Test1(4) S12

Student_______________________________ ID________________

SET OF PROBLEMS

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

Problem 1. (max 6 pts)

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

	S1 (0.25)	S2 (0.35)	S3 (0.45)
d1	0.51	0.2	-0.41
d2	0.4	-0.37	0.3
d3	-0.42	0.43	0.52
d4	0.2	-0.29	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 5.5pts)

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	650	400	220
Investment B, d2	400	400	400
Investment C, d3	900	220	-570
Probabilities	0.25	0.60	0.15

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

2. (max 0.5pts) What lottery would be used to assess utilities?

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

Profit	Indifference Probability
$650,000		0.85
$400,000		0.70
$220,000		0. 55

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 5pts)

Most companies offer their employees a variety of health care plans to choose from, e.g., preferred provider organizations (PPOs) and health maintenance organizations (HMOs). a survey of 100 large, 100 medium, and 100 small companies that offer their employees HMOs, PPOs, and fee-for-service plans was conducted; each firm pro­vided information on the plans chosen by their employ­ees. These companies had a total employment of 830,453 people. A breakdown of the number of employees in each category by firm size and plan is pro­vided in the table.

Company Size	Fee-for- Service	PPO & HMO
Small	1,875	3,224
Medium	8,951	13,523
Large	332,405	470,475

One employee from the 830,453 total employees is to be chosen at random for further analysis. Define the events a and b as follows:

a:(Observe an employee that chose preferred provider organization and health maintenance organizations (PPO&HMO)

b: (Observe an employee from a medium company)

1. (max 3.5 pts) Find, ,,,,, .

2. (max 0.5pts) Are eventsand mutually exclusive? Explain.

3. (max 1 pt) Are eventsand independent? Explain

Problem 4. (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	19.7	8.75	16.8	11.1
a2	19.8	9	16.9	15
a3	19.6	20.14	16.5	-4
a4	19.9	21	16.7	-3

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 4 pts) Determine the optimal mixed strategy solution.

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

Problem 5. (max 7 pts)

The fixed cost for the all production and selling process of a product is 39, the cost to produce and sell one unit of the product is 5. 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 9% per year compounded annually for the past 3 years. A house with a $350,000 value now would have had what value 3 years ago?