Clancy has $4,200. He plans to bet on a boxing match between Sullivan and Flanagan. He finds that he can buy coupons for $7 each that will pay off $10 each if Sullivan wins. He also finds in another store some coupons that will pay off $10 if Flanagan wins. The Flanagan tickets cost $3 each. Clancy believes that the two fighters each have a probability of of winning. Clancy is a risk averter who tries to maximize the expected value of the natural log of his wealth. Which of the following strategies would maximize his expected utility?
A) Don't gamble at all.
B) Buy 150 Sullivan tickets and 350 Flanagan tickets.
C) Buy 300 Sullivan tickets and 700 Flanagan tickets.
D) Buy exactly as many Flanagan tickets as Sullivan tickets.
E) Buy 150 Sullivan tickets and 700 Flanagan tickets.

Question

Clancy has $4,200. He plans to bet on a boxing match between Sullivan and Flanagan. He finds that he can buy coupons for $7 each that will pay off $10 each if Sullivan wins. He also finds in another store some coupons that will pay off $10 if Flanagan wins. The Flanagan tickets cost $3 each. Clancy believes that the two fighters each have a probability of  of winning. Clancy is a risk averter who tries to maximize the expected value of the natural log of his wealth. Which of the following strategies would maximize his expected utility?
A) Don't gamble at all. 
B) Buy 150 Sullivan tickets and 350 Flanagan tickets. 
C) Buy 300 Sullivan tickets and 700 Flanagan tickets. 
D) Buy exactly as many Flanagan tickets as Sullivan tickets. 
E) Buy 150 Sullivan tickets and 700 Flanagan tickets.

Quizplus · Accepted Answer

Let's first calculate the expected values for each betting option. 
For Sullivan: 
- Probability of winning: 11/17 
- Cost per coupon: $7 
- Payoff per coupon: $10

Expected value per coupon: (11/17)($10) - ($7) = $1.06

For Flanagan: 
- Probability of winning: 6/17 
- Cost per coupon: $3 
- Payoff per coupon: $10

Expected value per coupon: (6/17)($10) - ($3) = $1.59

Therefore, buying Flanagan coupons has a higher expected value than buying Sullivan coupons.

Now, let's consider the different strategies:

A) Don't gamble at all - This would result in no change in wealth or utility.

B) Buy 150 Sullivan tickets and 350 Flanagan tickets - This would result in a cost of ($7)(150) + ($3)(350) = $1,650 and an expected value of (150)($1.06) + (350)($1.59) = $703.50.

C) Buy 300 Sullivan tickets and 700 Flanagan tickets - This would result in a cost of ($7)(300) + ($3)(700) = $3,100 and an expected value of (300)($1.06) + (700)($1.59) = $1,417.

D) Buy exactly as many Flanagan tickets as Sullivan tickets - This would result in equal costs for both types of coupons, but as we calculated earlier, the Flanagan coupons have a higher expected value.

E) Buy 150 Sullivan tickets and 700 Flanagan tickets - This would result in a cost of ($7)(150) + ($3)(700) = $2,550 and an expected value of (150)($1.06) + (700)($1.59) = $1,417.50.

Therefore, the strategy that maximizes expected utility is to buy 300 Sullivan coupons and 700 Flanagan coupons.

Clancy Has $4,200