.8

B: Win $3,000 with a probability of 0.9 or lose $2,000 with a probability of 0.1

a. If the investor currently has $2,500, should they choose A or B?

b. Find the exact Certainty Equivalent for the alternative A and its risk premium.

c. Repeat a, assuming the investor has $5,000.

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