Test1(3)S12

Student_______________________________ ID________________

SET OF PROBLEMS

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

Problem 1. (max 7pts)

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	230	230	230
Investment B, d2	350	230	150
Investment C, d3	490	150	-110
Probabilities	0.25	0.40	0.35

1. (max 2.5pts) 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 (p)
$350,000		0.65
$230,000		0.35
$150,000		0.15

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

4. (max 2.5 pts) Use expected utility to make a recommended decision.

Problem 2. (max 8 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	7.4	-6.3	12.7	15.1
a2	-6	4	-5.4	-5.17
a3	7.25	1.15	14.76	17.17
a4	8	2	15.8	18.3

Company A

1. (max 1 pt) Does the game have a saddle point and a pure strategy?

b. (max 2 pt) Reduce the game to 2x2 game.

c. (max 4 pts) Determine the optimal mixed strategy solution.

d. (max 1 pts) What is the value of the game?

Problem 3. (max 8 pts)

The data in the table are typical prices for a barrel of crude oil for the indicated years:

Year	Crude oil($per barrel)
2005	92
2006	91
2007	92
2008	95
2009	100
2010	105
2011

1. (max 2pts) Graph this time series. Does a linear trend appear?

b. (max 4pts) Develop a linear trend equation for this time series.

c. (max 2pts) Draw graph of the trend. Use the trend equation to estimate the rating for 2011.

Problem 4. (max 6 pts)

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

	S1 (0.3)	S2 (0.45)	S3 (0.25)
d1	0.37	0.1	-0.31
d2	0.34	-0.22	0.2
d3	-0.35	0.33	0.4
d4	0.1	-0.1	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?

BONUS (max 3pts)

Rental costs for office space have been going up at 7% per year compounded annually for the past 3 years. If office rent now is $90 per square meter per month, what were the rental rates 3 years ago?