Industrial Organisation
SET EXERCISES #2
Instructions:
Answer ALL three problems below. Problem 1 is worth 28 marks. Problems 2 and
3 are worth 36 marks each.
Submission is via Moodle.
Deadline: Tuesday 15th December by 4pm.
Problem 1. Consider a Salop model with a unit mass of consumers uniformly distrib-
uted over a circle of circumference 1 km. Each consumer wants to buy one unit of a
homogeneous good, which they value at R. Four
rms sell this homogeneous good at
locations that correspond to 12 oclock, 3 oclock, 6 oclock and 9 oclock. These loca-
tions are
xed and cannot be changed. The production costs are zero. Consumers face
quadratic transportation costs: they incur d2 for every d units travelled. Assume R is
large enough in all con
gurations to ensure that the market is fully covered.
a. Calculate the optimal prices and the resulting pro
ts in a symmetric equilibrium
when all four
rms are active. Carefully explain your derivation and provide economic
reasoning where necessary. [8 marks]
b. Suppose now that each
rm faces a
xed operating cost of F > 0. For which values
of F all four
rms are able to earn enough pro
ts to cover their operating costs? For
which values of F only three of the
rms are able to earn enough pro
ts to cover their
operating costs? For which values of F only two of the
rms are able to earn enough
pro
ts to cover their operating costs? Carefully explain your derivation and provide
economic reasoning where necessary. [20 marks]
Problem 2. Consider a Hotelling model with linear transportation costs. The consumers
are located uniformly along a segment of unit length. There are two
rms, A and B,
located at the opposite ends of the segment. Each
rm has zero marginal costs. The
prices of the two
rms are equal to 1. The quality of each
rm is denoted qi, i = A;B,
and each qi is uniformly and independently distributed over [2; 3]. Each
rm knows the
values of both qualities while consumers know only the distribution (unless
rms disclose
the quality). The gross valuation of the consumers for each
rm is the expected quality
of that
rm given the available information. Their net utility is their gross valuation
minus the transportation cost minus the price. Unit transportation costs are equal to 1.
a. Suppose that
rms can simultaneously disclose their own quality qi at zero cost.
Consumers then decide which product to buy. What is the equilibrium? Carefully explain
your derivation and provide economic reasoning where necessary. [8 marks]
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b. Suppose now that disclosure is costly: it costs a 2 (0; 1=4] to disclose the quality;
this cost is the same for both
rms. Suppose that each
rm conditions its action on
its quality only. Find the equilibrium of the game in which
rms
rst simultaneously
decide whether to disclose their own quality truthfully or not to disclose any information,
and then consumers make their choices. Carefully explain your derivation and provide
economic reasoning where necessary. [8 marks]
c. Suppose that instead of advertising their own quality,
rms engage in comparative
advertising: they can advertise only the quality di¤erence qA ? qB, still at a cost a 2 (0; 1=4]. Find the equilibrium of the game in which
rms
rst simultaneously decide
whether to disclose the quality di¤erence or not to disclose any information and then
consumers make their choices. Carefully explain your derivation and provide economic
reasoning where necessary. [10 marks]
d. From a social welfare point of view, what are the bene
ts of advertising here? In
which case, (b) or (c), do you expect the equilibrium level of advertising to be closer to
the social optimum? No computations needed, carefully explain your answer in words
and provide su¢ cient economic reasoning. [10 marks]
Problem 3. Consider a good for which the per-period demand is Q = 1 ? p. There
are two periods and no discounting. There is an incumbent
rm I that has marginal
production cost c1 < 1 in the
rst period. In the second period, its marginal production
cost is c2 = c1 ? q1, where q1 is its output in the
rst period and 2 (0; 2).
a. Write down the pro
t maximization problem of the incumbent and calculate
the optimal quantities it will produce in periods 1 and 2. How do the optimal quantities
depend on and change with . What exactly is the economic interpretation of . Carefully
explain your derivations and provide economic reasoning where necessary. [12 marks]
Suppose now that there is a potential entrant E that might enter the market in the
second period. It has marginal production cost cE = c1 and no cost of entry. Because of
the latter, for the sake of clarity, suppose that E always enters but may produce zero (in
which case it does not enter de facto). The two
rms compete in quantities a la Cournot.
b. Derive the equilibrium of the second-period game for some given c2. What are
the equilibrium quantities produced by the incumbent and by the entrant and how do
they depend on q1? How do (second-period) pro
ts depend on q1? Carefully explain your
derivations and provide economic reasoning. [12 marks]
c. Now write down the
rst-period game pro
t maximization problem of the incum-
bent (with potential entry forthcoming in the second period) and calculate the equilib-
rium value of q1. When is the entry blockaded, deterred and accommodated, respectively?
Explain each case carefully and provide economic reasoning. [12 marks]
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