Practice Session 3
Price Discrimination
INDUSTRIAL ORGANIZATION
Economics Department, Universidad Carlos III de Madrid
1.
Key Questions
1. What is price discrimination?
2. What is the purpose of price discrimination?
3. What types of price discrimination exist?
4. What kind of information is necessary to perform each type of price discrimination?
5. What can make price discrimination challenging to implement?
6. Which mechanisms can we employ in order to implement each type of price discrimination?
7. Who are the winners and losers in each type of discrimination, with respect to a
perfectly competitive outcome?
8. How is total surplus distributed under first-degree discrimination?
9. What is a two-part tariff? In what type of discrimination is it used?
10. Under which type of price discrimination does the firm use two different prices, each
in a market with different demand, conditional on consumers not having arbitrage
possibilities between the two markets?
11. Below there are some examples of price discrimination in practice. Can you please
discuss which type of price discrimination applies to each case?
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2.
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Problems
1. A monopolist faces a single consumer whose demand function is q = 74−p. Marginal
costs equal zero.
a) What is the optimal price strategy in case of a linear tariff (that is, when a
single price is chosen)? What about the case of a two-part tariff? Compare
both cases in terms of social welfare and discuss.
b) Now suppose there are two types of consumers. Their aggregate demands have
equal shares, given by q1 = 66 − p1 y q2 = 82 − p2 . Suppose there is perfect
arbitrage between consumers of the same type, but there is no arbitrage between
consumers of different types. Moreover, the monopolist can recognize the type
of consumer that enters the shop. What type of price discrimination can the
monopolist use? Calculate his surplus, explaining all the necessary steps to
obtain the result. Does welfare increase if the government forbids all types of
price discrimination?
c) Now, suppose the monopolist cannot recognize the type of consumer who enters
his shop. Moreover, there is no arbitrage between consumers of the same type
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nor between consumers of different types. What type of price discrimination
can the monopolist use now? Calculate the optimal two-part tariff and the
monopolist’s surplus.
2. Consider a monopolist who faces a linear demand p = a − bx. Production costs are
C(x) = cx.
a) Show that the elasticity of demand is an increasing function of x.
b) Compute the welfare loss due to monopoly (compare total surplus in the case
of pure monopoly with the perfect competition case). How does this loss change
when b changes? (Use a graph in order to represent changes in surplus).
c) Suppose the monopolist performs first-degree price discrimination. Compute
consumer and producer surplus and compare them to the perfect competition
case. Are there welfare losses?
d ) Suppose now that the monopolist faces a linear demand p = 90−x, and has total
production costs C(x) = 2x+F , where F = 90 is the fixed cost that he must pay
in order to produce a positive amount of the good. The Regulation Authority
wants to reach the first-best. The Authority suggests the monopolist follows
the rule “price equal to marginal cost”. Compute the monopolist’s surplus and
total surplus.
e) Suppose there is no regulation; what is the monopoly equilibrium? Is it possible
to reach the first-best? Compute the difference in welfare terms between the
initial allocation (with regulation) and the alternative allocation.
3. AMERITH is a firm that has obtained a patent over a new material, used to produce
surgery tools. The marginal cost of each tool is 50 euros, and the demand for such
tools in Madrid (M ) and Barcelona (B) are the following:
PM
= 300 − 0,2qM
PB = 250 − 0,1qB
a) Compute equilibrium prices, quantities, profits, consumer’s surplus and welfare
loss, if any, in each market.
b) List the types of price discrimination and explain each of them.
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c) If AMERITH performs price discrimination, what type of discrimination would
it choose?
d ) Suppose that in London, the demand is segmented into two parts, and that
arbitrage is impossible: the demand for those firms who rent materials in public
hospitals P and the demand for hospitals who do not want to rent R. Such
demands are the following:
PP
= 250 − 0,125qP
PR = 350 − 0,05qR
e) As a consequence of the new regulation, selling equipment between firms who
rent and those who do not rent is no longer forbidden. How do the profits of
AMERITH change?
4. Suppose that SUIZA HISPANIA (from now on SH) is a firm that produces and
sells sports cars. Using information obtained from a market study, the firm must
decide how many models of cars to produce and sell. The market study concluded
that 2 types of buyers are interested in the firm’s prototypes: those who, in relative
terms, are willing to pay more for the AVENTADOR prototype (consumers of type
GILITO) and those who are willing to pay less (consumers of type RATA). The
following table summarizes the willingness to pay and the number of consumers of
each type:
N. of Individuals
Aventador
Lanza
Consumers type GILITO
20.000
80.000 e
35.000 e
Consumers type RATA
340.000
40.000 e
25.000 e
SH’s marginal production costs depend on the quality of the product. The marginal
cost of the Lanza model equals 15.000, while the marginal cost of the Aventador
model equals 20.000.
a) Suppose that SH only has the possibility of selling a single model, that is, the
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high-quality or low-quality model. Derive the optimal quality, the optimal price,
and the firm’s profits. Justify your answer.
b) Suppose that SH can offer two different models. Derive the optimal prices and
compute the firm’s profits. Justify your answer.
c) How many models of vehicles would SH sell if it could decide between selling
one or two models? Suppose 160.000 consumers of type RATA become of type
GILITO: how many models of vehicles would SH sell if it could decide between
selling one or two models? Justify your answer.
5. * The owner of a club knows that the demand for drinks is more elastic among
young consumers than among older consumers, and is trying to determine which is
the price scheme that would maximize his profits. In particular, the owner estimated
that the individual demand functions of each group are the following:
People younger than 25 years (“young”): qY = 18 − 5pY
People older than 25 years (“old”): qO = 20 − 4pO
Every night, 100 people of each age group visit the club. The owner has a cost
of 2 euros for each drink.
a) Suppose that the owner can charge an entry fee to the club, Ai , and a price
for every drink, pi , for each age group, where i = Y, O. Compute the entry fee
Ai and the price of drinks pi , for each age group, that maximize the owner’s
profits.
b) Suppose now that, to charge for entry to the club (Ai ), the owner has to hire
private guards, who cost 2000 euro per night. If there are no guards, the owner
cannot charge for entry and can only put a price pi on drinks (but can still
charge a different price for each age group). Would you suggest to hire private
guards or not? Why?
c) Now suppose that, by a municipal ruling, the club owner cannot charge different
entry fees or prices by age group. Of course, he can still charge entry fees A
and a price p for each drink. As before, in order to charge for entry, he still has
to pay the cost of 2000 euros for the guards (and if he does not pay the guards,
he can only put a price p on each drink). Should he hire guards in this case?
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Why? [Hint: There are two ways to solve this problem: 1) obtain the owner’s
profits for each case and compare them; or 2) obtain the owner’s profits in the
case of no entry fee, compare it to the profits of not having guards of case b),
and comment on your answer starting from this point].