1
Chapter Twenty-Four
Monopoly
垄断
2
Structure
What causes monopoly
Profit-maximizing choices of
monopoly
Markup pricing
Taxing a monopoly
Inefficiency of monopoly
Natural monopoly (自然垄断 )
3
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.
4
Pure Monopoly
Output Level,y
$/output unit
p(y) Higher output y causes alower market price,p(y).
5
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.
6
Pure Monopoly
Suppose that the monopolist seeks
to maximize its economic profit,
What output level y* maximizes
profit?
( ) ( ) ( ).y p y y c y
7
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( ) ( ),?
8
y
$ R(y) = p(y)y
Profit-Maximization
9
$ R(y) = p(y)y
c(y)
Profit-Maximization
y
10
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
(y)
11
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
(y)
y*
12
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
(y)
y*
13
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
(y)
y*
14
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*).
15
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( ) ( ) ( ) ( ),
16
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.
17
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.
18
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
19
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
20
Marginal Cost
F
y
y
c(y) = F + ay + by2
$
MC(y) = a + 2by
$/output unit
a
21
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
22
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
23
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
24
Profit-Maximization; An Example
$/output unit
y
MC(y) = a + 2by
p(y) = a - by
MR(y) = a - 2by
a
a
25
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
26
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
27
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?
28
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
29
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( ) ( )
30
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?
31
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
32
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.
33
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),
1 1?
p y( *) 1 1 0
34
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),
1 1?
p y( *) 1 1 0 1 1 0
35
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
36
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
,
37
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.
38
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?
39
Markup Pricingp y k p y
k k( *) ( *)1 1
1 1 1
is the monopolist’s price.
40
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
41
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.
42
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.
43
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
）,
44
Linear Demand Curve
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
45
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
Linear Demand Curve
46
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
yt
p(yt)
Linear Demand Curve
47
$/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
48
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
49
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
50
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
51
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
52
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.
53
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
54
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
55
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
56
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
57
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
58
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
59
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
60
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
61
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
62
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.
63
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.
64
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.
65
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.
66
Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
67
Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
y* MR(y)
p(y*)
68
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.
69
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.
70
Entry Deterrence by a Natural
Monopoly
y
$/output unit
ATC(y)
MC(y)
DI
DE
p(y),total demand = DI + DE
71
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
72
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,
73
Inefficiency of a Natural Monopolist
Like any profit-maximizing
monopolist,the natural monopolist
causes a deadweight loss.
74
y
$/output unit
ATC(y)
p(y)
y* MR(y)
p(y*)
MC(y)
Inefficiency of a Natural Monopoly
75
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
76
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
77
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?
78
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)
79
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
80
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.
81
Regulating a Natural Monopoly
Average cost pricing
–2nd best solution
–Difficulty,How to measure costs?
Government-ownership
82
y
$/output unit
ATC(y)
MC(y)
p(y)
MR(y) yAC
Average Cost Pricing
PAC
83
Underlying technology
–Minimum efficient scale
Market size
–Openness
Collusion
What Causes Monopolies
84
What Causes Monopolies
AC
y
p
MES
Demand
p?
85
y
Demand
MES
AC
What Causes Monopolies
p?
Chapter Twenty-Four
Monopoly
垄断
2
Structure
What causes monopoly
Profit-maximizing choices of
monopoly
Markup pricing
Taxing a monopoly
Inefficiency of monopoly
Natural monopoly (自然垄断 )
3
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.
4
Pure Monopoly
Output Level,y
$/output unit
p(y) Higher output y causes alower market price,p(y).
5
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.
6
Pure Monopoly
Suppose that the monopolist seeks
to maximize its economic profit,
What output level y* maximizes
profit?
( ) ( ) ( ).y p y y c y
7
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( ) ( ),?
8
y
$ R(y) = p(y)y
Profit-Maximization
9
$ R(y) = p(y)y
c(y)
Profit-Maximization
y
10
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
(y)
11
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
(y)
y*
12
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
(y)
y*
13
Profit-Maximization
$ R(y) = p(y)y
c(y)
y
(y)
y*
14
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*).
15
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( ) ( ) ( ) ( ),
16
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.
17
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.
18
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
19
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
20
Marginal Cost
F
y
y
c(y) = F + ay + by2
$
MC(y) = a + 2by
$/output unit
a
21
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
22
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
23
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
24
Profit-Maximization; An Example
$/output unit
y
MC(y) = a + 2by
p(y) = a - by
MR(y) = a - 2by
a
a
25
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
26
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
27
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?
28
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
29
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( ) ( )
30
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?
31
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
32
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.
33
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),
1 1?
p y( *) 1 1 0
34
Monopolistic Pricing & Own-Price
Elasticity of Demand
Notice that,sinceMR y p y k( *) ( *),
1 1?
p y( *) 1 1 0 1 1 0
35
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
36
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
,
37
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.
38
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?
39
Markup Pricingp y k p y
k k( *) ( *)1 1
1 1 1
is the monopolist’s price.
40
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
41
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.
42
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.
43
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
）,
44
Linear Demand Curve
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
45
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
Linear Demand Curve
46
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
yt
p(yt)
Linear Demand Curve
47
$/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
48
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
49
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
50
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
51
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
52
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.
53
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
ye
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
54
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
55
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
56
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
57
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)
58
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
59
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
60
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
61
The Inefficiency of Monopoly
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*) CS
PS
62
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.
63
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.
64
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.
65
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.
66
Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
67
Natural Monopoly
y
$/output unit
ATC(y)
MC(y)
p(y)
y* MR(y)
p(y*)
68
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.
69
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.
70
Entry Deterrence by a Natural
Monopoly
y
$/output unit
ATC(y)
MC(y)
DI
DE
p(y),total demand = DI + DE
71
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
72
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,
73
Inefficiency of a Natural Monopolist
Like any profit-maximizing
monopolist,the natural monopolist
causes a deadweight loss.
74
y
$/output unit
ATC(y)
p(y)
y* MR(y)
p(y*)
MC(y)
Inefficiency of a Natural Monopoly
75
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
76
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
77
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?
78
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)
79
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
80
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.
81
Regulating a Natural Monopoly
Average cost pricing
–2nd best solution
–Difficulty,How to measure costs?
Government-ownership
82
y
$/output unit
ATC(y)
MC(y)
p(y)
MR(y) yAC
Average Cost Pricing
PAC
83
Underlying technology
–Minimum efficient scale
Market size
–Openness
Collusion
What Causes Monopolies
84
What Causes Monopolies
AC
y
p
MES
Demand
p?
85
y
Demand
MES
AC
What Causes Monopolies
p?
