Download Monopoly

Outline of Presentation
1. Definition of monopoly.
2. Barriers to entry.
3. Theory of a single price monopoly.
4. Comparative statics: The effect of increasing costs.
5. Monopoly and Welfare.
6. Monopoly and Quality.
7. Price discrimination.
8. Why do natural monopolies exist?
Chapter 14:
Monopoly
Teemu Nyholm
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1. Definition of monopoly
Dictionary:
Exclusive control by one group of the means of producing or
selling a commodity or service.
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2. Barriers to Entry
Definition:
Barriers to entry protect a firm from the competition. The existence
of monopolies is always based on some kind of barriers to entry.
Legal barriers to entry: law, license, patent.
=> Legal Monopoly.
Economics:
The amount of output a monopoly is selling responds
continuously as a function of the price it charges.
• In a competitive markets a firm is a price-taker.
Natural barriers to entry: unique source of supply, economies of
scale, economies of scope.
=> Natural Monopoly.
• In monopolistic market a firm is a price-maker.
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First order condition can be written using elasticity of demand
3. Theory of single price
monopoly
1 
dc( y ) 
= 1 +
 p( y )
dy
 ε ( y) 
Monopoly’s maximization problem:
Monopoly is choosing optimal output in order to maximize
profit.
max p ( y ) y − c( y )
y
I
Monopolist is producing such amount, that marginal
cost equals to marginal revenue.
II
Monopolist is able to sell at a price level, that exceeds its
marginal costs. Thus monopoly price exceeds
competitive-market-price and the amount produced is less.
III
The difference between monopoly price and
competitive-market-price depends on the commodity’s
elasticity of demand.
First and second order conditions:
p ( y ) + p ' ( y ) y − c' ( y ) = 0
2 p ' ( y ) + p' ' ( y ) y − c ' ' ( y ) ≤ 0
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Linear example:
4. Comparative statics
p
The effect of a cost change on price:
MC
p*
dp dp dy
1
=
=
>0
dc dy dc 2 + yp' ' ( y )
p' ( y )
D
Part of a monopoly’s cost increase is passed a long in the
form of increased prices.
MR
y*
y
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5. Monopoly and Welfare
Social objective function:
6. Monopoly and Quality
Let q be product quality and let’s suppose that costs and utility
depend on quality. Social objective function:
W ( x ) = max
u( x ) − c( x )
x
Let x* be the level of monopoly output. Then
W ( x , q ) = u ( x , q ) − c ( x, q )
Let (x*, q*) be monopolist’s profit maximizing points. Then
W ' ( x*) = − u ' ' ( x*) x* > 0
=> x* does not maximize welfare.
IV
∂W ( x*, q*)
∂p ( x*, q*) * 0
x >
=−
∂x
∂x
∂W ( x*, q*)  ∂  u ( x*, q*)  ∂p ( x*, q*)  *
= 
−
 x
∂q
∂q
 ∂q  x * 
Monopolist produces too little output relative to
the social optimum.
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If the derivative of average willingness to pay exceeds
the derivative of marginal willingness to pay for the quality
change, so monopolist’s quality choice will not be optimal
from the social viewpoint.
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7. Price discrimination
Definition:
Price discrimination is the practice of charging some customers a
higher price than others for an identical good or of charging an
individual customer higher price on a small purchase than on a
large one.
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7.1 First-degree price
discrimination
VI
In the perfect price discrimination the price charged for each unit
is equal to the maximum willingness to pay for that unit.
If a firm is perfectly price discriminating, it will choose
to produce a Pareto efficient level of output, that is the
same level as a firm in the competitive markets would
produce. A perfectly price discriminating firm gains all
the surplus from the trade.
Monopolist’s maximizing problem, when perfectly price
discriminating:
max r − cx such that u ( x) ≥ r.
r,x
Let (r*,x*) be the optimal price and amount combination.
Then from f.o.c:
u ' ( x*) = c
r* = u ( x*)
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7.2 Second-degree price
discrimination
Second-degree price discrimination occurs when prices differ
only depending on the number of commodities bought. It is
known as nonlinear pricing.
Let’s suppose two consumers with utility functions u1(x) and
u2(x) for product x such that
u1 ( x ) > u2 ( x) and u '1 ( x ) > u '2 ( x)
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Self-selection constraints:
Consumers choose ( x1, r1=p(x1) x1 ) and ( x2, r2=p(x2) x2 ).
Because they want to consume amount xi and are willing to
pay r1
u1 ( x1 ) − r1 ≥ 0 and u2 ( x2 ) − r2 ≥ 0
And because they prefer their own consumption choice
u1 ( x1 ) − r1 ≥ u1 ( x2 ) − r2
u2 ( x2 ) − r2 ≥ u2 ( x1 ) − r1.
Now monopolist’s optimization problem takes the form
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max r1 + r2 − cx1-cx2
such, that self - selection constraint s hold.
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From the first order conditions
VII
u1 ' ( x1 ) = c + u2 ' ( x1 ) − u1 ' ( x1 ) > c
u2 ' ( x2 ) = c
If a firm is using nonlinear pricing, then the consumer with
the highest demand pays marginal cost and others pays
more. Thus only the consumer with the highest demand
consumes socially efficient amount.
7.3 Third degree price
discrimination
Third-degree price discrimination occurs when consumers are
charged different prices, but each consumer faces a constant price
for all units of output purchased.
Let’s suppose that a firm is price discriminating among two groups
with different demand curves p1(x1) and p2(x2). Now the profit
maximization problem takes the form
max p1 ( x1 ) x1 + p2 ( x2 ) x2 − cx1 − cx2
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The first order conditions:

1 
p1 ( x1 ) + p1 ' ( x1 ) x1 = p1 ( x1 ) 1 −
=c
 ε1 ( x1 ) 

1 
p 2 ( x2 ) + p2 ' ( x2 ) x2 = p2 ( x2 ) 1 −
=c
 ε 2 ( x2 ) 
which implies that
p1( x1 ) > p2 ( x2 ) ⇔ ε1 < ε 2
VIII
If a firm is price discriminating among consumers, then the
consumers with the more elastic demand are charged a
lower price.
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8. Why do natural monopolies
exist?
A natural monopoly exists when a single firm can supply an entire
market with lower costs than can any number of competitive firms.
Definition:
Strict economies of scale in the production of outputs in N are
present if for any initial input -output vector (x1,…,xm;y1,…,yn) and
for any w > 1, there is a feasible input output-vector
(wx1,…,wxm;v1y1,…vnyn) where all vi>w.
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In the case of a single product firm, the existence of scale
economies is sufficient but not necessary condition for natural
monopoly. In the case of a multi-product firm, economies of
scale are neither sufficient condition for natural monopoly.
Definition: Strict and global subadditivity of costs.
C(y) is strictly and globally subadditive in the set of N=1…n
commodities, if for any m output vectors y1, … , ym we have
C(y1 +…+ ym) < C(y1)+…+C(ym).
IX
Strict and global subadditivity is necessary and sufficient
condition for natural monopoly of any output combination
in the industry producing commodities in N.
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