1.) In a certain lottery, a lottery ticket cost $2. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following pay off table applies:
a. A realistic estimate of the chances of winning is 1 in 250,000. Use the expected value approach to recommend a decision
Given:
Realistic estimate of the probability of winning: 0.000004 (1/250,000)
Realistic estimate of the probability of loosing: 0.999996 (1- 0.000004)
Thus, the expected values for the two decision alternatives are:
EV (d1) = 0.000004 (300,000) + 0.999996 (-2) + (-1.999992) = -0.799992
EV (d2) = 0.000004 (0) + 0.999996 (0) = 0.00
Using the expected value approach, the optimal decision is to select (d2), which is not to purchase a lottery ticket with the expected monetary value of $0.
b. If a particular decision maker assigns an indifference probability of 0.000001 to the $0 payoff, would the individual purchase a lottery ticket? Use the expected utility to justify your answer.
Best payoff is $300,000; we assign a utility value of 10. U ($300,000) = 10.00
Worst payoff is -$2.00, we assign a utility value of 0.0 U (-$2.00) = 0.00
We calculate U (M):
U (M) = pU ($300,000) + (1 - p) U((-$2.00) = p (10) + (1 - p) 0.00 = 10p
Therefore, U ($0.00) = 10p = 10 x 0.000001 = 0.00001
| Monetary Value |
Indifference Value of p |
Utility Value |
| $300,000 |
N/A |
10 |
| $0.00 |
0.000001 |
0.00001 |
| -$2.00 |
N/A |
0 |
2.) Suppose that the point spread for a particular sporting event is 10 point and that with this spread you are convinced you would have a 0.60 probability of a bet on your team. However, the local bookie will accept only a $1000 bet. Assuming that such bet are legal, would you bet on team? (Disregard any commission charged by the bookie) Remember that you must pay losses out of your own pocket. Your payoff table is as follows
|
|
State of Nature
|
|
Decision Alternative
|
You Win
|
You Loss
|
|
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 $0.00 payoff? (Although this choice isn't easy, be realistic as possible. It requires for an analysis that reflects your attitude toward risk.)
c. What decision would you make based on the expected utility approach? In this case are you a risk taker or risk avoider?
d. Would other individual assess the same utility value you do? Explain
e. If you decision in part (c) was to place the bet, repeat the analysis assuming a minimum bet of $10,000
3.) 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 the 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 a risk avoider?
Profit Indifference Probability
$100,000 .95
$ 50,000 .70
0 .50
-$50,000 .25
d. Use expected utility to make a recommended decision.
e. Should decision maker feel comfortable with the final decision recommended by the analysis?
4.) Two Indiana state senate candidates must decide which city to visit the day before the November election. The same four citiesIndianapolis, Evansville, Fort Wayne, and South Bendare available for both candidates. These cities are listed as strategies 1 to 4 for each candidate. Travel plans must be made in advance, so the candidates must decide which city to visit prior to knowing the other candidates plans. Values in the following table show thousands of voters for the Republican candidate based on the strategies selected by the two candidates. Which city should each candidate visit, and what is the value of thegame?