Chapter Twenty-Four
Monopoly
垄断
Structure
?What causes monopoly
?Profit-maximizing choices of
monopoly
?Markup pricing
?Taxing a monopoly
?Inefficiency of monopoly
?Natural monopoly (自然垄断 )
Pure Monopoly
?A monopolized market has a single
seller.
?The monopolist’s demand curve is
the (downward sloping) market
demand curve.
?So the monopolist can alter the
market price by adjusting its output
level.
Pure Monopoly
Output Level,y
$/output unit
p(y) Higher output y causes alower market price,p(y).
What causes monopolies?
?A legal fiat; e.g,US Postal Service
?A patent; e.g,a new drug
?Sole ownership of a resource; e.g,a
toll highway
?Formation of a cartel; e.g,OPEC
?Large economies of scale; e.g,local
utility companies.
Pure Monopoly
?Suppose that the monopolist seeks
to maximize its economic profit,
?What output level y* maximizes
profit?
? ( ) ( ) ( ).y p y y c y? ?
Profit-Maximization
? ( ) ( ) ( ).y p y y c y? ?
At the profit-maximizing output level y*
? ?d ydy ddy p y y dc ydy? ( ) ( ) ( )? ? ? 0
so,for y = y*,
? ?ddy p y y dc ydy( ) ( ),?
y
$ R(y) = p(y)y
Profit-Maximization
$ R(y) = p(y)y
c(y)
Profit-Maximization
y
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
y*
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
y*
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
y*
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
y*
At the profit-maximizing
output level the slopes of
the revenue and total cost
curves are equal; MR(y*) = MC(y*).
Marginal Revenue
Marginal revenue is the rate-of-change of
revenue as the output level y increases;
? ?MR y ddy p y y p y y dp ydy( ) ( ) ( ) ( ),? ? ?
Marginal Revenue
Marginal revenue is the rate-of-change of
revenue as the output level y increases;
? ?MR y ddy p y y p y y dp ydy( ) ( ) ( ) ( ),? ? ?
dp(y)/dy is the slope of the market inverse
demand function so dp(y)/dy < 0,Therefore
MR y p y y dp ydy p y( ) ( ) ( ) ( )? ? ?
for y > 0.
Marginal Revenue
E.g,if p(y) = a - by then
R(y) = p(y)y = ay - by2
and so
MR(y) = a - 2by < a - by = p(y) for y > 0.
Marginal Revenue
E.g,if p(y) = a - by then
R(y) = p(y)y = ay - by2
and so
MR(y) = a - 2by < a - by = p(y) for y > 0.
p(y) = a - bya
ya/b
MR(y) = a - 2by
a/2b
Marginal Cost
Marginal cost is the rate-of-change of total
cost as the output level y increases;
MC y dc ydy( ) ( ),?
E.g,if c(y) = F + ay + by2 then
MC y y( ),? ?a b2
Marginal Cost
F
y
y
c(y) = F + ay + by2
$
MC(y) = a + 2by
$/output unit
a
Profit-Maximization; An Example
At the profit-maximizing output level y*,
MR(y*) = MC(y*),So if p(y) = a - by and
c(y) = F + ay + by2 then
MR y a by y MC y( *) * * ( *)? ? ? ? ?2 2a b
Profit-Maximization; An Example
At the profit-maximizing output level y*,
MR(y*) = MC(y*),So if p(y) = a - by and if
c(y) = F + ay + by2 then
MR y a by y MC y( *) * * ( *)? ? ? ? ?2 2a b
and the profit-maximizing output level is y a
b* ( )?
?
?
a
b2
Profit-Maximization; An Example
At the profit-maximizing output level y*,
MR(y*) = MC(y*),So if p(y) = a - by and if
c(y) = F + ay + by2 then
MR y a by y MC y( *) * * ( *)? ? ? ? ?2 2a b
and the profit-maximizing output level is y a
b* ( )?
?
?
a
b2
causing the market price to bep y a by a b a
b( *) * ( ),? ? ? ?
?
?
a
b2
Profit-Maximization; An Example
$/output unit
y
MC(y) = a + 2by
p(y) = a - by
MR(y) = a - 2by
a
a
Profit-Maximization; An Example
$/output unit
y
MC(y) = a + 2by
p(y) = a - by
MR(y) = a - 2by
y
a
b
*
( )
?
?
?
a
b2
a
a
Profit-Maximization; An Example
$/output unit
y
MC(y) = a + 2by
p(y) = a - by
MR(y) = a - 2by
y
a
b
*
( )
?
?
?
a
b2
p y
a b a
b
( *)
( )
?
? ?
?
a
b2
a
a
Monopolistic Pricing & Own-Price
Elasticity of Demand
?Suppose that market demand
becomes less sensitive to changes in
price (i.e,the own-price elasticity of
demand becomes less negative),
Does the monopolist exploit this by
causing the market price to rise?
Monopolistic Pricing & Own-Price
Elasticity of Demand
? ?MR y
d
dy
p y y p y y
dp y
dy
p y
y
p y
dp y
dy
( ) ( ) ( )
( )
( )
( )
( )
.
? ? ?
? ?
?
?
?
?
?
?
1
Monopolistic Pricing & Own-Price
Elasticity of Demand
? ?MR y
d
dy
p y y p y y
dp y
dy
p y
y
p y
dp y
dy
( ) ( ) ( )
( )
( )
( )
( )
.
? ? ?
? ?
?
?
?
?
?
?
1
Own-price elasticity of demand is
? ? p yy dydp y( ) ( )
Monopolistic Pricing & Own-Price
Elasticity of Demand
? ?MR y
d
dy
p y y p y y
dp y
dy
p y
y
p y
dp y
dy
( ) ( ) ( )
( )
( )
( )
( )
.
? ? ?
? ?
?
?
?
?
?
?
1
Own-price elasticity of demand is
? ? p yy dydp y( ) ( )so MR y p y( ) ( ),? ??
??
?
??
1 1?
Monopolistic Pricing & Own-Price
Elasticity of Demand
MR y p y( ) ( ),? ??
??
?
??
1 1?
Suppose the monopolist’s marginal cost of
production is constant,at $k/output unit.
For a profit-maximum
MR y p y k( *) ( *)? ??
??
?
??
?1 1?which isp y
k
( *),?
?1
1
?
Monopolistic Pricing & Own-Price
Elasticity of Demandp y k( *),?
?1
1
?
E.g,if ? = -3 then p(y*) = 3k/2,
and if ? = -2 then p(y*) = 2k,
So as ? rises towards -1 the monopolist
alters its output level to make the market
price of its product to rise.
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0??
??
?
??
??
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0 1 1 0??
??
?
??
? ? ? ?? ?
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0 1 1 0??
??
?
??
? ? ? ?? ?
That is,
1 1
? ? ?
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0 1 1 0??
??
?
??
? ? ? ?? ?
That is,
1 1 1
? ?? ? ? ? ?,
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0 1 1 0??
??
?
??
? ? ? ?? ?
That is,
1 1 1
? ?? ? ? ? ?,
So a profit-maximizing monopolist always
selects an output level for which market
demand is own-price elastic.
Markup Pricing
?Markup pricing,Output price is the
marginal cost of production plus a
“markup.”
?How big is a monopolist’s markup
and how does it change with the
own-price elasticity of demand?
Markup Pricingp y k p y
k k( *) ( *)1 1
1 1 1
??
??
?
??
? ? ?
?
?
??
?
?
?
is the monopolist’s price.
Markup Pricingp y k p y
k k( *) ( *)1 1
1 1 1
??
??
?
??
? ? ?
?
?
??
?
?
?
is the monopolist’s price,The markup is
p y k k k k( *),? ? ? ? ? ? ?? ? ?1 1
Markup Pricingp y k p y
k k( *) ( *)1 1
1 1 1
??
??
?
??
? ? ?
?
?
??
?
?
?
is the monopolist’s price,The markup is
p y k k k k( *),? ? ? ? ? ? ?? ? ?1 1
E.g,if ? = -3 then the markup is k/2,
and if ? = -2 then the markup is k,
The markup rises as the own-price
elasticity of demand rises towards -1.
A Profits Tax Levied on a Monopoly
?A profits tax levied at rate t reduces
profit from ?(y*) to (1-t)?(y*).
?Q,How is after-tax profit,(1-t)?(y*),
maximized?
?A,By maximizing before-tax profit,?(y*).
?So a profits tax has no effect on the
monopolist’s choices of output level,
output price,or demands for inputs.
?I.e,the profits tax is a neutral tax.
Quantity Tax Levied on a Monopolist
?A quantity tax of $t/output unit raises
the marginal cost of production by $t.
?So the tax reduces the profit-
maximizing output level,causes the
market price to rise,and input
demands to fall.
?The quantity tax is distortionary（ 扭曲
）,
Linear Demand Curve
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
Linear Demand Curve
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
yt
p(yt)
Linear Demand Curve
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
yt
p(yt)
The quantity tax causes a drop
in the output level,a rise in the
output’s price and a decline in
demand for inputs.
Linear Demand Curve
? p=a-by
? MR=a-2by
? With tax,MC=c+t
? Profit maximization,a-2by=c+t
y=(a-c-t)/2b
p(y)=a-by=a-(a-c-t)/2
? dp/dt=1/2
? The monopolist passes on half of the tax.
Linear Demand Curve
Constant Elasticity Demand
?Can a monopolist,pass” all of a $t
quantity tax to the consumers?
?Suppose the marginal cost of
production is constant at $k/output
unit.
?With no tax,the monopolist’s price is
p y k( *),? ???1
?The tax increases marginal cost to
$(k+t)/output unit,changing the
profit-maximizing price to
?The amount of the tax paid by buyers
is
p y k tt( ) ( ),? ?? ??1
p y p yt( ) ( * ),?
Constant Elasticity Demand
p y p y k t k tt( ) ( *) ( )? ? ?? ? ? ? ??? ? ? ? ?1 1 1
is the amount of the tax passed on to
buyers,E.g,if ? = -2,the amount of
the tax passed on is 2t.
Because ? < -1,? /?1??) > 1 and so the
monopolist passes on to consumers more
than the tax!
Constant Elasticity Demand
The Inefficiency of Monopoly
?A market is Pareto efficient if it
achieves the maximum possible total
gains-to-trade.
?Otherwise a market is Pareto
inefficient.
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
CS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
Total gains-to-trade is
maximized.CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
MC(y*+1) < p(y*+1) so both
seller and buyer could gain
if the (y*+1)th unit of output
was produced,Hence the
market
is Pareto inefficient.
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
DWL
Deadweight loss measures
the gains-to-trade not
achieved by the market.
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
ye
p(ye) DWL
The monopolist produces
less than the efficient
quantity,making the
market price exceed the
efficient market
price.
Natural Monopoly
?A natural monopoly arises when the
firm’s technology has economies-of-
scale （ 规模经济） large enough for it
to supply the whole market at a lower
average total production cost than is
possible with more than one firm in
the market.
Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
y* MR(y)
p(y*)
Entry Deterrence by a Natural
Monopoly
?A natural monopoly deters entry by
threatening predatory pricing （ 掠夺性
定价） against an entrant.
?A predatory price is a low price set by
the incumbent firm when an entrant
appears,causing the entrant’s
economic profits to be negative and
inducing its exit.
Entry Deterrence by a Natural
Monopoly
?E.g,suppose an entrant initially
captures one-quarter of the market,
leaving the incumbent firm the other
three-quarters.
Entry Deterrence by a Natural
Monopoly
y
$/output unit
ATC(y)
MC(y)
DI
DE
p(y),total demand = DI + DE
Entry Deterrence by a Natural
Monopoly
y
$/output unit
ATC(y)
MC(y)
DI
DE
pE
p(y*)
An entrant can undercut the
incumbent’s price p(y*) but,..
p(y),total demand = DI + DE
Entry Deterrence by a Natural
Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y),total demand = DI + DE
DI
DE
pE
pI
p(y*)
An entrant can undercut the
incumbent’s price p(y*) but
the incumbent can then
lower its price as far
as pI,forcing
the entrant
to exit,
Inefficiency of a Natural Monopolist
?Like any profit-maximizing
monopolist,the natural monopolist
causes a deadweight loss.
y
$/output unit
ATC(y)
p(y)
y* MR(y)
p(y*)
MC(y)
Inefficiency of a Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
y* MR(y)
p(y*)
p(ye)
ye
Profit-max,MR(y) = MC(y)
Efficiency,p = MC(y)
Inefficiency of a Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
y* MR(y)
p(y*)
p(ye)
ye
Profit-max,MR(y) = MC(y)
Efficiency,p = MC(y)
DWL
Inefficiency of a Natural Monopoly
Regulating a Natural Monopoly
?Why not command that a natural
monopoly produce the efficient
amount of output?
?Then the deadweight loss will be
zero,won’t it?
y
$/output unit
ATC(y)
MC(y)
p(y)
MR(y)
p(ye)
ye
Regulating a Natural Monopoly
At the efficient output
level ye,ATC(ye) > p(ye)
ATC(ye)
y
$/output unit
ATC(y)
MC(y)
p(y)
MR(y)
p(ye)
ye
Regulating a Natural Monopoly
At the efficient output
level ye,ATC(ye) > p(ye)
so the firm makes an
economic loss.
ATC(ye) Economic loss
Regulating a Natural Monopoly
?So a natural monopoly cannot be
forced to use marginal cost pricing,
Doing so makes the firm exit,
destroying both the market and any
gains-to-trade.
?Regulatory schemes can induce the
natural monopolist to produce the
efficient output level without exiting.
Regulating a Natural Monopoly
?Average cost pricing
–2nd best solution
–Difficulty,How to measure costs?
?Government-ownership
y
$/output unit
ATC(y)
MC(y)
p(y)
MR(y) yAC
Average Cost Pricing
PAC
?Underlying technology
–Minimum efficient scale
?Market size
–Openness
?Collusion
What Causes Monopolies
What Causes Monopolies
AC
y
p
MES
Demand
p?
y
Demand
MES
AC
What Causes Monopolies
p?
Monopoly
垄断
Structure
?What causes monopoly
?Profit-maximizing choices of
monopoly
?Markup pricing
?Taxing a monopoly
?Inefficiency of monopoly
?Natural monopoly (自然垄断 )
Pure Monopoly
?A monopolized market has a single
seller.
?The monopolist’s demand curve is
the (downward sloping) market
demand curve.
?So the monopolist can alter the
market price by adjusting its output
level.
Pure Monopoly
Output Level,y
$/output unit
p(y) Higher output y causes alower market price,p(y).
What causes monopolies?
?A legal fiat; e.g,US Postal Service
?A patent; e.g,a new drug
?Sole ownership of a resource; e.g,a
toll highway
?Formation of a cartel; e.g,OPEC
?Large economies of scale; e.g,local
utility companies.
Pure Monopoly
?Suppose that the monopolist seeks
to maximize its economic profit,
?What output level y* maximizes
profit?
? ( ) ( ) ( ).y p y y c y? ?
Profit-Maximization
? ( ) ( ) ( ).y p y y c y? ?
At the profit-maximizing output level y*
? ?d ydy ddy p y y dc ydy? ( ) ( ) ( )? ? ? 0
so,for y = y*,
? ?ddy p y y dc ydy( ) ( ),?
y
$ R(y) = p(y)y
Profit-Maximization
$ R(y) = p(y)y
c(y)
Profit-Maximization
y
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
y*
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
y*
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
y*
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
?(y)
y*
At the profit-maximizing
output level the slopes of
the revenue and total cost
curves are equal; MR(y*) = MC(y*).
Marginal Revenue
Marginal revenue is the rate-of-change of
revenue as the output level y increases;
? ?MR y ddy p y y p y y dp ydy( ) ( ) ( ) ( ),? ? ?
Marginal Revenue
Marginal revenue is the rate-of-change of
revenue as the output level y increases;
? ?MR y ddy p y y p y y dp ydy( ) ( ) ( ) ( ),? ? ?
dp(y)/dy is the slope of the market inverse
demand function so dp(y)/dy < 0,Therefore
MR y p y y dp ydy p y( ) ( ) ( ) ( )? ? ?
for y > 0.
Marginal Revenue
E.g,if p(y) = a - by then
R(y) = p(y)y = ay - by2
and so
MR(y) = a - 2by < a - by = p(y) for y > 0.
Marginal Revenue
E.g,if p(y) = a - by then
R(y) = p(y)y = ay - by2
and so
MR(y) = a - 2by < a - by = p(y) for y > 0.
p(y) = a - bya
ya/b
MR(y) = a - 2by
a/2b
Marginal Cost
Marginal cost is the rate-of-change of total
cost as the output level y increases;
MC y dc ydy( ) ( ),?
E.g,if c(y) = F + ay + by2 then
MC y y( ),? ?a b2
Marginal Cost
F
y
y
c(y) = F + ay + by2
$
MC(y) = a + 2by
$/output unit
a
Profit-Maximization; An Example
At the profit-maximizing output level y*,
MR(y*) = MC(y*),So if p(y) = a - by and
c(y) = F + ay + by2 then
MR y a by y MC y( *) * * ( *)? ? ? ? ?2 2a b
Profit-Maximization; An Example
At the profit-maximizing output level y*,
MR(y*) = MC(y*),So if p(y) = a - by and if
c(y) = F + ay + by2 then
MR y a by y MC y( *) * * ( *)? ? ? ? ?2 2a b
and the profit-maximizing output level is y a
b* ( )?
?
?
a
b2
Profit-Maximization; An Example
At the profit-maximizing output level y*,
MR(y*) = MC(y*),So if p(y) = a - by and if
c(y) = F + ay + by2 then
MR y a by y MC y( *) * * ( *)? ? ? ? ?2 2a b
and the profit-maximizing output level is y a
b* ( )?
?
?
a
b2
causing the market price to bep y a by a b a
b( *) * ( ),? ? ? ?
?
?
a
b2
Profit-Maximization; An Example
$/output unit
y
MC(y) = a + 2by
p(y) = a - by
MR(y) = a - 2by
a
a
Profit-Maximization; An Example
$/output unit
y
MC(y) = a + 2by
p(y) = a - by
MR(y) = a - 2by
y
a
b
*
( )
?
?
?
a
b2
a
a
Profit-Maximization; An Example
$/output unit
y
MC(y) = a + 2by
p(y) = a - by
MR(y) = a - 2by
y
a
b
*
( )
?
?
?
a
b2
p y
a b a
b
( *)
( )
?
? ?
?
a
b2
a
a
Monopolistic Pricing & Own-Price
Elasticity of Demand
?Suppose that market demand
becomes less sensitive to changes in
price (i.e,the own-price elasticity of
demand becomes less negative),
Does the monopolist exploit this by
causing the market price to rise?
Monopolistic Pricing & Own-Price
Elasticity of Demand
? ?MR y
d
dy
p y y p y y
dp y
dy
p y
y
p y
dp y
dy
( ) ( ) ( )
( )
( )
( )
( )
.
? ? ?
? ?
?
?
?
?
?
?
1
Monopolistic Pricing & Own-Price
Elasticity of Demand
? ?MR y
d
dy
p y y p y y
dp y
dy
p y
y
p y
dp y
dy
( ) ( ) ( )
( )
( )
( )
( )
.
? ? ?
? ?
?
?
?
?
?
?
1
Own-price elasticity of demand is
? ? p yy dydp y( ) ( )
Monopolistic Pricing & Own-Price
Elasticity of Demand
? ?MR y
d
dy
p y y p y y
dp y
dy
p y
y
p y
dp y
dy
( ) ( ) ( )
( )
( )
( )
( )
.
? ? ?
? ?
?
?
?
?
?
?
1
Own-price elasticity of demand is
? ? p yy dydp y( ) ( )so MR y p y( ) ( ),? ??
??
?
??
1 1?
Monopolistic Pricing & Own-Price
Elasticity of Demand
MR y p y( ) ( ),? ??
??
?
??
1 1?
Suppose the monopolist’s marginal cost of
production is constant,at $k/output unit.
For a profit-maximum
MR y p y k( *) ( *)? ??
??
?
??
?1 1?which isp y
k
( *),?
?1
1
?
Monopolistic Pricing & Own-Price
Elasticity of Demandp y k( *),?
?1
1
?
E.g,if ? = -3 then p(y*) = 3k/2,
and if ? = -2 then p(y*) = 2k,
So as ? rises towards -1 the monopolist
alters its output level to make the market
price of its product to rise.
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0??
??
?
??
??
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0 1 1 0??
??
?
??
? ? ? ?? ?
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0 1 1 0??
??
?
??
? ? ? ?? ?
That is,
1 1
? ? ?
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0 1 1 0??
??
?
??
? ? ? ?? ?
That is,
1 1 1
? ?? ? ? ? ?,
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),? ?
?
??
?
??
?1 1?
p y( *) 1 1 0 1 1 0??
??
?
??
? ? ? ?? ?
That is,
1 1 1
? ?? ? ? ? ?,
So a profit-maximizing monopolist always
selects an output level for which market
demand is own-price elastic.
Markup Pricing
?Markup pricing,Output price is the
marginal cost of production plus a
“markup.”
?How big is a monopolist’s markup
and how does it change with the
own-price elasticity of demand?
Markup Pricingp y k p y
k k( *) ( *)1 1
1 1 1
??
??
?
??
? ? ?
?
?
??
?
?
?
is the monopolist’s price.
Markup Pricingp y k p y
k k( *) ( *)1 1
1 1 1
??
??
?
??
? ? ?
?
?
??
?
?
?
is the monopolist’s price,The markup is
p y k k k k( *),? ? ? ? ? ? ?? ? ?1 1
Markup Pricingp y k p y
k k( *) ( *)1 1
1 1 1
??
??
?
??
? ? ?
?
?
??
?
?
?
is the monopolist’s price,The markup is
p y k k k k( *),? ? ? ? ? ? ?? ? ?1 1
E.g,if ? = -3 then the markup is k/2,
and if ? = -2 then the markup is k,
The markup rises as the own-price
elasticity of demand rises towards -1.
A Profits Tax Levied on a Monopoly
?A profits tax levied at rate t reduces
profit from ?(y*) to (1-t)?(y*).
?Q,How is after-tax profit,(1-t)?(y*),
maximized?
?A,By maximizing before-tax profit,?(y*).
?So a profits tax has no effect on the
monopolist’s choices of output level,
output price,or demands for inputs.
?I.e,the profits tax is a neutral tax.
Quantity Tax Levied on a Monopolist
?A quantity tax of $t/output unit raises
the marginal cost of production by $t.
?So the tax reduces the profit-
maximizing output level,causes the
market price to rise,and input
demands to fall.
?The quantity tax is distortionary（ 扭曲
）,
Linear Demand Curve
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
Linear Demand Curve
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
yt
p(yt)
Linear Demand Curve
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
yt
p(yt)
The quantity tax causes a drop
in the output level,a rise in the
output’s price and a decline in
demand for inputs.
Linear Demand Curve
? p=a-by
? MR=a-2by
? With tax,MC=c+t
? Profit maximization,a-2by=c+t
y=(a-c-t)/2b
p(y)=a-by=a-(a-c-t)/2
? dp/dt=1/2
? The monopolist passes on half of the tax.
Linear Demand Curve
Constant Elasticity Demand
?Can a monopolist,pass” all of a $t
quantity tax to the consumers?
?Suppose the marginal cost of
production is constant at $k/output
unit.
?With no tax,the monopolist’s price is
p y k( *),? ???1
?The tax increases marginal cost to
$(k+t)/output unit,changing the
profit-maximizing price to
?The amount of the tax paid by buyers
is
p y k tt( ) ( ),? ?? ??1
p y p yt( ) ( * ),?
Constant Elasticity Demand
p y p y k t k tt( ) ( *) ( )? ? ?? ? ? ? ??? ? ? ? ?1 1 1
is the amount of the tax passed on to
buyers,E.g,if ? = -2,the amount of
the tax passed on is 2t.
Because ? < -1,? /?1??) > 1 and so the
monopolist passes on to consumers more
than the tax!
Constant Elasticity Demand
The Inefficiency of Monopoly
?A market is Pareto efficient if it
achieves the maximum possible total
gains-to-trade.
?Otherwise a market is Pareto
inefficient.
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
CS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
Total gains-to-trade is
maximized.CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
MC(y*+1) < p(y*+1) so both
seller and buyer could gain
if the (y*+1)th unit of output
was produced,Hence the
market
is Pareto inefficient.
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
DWL
Deadweight loss measures
the gains-to-trade not
achieved by the market.
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
ye
p(ye) DWL
The monopolist produces
less than the efficient
quantity,making the
market price exceed the
efficient market
price.
Natural Monopoly
?A natural monopoly arises when the
firm’s technology has economies-of-
scale （ 规模经济） large enough for it
to supply the whole market at a lower
average total production cost than is
possible with more than one firm in
the market.
Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
y* MR(y)
p(y*)
Entry Deterrence by a Natural
Monopoly
?A natural monopoly deters entry by
threatening predatory pricing （ 掠夺性
定价） against an entrant.
?A predatory price is a low price set by
the incumbent firm when an entrant
appears,causing the entrant’s
economic profits to be negative and
inducing its exit.
Entry Deterrence by a Natural
Monopoly
?E.g,suppose an entrant initially
captures one-quarter of the market,
leaving the incumbent firm the other
three-quarters.
Entry Deterrence by a Natural
Monopoly
y
$/output unit
ATC(y)
MC(y)
DI
DE
p(y),total demand = DI + DE
Entry Deterrence by a Natural
Monopoly
y
$/output unit
ATC(y)
MC(y)
DI
DE
pE
p(y*)
An entrant can undercut the
incumbent’s price p(y*) but,..
p(y),total demand = DI + DE
Entry Deterrence by a Natural
Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y),total demand = DI + DE
DI
DE
pE
pI
p(y*)
An entrant can undercut the
incumbent’s price p(y*) but
the incumbent can then
lower its price as far
as pI,forcing
the entrant
to exit,
Inefficiency of a Natural Monopolist
?Like any profit-maximizing
monopolist,the natural monopolist
causes a deadweight loss.
y
$/output unit
ATC(y)
p(y)
y* MR(y)
p(y*)
MC(y)
Inefficiency of a Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
y* MR(y)
p(y*)
p(ye)
ye
Profit-max,MR(y) = MC(y)
Efficiency,p = MC(y)
Inefficiency of a Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
y* MR(y)
p(y*)
p(ye)
ye
Profit-max,MR(y) = MC(y)
Efficiency,p = MC(y)
DWL
Inefficiency of a Natural Monopoly
Regulating a Natural Monopoly
?Why not command that a natural
monopoly produce the efficient
amount of output?
?Then the deadweight loss will be
zero,won’t it?
y
$/output unit
ATC(y)
MC(y)
p(y)
MR(y)
p(ye)
ye
Regulating a Natural Monopoly
At the efficient output
level ye,ATC(ye) > p(ye)
ATC(ye)
y
$/output unit
ATC(y)
MC(y)
p(y)
MR(y)
p(ye)
ye
Regulating a Natural Monopoly
At the efficient output
level ye,ATC(ye) > p(ye)
so the firm makes an
economic loss.
ATC(ye) Economic loss
Regulating a Natural Monopoly
?So a natural monopoly cannot be
forced to use marginal cost pricing,
Doing so makes the firm exit,
destroying both the market and any
gains-to-trade.
?Regulatory schemes can induce the
natural monopolist to produce the
efficient output level without exiting.
Regulating a Natural Monopoly
?Average cost pricing
–2nd best solution
–Difficulty,How to measure costs?
?Government-ownership
y
$/output unit
ATC(y)
MC(y)
p(y)
MR(y) yAC
Average Cost Pricing
PAC
?Underlying technology
–Minimum efficient scale
?Market size
–Openness
?Collusion
What Causes Monopolies
What Causes Monopolies
AC
y
p
MES
Demand
p?
y
Demand
MES
AC
What Causes Monopolies
p?
