9. Imagine making choices in the following situation to test your degree of risk aversion.

Someone offers you the choice between the following game and a sure thing.

The game: A coin is tossed. If it turns up heads, you get a million dollars.

If tails, you get nothing.

The sure thing: You’re given $500,000.

a. What is the expected value of each option?

b. Which option would you choose?

c. Viewing the options as probability distributions, which has the larger variance?
What is the variance of the sure thing? (No calculations.)

d. Suppose the game is changed to offer a payoff of $1.2 million for a head but still offers nothing for a tail. The sure thing remains $500,000. What is the expected value of each option now? Which option would you choose now?

e. Most people will have chosen the sure thing in part (d). Assuming you did too, how much would the game’s payoff have to increase before you would choose it over the sure thing?

f. Relate this exercise to Figure 9.6 on page 382.