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4. Market Structure
4.1 Monopoly
4.1.1 Monopolistic Competition
5. Externalities
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• Mandatory: Varian, H., Intermediate Microeconomics, 5th
edition, Norton, 1999. Chapter 24.
1
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In previous lectures we have seen how firms choose the pricequantity combination in
FRPSHWLWLYH
PDUNHWV
, a market
structure characterised by a great number of firms. We are now
going to study the behaviour of a firm that faces no competition,
i.e. the behaviour of a PRQRSROLVW.
In the case of monopoly, the firm has control over the price of
output. Therefore, it will choose the level of price and output
that maximises profits. Remember that in the situation of perfect
competition, firms could only choose the quantity, since the
control over the price was out of their reach.
Since the monopolists supplies the whole market, it can either
choose the price and let consumers pick the quantity transacted
in the market, or it can choose the quantity and see what price
consumers are willing to pay for that quantity. Either way, we
will get the same outcome.
2
0D[LPLVLQJ3URILWV
• Denoting the inverse demand function by
cost function by
0 5, we can write the revenue function
F \
0 5= 0 5 .
U \
as
0 5 and the
S \
S \ \
Thus,
the
monopolist’s
profit-
maximisation problem can be defined as:
max U
\
0 5− 0 5
\
F \
• By setting the problem in this way, we immediately see
that the optimality condition implies having the marginal
revenue equal to the marginal cost:
05
= 0&
RU
GU
G\
=
GF
G\
• Notice that the same optimality condition holds for the
competitive firm. The difference is now in the marginal
revenue function. For the competitive firm, the marginal
revenue is just equal to the market price, which is constant
and unaffected by the actions of any individual firm.
• For the monopolist, the marginal revenue is not constant
and that is precisely because the demand curve it faces is
the market demand curve. Thus, when the monopolist
increases output by G\ , there are two effects on revenues:
3
- First, it sells more output and so gets extra revenue,
SG\
.
- Second, because it increases the quantity of output in
the market, it drives the price down, which means
that it will receive less for HYHU\ unit sold,
\GS
.
• Therefore, the total change in revenue that follows an
increase in output is given by:
GU
=
SG\
0 5=
05 \
• Since
+ \GS, so that the effect on marginal revenue is:
GU
G\
=
GS G\
S
+
GS
G\
\
< 0 , it turns out that there are two
contradictory effects. On one side, if the monopolist
produces more, it sells more. On the other side, by
expanding output it lowers the price on all units sold, not
just the extra units produced.
• Using the last expression, the optimality condition can be
re-written as:
1 "
1
−
0 5 0 5 ε 0 5 # = 0 5, where ε 0 5 is the
!
$
05 \
=
S \
\
0& \
\
demand elasticity.
4
• This implies that:
- Since in a competitive market, the firm faces an
horizontal
ε
curve
(infinitely
elastic,
0 5 = ∞ ). Thus the optimality condition is just
=
0 5.
For the monopolist, if ε 0 5 < 1, then 1 ε 0 5 > 1 and
\
S
-
demand
0& \
\
\
so MR is negative, meaning that \ cannot be a
maximising level. It turns out that the monopolist
will never position itself on the inelastic section of
the demand curve, since in this case reducing output
will increase revenues and reduce marginal costs,
thereby raising profits.
- It follows, that profit maximisation will occur
somewhere in the curve where ε
0 5 ≥ 1.
\
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• Suppose that the monopolist faces the following linear
inverse demand curve:
0 5=
S \
D
− E\ . The revenue function is then:
5
0 5= 0 5
U \
S \ \
= D\ − E\ 2 , and the marginal revenue
function is:
0 5=
05 \
D
− 2 E\
• As we have seen previously, the marginal revenue curve
has the same intercept, but twice the slope of the demand
curve.
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3
0&
$&
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slope=-b
05
slope=-2b
4
• The optimal level of output,
\
*
is where the MR curve
crosses the MC curve. The monopolist will charge the
maximum price it can for that level of output,
*
2 7. This
S \
6
costs,
*
2 7
$& \
\
*
*
2 7
S \
yields a revenue
\
*
, from which we subtract total
to get profits.
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• From the optimality condition, we can work out the price
correspondent to the optimal quantity,
\
*
:
*
0 5 = 1 − 1 2ε 0 75 , where 1 − 11ε 0 5 is the
S \
0& \
\
\
PDUNXS
• Since the monopolist is operating where ε
.
0 5 ≥ 1, the
\
mark-up is greater than one, meaning that the price is
greater than MC, a situation that contrasts with that of a
competitive firm.
7KH,PSDFWRI7D[HVRQD0RQRSROLVW
• Consider that a quantity tax is levied on the monopolist,
which has constant MC,
curve,
0 5=
S \
D
F
, and faces a linear demand
− E\ . Clearly, the MC goes up by the
amount of the tax, but what happens to the price?
• The optimality condition is now:
7
D
− 2E\ = F + W . Solving for \, yields:
\
=
D
−F−W
.
2E
Thus, the change in output is:
G\
GW
=−
1
.
2E
Using the demand curve we find that the change in price is
given by:
GS
GW
=D−E
G\
GW
= −E × −
1 1
= .
2E 2
/,1($5'(0$1'$1'7$;$7,21
3
S
’
S
*
0&W
W
0&
05
\
’
\
*
'HPDQG
4
• In graphical terms, this result can be explained by the fact
that, since the demand curve is half as steep as the MR
curve, the price goes up by half the amount of the tax.
8
• This result, however, is not general but stems from
constant MC and the linearity of the demand curve. If, for
example, the monopolist faces a constant-elasticity
demand curve, then we have that:
S
=
GS
GW
+W
, and so,
1−1 ε
=
F
1
, which is greater than one, so that the
1−1 ε
monopolist passes on PRUH than the amount of the tax.
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• Since the monopolist operates where the price is greater
than MC, in general the price will be higher and output
lower than in the competitive market environment. Thus,
consumers are worse-off under monopoly than under
perfect competition.
• In contrast, the firm is better-off under monopoly, as it can
manipulate price to increase profits. This naturally raises
the question of how does the monopoly system compare
with perfect competition for the society as a whole
(consumers + producers). That is, is the monopoly Pareto
efficient?
9
• The answer is NO! And that is because
S
> 0& , meaning
that there is some consumer willing to pay more for an
extra unit of output than it costs to produce. In other
words, if extra output could be sold at a price lower than
the market price, but still higher than MC, the utility of
consumers would increase and so would the profits of the
firm.
• Therefore, the reason why monopoly is not Pareto efficient
is that the monopolist cannot lower the price of the extra
units without lowering the price of all units, which can
lower it profits.
10
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• To ascertain how inefficient monopoly is, we can try to
measure the difference between the consumers’ utility loss
and the producers’ profit gain associated with the change
from monopoly to perfect competition.
• We will do that by measuring the consumers’ and
producers’ surpluses variations and work out the net (or
society) gain from imposing perfect competition to a
monopoly situation.
• The consumer surplus goes up for two reason. First, under
perfect competition they pay less for the units they were
already consuming under monopoly (area A). Second,
11
their utility is boosted by the fact that they are consuming
extra units of the good (area B).
• The producer surplus is affected in contradictory ways.
First, its profits are driven downwards by the fact that it
receives less for the units it was selling under monopoly
(area A). However, because it is selling more, it gets extra
profits (area C).
• The accountancy of the effects can be made as follows:
- The area A is just a transfer of the surplus from the
monopolist to the consumers and so cancels out in
society’s perspective.
- The area B + C represents the net gain from moving
from monopoly to perfect competition, since it
measure the value that consumers and producers
attach to the extra units that are transacted in the
market because of the change from monopoly to
perfect competition.
• Thus, the area B + C measures the deadweight loss due to
the monopoly. This deadweight loss gives the society’s
cost of monopoly and is derived as the value of the
forgone units of output, valued at the price consumers are
willing to pay for it.
12
• Every time the government concedes monopoly rights, it
has to balance the benefits that result form that with the
inevitable deadweight loss that accrues from monopoly.
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• Even though monopoly is inefficient, forcing the
monopolist to equate price to MC will sometimes
determine negative profits. That happens whenever the
demand curve intersects the MC curve beneath the AC
curve.
• This situation often arises with public utilities, such as gas
and electricity companies, motorways, telecommunication
companies, etc.. These companies have huge fixed costs
(in buying and maintaining its equipment) and very low
marginal costs.
• A situation in which the industry presents large fixed costs
and low marginal costs is referred to as
PRQRSRO\
QDWXUDO
. It is so-called because the initial investment are
so huge that they constitute a
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barrier to entry by
competitors.
13
• If the government forces the monopolist to set
S
=
0&
the monopolist goes out of business, which is even more
inefficient than letting the monopolist setting
05
= 0& .
• As far as natural monopolies are concerned, the
government typically has three choices:
D
It either let the
monopolist set the price-quantity combination that
maximises its profits, or
S
=
0&
E
forces the monopolist to set
and gives a lump-sum subsidy in order to make
up for the monopolist losses, or
F
the governments takes
charge of the business itself.
14
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• Under which circumstances should we expect the
market to be organised as a monopoly rather than
competitively?
• The crucial factor is the
PLQLPXP HIILFLHQW VFDOH
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, i.e. the level of output that minimises average
costs, relative to the size of demand. The MES is
determined by the shape of the AC curve, which in turn
depends on the technology.
• If the MES, the level of output that minimises AC is
small relative to the market, the conditions are laid for
many firms to operate within the market. Otherwise, a
situation of monopoly (or oligopoly) may arise.
15
• Since the size of the market can be influenced by
government policy, the emergence of monopolies are
more likely in those countries where the government
pursues
policies
that
restrict
internal/external
competition.
• The government can also force the monopolist to act as
in a competitive market. However, regulation and
intervention also involves costs, implying that the
government has to weight the deadweight loss of
monopoly against the costs of regulation.
• Monopolies can also arise in situations where the
incumbent threats to reduce prices drastically so as to
scare off possible entrants.
• Monopolies or other forms of market-power can also be
created by the strategic interaction of the incumbents,
who might collude to decrease output so to increase the
price and so boost joint profits. In this case, the industry
is organised as a FDUWHO, which is normally unlawful.
16
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• We have described a monopolistic industry as one with a
single large producer. However, defining an industry as
consisting of all firms producing the same product, is
somehow misleading. The fact that only Nokia produces
Nokia mobile phones does not mean that Nokia is a
monopolist.
• In fact, we should view an industry as the set of firms that
produce products that are viewed as close substitutes by
consumers. Each firms has monopoly rights over its brand,
but brands are viewed as substitutes.
• In the case where an industry congregates several firms
producing unique products that are close substitutes, the
demand curve facing the firm depends on the output the
competitors are producing and also on the degree of
substitutability of brands/products.
• If the products are very similar, the demand curve facing
the curve is essentially horizontal, because if the firm
raises its price too much, consumers will cease to buy its
product. The lower the elasticity of substitution between
brands/products, the steeper the demand curve facing the
firm.
17
• Thus, the more successfully the firm is able to do SURGXFW
GLIIHUHQWLDWLRQ
, the higher the market-power it will attain,
as the elasticity of the demand for its brand will be lower.
• The situation we are describing is known as
PRQRSROLVWLF
FRPSHWLWLRQ
, since each firm faces a downward sloping
demand curve and so have some market-power, i.e.
capacity to influence the market price of its own product.
• The monopolistic competitor is a monopolist of its own
product but has to endure the competition of the firms
producing close substitutes. Furthermore, there are no
restrictions to entry.
• Monopolistic competition is the most prevalent form of
industry structure. Bur unfortunately is very difficult to
analyse in abstract terms as it depends on the degree of
product substitution, the strategic interaction of firms, the
institutional environment, etc.
•
But there certain conjectures we can make about the
behaviour of monopolistic competition. More entrants will
necessarily decrease the elasticity of substitution among
products, making the demand curve facing the firm more
horizontal. This implies that as more and more firms enter
the market, profits (in the economic sense) are driven
down to zero.
18
(;7(51$/,7,(6
•
([WHUQDOLW\
can be roughly defined as a situation in which
the actions of one consumer/producer affect third parties
(consumers or producers).
• A
FRQVXPSWLRQ H[WHUQDOLW\
obtains when one consumer
cares directly about another agent’s production or
consumption (e.g. neighbour’s garden). A
H[WHUQDOLW\
SURGXFWLRQ
can be characterised as a situation in which the
production possibilities of one firm are influenced by the
actions of other producers or consumers (e.g. Orchard and
beekeeper).
• The crucial feature of externalities is that they are
goods/services which are valued by people but are not
transacted in the market. Its main problem is therefore that
the equilibrium allocation might not be efficient.
• In what follows, we will concentrate our analysis on the
production
externalities,
since
the
consumption
externalities are less relevant for the topics you will be
working on in this Master.
19
3URGXFWLRQ([WHUQDOLWLHV
• Suppose there are two firms, S and F. Firm S produces
steel, V , and also pollution,
[
, which is dumped into the
river. Its cost function is given by
fishery that catches fish,
I
F
V
( V, [ ) . Firm F is a
, and so is adversely affected by
pollution. Thus, pollution enters the cost function of F,
which is given by, F ( I , [ ).
I
• Assuming, realistically, that pollution decreases the costs
of steel production (over some range) and increases the
cost of producing fish, we have:
∂F
∂F
≤ 0 and
>0
∂[
∂[
I
V
• Now, profit-maximisation problems of firms F and S is
given respectively by:
max S V − F ( V, [ ) and
V [
,
V
max S
I
I
V
I
−F
I
0,5
I
[
• Notice that only firm S has control over the quantity of
pollution produced, even though firm F is affected by it.
This constitutes a typical case of production externalities.
• The optimal conditions for firm S are:
20
S
V
=
∂F
V
2
V
*
, [*
∂V
7 and 0 = ∂ 2
F
V
V
*
, [*
7
∂[
For firm F, the optimum is found where
S
I
=
∂F
I
2
V
*
, [*
7
∂I
• From those conditions we can immediately identify the
source of the problem. Since the price of pollution is
assumed to be zero, pollution will be produced until its
marginal cost is zero. The problem is that, when choosing
[
*
, the firm S is only evaluating its own cost function, in
spite of
[
*
affecting the cost function of F.
• In fact, the increase in the cost of fishing caused by
pollution is part of the
VRFLDO FRVW
of producing steel,
which is not being accounted for. Thus, we would expect
the equilibrium amount of pollution produced to be greater
than the social optimum, meaning that the market is
inefficient.
• To check whether the described situation is efficient or
not, let’s suppose that the two firms merge to jointly
produce steel, fish and eventually pollution. In this case,
there is no externality as the costs of pollution to the
fishing activity has been LQWHUQDOLVHG.
• The merged firm’s profit-maximisation problem is:
21
max S V +
V
S
V
, I ,[
− F (V, [ ) − F
I
I
V
I
0 , 5,
I
[
which yields the following optimality conditions:
S
V
=
∂F
’
V
V
[
∂F
’
2 , 7,
∂V
S
=
I
I
2
I
’
, [’
∂I
7, 0 = ∂ 2 , 7 + ∂ 2
F
V
’
V
[
’
F
∂[
I
firm will take into account the effect of pollution in the
cost function of fish production, i.e. it takes the social cost
of producing steel into account in its optimisation problem.
• What does this imply to the quantity of pollution
produced? Before the merge, firm S was producing
is
0&
6
2
V
*
, [ * = 0 . After the merge the firm
7
producing
− 0&
6
2 , 7=
V
’
[
’
pollution
0&
)
2
I
’
, [’ . Since
7
according
0&
)
2
I
’
to,
, [’ > 0 ,
7
then the firm will be producing pollution in the region
where
0&
6
2 , 7 < 0 . This means that the optimum
V
’
[
’
amount of pollution will be lower after the merge, i.e.
when the
VRFLDO FRVW
’
∂[
• The crucial term is last one as it shows that the merged
according to,
I
is taken into account, pollution is
reduced relative to the situation where the firm only
considers its SULYDWHFRVWV.
22
, [’
7
• Since Pareto efficiency requires the firm to minimise the
social costs where the
VXP
of the MCs is equal to zero, it
turns out that the competitive market is not efficient when
externalities are present.
• Notice that the same would be true if the externality was
positive rather than negative. In that case the optimal
amount of the externality good that would produced in a
private logic would be too small, since the firm would not
take into account the benefit other firms would be reaping.
Price
-MCS
62&,$/&267$1'35,9$7(&267
Socially
optimal
amount
MCF
Privately
optimal
amount
[
’
[
*
Pollution
23
,QWHUSUHWLQJWKH&RQGLWLRQV
There are several interpretations for the conditions of Pareto
efficiency presented above. Each provides a scheme to correct
the efficiency loss due to the presence of externalities.
• The first is that the firm faces the wrong price for
pollution. For the polluting firm, pollution cost nothing,
meaning that the firm is not assuming the social cost it is
generating. Thus, the situation can be corrected by
ensuring that the firm covers that social cost by paying a
tax on pollution.
• If the firm has to pay
W
euros for each quantity of
pollution1, its optimising problem becomes:
max S V − F ( V, [ ) - W[ , and the optimality condition are:
V [
,
S
V
=
V
V
∂F
V
2
V
*
, [*
∂V
7 and
W
=
∂F
V
2
V
*
, [*
7
∂[
• The authorities problem is then to find the value of
W
that
induces the firm to produce the optimum social amount of
pollution.
• Another possible interpretation is that there is a market
missing – the market for pollution. In this market some
1
This kind of tax that corrects an inefficient situation is known as a Pigouvian
tax after the economist named Arthur Pigou.
24
agents would be willing to pay to have the quantity of
pollution produced reduced. Thus, pollution would have a
negative price.
• To illustrate suppose that firm F has the right to a clean
water but has also the right to allow production of
pollution for a certain price. Let that price be
T
. Then the
profit-maximisation problems of both firms would be:
max S V − F ( V, [ ) - T[ and max S
V
V [
,
V
I
,[
I
I
+ T[ − F
I
0,5
I
[
• The optimality conditions are then:
S
V
S
I
=
∂F
=
2
V
V
*
, [*
∂V
∂F
I
2
I
*
7 and
, [*
∂I
T
7 and
=
T
∂F
V
2
V
*
, [*
7
∂[
=
∂F
I
2
I
*
, [*
7
∂[
• Together, these conditions imply that:
T
=−
∂F
V
2
V
*
, [*
∂[
7=∂ 2
F
I
I
*
∂[
, [*
7,
which
can
be
interpreted as saying that the MC to the steel firm of
reducing pollution is equal to the marginal benefit to the
fishery firm of that pollution reduction.
• Again, this situation would produce a Pareto efficient
outcome.
25