Consider the following problem with four states of nature, three decision alternatives, and the following payoff table (in \$’s):

The indifference probabilities for three individuals are:

 Payoff Person 1 Person 2 Person 3 \$ 2600 1.00 1.00 1.00 \$ 400 .40 .45 .55 \$ 200 .35 .40 .50 \$ 0 .30 .35 .45 -\$ 200 .25 .30 .40 -\$1400 0 0 0

a. Classify each person as a risk avoider, risk taker, or risk neutral.

b. For the payoff of \$400, what is the premium the risk avoider will pay to avoid risk? What is the premium the risk taker will pay to have the opportunity of the high payoff?

c. Suppose each state is equally likely. What are the optimal decisions for each of these three people?

 s1 s2 s3 s4 d1 200 2600 -1400 200 d2 0 200 – 200 200 d3 -200 400 0 200

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Joe is contemplating either opening another store or expanding its existing location. The payoff table for these two decisions is:

 State of Nature Decision s1 s2 s3 New Store -\$80,000 \$20,000 \$160,000 Expand -\$40,000 \$20,000 \$100,000

Paul has calculated the indifference probability for the lottery having a payoff of \$160,000 with probability p and -\$80,000 with probability (1-p) as follows:

 Amount Indifference Probability (p) -\$40,000 .4 \$20,000 .7 \$100,000 .9
 a. Is Joe a risk avoider, a risk taker, or risk neutral? b. Suppose Joe has defined the utility of -\$80,000 to be 0 and the utility of \$160,000 to be 80. What would be the utility values for -\$40,000, \$20,000, and \$100,000 based on the indifference probabilities? c. Suppose P(s1) = .4, P(s2) = .3, and P(s3) = .3. Which decision should Joe make? Why? Compare with the decision using the expected value approach. =========================================================

The table shows both prospective profits and losses for a company, depending on what decision is made and what state of nature occurs. Use the information to determine what the company should do.

 State of Nature Decision s1 s2 s3 d1 30 80 -30 d2 100 30 -40 d3 -80 -10 120 d4 20 20 20
 a. if an optimistic strategy is used. b. if a conservative strategy is used. c. if minimax regret is the strategy.
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A technology company is considering expanding its production capacity to meet a growing demand for its product line of cell phones. The alternatives are to build a new cell phone, expand a line of existing cell phones, or do nothing. The marketing department estimates a 35 percent probability of a market upturn, a 40 percent probability of a stable market, and a 25 percent probability of a market downturn. The firm’s analyst, estimates the following annual returns for these alternatives:

 Market Upturn Stable Market Market Downturn Build new cell phone \$690,000 \$(130,000) \$(150,000) Expand existing phone 490,000 (45,000) (65,000) Do nothing 50,000 0 (20,000)

a. Use a decision tree analysis to analyze these decision alternatives.

b. What should the company do?

c. What returns will accrue to the company if your recommendation is followed?

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