The course grade consists of a final exam and two individual homework assignments (both 10%). This document contains handwritten computations and solutions to the first homework assignment. The solutions are given in green. This homework assignment was graded with a 10. Please check if the question...
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1
,Problem set
0. Write down your student number.
1. Firms 1, 2, and 3 are Bertrand competitors in a market, where demand is characterized
by P (Q) = 300 2Q. Marginal costs are constant at c1 = A, c2 = 100, and c3 = 120.
Fixed costs are zero. Find the equilibrium profit of firm 1.
2. Two companies compete by setting production levels simultaneously. Market demand is
given by P (Q) = 100 4Q. Marginal costs are constant at c1 = B and c2 = 20. Find the
equilibrium market price.
3. Firm 1 is the Stackelberg leader in a market and Firm 2 is the follower. Firm 1 has a
marginal cost of c1 = C. Firm 2 has a marginal cost of c2 = 10. Market demand is given
by P (Q) = 200 2Q. Find the equilibrium price.
4. Anna and Elsa are the owners of two competing ice cream shops in the imaginary town
of Arenstrip. They are located at the two opposing ends of the town’s 1-km-long Main
Street. The 100 inhabitants of the town are distributed uniformly on Main Street and
each of them eats one scoop of ice cream for desert each Sunday, regardless of its price.
People’s disutility from getting to an ice cream shop and back home amounts to 2 EUR
per km of distance to the stand. Anna’s marginal cost of producing one scoop of ice
cream is c1 = D. Elsa’s marginal cost of producing one scoop of ice cream is c2 = 3. Find
Anna’s equilibrium price for on scoop of ice cream.
5. A market is currently supplied by a monopolist with constant average and marginal cost
of c1 = E. Demand is given by P (Q) = 100 Q. There is a potential entrant with a
constant marginal cost of c2 = 4 and a fixed cost of F. The timing of the entry game is
as follows. First, the incumbent firm can announce a future production level and sign up
prospective buyers with binding contracts, therefore making the announcement credible.
Second, the entrant decides about entry. If it expects to earn strictly positive profits, it
enters the industry and produces optimally given the incumbent’s quantity announcement.
Otherwise, the entrant stays out and the incumbent remains a monopolist. Find the
equilibrium profit of firm 1 if it does not deliberately deter entry.
6. Using the same parameters and context as in the previous problem (Problem 5.), find the
entry-deterring production level of firm 1.
7. N firms produce homogeneous products and compete by setting prices simultaneously.
The aggregate demand function is given by Q(P ) = 100 P . Marginal costs are equal
to c = 20 for all firms. Through a trade union, all the executives meet in a closed
meeting, and contemplate forming a collusive agreement at the jointly profit maximizing
prices. Find the threshold value for the probability-adjusted discount factor above which
collusion is sustainable by the trigger strategy.
8. Two firms produce di↵erentiated products and compete by setting prices simultaneously.
Each of them faces the demand function: qi (pi ; pj ) = 150 2 · pi + pj , where qi and pi are
own quantity and price, and pj is the price that the rival firm sets. Marginal costs are
2
, equal to G for both firms. One day, the two executives sit down to lunch together and
contemplate forming a collusive agreement at the jointly profit maximizing prices. Find
the price of firm i if it adheres to the cartel agreement.
9. Consider the following stage game of an infinitely repeated game: Two firms simulta-
neously make the choice of whether they cooperate in a collusive agreement with their
opponent, or whether they deviate from the collusive agreement. The firms’ pay-o↵s are
given by the following table:
Find the threshold value for the probability-adjusted discount factor above which collusion
is sustainable by the trigger strategy.
10. Consider the same competitive context as in the previous problem (Problem 9), but now
assume that H = 2. Furthermore, assume that each firm has a probability-adjusted
discount factor of I. The antitrust authority puts considerable e↵ort into monitoring the
market, with the e↵ect that any collusive agreement between the firms is detected and
prosecuted with a probability of 10%. After a successful prosecution, colluding firms must
each pay a fine and will never be able to form a cartel again. Find the lowest fine that
would deter the firms from forming a cartel.
, 2 Cournot model simultaneity
PIQI
t
100 40
C 1 C2 20
Q 9 92
Ti C1
p 911 9
1100
419 921191 9
1009 491 49192 9
999 491 49192
f O.c
for profit maximization
99 0
2111291 891 492
99
89 492
best response
firm 1
91 9918 11292
Ta C1
Ip 921 92
1100
4191 921192 2092
8092 49192 4922
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