Monopoly
Monopoly
Monopoly
MODELS OF MONOPOLY
Dr. S. Chen
Microeconomics, Ec2201
2009 Spring
1
Monopoly
2
Barriers to Entry
• The reason why a monopoly exists is
that other firms find it unprofitable or
impossible to enter the market
• Barriers to entry are the source of all
monopoly power
– there are two general types of barriers to
entry
• technical barriers
• legal barriers
3
Technical Barriers to Entry
• The production of a good may exhibit
decreasing marginal and average costs over a
wide range of output levels
– in this situation, relatively large-scale firms
are low-cost producers
• firms may find it profitable to drive others out of
the industry by cutting prices
• this situation is known as natural monopoly
• once the monopoly is established, entry of new
firms will be difficult
– Antitrust case: Microsoft Word (NYT1, 2)
4
Technical Barriers to Entry
• Another technical basis of monopoly is
special knowledge of a low-cost
productive technique
– it may be difficult to keep this knowledge
out of the hands of other firms
– Patents of drugs; expensive health care
and insurance in US
• Ownership of unique resources may
also be a lasting basis for maintaining a 5
monopoly
Legal Barriers to Entry
• Many pure monopolies are created as a
matter of law
– with a patent, the basic technology for a
product is assigned to one firm
– the government may also award a firm an
exclusive franchise to serve a market
6
Creation of Barriers to Entry
• Some barriers to entry result from actions
taken by the firm
– research and development of new products
or technologies
– purchase of unique resources
– lobbying efforts to gain monopoly power
• The attempt by a monopolist to erect
barriers to entry may involve real
resource costs 7
Profit Maximization
• To maximize profits, a monopolist will
choose to produce that output level for
which marginal revenue is equal to
marginal cost
– marginal revenue is less than price because
the monopolist faces a downward-sloping
demand curve
• he must lower its price on all units to be sold if it
is to generate the extra demand for this unit
8
Marginal Revenue Curve
Price
• A monopolist
must have
P > MR
D
MR
Quantity
Profit Maximization
• Since MR = MC at the profit-maximizing
output and P > MR for a monopolist, the
monopolist will set a price greater than
marginal cost P>MC.
10
Profit Maximization
Price MC The monopolist will maximize
profits where MR = MC
AC
P* The firm will charge a price
of P*
AC*
11
The Inverse Elasticity Rule
• The gap between a firm’s price and its
marginal cost is inversely related to the
price elasticity of demand facing the
firm P − MC 1
=−
P eQ,P
15
Monopoly Profits
Price Price
MC MC
AC
AC
P* P*=AC
D D
MR MR
Q* Quantity Q* Quantity
Positive profits Zero profit
16
No Monopoly Supply Curve
• With a fixed market demand curve, the
supply “curve” for a monopolist will only
be one point
– the price-output combination where MR =
MC
• If the demand curve shifts, the marginal
revenue curve shifts and a new profit-
maximizing output will be chosen
17
Monopoly with Linear Demand
• Suppose that the market for frisbees
has a linear demand curve of the form
Q = 2,000 - 20P
or
P = 100 - Q/20
• The total costs of the frisbee producer
are given by
C(Q) = 0.05Q2 + 10,000
18
Monopoly with Linear Demand
• To maximize profits, the monopolist
chooses the output for which MR = MC
• We need to find total revenue
TR = P⋅Q = 100Q - Q2/20
• Therefore, marginal revenue is
MR = 100 - Q/10
while marginal cost is
MC = 0.1Q
19
Monopoly with Linear Demand
• Thus, MR = MC where
100 - Q/10 = 0.1Q
Q* = 500 P* = 75
• At the profit-maximizing output,
C(Q) = 0.05(500)2 + 10,000 = 22,500
AC = 22,500/500 = 45, MC=0.1⋅500=50
π = (P* - AC)Q = (75 - 45)⋅500 = 15,000
20
Monopoly with Linear Demand
• To see that the inverse elasticity rule
holds, we can calculate the elasticity of
demand at the monopoly’s profit-
maximizing level of output
∂Q P 75
eQ,P = ⋅ = −20 = −3
∂P Q 500
21
Monopoly with Linear Demand
• The inverse elasticity rule specifies that
P − MC 1 1
= =
P eQ,P 3
22
Monopoly and Resource
Allocation
• To evaluate the allocational effect of a
monopoly, we will use a perfectly
competitive, constant-cost industry as a
basis of comparison
– the industry’s long-run supply curve is
infinitely elastic with a price equal to both
marginal and average cost
23
Monopoly and Resource
Allocation
Price
If this market was competitive, output would
be Q* and price would be P*
P* MC=AC
D
MR
Q** Q* Quantity
24
Monopoly and Resource
Allocation
Price Competitive Monopoly
market market
Consumer surplus A+B+C A
A
P** Producer surplus 0 B
B Social gain A+B+C A+B
C
P* MC=AC
CS=the area under D
and above P
MR
D PS=the area under P
and above MC
Q** Q* Quantity
25
Monopoly and Resource
Allocation
Price Consumer surplus would fall (by B+C)
Q** Q* Quantity
26
Welfare Losses and Elasticity
Example: Assume that
• MC=AC=10 for a monopolist and
• The demand curve is given by:
Q =100-2P
Because a monopolist must choose to
operate only if the market demand
curve is elastic (i.e. e<-1), we have
P*>Q*/2. 27
Welfare Losses and Elasticity
• The competitive price in this market will
be,
Pc =MRc=MC= 10,
and the monopoly price is given by
(using the inverse elasticity rule)
10
Pm =
1
1+
e
which must be >10 because e<-1. 28
Welfare Losses and Elasticity
• Similar to the previous class example,
we can use
– the demand function and
– the MC function
to derive the monopoly price and quantity:
Pm = 30 and Qm = 40
Welfare Losses and Elasticity
Price For a competitive market,
50
consumer surplus= A+B+C
= 80 (50-10)/2 =1600
A
Pm=30
Producer surplus =0
B
C MC=AC=10
Pc=10 So the social gain=1600
Q=100-2P
MR = 50-P
Qm=40 Qc=80 Quantity
30
Welfare Losses and Elasticity
Price For a monopoly market,
50
consumer surplus= A
= 40 (50-30)/2 =400
A
Pm=30
Producer surplus =B=40(30-10)=800
B
C MC=AC=10
Pc=10 So the social gain=1200
B
C MC=AC=10
Pc=10
Q=100-2P
MR = 50-P
Qm=40 Qc=80 Quantity
32
Monopoly and Product Quality
• The market power enjoyed by a monopoly
may be exercised along dimensions other
than the market price of its product
– type, quality, or diversity of goods
• Whether a monopoly will produce a
higher-quality or lower-quality good than
would be produced under competition
depends on demand and the firm’s costs
33
Monopoly and Product Quality
(optional)
• Suppose that consumers’ willingness to
pay for quality (X) is given by the inverse
demand function P(Q,X) where
∂P/∂Q < 0 and ∂P/∂X > 0
• If costs are given by C(Q,X), the
monopoly will choose Q and X to
maximize
π = P(Q,X)Q - C(Q,X)
34
Monopoly and Product Quality
(optional)
First-order conditions for a maximum are
∂π ∂P
= P (Q, X ) + Q − CQ = 0
∂Q ∂Q
∂π ∂P
=Q − CX = 0
∂X ∂X
38
Price Discrimination
• A monopoly engages in price
discrimination if it is able to sell otherwise
identical units of output at different prices
• Whether a price discrimination strategy is
feasible depends on the inability of
buyers to practice arbitrage
– profit-seeking middlemen will destroy any
discriminatory pricing scheme if possible
• price discrimination becomes possible if resale is
costly 39
Perfect Price Discrimination
• If each buyer can be separately
identified by the monopolist, it may be
possible to charge each buyer the
maximum price he would be willing to
pay for the good
– perfect or first-degree price discrimination
• extracts all consumer surplus
• no deadweight loss
40
Perfect Price Discrimination
Under perfect price discrimination, the monopolist
Price charges a different price to each buyer
The first buyer pays P1 for Q1 units
P1
P2 The second buyer pays P2 for Q2-Q1 units
MC
The monopolist will
April
marginal buyer is no
Eric
D (23,347.2>15,000)
• Monopoist extracts
Quantity all the CS.
Q1 Q2 Q* 43
Market Separation
• Perfect price discrimination requires the
monopolist to know the demand function
for each potential buyer
• A less stringent requirement would be to
assume that the monopoly can separate its
buyers into a few (two) identifiable markets
– can follow a different pricing policy in each
market
– third-degree price discrimination
44
Market Separation
• All the monopolist needs to know in this
case is the price elasticities of demand
for each market
• set price according to the inverse elasticity
rule; (P-MC)/P=-1/e
• that is: MC=P(1+1/e)
• If the marginal cost is the same in all
markets, 1 1
Pi (1 + ) = Pj (1 + )
ei ej
45
Market Separation
• This implies that
1
(1 + )
Pi ej
=
Pj (1 + 1 )
ei
MC1 MC2
D1 D2
MR1 MR2
49
Third-Degree Price
Discrimination(optional)
• The allocational impact of this policy can be
evaluated by calculating the deadweight
losses in the two markets
– the competitive output would be 18 in market 1
and 12 in market 2
DW1 = 0.5(P1-MC)(18-Q1) = 0.5(15-6)(18-9) = 40.5
52
Two-Part Tariffs(optional)
• A linear two-part tariff occurs when
buyers must pay a fixed fee for the right
to consume a good and a uniform price
for each unit consumed
T(q) = a + pq
• The monopolist’s goal is to choose a
and p to maximize profits, given the
demand for the product
53
Two-Part Tariffs(optional)
• Because the average price paid by any
demander is
p’ = T/q = a/q + p
this tariff is only feasible if those who
pay low average prices (those for whom
q is large) cannot resell the good to
those who must pay high average
prices (those for whom q is small)
54
Two-Part Tariffs(optional)
• One feasible approach for profit
maximization would be for the firm to set
p = MC and then set a equal to the
consumer surplus of the least eager
buyer
– this might not be the most profitable
approach
– in general, optimal pricing schedules will
depend on a variety of contingencies
55
Two-Part Tariffs(optional)
• Suppose there are two different buyers
with the demand functions
q1 = 24 - p1
q2 = 24 - 2p2
• If MC = 6, one way for the monopolist to
implement a two-part tariff would be to
set p1 = p2 = MC = 6
q1 = 18 q2 = 12
56
Two-Part Tariffs(optional)
• With this marginal price, demander 2
obtains consumer surplus of 36
– this would be the maximum entry fee that
can be charged without causing this buyer
to leave the market
• This means that the two-part tariff in this
case would be
T(q) = 36 + 6q
57
Regulation of Monopoly
• Natural monopolies such as the utility,
communications, and transportation
industries are highly regulated in many
countries
58
Regulation of Monopoly
• Many economists believe that it is
important for the prices of regulated
monopolies to reflect marginal costs of
production accurately
• An enforced policy of marginal cost
pricing will cause a natural monopoly to
operate at a loss
– natural monopolies exhibit declining
average costs over a wide range of output
59
Regulation of Monopoly
Because natural monopolies exhibit
Price decreasing costs, MC falls below AC
An unregulated monopoly will
maximize profit at Q1 and P1
If regulators force the
P1
monopoly to charge a
C1 price of P2, the firm will
suffer a loss because
C2
AC P2 < C2
P2 MR MC
Quantity
Q1 Q2 D
60
Regulation of Monopoly
Suppose that the regulatory commission allows the
Price monopoly to charge a price of P1 to some users
61
Regulation of Monopoly
• Another approach followed in many
regulatory situations is to allow the
monopoly to charge a price above
marginal cost that is sufficient to earn a
“fair” rate of return on investment
– if this rate of return is greater than that
which would occur in a competitive market,
there is an incentive to use relatively more
capital than would truly minimize costs
62
Regulation of Monopoly
• Suppose that a regulated utility has a
production function of the form
q = f (k,l)
• The firm’s actual rate of return on
capital is defined as
pf (k , l ) − wl
s=
k
63
Regulation of Monopoly
• Suppose that rate of return on capital s
is constrained by regulation to be equal
to s0, then the firm’s problem is to
maximize profits
π = pf (k,l) – wl – vk
subject to the constraint wl + s0k = pf (k,l).
• The Lagrangian for this problem is
L = pf (k,l) – wl – vk + λ[wl + s0k – pf (k,l)]
64
Regulation of Monopoly
• If λ=0, regulation is ineffective and the
monopoly behaves like any profit-
maximizing firm
• If λ=1, the Lagrangian reduces to
L = (s0 – v)k
which (assuming s0>v), will mean that
the monopoly will hire infinite amounts
of capital – an implausible result.
65
Regulation of Monopoly
• Therefore, 0<λ<1 and the first-order
conditions for a maximum are:
∂L
= pfl − w + λ(w − pfl ) = 0
∂l
∂L
= pfk − v + λ(s0 − pfk ) = 0
∂k
∂L
= wl + s0 − pf (k , l ) = 0
∂λ
66
Regulation of Monopoly
• Because s0>v and λ<1, this means that
pfk < v
• The firm will hire more capital than it
would under unregulated conditions
– it will also achieve a lower marginal
productivity of capital than the unregulated
markets.
67
Dynamic Views of Monopoly
• Some economists have stressed the
beneficial role that monopoly profits can
play in the process of economic
development
– these profits provide funds that can be
invested in research and development
– the possibility of attaining or maintaining a
monopoly position provides an incentive to
keep one step ahead of potential competitors
68
Important Points to Note:
• The most profitable level of output for
the monopolist is the one for which
marginal revenue is equal to marginal
cost
– at this output level, price will exceed
marginal cost
– the profitability of the monopolist will
depend on the relationship between price
and average cost
69
Important Points to Note:
• Relative to perfect competition,
monopoly involves a loss of consumer
surplus for demanders
– some of this is transferred into monopoly
profits, whereas some of the loss in
consumer surplus represents a
deadweight loss of overall economic
welfare
– it is a sign of Pareto inefficiency
70
Important Points to Note:
• Monopolies may opt for different levels
of quality than would perfectly
competitive firms
• Durable good monopolists may be
constrained by markets for used goods
71
Important Points to Note:
• A monopoly may be able to increase
its profits further through price
discrimination – charging different
prices to different categories of buyers
– the ability of the monopoly to practice
price discrimination depends on its ability
to prevent arbitrage among buyers
72
Important Points to Note:
• Governments often choose to regulate
natural monopolies (firms with
diminishing average costs over a broad
range of output levels)
– the type of regulatory mechanisms
adopted can affect the behavior of the
regulated firm
73