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# Utility and Decision Making

Frank is faced with a decision about whether to take a bet with a friend or get \$20 for sure. If he wins the bet, he gets \$50, if he loses the bet, he has to pay \$50. For Frank, the utility of \$50 is 10 and the utility of paying \$50 is 0. The utility of the \$20 sure thing is:

U(\$20) = p*U(\$50) + (1-p)*U(-\$50)

When p = .8, Frank is indifferent between the bet and the guaranteed \$20.

What is the utility of \$20 to Frank?

What is the expected value of the bet?

Would you say Frank is a risk avoider?
A) YES
B) NO

What is the risk premium that Frank is willing to pay???

The following shows the payout table for two soda companies, Coca-Cola and Jones Soda. Both companies are deciding whether to build a large plant or build a small plant. The numbers shown are the change in market share for Coca-Cola. (A positive number increases Coca-Cola's market share). Also, this game is zero sum, meaning that whatever Coca-Cola gains, Jones Soda loses.

Jones Soda
build large build small

Cocal_Cola build large 0 7
build small -2 1

If Coca-Cola builds a large plant and Jones builds a small plant, how much does Jones' market share change?

Coca-Cola is in such a poor financial position that any loss in market share would mean the demise of the business. What would you advise the company to do?
A) Build large
B) Build small
C) Take no action

#### Solution Preview

1.
U(\$20) = 0.8*U(\$50) + (0.2)*U(-\$50) = 8

Expected value of the bet is 0.8 X 50 + 0.2 X (-50) = \$30

Yes, Frank is a risk avoider ...

#### Solution Summary

Utility and Decision Making

\$2.19