Four Business Problems Assignment
5. Three decisions makers have accessed utilities for the following decision problem (payoff in dollars):
State of Nature
Decision Alternative s1 s2 s3
d1 20 50 -20
d2 80 100 -100
The indifference probabilities are as follows:
Indifference Probability (p)
Payoff Decision Maker A Decision Maker B Decision Maker C
100 1.00 1.00 1.00
80 0.95 0.70 0.90
50 0.90 0.60 0.75
20 0.70 0.45 0.60
-20 0.50 0.25 0.40
-100 0.00 0.00 0.00
a. Plot the utility function for money for each decicion maker.
b. Classify each decision maker as risk avoider, a risk taker, or risk neutral.
c. For the payoff at 20, what is the premium that the risk avoider will pay to avoid risk?
What is the premium that the risk taker will pay to have the opportunity of the high payoff?
6. In Problem 5, if P(s1) = 0.25, P(s2) = 0.50, and P(s3) = 0.25, find a recommended decision for each of the three decision makers. (Note: For the same decision problem, different utilities can lead to different decisions.)
7. Suppose that the point spread for a particular sporting event is 10 points and that with this spread you are convinced you would have a 0.60 probability of winning a bet on your team. However, the local bookie will accept only a $1000 bet. Assuming that such bets are legal, would you bet on your team? (Disregard any commission charged by the bookie.) Remember that you must pay losses out of your own pocket. Your payoff take is as follows:
State of Nature
Decision Alternatives You Win You Lose
Bet $1000 -$1000
Don’t Bet $0 $0
a. What decision does the expected value approach recommend?
b. What is your indifference probability for the $0 payoff? (Although this choice isn’t easy, be as realistic as possible. It is required for an analysis that reflects your attitude towards risk.)
c. What decision would you make based on the expected utility approach? In this case are you a risk taker or a risk avoider?
d. Would other individuals assess the same utility values you do? Explain.
e. If your decision in part (c) was to place the bet, repeat the analysis assuming a minimum bet of $10,000.
9. A new product has the following profit projections and associated probabilities:
a. Use the expected value approach to decide whether to market the new product.
b. Because of high dollar values involved, especially the possibility of a $100,000 loss, the marketing vice president has expressed some concern about the use of the expected value approach. As a consequence, if a utility analysis is performed, what is the appropriate lottery?
c. Assume that the following indifference probabilities are assigned. Do the utilities reflect the behavior of a risk taker or risk avoider?
Profit Indifference Probability (p)
$ 50,000 0.70
$ 0 0.50
-$ 50,000 0.25
d. Use expected utility to make a recommended decision.
e. Should the decision maker feel comfortable with the final decision recommended by the analysis?
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