Transcript p(y)

Chapter 24
Monopoly
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.

2
Pure Monopoly
$/output unit
p(y)
Higher output y causes a
lower market price, p(y).
Output Level, y
3
Why Monopolies?

Some examples:
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.
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Pure Monopoly

Suppose that the monopolist seeks to maximize
its economic profit,
( y)  p( y)y  c( y).

What output level y* maximizes profit?
5
Profit-Maximization
( y)  p( y)y  c( y).
At the profit-maximizing output level y*
d( y) d
dc( y)

0
p( y)y 
dy
dy
dy
so, for y = y*,
d
dc( y)
.
p( y)y 
dy
dy
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Profit-Maximization

At the profit-maximizing output level the slopes
of the revenue and total cost curves are equal:
MR(y*) = MC(y*).
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Marginal Revenue
Marginal revenue is the rate-of-change of revenue
as the output level y increases:
d
dp( y)
MR( y) 
.
p( y)y  p( y)  y
dy
dy
dp(y)/dy is the slope of the market inverse
demand function so dp(y)/dy < 0. Therefore
dp( y)
MR( y)  p( y)  y
 p( y)
dy
for y > 0.
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Marginal Revenue
E.g. if p(y) = a - by then
R(y) = p(y)y = ay - by2
and therefore
MR(y) = a - 2by < a - by = p(y) for y > 0.
a
p(y) = a - by
a/2b
a/b y
MR(y) = a - 2by
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Marginal Cost
Marginal cost is the rate-of-change of total cost
as the output level y increases;
dc( y)
MC( y) 
.
dy
E.g. if c(y) = F + ay + by2 then
MC( y)  a  2by.
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Marginal Cost
$
c(y) = F + ay + by2
F
$/output unit
y
MC(y) = a + 2by
a
y
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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  2by*  a  2by*  MC( y*)
and the profit-maximizing output level is
aa
y* 
2(b  b )
causing the market price to be
aa
p( y*)  a  by*  a  b
.
2(b  b )
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Profit-Maximization;
An
Example
$/output unit
a
p(y) = a - by
MC(y) = a + 2by
a
y
MR(y) = a - 2by
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Profit-Maximization;
An
Example
$/output unit
a
p(y) = a - by
MC(y) = a + 2by
a
y* 
aa
2(b  b )
y
MR(y) = a - 2by
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Profit-Maximization;
An
Example
$/output unit
a
p(y) = a - by
p( y*) 
aa
ab
2(b  b )
MC(y) = a + 2by
a
y* 
aa
2(b  b )
y
MR(y) = a - 2by
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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?
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Monopolistic Pricing & Own-Price
Elasticity of Demand
d
dp( y)
MR( y) 
p( y)y  p( y)  y
dy
dy
y dp( y) 

 p( y) 1 
.

 p( y) dy 
Own-price elasticity of demand is
p( y) dy
1

so MR( y)  p( y) 1  .

  
y dp( y)
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Monopolistic Pricing & Own-Price
Elasticity of Demand
1

MR( y)  p( y) 1   .
 
Suppose the monopolist’s marginal cost of
production is constant, at $k/output unit. For
a profit-maximum
1

MR( y*)  p( y*) 1    k


which is
k
p( y*) 
.
1
1

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Monopolistic Pricing & Own-Price
Elasticity of Demand
p( 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.
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Monopolistic Pricing & Own-Price
Elasticity of Demand
 1
Notice that, since MR ( y*)  p( y*)1    k ,
 
1
1

p( y*) 1    0  1   0



1
 1    1.
That is,

So a profit-maximizing monopolist always selects
an output level for which market demand is
own-price elastic.
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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?

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Markup Pricing
1

p( y*) 1    k



k
p( y*) 

1 1 
1

k
is the monopolist’s price. The markup is
k
k
p( y*)  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.
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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.

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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.

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Quantity Tax Levied on a
Monopolist
$/output unit
p(y)
p(y*)
MC(y)
y
y*
MR(y)
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Quantity Tax Levied on a
Monopolist
$/output unit
p(y)
MC(y) + t
p(y*)
t
MC(y)
y
y*
MR(y)
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Quantity Tax Levied on a
Monopolist
$/output unit
p(y)
p(yt)
p(y*)
MC(y) + t
t
MC(y)
y
yt y*
MR(y)
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Quantity Tax Levied on a
Monopolist The quantity tax causes a drop
$/output unit
p(y)
p(yt)
p(y*)
yt y*
in the output level, a rise in the
output’s price and a decline in
demand for inputs.
MC(y) + t
t
MC(y)
MR(y)
y
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Linear Demand
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.

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Linear Demand
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Constant Elasticity Demand
Can a monopolist “pass” all of a $t quantity tax
to the consumers in the case of constant
elasticity demand?
 Suppose the marginal cost of production is
constant at $k/output unit.
 With no tax, the monopolist’s price is

k
p( y*) 
.
1 
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Constant Elasticity Demand

The tax increases marginal cost to
$(k+t)/output unit, changing the profitmaximizing price to
(k  t ) 
p( y ) 
.
1 
t

The amount of the tax paid by buyers is
p( yt )  p( y*).
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Constant Elasticity Demand
(k  t ) 
k
t
p( y )  p( y*) 


1 
1  1 
t
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!
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The Inefficiency of Monopoly
Social welfare=consumer surplus+ producer
surplus
 A market is Pareto efficient if it achieves the
maximum possible total gains-to-trade (i.e.
social welfare).
 Otherwise a market is Pareto inefficient.

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The
Inefficiency
of
Monopoly
$/output unit
The efficient output level
ye satisfies p(y) = MC(y).
p(y)
MC(y)
p(ye)
ye
y
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The
Inefficiency
of
Monopoly
$/output unit
The efficient output level
ye satisfies p(y) = MC(y).
p(y)
CS
MC(y)
p(ye)
ye
y
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The
Inefficiency
of
Monopoly
$/output unit
The efficient output level
ye satisfies p(y) = MC(y).
p(y)
CS
p(ye)
MC(y)
PS
ye
y
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The
Inefficiency
of
Monopoly
$/output unit
p(y)
CS
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
Total gains-to-trade is
maximized.
MC(y)
PS
ye
y
38
The
Inefficiency
of
Monopoly
$/output unit
p(y)
p(y*)
MC(y)
y
y*
MR(y)
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The
Inefficiency
of
Monopoly
$/output unit
p(y)
p(y*)
CS
MC(y)
y
y*
MR(y)
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The
Inefficiency
of
Monopoly
$/output unit
p(y)
p(y*)
CS
MC(y)
PS
y
y*
MR(y)
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The
Inefficiency
of
Monopoly
$/output unit
p(y)
p(y*)
CS
MC(y)
PS
y
y*
MR(y)
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The
Inefficiency
of
Monopoly
$/output unit
p(y)
p(y*)
CS
MC(y)
PS
y
y*
MR(y)
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The
Inefficiency
of
Monopoly
$/output unit
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
MC(y)market
is Pareto inefficient.
p(y)
p(y*)
CS
PS
y
y*
MR(y)
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The
Inefficiency
of
Monopoly
$/output unit
Deadweight loss measures
the gains-to-trade not
achieved by the market.
p(y)
p(y*)
MC(y)
DWL
y
y*
MR(y)
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The
Inefficiency
of
Monopoly
$/output unit
The monopolist produces less
than the efficient quantity,
making the market price exceed
the efficient market price.
p(y)
p(y*)
p(ye)
MC(y)
DWL
y*
y
ye
MR(y)
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Natural Monopoly
A natural monopoly occurs when a firm cannot
operate at an efficient level of output without
losing money.
 When there are large fixed costs and small
marginal costs, you can easily get the kind of
situation described above.
 Many public utilities are natural monopolies of
this sort.

47
Natural Monopoly
48
Inefficiency of a Natural Monopoly
Like any profit-maximizing monopolist, the
natural monopolist causes a deadweight loss.
 If allowing a natural monopolist to set the
monopoly price is undesirable due to the Pareto
inefficiency, and forcing the natural monopoly
to produce at the competitive price is infeasible
due to negative profits, what is left?
 For the most part natural monopolies are
regulated or operated by governments.

49
Natural Monopoly: Solutions
Pricing policy: Set the prices that just allow the
firm to break even – produce at a point where
price equals average costs. But it is difficult to
determine the true costs of the firm…
 The other solution is to let the government
operate it at price equals marginal cost and
provide a lump-sum subsidy to keep the firm in
operation.

50
What Causes Monopolies?

1. Nature of technology.
If the minimum efficient scale (MES) is large
relative to demand, then the market is likely to
be monopolized. But if the MES is small
relative to demand, there is room for many
firms in the industry, and there is a hope for a
competitive market structure.
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What Causes Monopolies?
52
What Causes Monopolies?

2. Cartel.
Several different firms in an industry might be
able to collude and restrict output in order to
raise prices and thereby increase their profits.
When firms collude in this way and attempt to
reduce output and increase price, we say the
industry is organized as a cartel.
Cartels are illegal.
53
What Causes Monopolies?

3. Entry deterrence.
An industry may have one dominant firm purely by
historical accident. If one firm is first to enter some
market, it may have enough of a cost advantage to be
able to discourage other firms from entering the
industry. The incumbent may be able to convince
potential entrants that it will cut its prices drastically if
they attempt to enter the industry.
By preventing entry in this manner, a firm can
eventually dominate a market.
54
What Causes Monopolies?

4. Patent.
A patent offers inventors the exclusive right to
benefit from their inventions for a limited
period of time.
Thus a patent offers a kind of limited
monopoly.
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