Industrial Organization Analysis
Final exam April 2019
For the 10 multiple choice questions you need only to write the answer alternative (i.e. no
motivations are necessary). For the long questions you need to carefully motivate your answers for
each subquestion. Included with the exam is a summary of some definitions, rules of calculus, and
derived expressions.
Definitions, rules of calculus, and derived expressions for IOA exam
Rules of calculus
𝑓(𝑥) = 𝑎𝑥 𝑛 , 𝑓 ′ (𝑥) =
𝑑𝑓(𝑥)
= 𝑎𝑛𝑥 𝑛−1
𝑑𝑥
𝑓(𝑥) = 𝑎𝑒 𝑏𝑥 , 𝑓 ′ (𝑥) =
𝑑𝑓(𝑥)
= 𝑎𝑏𝑒 𝑏𝑥
𝑑𝑥
𝑓(𝑥) = 𝑎 ln(𝑥) , 𝑓 ′ (𝑥) =
𝑓(𝑥) = 𝑔(𝑥)ℎ(𝑥), 𝑓 ′ (𝑥) =
𝑑𝑓(𝑥) 𝑎
=
𝑑𝑥
𝑥
𝑑𝑓(𝑥)
= 𝑔(𝑥)ℎ′ (𝑥) + 𝑔′ (𝑥)ℎ(𝑥)
𝑑𝑥
𝑓(𝑥) = 𝑔(ℎ(𝑥)), 𝑓 ′ (𝑥) =
𝑑𝑓(𝑥)
= 𝑔′ (ℎ(𝑥))ℎ′(𝑥)
𝑑𝑥
Own price elasticity (some textbooks define the own price elasticity with a minus sign, I follow that
convention in my slides etc)
𝜖=
𝑑𝑞 𝑝
𝑑𝑝 𝑞
Own price elasticity with mid-point (“arc”) formula (some textbooks define the own price elasticity with a
minus sign, I follow that convention in my slides etc)
𝑞1 − 𝑞 0
(𝑞1 + 𝑞 0 )
𝜖= 1
𝑝 − 𝑝0
(𝑝1 + 𝑝0 )
Own price elasticity with logarithms (some textbooks define the own price elasticity with a minus sign, I
follow that convention in my slides etc)
𝜖=
ln(𝑞1 ) − ln(𝑞 0 )
ln(𝑝1 ) − ln(𝑝0 )
Cross price elasticity
𝜖=
𝑑𝑞1 𝑝2
𝑑𝑝2 𝑞1
Inverse elasticity rule (some textbooks define the own price elasticity with a minus sign, I follow that
convention in my slides etc)
𝑝 − 𝑚𝑐
1
=−
𝑝
𝜖
Cournot Nash equilibrium with n symmetric firms, constant marginal cost, and linear inverse demand 𝑝 =
𝑎 − 𝑏𝑄, where Q is the sum of all firms’ outputs
𝑞=
𝑎 − 𝑚𝑐
(𝑛 + 1)𝑏
Expression for price cost margin of firm i in a Cournot market with n asymmetric firms with constant but
different marginal costs, where 𝑠𝑖 = 𝑞𝑖 /𝑄 (some textbooks define the own price elasticity with a minus
sign, I follow that convention in my slides etc)
𝑝 − 𝑚𝑐𝑖
𝑠𝑖
=−
𝑝
𝜖
Expression for market share weighted price cost margin of firms in a Cournot market with n asymmetric
firms with constant but possibly different marginal costs, where 𝐻 = ∑𝑛𝑖=1(𝑠𝑖 )2 (some textbooks define the
own price elasticity with a minus sign, I follow that convention in my slides etc)
𝑛
∑ 𝑠𝑖
𝑖=1
𝑝 − 𝑚𝑐𝑖
𝐻
=−
𝑝
𝜖
Net present value of a stream of profits 𝜋
∞
∑ 𝜋𝛿 𝑡 =
𝑡=0
∞
∑ 𝜋𝛿 𝑡 =
𝑡=1
𝜋
1−𝛿
𝛿𝜋
1−𝛿
1) Polysilicon is a hyper-pure form of silicon and is the basic raw material in the production of
solar panels that can generate electricity from solar light. About 60 percent of the world’s
production capacity is in China. Recently the Chinese government has implemented stricter
environmental standards and this is predicted to result in the closure of 10 percent of the
Chinese polysilicon producing plants. Assuming that the world polysilicon market is
perfectly competitive we expect ceteris paribus (all else equal) that the closing down of
Chinese producing polysilicon plants will in the short-run
a) lead to higher price and lower sold quantity of polysilicon.
b) lead to a higher price and higher sold quantity of polysilicon.
c) lead to a lower price and higher sold quantity of polysilicon.
d) have an ambiguous effect on the price of polysilicon.
2) A local video store knows that each customer's demand per year is given by
Q = 12.00 – 1.00P, and knows the marginal cost of each rental is $2.00. How much should
the store charge for an annual membership in order to extract the entire consumer surplus
via an optimal two-part pricing strategy?
a) $7.00
b) $50.00
c) $100.00
d) None of the above
3) There are 1000 potential travellers each day on the Copenhagen - Oslo route, of which 500
are yuppies and 500 are hippies. Yuppies are willing to pay 700.00 for an unrestricted ticket
and 400.00 for a restricted ticket. Hippies are willing to pay 500.00 for an unrestricted ticket
and 300.00 for a restricted ticket. Travellers buy the ticket that gives them the highest
surplus (equal to the difference between the willingness to pay and the price), provided that
this surplus is positive. Among the following price policies, which one results in the highest
revenues?
a) 700.00 for an unrestricted ticket and 300.00 for a restricted ticket.
b) 699.00 for an unrestricted ticket and 299.00 for a restricted ticket.
c) 598.00 for an unrestricted ticket and 299.00 for a restricted ticket.
d) 498.00 for an unrestricted ticket and 199.00 for a restricted ticket.
4) The “merger paradox” is that
a) mergers in markets with many firms may decrease profits for all firms.
b) mergers in markets with differentiated products and price competition are usually
profitable for the firms that merge but increases profits for other firms even more.
c) a merger between two firms may lead to higher profits for all other firms.
d) None of the above.
5) Firm A and Firm B are choosing independently and simultaneously whether or not to launch
promotion campaigns. For a firm, a promotion campaign costs $30m; all other costs are zero.
If both firms do promotion campaigns then they each get revenue equal to $70m. If neither
firm does promotion then they each get revenue equal to $60m. If Firm A promotes and Firm
B does not promote, Firm A gets revenue equal to $80m and Firm B gets revenue equal to
$30m. If Firm B promotes and Firm A does not promote, Firm B gets revenue equal to $100m
and Firm A gets revenue equal to $30m. The Nash equilibrium in this simultaneous move
one-shot interaction is that
a) Firm A promotes and Firm B promotes.
b) Firm A does not promote and Firm B does not promote.
c) Firm A promotes and Firm B does not promote.
d) Firm A does not promote and Firm B promotes.
6) Firm A and Firm B are choosing sequentially whether launch promotion campaigns. Firm B
decides first, and Firm A can observe whether or not Firm B has launched a promotion
campaign. For a firm, a promotion campaign costs $30m; all other costs are zero. If both
firms do promotion campaigns then they each get revenue equal to $70m. If neither firm
does promotion then they each get revenue equal to $60m. If Firm A promotes and Firm B
does not promote, Firm A gets revenue equal to $80m and Firm B gets revenue equal to
$30m. If Firm B promotes and Firm A does not promote, Firm B gets revenue equal to $100m
and Firm A gets revenue equal to $30m. In the sub-game perfect Nash equilibrium in this
sequential game
a) Firm A promotes and Firm B promotes.
b) Firm A does not promote and Firm B does not promote.
c) Firm A promotes and Firm B does not promote.
d) Firm A does not promote and Firm B promotes.
7) Assume that a market contains 5 firms. The market shares of the two largest are 50 percent
and 35 percent, respectively, and the sum of the market shares of the three smallest is 15
percent. The upper bound of the Herfindahl index for this market is
a) 0.340 (or 3400 with alternative definition)
b) 0.380 (or 3800 with alternative definition)
c) 0.395 (or 3950 with alternative definition)
d) None of the above.
8) Assume that two firms compete by setting quantities independently and simultaneously
(Cournot). The inverse demand for the homogenous product is = 1 − 𝑞1 − 𝑞2 . The two
firms have constant but different marginal costs 𝑐1 = 0.05, 𝑐2 = 0.10. In the Nash
equilibrium
a) firm 1 will have the lowest ratio (𝑃 − 𝑐𝑖 )/𝑃
b) firm 1 will have the lowest market share
c) firm 1 will have the highest profit
d) None of the above.
9) Assume firms compete by setting quantities independently and simultaneously (Cournot).
The inverse demand for the homogenous product is 𝑃 = 1 − ∑𝑁
𝑖=1 𝑞𝑖 , where N is the number
of firms. The marginal cost is c=0.01. To enter the market a firm needs to pay an entry cost
F=0.03 . In the “free entry equilibrium”
a) all firms that have entered make zero profits.
b) the price is equal to 0.01 .
c) no new firm will enter.
d) All of the above.
10) The ”characteristics approach” to product demand is useful when
a)
b)
c)
d)
products are homogenous.
the character of a product is difficult to measure.
products can be defined as different combinations of characteristics.
None of the above.
LONG QUESTION A
A market contains two firms. The demand for firm 1 is is 𝑞1 = 9 − 2𝑝1 + 𝑝2 and for firm 2 it is
𝑞2 = 9 − 2𝑝2 + 𝑝1 . The marginal cost of production is constant and equal to 2.0 for both firms.
Fixed costs are assumed to be zero for each firm. Assume that the firms compete in prices.
a)
Derive the best response function for firm 1.
b)
Assume that firms set prices independently and simultaneously and meet only once.
Calculate the Nash equilibrium prices and profits.
c)
At the Nash equilibrium prices, are the products a) horizontally differentiatied, or b)
vertically differentiated? Motivate briefly.
d)
Assume that firm 1 sets its price first and then firm 2 sets its price after having
observed firm 1’s price. Calculate the (subgame perfect) Nash equilibrium prices for
both firms.
e)
Assume that the two firms would merge and form a monopoly. Calculate the profit
maximizing prices for the monopoly.
LONG QUESTION B
The following questions relate to the disposable diaper market in the U.S. and are based on an
article from CNN.Money.com (June 2018). The article has been lightly edited and shortened, and
some supplementary information has been added as “Useful facts and assumptions” and in one
figure. Please base your answers on the information, and facts and assumptions provided in the
sources mentioned above, the learning and course materials from the course Industrial
Organization Analysis and general logical and economic reasoning.
Useful facts and assumptions (collected from various sources)
A disposable diaper mainly consists of absorbent pad made of material based on paper pulp,
which is compressed by two sheets of fabrics. Innovations in diaper design are becoming more
important and the leading diaper manufacturers are investing heavily in research and
development to develop diapers that can absorb more efficiently and can offer dryness for a
longer time. Disposable diapers come in many different shapes and qualities. Disposable diaper
sizes are based on the child's weight.
Sales of “disposable baby diapers” in the U.S. was about US$6bn in 2018.
Procter & Gamble (P&G) is an American multi-national consumer goods corporation. P&G
produces and sells disposable diapers under the brand names “Pampers” (premium) and “Luvs”
(basic). P&G has a 43 percent market share in the U.S. disposable diaper market. P&G spends
about 7 percent of its disposable diaper sales revenue on marketing.
Kimberly-Clark is an American multi-national personal care corporation. Kimberly Clark produces
and sells disposable diapers under the brand name “Huggies”. Kimberly Clark has a 35 percent
market share in the U.S. disposable diaper market. Kimberly Clark spends about 6 percent of its
disposable diaper sales revenue on marketing.
Other producers of branded disposable diapers include The Honest Company, and Seventh
Generation (owned by Unilever, a multi-national consumer goods corporation), but their market
shares are less than 2 percent each.
A range of different companies produce disposable diapers that are sold to retailers such as Aldi,
Amazon, Target, and Walmart, which market these under their own names (“private labels”).
Retailers with their own private labels also sell branded disposable diapers from P&G, and
Kimberly Clark. Private label disposable diapers typically have simpler shapes and use cheaper
materials than e.g. Pampers and Huggies. Private labels have grown over the last few years and
now have about 10 percent market share in the disposable diaper market. The marketing budgets
for private label disposable diapers is negligible.
Questions
a) Define the terms “horizontal product differentiation” and “vertical product
differentiation”. Use disposable diapers to exemplify both types of product differentiation.
b) “The price of pulp, a fibrous material used in many personal-care products such as
disposable diapers, has risen over the past year.” Assume that P&G has a monopoly with its
Pampers brand in the market for disposable diapers. Explain briefly how higher prices of
pulp will change P&G’s pricing of Pampers and its profits. Illustrate graphically. Hint: You
may assume that there is only one model of Pampers.
c) “The price of pulp, a fibrous material used in many personal-care products such as
disposable diapers, has risen over the past year.” Assume that P&G and Kimberly Clark are
the only producers of disposable diapers and that their respective products, Pampers and
Huggies, are differentiated and that the two firms compete in prices. Illustrate graphically
how their best response functions will change following higher pulp prices and how the
Nash equilibrium prices will change. Discuss briefly how profits of P&G and Kimberly Clark
will be affected by the higher pulp prices. Hint: You may assume that there is only one
model of Pampers and Huggies, respectively.
d) “Why diapers are in trouble: Americans are having fewer babies”. Assume that P&G has a
monopoly with its Pampers brand in the market for disposable diapers. Explain how the
demand for disposable diapers will change in response to fewer newborn babies. Explain
briefly how fewer newborn babies will affect P&G’s profits and discuss whether P&G
should adjust its pricing. Illustrate graphically. Hint 1: You may assume that there is only
one model of Pampers. Hint 2: You may assume that the demand per baby is q=a-b*p and
that it remains the same as before but that there are fewer babies now. Hint 3: You may
assume that marginal cost of production is constant.
e) “Why diapers are in trouble: Americans are having fewer babies”. Assume that P&G and
Kimberly Clark are the only producers of disposable diapers and that their respective
products, Pampers and Huggies, are differentiated and that the two firms compete in
prices. Illustrate graphically their best response functions before and after the change in
the number of newborn babies, and compare the prices and profits in old and new Nash
equilibrium. Hint: You may assume that there is only one model of Pampers and Huggies,
respectively.
f) Amazon.com (the largest e-commerce market place in the U.S.) has begun to sell
disposable diapers as part of its Mama Bear range of products. The quality of
Amazon.com’s disposable diapers is somewhat lower than P&G’s Luvs. Explain briefly how
entry by Amazon.com will affect profits of P&G. Illustrate graphically. Hint: Consider both
the effect on P&G’s Luvs and Pampers.
g) Kimberly Clark decided to produce the disposable diapers for Amazon.com. Discuss briefly
the effects on Kimberly Clark’s profits by Amazon.com’s entry. Comment briefly on the
quotes in the final paragraph "In a tough, competitive environment, where it's really hard
to grow sales, why not?", "If they [Kimberly Clark] don't do it, somebody else will.".
Why diapers are in trouble: Americans are having fewer babies
CNNMoney, June 2018
America's birth rate is at its lowest level in three decades. That's a problem for Pampers and
Huggies.
Birth rates began dropping in 2008 as the economy sank into a recession. Better access to
contraceptives and younger Americans having children later in their lives have extended the
decline, the National Center for Health Statistics found. The downturn caused disposable diaper
sales to fall almost 6% from April 2017 to 2018, according to Nielsen's most recent retail scanner
data. "This new reality is beginning to take a substantial toll," said Svetlana Uduslivaia, the head of
industry research at Euromonitor International. The diaper slump will probably be the "normal for
the foreseeable future."
Diaper wars
Fewer babies mean falling sales for Procter & Gamble (P&G) and Kimberly-Clark, the country's
leading diaper suppliers. (P&G makes Pampers and Luvs, and Kimberly produces Huggies.)
In January, Kimberly said it would lay off around 13% of its workers and shutter 10 manufacturing
plants to save money in the pinch. "You can't encourage moms to use more diapers in a developed
market where the babies aren't being born," chief executive Thomas Falk told analysts.
Diapers are key businesses for both companies.
Huggies accounts for about a third of Kimberly $18 billion in sales globally, according to
AllianceBernstein analyst Ian Gordon. Pampers is P&G's top-selling brand, bringing in more than
$8 billion a year globally. The conglomerate's baby care unit was its second largest business in
2017. It made up 14% of P&G's $65 billion worth of sales.
Huggies and Pampers have cornered the market by convincing parents that their diapers are the
safest and most reliable for newborns and toddlers. Last year, P&G controlled 43% of the U.S.
market and Kimberly grabbed 35%, according to Euromonitor.
"Parents are brand loyal when it comes to products for their kids," said Morningstar analyst Erin
Lash. "If a diaper works and you don't have accidents or issues when you're out with your child,
you probably will stick with it."
The rewards of retaining shoppers are huge for diaper makers. "If you have multiple children, and
it works for one kid, you're going to start there for your second child," Lash said. "There aren't as
many expenditures for a household as big as diapers," said Leonard Lodish, a professor emeritus at
the Wharton School of Business. Parents can spend more than $700 on diapers for babies during
the first year of their lives, Uduslivaia said.
Pampers Pure
P&G has taken several steps to respond to the demographic changes. The company has extended
its reach to parents concerned about diaper materials and ingredients. In February, it unveiled
Pampers Pure diapers and wipes, a "natural" collection with zero fragrance, lotion or chlorine.
Pampers Pure will compete with Unilever-owned Seventh Generation and The Honest Company
brands that have gained traction with eco-friendly marketing. Pampers Pure has already become
the top-selling natural diaper, P&G's chief financial officer Jon Moeller said at a conference this
week.
The brand is more expensive than P&G's regular line, but raising prices is difficult. Promotions and
discounts are a staple of diaper marketing, and shoppers want to save money on big-ticket
purchases. "If you are going to raise the price, you have to justify why," Uduslivaia said. "What is
so unbelievably great about that diaper that people would be willing to spend more?"
Price of pulp
The price of pulp, a fibrous material used in many personal-care products such as disposable
diapers, has risen over the past year. Rising demand from other sectors and some unplanned
shutdowns at mills - including from a trucker strike in Brazil - have led to tighter supplies.
Private labels and Amazon
To add to the challenges, P&G and Kimberly are also grappling with retailers' private labels and
Amazon. "The market is changing and some retailers are aggressively pursuing private label," P&G
CEO David Taylor said in April. Private label brands are as much as 20% cheaper — a threat to Luvs,
P&G's value line. P&G has responded by lowering Luvs' prices, but that hasn't stopped the
bleeding. "The lower private-label pricing has been a real challenge," Taylor said. "While we've
taken some steps to restore Luvs' competitiveness, it hasn't had the desired effect yet."
Kimberly, looking for ways to fuel growth, has turned to a risky source: Amazon. Amazon quietly
added diapers to its Mama Bear baby line last year, and analysts confirmed that Kimberly is
manufacturing the label. Although Mama Bear will to some extent compete with Huggies,
Kimberly has decided that producing for private labels is the best choice. "In a tough, competitive
environment, where it's really hard to grow sales, why not?" said Euromonitor’s Uduslivaia. "If
they don't do it, somebody else will."
Figure 1: Average prices per different disposable diapers (sold in packs of 48 in comparable diaper size)