Test1(1) S12

Student_______________________________ ID________________

SET OF PROBLEMS

MaxGrade = (30% +3%) of Total Grade

Problem 1. (max 6 pts)

Consider the following payoff table of Profits(prior probabilities are in parentheses)

	S1 (0.3)	S2 (0.45)	S3 (0.25)
d1	0.49	0.2	-0.41
d2	0.4	-0.3	0.3
d3	-0.4	0.4	0.5
d4	0.2	-0.2	0.3

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?

Problem 2. (max 6pts)

A firm has three investment alternatives. Payoffs are in thousands of dollars.

	Economic Conditions
Decision Alternative	Up s1	Stable s2	Down s3
Investment A, d1	1000	250	-200
Investment B, d2	500	500	500
Investment C, d3	750	500	250
Probabilities	0.30	0.50	0.20

1. (max 2pts) What is the best expected value decision?

2. (max 1pts) What lottery would be used to assess utilities?

3. (max 1pt) Assume that the following utilities are assigned.

Profit	Indifference Probability
$750,000		0.85
$500,000		0.65
$250,000		0.3

Do the utilities re­flect the behavior of a risk taker or a risk avoider?

4. (max 2 pts) Use expected utility to make a recommended decision.

Problem 3. (max 6 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	21	9	18	15
a2	3	-3	6	9
a3	15	21	0	-3
a4	15	3	9	12

Company A a. (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 3.5 pts) Determine the optimal mixed strategy solution.

d. (max 0.5 pts) What is the value of the game?

Problem 4. (max 7 pts)

The fixed cost for the all production and selling process of a product is 216, the cost to produce and sell one unit of the product is 20. The demand function has the following form .

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?

BONUS (3pts max)

In a suburb of Astana, housing have been decreasing at 12% per year compounded annually for the past 2 years. A house with a $200,000 value now would have had what value 2 years ago?