Assignment 2
Industrial Organization
May 2023
Instructions
Please, adhere to the following conventions when writing out your solutions.
• Round your final answers to 2 digits, when necessary, (e.g. 2.341 to 2.34) and your
intermediate calculations to 4 digits or more. Show all of your work.
• Write out your solutions to each question by hand, as neatly as you can manage.
• Highlight your final answer to each question with a color that stands out.
• Take a good-quality picture of each page under favorable lighting conditions. Put the
questions in order, and hand them in as a single PDF file. (There are several free apps
that allow you to do so with your phone, e.g. Genius Scan, or you can use a scanner.)
As this is an individual assignment, each problem contains one parameter (in blue text color).
On canvas, you will find a table named ”Parameter values by student number - Assignment 2”.
In the table, you can look up your student number to find what parameter values you need to
use. This implies that the correct answers to the problems below are di↵erent for each student.
You will get 1 point for each correct answer to problems 1-10. You may get up to 0.75 points
to a problem, where you have used a correct approach, but made minor algebra errors that
result in a wrong answer. Illegible submissions will result in 0 points for the given problem.
Submissions that do not adhere to the above listed conventions may get a point deduction of
up to 2 points.
The deadline for submitting your answers is Friday, 26.05.2023 at 17:00. It is your respon-
sibility to upload and submit the problems before the deadline. Therefore, make sure that you
start your uploading process sufficiently early, in case you encounter unforeseen delays (e.g.
network problems, computer problems, etc.).
1
,Problem set
0. Write down your student number.
1. In a market where 10 firms act as Cournot competitors, demand is characterized by
P (Q) = 500 10·Q. All firms have constant marginal costs equal to A. Two firms propose
a merger, after which the merged entity becomes a Stackelberg leader in the market. The
non-merged follower firms all continue to play simultaneous quantity competition among
each other. Find the market price after the merger.
2. Think of a Hotelling model with three firms: one at the West end (W ), one in the middle
(M ), and one at the East end (E). The length of the town is 10 miles and it has 3600
evenly distributed inhabitants. People’s disutility from traveling to a seller equals $5 for
each mile of distance between the two locations. The marginal cost of production is B,
and valuations are high enough for everyone to buy exactly one product each day. Firms
W and M are considering a merger. Find the change in the price of W after the merger.
In a market where 6 firms act as Cournot competitors, demand is characterized by P (Q) =
200 Q. All firms but one have constant marginal costs equal to 20 (efficient firms), while
one firm has a constant marginal cost that exceeds the marginal costs of the efficient firms
by C (inefficient firm). One of the efficient firms is proposing a merger with the inefficient
firm.
3. Do consumers benefit from the merger? Justify your answer.
4. Does the efficient merging firm benefit from the merger (Assume that it makes half of the
merged firm’s profit after the merger)? Justify your answer.
5. Market demand for a product is given by P (Q) = 400 Q. The supply side of the market
is vertically segmented: a single manufacturer sells to 3 retailers, who take the wholesale
price (w) as given and sell the product on to final consumers. The marginal cost of
manufacturing is D and the marginal cost of retailing is 50 (both constant). The retailers
compete with each other by setting production levels simultaneously. The manufacturer
has just announced that it intends to acquire one of the retail firms. Find the equilibrium
consumer price before the acquisition.
6. Market demand for a homogeneous product is given by P (Q) = 300 Q. The supply
side of the market is vertically segmented: a single manufacturer sells to two retailers,
who sell the product on to final consumers. The manufacturer exercises resale price
maintenance (RPM), so retailers take both the wholesale and the maintained retail price
as given and share the market equally, regardless of their marginal costs. The marginal
cost of manufacturing is E and the marginal cost of retailing is 40 (both constant). One
of the retail firms is considering an investment into training and expanding its sta↵ to
provide high-quality customer advice about the usage of the product. As a result, total
market demand at any price would increase by a factor of 2, but the marginal cost of
the investing retailer would also increase by 15. The retailer would not invest into sta↵
training and expansion if it expected to end up with a profit decrease as a consequence.
Find the profit-maximizing wholesale price that induces investment.
2
,7. William and Norah are competing po↵ertjes sellers in Langstad. They are located at the
two opposing ends of the town’s 3-mile-long main street. The 300 inhabitants of the town
are distributed uniformly along the street and each of them eats at most one portion
of po↵ertjes after lunch each day. People’s disutility from getting to a po↵ertjes stand
and back home amounts to $2 for each mile of distance to the stand. The marginal cost
of producing one portion of po↵ertjes is $6. Unfortunately, the town’s residents are not
equally informed about their options to get their favorite after-lunch snack. F people know
about both William and Norah, whereas the rest of the population does not know about
either of them (and hence buys no po↵ertjes). Both the informed and the uninformed
consumers are uniformly distributed along the street. Each consumer has a valuation of
$50 for the product. Suppose that both Norah and William can advertise at zero cost to
inform everyone about their business. Find the equilibrium price of William if William
advertises, but Norah does not.
3
,1 Cournot competition 110
firms
500 10 Q
PIQ
C 437
Cournot
post merger Stackleberg
with 1 leader and 8
equilibrium
backward induction
followers use
profit of a
single follower firm
Ti _500 10
19 QI 91 4317 9
63 10
19T QI 91 _9T
f 0 c
for profit maximization
IT 29 63 209 100Ei 1091 0
Symmetry implies
Ei 79T
, Substitute
63 909 1091 0
BR
Single follower firm
163 90
Git 1091
BR entire
follower segment
Q 8
Git 8190 163 1091
leader
profit merger Stackleberg
Tk 63 10 Q _9L
19
_63 10 18190 163 1091
1091
9
7 I
111191 9L
f 0 c
for profit maximization
7Th 291 17 0
2.22229L
, 9 9
Equilibrium
3.15
91
QT 8190 163 10 3.15
2.8
3.15 t 2.8 5.95
Market
price after merger
500 10 5.95 440.5
p
2
Hoteuing game
l 10 Miles
N 3600
t 5 nile
per
30
Industrial Organization
May 2023
Instructions
Please, adhere to the following conventions when writing out your solutions.
• Round your final answers to 2 digits, when necessary, (e.g. 2.341 to 2.34) and your
intermediate calculations to 4 digits or more. Show all of your work.
• Write out your solutions to each question by hand, as neatly as you can manage.
• Highlight your final answer to each question with a color that stands out.
• Take a good-quality picture of each page under favorable lighting conditions. Put the
questions in order, and hand them in as a single PDF file. (There are several free apps
that allow you to do so with your phone, e.g. Genius Scan, or you can use a scanner.)
As this is an individual assignment, each problem contains one parameter (in blue text color).
On canvas, you will find a table named ”Parameter values by student number - Assignment 2”.
In the table, you can look up your student number to find what parameter values you need to
use. This implies that the correct answers to the problems below are di↵erent for each student.
You will get 1 point for each correct answer to problems 1-10. You may get up to 0.75 points
to a problem, where you have used a correct approach, but made minor algebra errors that
result in a wrong answer. Illegible submissions will result in 0 points for the given problem.
Submissions that do not adhere to the above listed conventions may get a point deduction of
up to 2 points.
The deadline for submitting your answers is Friday, 26.05.2023 at 17:00. It is your respon-
sibility to upload and submit the problems before the deadline. Therefore, make sure that you
start your uploading process sufficiently early, in case you encounter unforeseen delays (e.g.
network problems, computer problems, etc.).
1
,Problem set
0. Write down your student number.
1. In a market where 10 firms act as Cournot competitors, demand is characterized by
P (Q) = 500 10·Q. All firms have constant marginal costs equal to A. Two firms propose
a merger, after which the merged entity becomes a Stackelberg leader in the market. The
non-merged follower firms all continue to play simultaneous quantity competition among
each other. Find the market price after the merger.
2. Think of a Hotelling model with three firms: one at the West end (W ), one in the middle
(M ), and one at the East end (E). The length of the town is 10 miles and it has 3600
evenly distributed inhabitants. People’s disutility from traveling to a seller equals $5 for
each mile of distance between the two locations. The marginal cost of production is B,
and valuations are high enough for everyone to buy exactly one product each day. Firms
W and M are considering a merger. Find the change in the price of W after the merger.
In a market where 6 firms act as Cournot competitors, demand is characterized by P (Q) =
200 Q. All firms but one have constant marginal costs equal to 20 (efficient firms), while
one firm has a constant marginal cost that exceeds the marginal costs of the efficient firms
by C (inefficient firm). One of the efficient firms is proposing a merger with the inefficient
firm.
3. Do consumers benefit from the merger? Justify your answer.
4. Does the efficient merging firm benefit from the merger (Assume that it makes half of the
merged firm’s profit after the merger)? Justify your answer.
5. Market demand for a product is given by P (Q) = 400 Q. The supply side of the market
is vertically segmented: a single manufacturer sells to 3 retailers, who take the wholesale
price (w) as given and sell the product on to final consumers. The marginal cost of
manufacturing is D and the marginal cost of retailing is 50 (both constant). The retailers
compete with each other by setting production levels simultaneously. The manufacturer
has just announced that it intends to acquire one of the retail firms. Find the equilibrium
consumer price before the acquisition.
6. Market demand for a homogeneous product is given by P (Q) = 300 Q. The supply
side of the market is vertically segmented: a single manufacturer sells to two retailers,
who sell the product on to final consumers. The manufacturer exercises resale price
maintenance (RPM), so retailers take both the wholesale and the maintained retail price
as given and share the market equally, regardless of their marginal costs. The marginal
cost of manufacturing is E and the marginal cost of retailing is 40 (both constant). One
of the retail firms is considering an investment into training and expanding its sta↵ to
provide high-quality customer advice about the usage of the product. As a result, total
market demand at any price would increase by a factor of 2, but the marginal cost of
the investing retailer would also increase by 15. The retailer would not invest into sta↵
training and expansion if it expected to end up with a profit decrease as a consequence.
Find the profit-maximizing wholesale price that induces investment.
2
,7. William and Norah are competing po↵ertjes sellers in Langstad. They are located at the
two opposing ends of the town’s 3-mile-long main street. The 300 inhabitants of the town
are distributed uniformly along the street and each of them eats at most one portion
of po↵ertjes after lunch each day. People’s disutility from getting to a po↵ertjes stand
and back home amounts to $2 for each mile of distance to the stand. The marginal cost
of producing one portion of po↵ertjes is $6. Unfortunately, the town’s residents are not
equally informed about their options to get their favorite after-lunch snack. F people know
about both William and Norah, whereas the rest of the population does not know about
either of them (and hence buys no po↵ertjes). Both the informed and the uninformed
consumers are uniformly distributed along the street. Each consumer has a valuation of
$50 for the product. Suppose that both Norah and William can advertise at zero cost to
inform everyone about their business. Find the equilibrium price of William if William
advertises, but Norah does not.
3
,1 Cournot competition 110
firms
500 10 Q
PIQ
C 437
Cournot
post merger Stackleberg
with 1 leader and 8
equilibrium
backward induction
followers use
profit of a
single follower firm
Ti _500 10
19 QI 91 4317 9
63 10
19T QI 91 _9T
f 0 c
for profit maximization
IT 29 63 209 100Ei 1091 0
Symmetry implies
Ei 79T
, Substitute
63 909 1091 0
BR
Single follower firm
163 90
Git 1091
BR entire
follower segment
Q 8
Git 8190 163 1091
leader
profit merger Stackleberg
Tk 63 10 Q _9L
19
_63 10 18190 163 1091
1091
9
7 I
111191 9L
f 0 c
for profit maximization
7Th 291 17 0
2.22229L
, 9 9
Equilibrium
3.15
91
QT 8190 163 10 3.15
2.8
3.15 t 2.8 5.95
Market
price after merger
500 10 5.95 440.5
p
2
Hoteuing game
l 10 Miles
N 3600
t 5 nile
per
30
