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ECON 101: Principles of Microeconomics – Discussion Section Week 12 – Spring 2015
Content for Today
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Monopoly
Price Discrimination
Monopoly and Price Discrimination Questions
1.
Suppose a monopoly faces a market demand curve of P = 42 – Q The
Marginal cost faced by him is given by the equation : MC = Q
(a) Derive the equation for marginal revenue curve.
The marginal revenue curve requires to take twice the slope of the demand
curve, hence MR=42-2Q
(b) Find the profit maximizing level of production for this monopolist.
The optimality condition for the monopolist is MR=MC, So 42-2Q=Q
This implies Q=42/3=14
(c) What should be the price charged by the monopolist?
Plugin back in the demand we get P=42-14=28
(d) What is the socially optimal price?
The Social optimal price holds when MC=P. Therefore P=Q. Plugin back in
the demand we get Q=42-Q. So Q=21. And so the price should be P=21
(e) What’s this monopolist’s total revenue?
PQ=(28)(14)=392
(f) Graph the producer surplus, the consumer surplus, and the dead-weight
loss for the market with the monopolist.
C.S.
42
42
28
28
D.W.L
P.S.
14 21
14 21
42
42
(g) Compare the Social Surplus had this industry been perfectly competitive.
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ECON 101: Principles of Microeconomics – Discussion Section Week 12 – Spring 2015
The
Social
Surplus=
P.S.+C.S.
in
the
monopoly
case
P.S.=(14)(14)/2+14(14)=294. C.S.=(14)(14)/2=98. So Social Surplus=392.
In the perfect competitive market. P.S.=(21)(21)=220.5 and
C.S.=(21)*(21)/2=220.5 so Social Surplus=441>392.
(h) Assume now that the monopolist can discriminate perfectly (first price
discrimination) what is the producer surplus? Is the social surplus greater
or less than in the perfect competitive case?
Now the monopolist can extract all the surplus from the consumers. Hence
P.S.=441=Social Surplus. Therefore the social surplus is the same as in
perfect competition.
2. Orange, the monopoly firm in computer market having a constant marginal
cost 30. There are two types of consumer in the market, corporate user and
personal user. The demand curves are given by the following equations Corporate
users: Q = 50 – P/3 Personal users: Q = 110 – P
(a) Suppose Orange can implement third degree price discrimination. Derive
the profit maximization prices, consumer surplus and Orange’s profit.
MR for corporate users is MR = 150 – 6Q. Thus, MR = MC implies Q = 20 and P =
90. Thus, corporate user’s consumer surplus is 600 and profit from corporate user is
1200. Similarly, MR for personal user is MR = 110 - 2Q. Thus, MR = MC implies Q
= 40 and P = 70. Thus, personal user’s consumer surplus is 800 and profit from
personal user is 1600.
(b) Derive the aggregated market demand. Then, derive the profit
maximization price, consumer surplus and Orange’s profit.
Aggregate demand is Q = 160 – 4P/3 if P<110 and Q = 50 – P/3 if P>110 or
equivalently, P = 120 – 3Q/4 if Q > 40/3 and P = 150 – 3Q if Q < 40/3. Since
aggregate demand has two parts, MR also has two parts,
MR = 120 – 3Q/2 if Q > 40/3 and MR = 150 – 6Q if Q < 40/3. Thus, MR = MC holds
at Q = 60. Thus P = 75. Consumer surplus is 1550
3. Consider the monopoly company in a car market Toyotaka. The Toyotaka’s
variable cost and marginal cost are given by VC = 10q and MC = 10. In addition to
that, Toyotaka needs to build a plant in order to operate. Building a plant costs the
firm 7000.
(a) Derive the total cost for the firm. Does the technology of the firm exhibit
economy of scale?
Fixed cost is 7000. Total cost, a sum of fixed cost and variable cost is 7000 + 10q.
ATC is 7000/q + 10 which is decreasing and hence, exhibits economy of scale.
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ECON 101: Principles of Microeconomics – Discussion Section Week 12 – Spring 2015
(b) The demand curve for car is given by Q = 210 – P. Derive MR and find
monopoly price, quantity and profit
MR is given by 210 - 2Q. Therefore, by MR = MC, monopoly quantity satisfies 210
- 2Q = 10. Thus, Q = 100. Demand is 100 at P = 110. Thus, monopoly price is 110.
Given monopoly quantity and price, monopolist revenue is PQ = 11000 and total cost
is 7000+10*100 = 8000. Thus, profit is 3000.
(c) Find the price, quantity and profit under marginal cost regulation. The
marginal cost regulation is the regulation under which the firm charges
price equal to average marginal cost.
Under marginal cost regulation P = 10. Thus Q = 200 and profit is -7000.
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