UNIVERSITY OF MANNHEIM
CC501 DECISION ANALYSIS
Sample Final Exam
REMARK: The point distribution of this sample exam might not
match the one in the actual exam! Note that this is not a previous
exam but a sample exam that is compiled for Fall 2015 semester.
INSTRUCTIONS
1. Please don’t open the exam until you are told to do so.
2. You are allowed to use ONLY a non-programmable calculator. Laptops and cell phones are
absolutely prohibited. Textbooks and class notes are NOT allowed.
3. The exam consists of 12 pages (including the cover page) and 4 parts with a total of 180
points. Make sure your exam has 12 pages and 4 parts.
4. Please write your answers ON the question sheet. ONLY the answers on the question sheet
will be graded. Page 12 is left blank for you to write your answers if you need more space.
If you need more sheets, raise your hand.
5. You can use the colored sheets as scratch paper. Colored sheets will NOT be graded.
6. In answering the questions, show all your calculations, so that you can receive partial credit.
7. Calculate with an accuracy of three decimal places if not indicated differently in the problem.
8. You have 90 minutes to complete the exam. Please use your time wisely.
9. Cross out ALL pages if you do not want your exam to be graded.
Last name:
Signature of the student:
First name:
Student ID:
Part
Q1
Q2
Q3
Q4
Total
Total Points
42
51
45
45
180
Your Score
Question 1 (42pts)
a) (6pts) What are the requirements for the existence of additive value functions? Explain them
with one or two sentences.
b) (7pts) Explain “conjunction fallacy” with one example.
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c) (6pts) What are the advantages and disadvantages of influence diagrams, decision matrices and
decision trees?
d) (10pts) Consider the investment alternatives given in the table below. When asked to choose
between A and B, most people choose alternative B. When asked to choose between C and D,
most people choose alternative C. Is this consistent with the EUT? Why? Why not? Explain.
Alternative
Outcome(s) and Probabilities
A
e2,500 with probability 0.33 e2,400 with probability 0.66
B
e2,400 for sure
C
e2,500 with probability 0.33
D
e2,400 with probability 0.34
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e0 with probability 0.01
e0 with probability 0.67
e0 with probability 0.66
e) (6pts) In January 2006, you met one of your college friends over dinner. You started talking
about the housing market, and your friend said that the rise in house prices since 2003 had been
normal, and he did not have any indication of a possible bubble. In the following two years, you
and your friend lost touch. In December 2008, you ran into your friend, and asked him what he
thought about the economy. He said: “Wasn’t it obvious that the bubble would burst?”. What
kind of a bias does your friend have? Explain this bias with one or two sentences.
f) (7pts) You are given the graph of your best friend’s utility function. What is your friend’s
certainty equivalent of a lottery that pays zero with probability 0.5 and 4e with probability 0.5?
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Question 2 (51pts)
Your boss wants you to buy a new coffee machine for the office. He only cares about three
attributes: price (to be minimized), capacity (to be maximized), and guarantee time (to be maximized). At the store, you find various coffee machines ranking in price from 29e to 529e, in
capacity from 2 to 12 cups, and in guarantee time from 0 to 24 months. Your boss made sure
that his preferences fulfill the conditions to justify the use of an additive value model. He further
determined that his attribute specific value functions for attributes “capacity” and “guarantee
time” are linear.
a) (6pts) Assume that the value function for the attribute “price” is given by:
1
x
Normalize the attribute value function v1 (x) such that the values attached to different price levels
lie between 0 and 1.
v1 (x) = 0.298 + 22.486
b) (10pts) Now assume that the attribute value function v1 is linear in price. You are given the
following indifference statements regarding your boss’s preferences:
Statement 1: (529e, *, 24 months) ∼ (429e, *, 0 months)
Statement 2: (*, 2 cups, 24 months) ∼ (*, 6 cups, 0 months)
Calculate the attribute weights (w1 , w2 , w3 ) with
5
P
wi = 1.
c) (10pts) As a robustness check, you repeated your analysis using the Swing Method, and you
realized that the weights you obtained using the Swing Method match exactly the ones that you
obtained in part a). If your boss assigns the alternative (29e, 2 cups, 0 months) a score of 100,
what should be the scores that he assigns to each of the alternatives (529e, 12 cups, 0 months)
and (529e, 2 cups, 24 months)?
d) (18pts) You are doubtful about your boss’s answers. Using a different method, you determined
the following upper and lower bounds for the attribute weights:
Attribute
Weight
Price
w1
Capacity
w2
Guarantee time
w3
Lower
bound
0.5
0.2
0.1
Upper
bound
0.7
0.3
0.2
Given this information, conduct a dominance test to see if any of the alternatives CoffeeMax (229e,
8 cups, 12 months) and CoffeeKing (529e, 12 cups, 24 months) dominates the other.
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e) (7pts) While you were running several consistency checks, you obtained the following preference
statements:
Statement 1: (*, 12 cups, 0 months) (*, 8 cups, 0 months)
Statement 2: (*, 12 cups, 24 months) ∼ (*, 8 cups, 24 months)
Can you still use the additive model? Why or why not? Explain.
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Question 3 (45pts)
You are planning on making a financial investment. There are two options: a stock and a risk-free
bond. You want to invest all your savings, a total of 1,000e, into one of these investment options.
There are two states of the world: “Up” and “Down” which are expected to happen with 60%
and 40% probability, respectively. The return on the stock is 25% in the up-state and -25% in the
down-state. The risk-free bond returns 1% in both states.
a) (12pts) Assume that you are an expected value maximizer. Would you invest your savings into
the stock or the bond? Draw an influence diagram that represents this problem.
b) (15pts) You have an analyst friend who could help you with your decision. You could ask your
friend to send you a copy of his report where he forecasts the market trends. Your friend’s track
record shows that if the market will actually rise, he predicts an “Up” market 85% of the time, and
if the market will fall, he predicts a “Down” market in 70% of the cases. What is the probability
that the market will go up conditional on your friend forecasting an “Up” market?
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c) (18pts) What is the maximum price that you would be willing to pay if your friend wants to
charge you for his help? Draw the decision tree for this problem.
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Question 4 (45pts)
An individual owns a house with a value equal to 200,000e. There is a 5% probability that the
house will burn down completely in a fire. The individual can insure his house against a loss from
this fire. The premium for full insurance is 20,000e. Also, the individual has savings equal to
25,000e. (The total wealth is equal to savings plus the value of the house).
a) (8pts) If the individual were an expected value maximizer (i.e. risk neutral), would he buy this
full insurance policy?
b) (16pts) Now assume that the individual is an expected utility maximizer with u(x) = 100ln(x).
Would he buy this full insurance policy? Calculate the risk premium. What is the maximum price
that he is willing to pay for full insurance?
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c) (21pts) What if the person had savings equal to 250,000e instead of 25,000e? Would he buy
this full insurance? How did the change in savings affect the decision and the risk premium? What
would you expect to happen if the decision maker had a CARA utility function (e.g. exponential
utility function)? Why? Explain.
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USE THIS ADDITIONAL PAGE TO WRITE YOUR ANSWERS THAT YOU WANT
TO BE GRADED
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