Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 31

Suppose a person must accept one of three bets:
Bet 1: Win $100 with probability V2; lose $100with probability 1/2.
Bet 2: Win $100 with probability 3/i; lose $300 with probability 1=4.
Bet 3: Win $100 with probability 9 10; lose $900with probability 1 10.
a. Show that all of these are fair bets.
b. Graph each bet on a utility of income curve similar to Figure.
FIGURE Risk Aversion
An individual characterized by the utility-of-income curve U will obtain a higher utility (U3) from a risk-free income of $35,000 than from a 50-50 chance of winning or losing $5,000 (U2). He or she will be willing to pay up to $2,000 to avoid having to take this bet. A fair bet of $15,000 provides even less utility (U1) than the $5,000 bet.
c. Explain carefully which bet will be preferred and why.