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UNIVERSITY OF CALIFORNIA BERKELEY
Hass School of Business
MBA 201A—Economic Analysis for Business Decisions—Fall 2009
Professors Steve Tadelis and Catherine Wolfram
FINAL EXAM
Instructions: The number in brackets (e.g., [5]) indicates the points for each question.
Total: 180 points. Note that you have 180 minutes to do the exam, so you should spend
no more than 1 minute per point.
Please Write Legibly. Briefly explain your answers (that is, don’t just write “yes” or “no”
and don’t just write down a numerical answer without showing how you derived it). Write
only on this exam and not on other sheets of paper.
Please sign the honor code oath at the bottom of the back page.
Short answer questions
The following three questions require only short answers (1-3 sentences). Use any
graphs that will help your explanation. Be sure to label graphs clearly.
1. [10] Even with a very small number of competitors, firms occasionally get locked in
bitter price competition and drive prices down to their marginal costs. Discuss two
factors that help firms avoid the “Bertrand Trap.”
Full credit given for discussion of two of any of the following factors:
 Cost leadership on the part of one of the firms,
 If the two firms manage to limit capacity,
 Product differentiation,
 Switching costs,
 Facilitating practices, such as most-favored customer clauses, and
 Repeated interactions, as long as firms care about the future.
MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
2. [10] Alice is a contractor bidding in a sealed-bid auction for a job to paint Bob's house.
Being an expert painter, Alice knows for sure (and is correct) that it will cost her exactly
$5,000 (labor and material) to paint Bob's house. The auction rules state that the
lowest bidder gets the job and gets paid the amount of the second lowest bid. Explain
to Alice, who does not know economics, why she should bid exactly $5,000.
Call the lowest bid by any other bidder besides Alice $X. If Alice bids below $5000 say,
$4900 then compared to truthful bidding that i) makes no difference if X > 5000, Alice
still gets the job and gets paid X, ii) makes no difference if X < 4900, Alice still doesn’t
get the job, iii) hurts Alice if 4900 < X < 5000, because she gets the job but it costs her
more to do the job than she receives in payment. If Alice overbids to, say, $5100, then
compared to truthful bidding it i) makes no difference if X < 5000, because Alice still
doesn’t get the job, ii) if X > 5100 makes no difference, Alice still gets the job and
receives X, iii) hurts Alice if 5000 < X < 5100 because now she doesn’t get the job but
with a truthful bid she would have won and been paid more than her cost.
3. [10] Two firms have to set their capacity in a market they are about to enter. Their
payoffs are described by the following matrix (the lower left number in each cell is the
payoff to Row Inc. and the upper right number is the payoff to Column Ltd.):
Column Ltd.
Small
6
Mid
7
Large
10
Small
7
Row Inc.
5
4
Mid
8
4
6
6
3
5
5
4
2
Large
11
5
3
What is (or are) the Nash equilibrium of this game?
Indicate best response of player 1 and
indicates best response of player 2.
The only Nash Equilibrium (where both firms are at a best response) is Mid-Mid.
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
Question 4
You run a photography company that specializes in weddings near your home in Carmel,
California. You have two types of clients: the wealthy, who own a single, year-round
house in Carmel, and the very wealthy, who own multiple houses, including one in
Carmel. You can distinguish between the two types of clients, but you feel that you would
lose considerable business, especially from the very wealthy, if you charged different
prices to consumers based on their wealth.
Your marginal costs are $2000 per wedding regardless of what type of client you’re
serving. This includes the cost of film and the cost of labor (either the opportunity cost of
your time if you do the wedding yourself, or the wages you pay to your associates). You
expect that in 2010 there will be 140 weddings, including 40 to the wealthy and 100 to the
very wealthy.
In order to try to distinguish the wealthy from the very wealthy, you are thinking of offering
two types of services: all black-and-white photos or half black-and-white, half color.
Based on your extensive interviews with potential clients, you estimate the following
valuations for these two types of services in 2010:
Number of weddings
Wealthy
Very wealthy
40
100
Half black-and-white,
half color
$5,000
$6,000
All black-and-white
$6,000
$10,000
Assume that the cost difference between color and black-and-white film is negligible,
although you might tell your clients otherwise to justify your new pricing scheme. Also
assume that couples in Carmel get married no more than once per year, so they will order
no more than one photography package.
a. [10] In 2010, what would be the profit-maximizing way to price all black-and-white and
half black-and-white, half color wedding photos?
Consider three options:
i) Uniform price, selling all black-and-white to everyone: profits = ($6,000 - $2,000)x140 =
$560,000
ii) Uniform price, selling all black-and-white only to the very wealthy: profits = ($10,000 $2,000)x100 = $800,000
iii) Separate prices: profits = ($5,000 - $2,000)x40 + ($9,000 - $2,000)x100 = $820,000
Option iii) yields the most profits, so charge:
$5,000 for half-half
$9,000 (actually $8,999) for black-white
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
b. [15] You learn that the reception location of choice for the wealthy is considering doing
a major renovation in 2010. This would drive the number of wealthy clients down to 20.
You believe that there’s a 50% chance that they will go through with the renovation, in
which case, you would have 20 wealthy clients and 100 very wealthy, still with the same
valuations listed in the table above. If they decide to delay their renovation (an event to
which you assign probability of 50%), then the number of clients will be exactly as in the
table above. You need to print up your new brochure with 2010 prices before you know
whether or not the renovation is going to take place. Assuming you are risk neutral, what
prices would you choose? In other words, what prices maximize expected profits?
If you use the prices found in part a:
your profits if there is no renovation will be: $820,000
your profits if there is a renovation will be: ($5,000-$2,000)x20 + ($9,000 $2,000)x100 = $760,000
Your expected profits will be .5x$820,000+.5x$760,000 = $790,000
If you charge $10,000 for black-and-white and sell only to the very wealthy, your profits
will be $800,000, and they will be unaffected by the renovation since you now don’t sell to
the wealthy. Your expected profits will be $800,000.
Since $800,000 > $790,000, the prices that maximize expected profits are charging
$10,000 for black-and-white and a price greater than $6,000 for half-and-half.
c. [5] Would you choose different prices than you did in part b. if you were risk averse?
Why or why not?
No, your answer would not change. The choice that maximizes profits also has less risk
associated with it.
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
d. [10] How much would you be willing to pay to learn whether or not the renovation would
take place before you printed your 2010 brochure?
You should be willing to pay up to $10,000 for the information. If you learn that the
renovation will go forward, you won’t change your pricing strategy—you would still charge
$10,000 for black-and-white and only serve the very wealthy. If you learn that the
renovation will not happen, however, you would price discriminate and earn $820,000
instead of $800,000. Since the information will make you change your decision 50% of
the time, and will earn you $20,000 when it does ($820,000 - $800,000), it is worth up to
$10,000 to you.
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
Question 5
You are the product manager of Macrohard's new student-targeted software line,
Dormroom 2009, which includes two components: Letter 2009, the new word-processor,
and Surpass 2009, the new spreadsheet analyzer. Your market research team tells you
that there are five student groups that compose the market with the following willingnessto-pays (WTP) for each product:
Engineering Majors
Econ Majors
Poli-Sci Majors
Pre-Med Majors
Humanities Majors
WTP for
Letter 2009
($)
10
40
45
70
55
WTP for
Surpass 2009
($)
55
70
45
40
10
There are an equal number of students in each of the 5 groups listed in the table above.
The company’s accountant presents the following table of per unit costs for both of the
products:
Unit Costs
Software development*
Promotion*
Manual development costs*
Manual printing costs
Customer Support Website*
CDs (each)
Total Unit Costs
*
Letter 2009
$1.00
$0.20
$1.00
$4.60
$0.30
$0.40
$7.50
Surpass 2009
$3.00
$0.20
$1.90
$6.60
$0.40
$0.40
$12.50
Amortized based on expected number of customers.
a. [10] What are the marginal costs of selling Letter 2009? Surpass 2009? Explain
your answer.
The only variable costs are manual printing costs and CDs so marginal costs are
equal to MC = $4.60 + $0.40 = $5.00 for Letter and MC = $6.60 + $0.40 = $7.00 for
Surpass.
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
[10] Macrohard's CEO insists on offering a single price per product without offering
the bundle of both products at a discount. With this restriction, what would be the
profit-maximizing prices for Letter 2009 and Surpass 2009?
For each of the two products we have the same demand and profit maximization is
at a price of $40 per product as can be calculated from the following table (this is
done for “Letter” where each student group is counted as 1):
Price
10
40
45
55
70
Quantity
5
4
3
2
1
Revenue
50
160
135
110
70
Costs
25
20
15
10
5
Profits
25
140
120
100
65
A similar table for “Surpass” would yield the optimal price to be the same but since
MC = 7 then “Surpass” profits are $132 and total profits are therefore $272.
b. [10] One of your company’s board members suggests that you should, “do what
Microsoft does” and only sell the products as a bundle. If you did as the director
suggested, what price would maximize profit? Whose suggestion is better – the
CEO’s or the director’s? (Assume that if sold as a bundle, technology prevents
customers from separating and reselling the products.)
We can use a similar approach to the bundle, but now the willingness to pay is the
sum over both products (now the marginal cost per bundle is $12 assuming that
each product has its own manual and CD):
Price
65
90
110
Quantity
5
3
2
Revenue
325
270
220
Costs
60
36
24
Profits
265
234
196
Total profits are therefore $265 which is less than what the CEO strategy achieves.
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
c. [10] Can you develop a pricing strategy that is better than those considered in
either b. or c.? What prices would you charge for the bundle? For the individual
products?
A quick observation suggests that Engineering and Humanities majors really like
one product and not the other. The other three majors have a higher willingness to
pay for the bundle. In this case we can try to sell the bundle to these three majors
and the individual products to the Engineering and Humanities students. For this
we can charge $90 for the bundle and $55 for each separate product. The PoliSci
majors are willing to buy the bundle but are uninterested in the individual products,
while the Engineering and Humanities majors are each willing to buy one product
but not the bundle. The Econ and PreMed majors get a surplus of $20 from he
bundle and only $15 from the individual product they like best, so each prefers the
bundle. Total profits are: 3$90 + 2$55 – 3$12 – $5 – $7 = $332.
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
Question 6
Consider the market for printed books in 16th century England. By this time, the
Gutenberg press has been in use for over 100 years and countless people have access to
the technology and have learned the art of printing. There are many printing companies,
and they are all price takers. Also, many people have the necessary income to enjoy
reading books. For simplicity, assume that all books have an equal number of pages,
thus cost the same to produce. The main inputs to book printing are paper and the
printer’s time. (The costs of the printing presses are sunk and the costs of the ink are
trivial.) Assume that each book printing company in the market has the following total cost
function TC(Q) = 500 + 4Q + 0.05 Q2 where Q is the number of books per year and costs
are measured in pounds.
Assume that people don’t care which book they read as long as they read a book. The
total demand for books in England is reflected by Q= 50,600-50P where Q is measured in
books per year and P is measured in pounds per book. People outside of England do not
value books printed in English.
a. [15] It is 1575 AD and the Queen of England, an avid reader who wants to
encourage literacy, would like to fix prices for books. She would like to set a price
of 10 pounds per book, but her advisors convince her that this would be a bad idea.
What might their reasons be? (Note: A full credit answer will be quantitative as well
as qualitative.)
At a price of 10 pounds, no book printers can profitably remain in the market (see below).
Existing firms that are in the market will gradually exit, and no new firms will enter the
market. Eventually, no books will be produced. At a price of 10 pounds, market demand
would be QD = 50,100. Since supply will eventually be zero, there will be a shortage of
50,100 books.
For an individual firm,
P=MC
10=4 + 0.1Q  Q=60
R=600
TC=500+240+180=920
Loss of 320 pounds.
Alternatively, we can see this by solving for the minimum of the AC and verifying that 10
pounds is below the minAC.
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
b. [15] The Queen’s advisors convince her that she should not regulate prices but instead
let the book market achieve a long run competitive equilibrium. What will be the market
price, how many books will be produced and how many firms will be in the market once
the market achieves a long run competitive equilibrium?
At the LR equilibrium, each firm will be making zero economic profits, and P=min(AC).
AC(Q)= 500/Q+4+0.05Q
MC(Q)=4+0.1Q
We can find the min of AC by solving for the point where MC=AC:
0.1Q= 500/Q+0.05Q0.05Q=500/QQ=100
AC(100)=5+4+5=14
Price in the long run will be 14 pounds. At this price quantity demanded will be
Q= 50,600-50(14) = 49,900
Since each firm will optimally produce 100, 499 firms will be in the market.
c. [10] In the summer of 1582 a fire in Central Europe eradicates a large tract of
forest, causing paper input prices to go up. Explain qualitatively what you think will
happen to the long run competitive equilibrium price. Will it go up, down or stay the
same, or is it impossible to tell? Assume that paper prices are expected to stay
high for longer than it takes the book market to achieve a new long run equilibrium.
The long run competitive equilibrium price will be higher. To be precise, it will be higher
by the change in the price of paper times the amount of paper that it takes to produce a
book, assuming that there is no substitute for paper in the book printing process. If the
printers are able to substitute, the LRCE price will still be higher, but not by quite as much
as the change in the paper costs.
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
Question 7
The Hard Rock Café in Merced only sells beer in one-pint glasses. The local demand from
adults over the age of 21 is quite accurately described by the following demand function:
qA= 1,600 – 100p where qA is measured in pint glasses and p is measured in dollars per
pint. The marginal cost of a pint of beer is $2.00.
a. [10] What is the profit-maximizing price and quantity of beer sold for the Hard Rock
Café? What is its profit?
For this demand p = 16 – 0.01qA and MR = 16 – 0.02qA. Equating MR to MC = 2 gives
qA = 700, and plugging this back into the demand gives p = 9. Profits are $4,900
(assuming no fixed costs).
A new university opens in Merced, and the demand by students (over the age of 21) is
quite accurately described by the following demand function: qS=800-100p.
b. [10] If Merced city code does not allow the Hard Rock Café to charge separate
prices for students or locals, what would be the profit-maximizing price and quantity
of beer sold? What is the profit?
For the student demand p = 8 – 0.01qs which means that for prices above $8 and
below $16 the demand is just the adult demand (as in part (a) above) and for prices
below $8 we need to aggregate the two demands which yields Q = 2400 – 200p, or
p = 12 – 0.005Q with MR = 12 – 0.01Q. Equating MR of the aggregated demand to
MC = 2 gives 2 = 12 – 0.01Q or Q = 1,000. Plugging this back into the aggregate
demand gives p = 12 – 0.0051000 = 7, which is in the correct price range to serve
both markets. Profits are $5,000 (assuming no fixed costs).
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MBA 201A
c.
Professors Tadelis and Wolfram
Fall 2009—Final
[10] After the student union successfully lobbies the city council in Merced, the
code was changed to allow the Hard Rock Cafe to offer student discounts so that it
can charge a standard price, and offer a discount to those who possess a student
ID. What is the profit maximizing price and student discount, and how much beer
does each group (adults and students) buy? What are the profits? (Local laws
prohibit consumers from reselling beer.)
Now the monopolist can do group discrimination. From part (a) above we know that
the price it charges adults is $9, qA = 700, and from that market alone it makes $4,900.
For student demand is p = 8 – 0.01qs and MR = 8 – 0.02qs. Equating MR to MC = 2 for
students gives qs = 300, and plugging this back into the demand gives p = 5. Profits
from the student market are $900, and hence total profits are $5,800 (assuming no
fixed costs). This would be implemented with a $9 price per pint, and a $4 student
discount.
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MBA 201A
Professors Tadelis and Wolfram
Fall 2009—Final
YOUR NAME: ______________________________
YOUR COHORT: ____________________________
Please Sign Honor Code Oath:
I understand that this exam is an individual effort exercise. I sweat on my honor that I
have not consulted with another person or made use of notes or other materials during the
exam.
Signature: _________________________________
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