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# expected value and variance

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1.The following table shows the expected value and variance for 5 projects a firm can undertake.

Project Expected Value Variance
A \$100 \$124
B \$220 \$110
C \$100 \$138
D \$180 \$138
E \$200 \$124
a. Project B dominates all others. True or False? Why? .
b. Project C is the least preferable. True or False? Why?
c. If the mean-variance rule is used for the decision, project D is preferable to C. True or False? Why?

2. If firms in a perfectly competitive industry are earning an economic profit, product price will because . After long-run competitive equilibrium comes about there will be (fewer, more, the same number of) firms in the industry and the industry will produce (less, more, the same amount of) output. In long-run competitive equilibrium each firm will earn economic profit.

3. Sony and Zenith must each decide which technology to utilize in building their high definition television (HDTV) sets: either Alpha technology or Beta technology. Sony has a technological advantage in using Alpha technology and Zenith has a technological advantage in using Beta technology. The payoff table below shows the profit outcomes for both firms in the various possible technology choice outcomes:
Zenith

Alpha
Beta
Sony

Alpha

A
\$16 \$12 B
\$11 \$10
Beta

C
\$9 \$8 D
\$13 \$15
Payoffs in billions of
Suppose the technology decision between Alpha and Beta will be made simultaneously. Answer the following questions:
a. Does Sony have a dominant strategy? If yes, which one? If not, why not? Explain. (4 pts)
b. Does Zenith have a dominant strategy? If yes, which one? If not, why not? Explain. (4 pts)
c. Identify the Nash equilibrium (equilibria) for this simultaneous decision. Explain. (8 pts)

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#### Solution Preview

1.The following table shows the expected value and variance for 5 projects a firm can undertake.

Project Expected Value Variance
A \$100 \$124
B \$220 \$110
C \$100 \$138
D \$180 \$138
E \$200 \$124
a. Project B dominates all others. True or False? Why? .
TRUE. This is so because the project has the highest expected value (\$220) and the lowest variance (\$110).
b. Project C is the least preferable. True or False? Why?
TRUE. This is so because the project has the lowest expected value (\$100) and the highest variance (\$138).
c. If the mean-variance rule is used for the decision, project D is preferable to C. True or False? Why?
TRUE. Both projects have the same variance (\$138) but project D has higher expected value (\$180) compared to project C (\$100).

2. If firms in a perfectly competitive industry are earning an economic profit, product price will FALL because FIRMS WILL ENTER THE MARKET. After long-run competitive equilibrium comes about there will be MORE(fewer, more, the same number of) firms in the industry and ...

#### Solution Summary

This solution reiterates expected value and variance.

\$2.19