The course grade consists of a final exam and two individual homework assignments (both 10%). This document contains handwritten computations and solutions to the second homework assignment. The solutions are given in green and the student specific parameter values are given in orange. This homewor...
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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.
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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.
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