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Chapter 25
Monopoly

Pure Monopoly
uA monopolized market has a single seller.
uThe monopolist’s demand curve is the (downward sloping) market demand curve.
uSo 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 a
lower market price, p(y).

Why Monopolies?
uWhat causes monopolies?
–a legal fiat; e.g. US Postal Service

Why Monopolies?
uWhat causes monopolies?
–a legal fiat; e.g. US Postal Service
–a patent; e.g. a new drug

Why Monopolies?
uWhat 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

Why Monopolies?
uWhat 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

Why Monopolies?
uWhat 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
uSuppose that the monopolist seeks to maximize its economic profit,
uWhat output level y* maximizes profit?

Profit-Maximization
At the profit-maximizing output level y*
so, for y = y*,

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
P(y)

Profit-Maximization
$
R(y) = p(y)y
c(y)
y
P(y)
y*

Profit-Maximization
$
R(y) = p(y)y
c(y)
y
P(y)
y*

Profit-Maximization
$
R(y) = p(y)y
c(y)
y
P(y)
y*

Profit-Maximization
$
R(y) = p(y)y
c(y)
y
P(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;


Marginal Revenue
Marginal revenue is the rate-of-change of revenue as the output level y increases;
dp(y)/dy is the slope of the market inverse
demand function so dp(y)/dy < 0.  Therefore
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 - by
a
y
a/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;
E.g. if c(y) = F + ay + by2 then

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

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
and the profit-maximizing output level is

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
and the profit-maximizing output level is
causing the market price to be

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
a
a

Profit-Maximization; An Example
$/output unit
y
MC(y) = a + 2by
p(y) = a - by
MR(y) = a - 2by
a
a

Monopolistic Pricing & Own-Price Elasticity of Demand
uSuppose 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



Monopolistic Pricing & Own-Price Elasticity of Demand
Own-price elasticity of demand is


Monopolistic Pricing & Own-Price Elasticity of Demand
Own-price elasticity of demand is
so

Monopolistic Pricing & Own-Price Elasticity of Demand
Suppose the monopolist’s marginal cost of
production is constant, at $k/output unit.
For a profit-maximum
which is

Monopolistic Pricing & Own-Price Elasticity of Demand
E.g. if e = -3 then p(y*) = 3k/2,
and if e = -2 then p(y*) = 2k.
So as e 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, since


Monopolistic Pricing & Own-Price Elasticity of Demand
Notice that, since


Monopolistic Pricing & Own-Price Elasticity of Demand
Notice that, since
That is,

Monopolistic Pricing & Own-Price Elasticity of Demand
Notice that, since
That is,

Monopolistic Pricing & Own-Price Elasticity of Demand
Notice that, since
That is,
So a profit-maximizing monopolist always
selects an output level for which market
demand is own-price elastic.

Markup Pricing
uMarkup pricing: Output price is the marginal cost of production plus a “markup.”
uHow big is a monopolist’s markup and how does it change with the own-price elasticity of demand?

Markup Pricing
is the monopolist’s price.


Markup Pricing
is the monopolist’s price.  The markup is


Markup Pricing
is the monopolist’s price.  The markup is
E.g. if e = -3 then the markup is k/2,
and if e = -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
uA profits tax levied at rate t reduces profit from P(y*) to (1-t)P(y*).
uQ: How is after-tax profit, (1-t)P(y*), maximized?

A Profits Tax  Levied on a Monopoly
uA profits tax levied at rate t reduces profit from P(y*) to (1-t)P(y*).
uQ: How is after-tax profit, (1-t)P(y*), maximized?
uA: By maximizing before-tax profit, P(y*).

A Profits Tax  Levied on a Monopoly
uA profits tax levied at rate t reduces profit from P(y*) to (1-t)P(y*).
uQ: How is after-tax profit, (1-t)P(y*), maximized?
uA: By maximizing before-tax profit, P(y*).
uSo a profits tax has no effect on the monopolist’s choices of output level, output price, or
demands for inputs.
uI.e. the profits tax is a neutral tax.

Quantity Tax Levied on a Monopolist
uA quantity tax of $t/output unit raises the marginal cost of production by $t.
uSo the tax reduces the profit-maximizing output level, causes the market price to rise, and input
demands to fall.
uThe quantity tax is distortionary.

Quantity Tax Levied on a Monopolist
$/output unit
y
MC(y)
p(y)
MR(y)
y*
p(y*)

Quantity Tax Levied on a Monopolist
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)

Quantity Tax Levied on a Monopolist
$/output unit
y
MC(y)
p(y)
MR(y)
MC(y) + t
t
y*
p(y*)
yt
p(yt)

Quantity Tax Levied on a Monopolist
$/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.

Quantity Tax Levied on a Monopolist
uCan a monopolist “pass” all of a $t quantity tax to the consumers?
uSuppose the marginal cost of production is constant at $k/output unit.
uWith no tax, the monopolist’s price is

Quantity Tax Levied on a Monopolist
uThe tax increases marginal cost to $(k+t)/output unit, changing the profit-maximizing price to
uThe amount of the tax paid by buyers is

Quantity Tax Levied on a Monopolist
is the amount of the tax passed on to
buyers.  E.g. if e = -2, the amount of
the tax passed on is 2t.
Because e < -1, e /(1+e) > 1 and so the
monopolist passes on to consumers more
than the tax!

The Inefficiency of Monopoly
uA market is Pareto efficient if it achieves the maximum possible total gains-to-trade.
uOtherwise 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
uA natural monopoly arises when the firm’s technology has economies-of-scale 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
uA natural monopoly deters entry by threatening predatory pricing against an entrant.
uA 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
uE.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
uLike 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
uWhy not command that a natural monopoly produce the efficient amount of output?
uThen 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
uSo 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.
uRegulatory schemes can induce the natural monopolist to produce the efficient output level without
exiting.