Repeat Problem 14.24 with U (x) = 0.0003 x – 8.48e – x = 2775. A utility function of this form is called linear-plus-exponential, because it contains both linear (0.0003 x) and exponential terms. It has a number of interesting and useful properties, including the fact that it switches only once among any pair of lotteries (such as those in Problem 14.24)as wealth increases.

Repeat problem 14.24

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

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

b. Repeat a, assuming the bettor has $5,000.

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?