Test1(2)S12
.docStudent_______________________________ ID________________
SET OF PROBLEMS
MaxGrade = (30% +3%) of Total Grade
Problem 1. (max 5.5pts)
A firm has three investment alternatives. Payoffs are in thousands of dollars.
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Economic Conditions
Decision Alternative
Up s1
Stable s2
Down s3
Investment A, d1
500
125
-100
Investment B, d2
375
250
125
Investment C, d3
250
250
250
Probabilities
0.20
0.50
0.30
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(max 2pts) What is the best expected value decision?
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(max 0.5pts) What lottery would be used to assess utilities?
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(max 1pt) Assume that the following utilities are assigned.
-
Profit
Indifference Probability (p)
$375,000
0.65
$250,000
0.35
$125,000
0.15
Do the utilities reflect the behavior of a risk taker or a risk avoider?
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(max 2 pts) Use expected utility to make a recommended decision.
Problem 2. (max 6.5 pts)
Company A and Company B, are competing for a given consumer market. Each company is considering four advertising options. Depending on the options used by each company, a certain percentage of consumers will switch from one company to the other. After performing market studies, it was determined that the entries in the payoff table (below) represent the percentage of Company B customers that will switch to Company A.
Company B
|
b1 |
b2 |
b3 |
b4 |
a1 |
-6 |
4 |
-5.4 |
-5.17 |
a2 |
7.4 |
-6.3 |
12.7 |
15.1 |
a3 |
8 |
2 |
15.8 |
18.3 |
a4 |
7.25 |
1.15 |
14.76 |
17.17 |
Company A
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(max 1 pt) Does the game have a saddle point and a pure strategy?
b. (max 1 pt) Reduce the game to 2x2 game.
c. (max 4 pts) Determine the optimal mixed strategy solution.
d. (max 0.5 pts) What is the value of the game?
Problem 3. (max 7 pts)
The fixed cost for the all production and selling process of a product is 64, the cost to produce and sell one unit of the product is 8. The number of units that is guaranteed to be sold at a price p can be calculated using formula(price-demand equation) .
a. (max 2 pts) Express revenue as a function of Q. Find the output that will produce the maximum revenue. What is the maximum revenue
b. (max 2 pts) Graph the cost function and the revenue function in the same coordinate system;
c. (max 1.5 pts) Find break-even points;
d. (max 1.5 pts) How many cameras should the company manufacture to maximize its profit? What is the maximum profit?
Problem 4. (max 5pts)
Several life insurance firms have policies geared to college students. To get more information about this group, a major insurance firm interviewed college students to find out the type of life insurance they preferred, if any. The accompanying table was produced. One student from the interviewed is to be chosen at random for further analysis.
Define the events a and b as follows:
a:(Observe a male student )
b: (Observe a student without preferences)
|
Preferred a Term Policy |
Preferred a Whole-life Policy |
No Preference |
Females |
109 |
25 |
634 |
Males |
202 |
31 |
499 |
a. (max 3.5 pts) Find, ,,,,, .
b. (max 0.5pts) Are eventsand mutually exclusive? Explain.
c. (max 1 pt) Are eventsand independent? Explain
Problem 5. (max 6 pts)
Consider the following payoff table of costs (prior probabilities are in parentheses)
-
S1 (0.35)
S2 (0.35)
S3 (0.3)
d1
0.1
-0.1
0.2
d2
0.3
-0.2
0.2
d3
-0.3
0.3
0.4
d4
0.39
0.1
-0.31
a. (max 0.5pts) Which decision is prescribed by the optimistic criterion?
b. (max 1pt) Which decision is prescribed by the conservative criterion?
c. (max 2.25pts) Which decision is prescribed by the minimax regret criterion?
d. (max 2.25pts) Which decision is prescribed by the expected value criterion?
BONUS (max 3pts)
Rental costs for office space have been going up at 5% per year compounded annually for the past 2 years. If office rent now is $90 per square meter per month, what were the rental rates 2 years ago?