Transcript Document

Chapter 3
Basic Monopoly Pricing
and
Product Strategies
Industrial Organization: Chapter 3
1
Introduction
• A monopolist has the power to set prices
• Consider how the monopolist exercises this power
–
–
–
–
–
Focus in this section on a single-product monopolist
What determines price?
What different pricing strategies might be used?
What product design strategies might be used?
What constraints are there on the monopolist’s ability to extract
consumer surplus?
Industrial Organization: Chapter 3
2
First-Degree Price Discrimination
First-degree price discrimination occurs when the seller is
able to extract the entire consumer surplus
– suppose that you own five antique cars and you meet two collectors
– each is willing to pay $10,000 for one car, $8,000 for a second car,
$6,000 for a third car, $4,000 for a fourth and $2,000 for a fifth
– sell the first two cars at $10,000, one to each buyer
– sell the second two cars at $8,000, one to each buyer
– sell the fifth car to one of the buyers at $6,000
– total revenue $42,000
• Highly profitable but requires
– detailed information
– ability to avoid arbitrage
• Leads to the efficient choice of output: since price equals
marginal revenue and MR = MC
Industrial Organization: Chapter 3
3
First-degree price discrimination (cont.)
• The information requirements appear to be insurmountable
• No arbitrage is less restrictive but potentially a problem
• But there are pricing schemes that will achieve the same
output
– non-linear prices
– two-part pricing as a particular example of non-linear prices
Industrial Organization: Chapter 3
4
Two-Part Pricing
Take an example:
Jazz club:
n identical consumers
Demand is P = V - Q
Cost is C(Q) = F + cQ
Marginal Revenue is
MR = V - 2Q
Marginal Cost is
MC = c
$
V
c
MC
MR
V
Industrial Organization: Chapter 3
Quantity
5
Two-Part Pricing
With a uniform price profit
is maximized by setting
Charging
an
marginal
revenue equal
entry
fee increases
to marginal
cost
profit by
2/8
(V
c)
V - 2Q = c
per consumer
So Q = (V - c)/2
P=V-Q
So P = (V + c)/2
Profit to the monopolist
is
n(V - c)2/4 - F
What if the seller
can charge an entry
fee?
$
V
(V+c)/2
c
The maximum entry fee that
each consumer will be willing
to pay is consumer surplus
MC
MR
(V-c)/2
V
Quantity
Consumer surplus for each
consumer is
(V - c)2/8
Industrial Organization: Chapter 3
6
Two-Part Pricing
Is this the best
the seller
can do?
$
V
This whole area is
now profit from each
consumer
(V+c)/2
Lower the unit price
c
This increases consumer
surplus and so increases
the entry charge
MC
MR
(V-c)/2
Industrial Organization: Chapter 3
V
Quantity
7
Two-Part Pricing
What is the best
the seller
can do?
Set the unit price equal
to marginal cost
This gives consumer
surplus of (V - c)2/2
$
V
c
The entry charge
converts consumer
surplus into profit
MC
Using two-part
MR
pricing increases
the
monopolist’s
V
V-c
Quantity
profit
Set the entry charge
to (V - c)2/2
Industrial Organization: Chapter 3
8
Two-part pricing (cont.)
• First-degree price discrimination through two-part pricing
– increases profit by extracting all consumer surplus
– leads to unit price equal to marginal cost
– causes the monopolist to produce the efficient level of output
• What happens if consumers are not identical?
• Assume that consumers differ in types and that the
monopolist can identify the types
– age
– location
– some other distinguishing and observable characteristic
• We can extend our example
Industrial Organization: Chapter 3
9
Two-part
with different consumers
• There ispricing
an alternative
approach
• Offer
older
customers
Older
Consumers
So
the
seller
can charge Younger Consumers
entry
plus 12
fort o each
an entry
feeunits
of $72
Demand:
P = 16
-Q
$120older
customer
and $32 Demand: P = 12 - Q
• and to
younger
customers$
each
If younger
unit price one
And
for converts
the
This
entry plus
8isunits
for
Consumer
surplus
Assume that
set at
$4 $64
younger customers
all
consumer
12
for the
older
And
marginal
younger
cost is
older
customers
consumer
surplus
surplus
intoat
customers
is $72
customers
each
each buy
12
is
$32constant
buyprofit
$4
8 units
per unit
units
$72
$72
$32
$32
$
16
4
MC
$48
4
MC
$32
12
Quantity
16
Industrial Organization: Chapter 3
8
12
Quantity
10
Second-Degree Price Discrimination
• What if the seller cannot distinguish between buyers?
– perhaps they differ in income (unobservable)
• Then the type of price discrimination just discussed is
impossible
• High-income buyer will pretend to be a low-income buyer
– to avoid the high entry price
– to pay the smaller total charge
• Confirm from the diagram
Industrial Organization: Chapter 3
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The example again
High-Demand
Consumers
Low-Demand
Consumers
Demand:NO!
P = 16
Q Could the seller
Demand:
preventP = 12 - Q
If a- high-demand
If
high-demand
consumer pays
theaby
lower
fee
this
limiting
the number
$
pays
the
lower
and gets the consumer
lower
quantity
of units
thathe
can
be bought?
fee and buys
12 units he
gets $32 of consumer
surplus
12
gets $40 of consumer
surplus
$32
$
16
8
$32
4
$32
$8
$32
MC
$16
8 12
Quantity
4
MC
$32
16
Industrial Organization: Chapter 3
8
12
Quantity
12
Second-Degree Price Discrimination
• The seller has to compromise
• A pricing scheme must be designed that makes buyers
– reveal their true types
– self-select the quantity/price package designed for them
• This is the essence of second-degree price discrimination
• It is “like” first-degree price discrimination
– The seller knows that there are buyers of different types
• But
– the seller is not able to identify the different types
• A two-part tariff is ineffective
– allows deception by buyers
• Use quantity discounting
Industrial Organization: Chapter 3
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The example again
High-Demand
$
16
8
4
Low-Demand
The low-demand consumers will be
Sohighany other package
So will the
Low demand
willing
to
buy
this
($64,
8) package
demand consumers:
offered
to
high-demand
consumers will not
This
is the
So they
can
be8)offered
a incentive
package
These
packages
exhibit
because
the
($64,
High
demand
consumers
are
$ - 32
consumers
must
offer
at Offer the
buylow-demand
the ($88, 12)
Profit
of
from
($88,
each
12)
(since
high$120
=
88)
compatibility
constraint
quantity
discounting:
highAnd
profit
from
package willing
gives them
$32
to
pay
up
to
$120
for
package
since they
least
$32
consumer
surplus
demand
consumer
and
they$7.33
will
is buy
this
consumers
a package
of
demand
pay
per
unit
and
each
low-demand
consumer
surplus
entry
plus
12
drinks
if
no
other
12
are8 willing
to pay
$40 ($88 - low-demand
12 x $4)
entryconsumer
plus
drinks
for
$64
pay
$8
is
package is available
only $72 for 12
$32 ($64 - 8x$4)
$32
drinks
$32
$40
$64
$32
$8
$24
$32
$32
MC
$16
8 12
Quantity
4
MC
$32
16
Industrial Organization: Chapter 3
$8
8
12
Quantity
14
The example again
A high-demand consumer will pay
up to $87.50 for
entry
andclub7 drinks does
High-Demand
Low-Demand
The
monopolist
better by
Can
the
So buying theowner
($59.50,do
7) package
reducing
the number of Suppose
units each low-demand
even
gives him $28 consumer surplus
offered
to low-demand
consumers
better than
this?
consumer is offered 7 drinks
So entry plus 12 drinks can be sold
him to increase
Each consumer will pay up to
for $92since
($120 -this
28 = allows
$92)
$
$59.50 for entry and 7 drinks
charge
to
high-demand
Profit from eachthe
($92,
12) package
ProfitReduce
from each
is $44: an increase of $4
per
Yes!
the($59.50,
number7)
consumers
12
package
$31.50: to
a reduction
consumer
of unitsisoffered
each
of $0.50 per consumer
$28
low-demand
consumer
$
16
$87.50
$44$92
$31.50
$59.50
4
MC
$28$48
4
MC
$28
7
12
Quantity
16
Industrial Organization: Chapter 3
7 8 12
Quantity
15
Second-degree price discrimination (cont.)
• Will the monopolist always want to supply both types of
consumer?
• There are cases where it is better to supply only highdemand
– high-class restaurants
– golf and country clubs
• Take our example again
– suppose that there are Nl low-income consumers
– and Nh high-income consumers
Industrial Organization: Chapter 3
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Second-degree price discrimination (cont.)
• Suppose both types of consumer are served
– two packages are offered ($57.50, 7) aimed at low-demand and
($92, 12) aimed at high-demand
– profit is $31.50xNl + $44xNh
• Now suppose only high-demand consumers are served
– then a ($120, 12) package can be offered
– profit is $72xNh
• Is it profitable to serve both types?
– Only if $31.50xNl + $44xNh > $72xNh  31.50Nl > 28Nh
This requires that
Nh
Nl
31.50
<
28
= 1.125
There should not be “too high” a proportion of high-demand consumers
Industrial Organization: Chapter 3
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Second-degree price discrimination (cont.)
• Characteristics of second-degree price discrimination
– extract all consumer surplus from the lowest-demand group
– leave some consumer surplus for other groups
• the incentive compatibility constraint
– offer less than the socially efficient quantity to all groups other
than the highest-demand group
– offer quantity-discounting
• Second-degree price discrimination converts consumer
surplus into profit less effectively than first-degree
• Some consumer surplus is left “on the table” in order to
induce high-demand groups to buy large quantities
Industrial Organization: Chapter 3
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Third-Degree Price Discrimination
• Consumers differ by some observable characteristic(s)
• A uniform price is charged to all consumers in a particular
group
• Different uniform prices are charged to different groups
– “kids are free”
– subscriptions to professional journals e.g. American Economic
Review
– airlines
• the number of different economy fares charged can be very large
indeed!
– early-bird specials; first-runs of movies
Industrial Organization: Chapter 3
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Third-degree price discrimination (cont.)
• Often arises when firms sell differentiated products
– hard-back versus paper back books
– first-class versus economy airfare
• Price discrimination exists in these cases when:
– “two varieties of a commodity are sold by the same seller to two
buyers at different net prices, the net price being the price paid by
the buyer corrected for the cost associated with the product
differentiation.” (Phlips)
• The seller needs an easily observable characteristic that
signals willingness to pay
• The seller must be able to prevent arbitrage
– e.g. require a Saturday night stay for a cheap flight
Industrial Organization: Chapter 3
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Third-degree price discrimination (cont.)
• The pricing rule is very simple:
– consumers with low elasticity of demand should be charged a high
price
– consumers with high elasticity of demand should be charged a low
price
• Illustrate with a simple example
–
–
–
–
monopolist has constant marginal costs of c per unit
two types of consumers, with the type being identifiable
all consumers of a particular type have identical demands
two pricing rules must hold
• marginal revenue must be equal on the last unit sold to each type of
consumer
• marginal revenue must equal marginal cost in each market
Industrial Organization: Chapter 3
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An example
Type 1 Demand: P = A1 - BQ1
Type 2 Demand: P = A2 - BQ2
MR1 = A1 - 2BQ1
MC
=c A >A
Since
1
2
 Q1 = (A1 - c)/2B
$
A1
MR2 = A2 - 2BQ2
MC = c
 Q2 = (A2 - c)/2B
Type 1
consumers are charged a
 P1 = (A1 + c)/2
 P2 = (A2 + c)/2
higher price than
$
Type 2 consumers
A2
(A1+c)/2
(A2+c)/2
c
MC
c
MC
MR2
MR1
(A1-c)/2B
Quantity
A1/B
(A2-c)/2B
Industrial Organization: Chapter 3
A2/B
Quantity
22
Third-degree price discrimination (cont.)
• What happens if marginal costs are not constant?
• The same principles apply
– marginal revenue equalized across consumer types
– marginal revenue equal to marginal cost where marginal cost is
measured at aggregate output
• Consider an example
Industrial Organization: Chapter 3
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The example
• Two markets
– Market 1: P = 20 - Q1
– Market 2: P = 16 - 2Q2
Now calculate
aggregate marginal
revenue
MR1 = 20 - 2Q1
MR2 = 16 - 4Q2
Note that this applies
only forof
prices
Invert these to give Q as a function
MR:less than
Q1 = 10 - MR/2
Q2 = 4 - MR/4
The consumers with
So aggregateless
marginal
revenue are
is
elastic demand
Q = Q1 + Q2 =charged
14 - 3MR/4
higher prices
Invert this to give marginal revenue:
MR = 56/3 - 4Q/3 for MR < $16
$16
MC = 2Q
MC = MR  2Q = 56/3 - 4Q/3
 Q = 5.6
 MR = $11.20
 Q1 = 4.4 and Q2 = 1.2
 P1 = $15.60 and P2 = $13.60
MR = 20 - 2Q for MR > $16
Industrial Organization: Chapter 3
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Third-degree price discrimination (cont.)
• A general rule characterizes third-degree price
discrimination
• Recall the formula for marginal revenue in market i:
– MRi = Pi(1 - 1/i) where i is the price elasticity of demand
• Recall also that when serving two markets profit
maximization requires that MR is equalized in each market
Prices are always
– so MR1 = MR2
–  P1(1 - 1/ 1) = P2(1 - 1/ 2) higher in markets where
demand is inelastic
P1
(1 - 1/ 2)

=
P2
(1 - 1/ 1)
Industrial Organization: Chapter 3
25
Price Discrimination and Welfare
• Does price discrimination reduce welfare?
• First- and second- degree: “not necessarily”
– because output is at or near to the efficient level
• Third-degree is less clear
– monopolist restricts output in the markets supplied
– but markets may be served that would otherwise be left unsupplied
• A necessary condition for third-degree price discrimination
not to reduce welfare is that it leads to an increase in
output
Industrial Organization: Chapter 3
26
Public Policy
• Uneven
– Robinson-Patman makes price discrimination illegal if it is
intended to create a monopoly
– One defense is if discriminatory prices are intended to “meet the
competition”
• Enforcement has been spotty
– weak in recent years
– but note the pharmaceutical case
– private actions are possible: see http://lawmall.com
• International restrictions also exist
– anti-dumping regulations
– these are currently pursued very actively
Industrial Organization: Chapter 3
27
Monopoly and Product Quality
• Firms can, and do, produce goods of different qualities
• Quality then is an important strategic variable
• The choice of product quality by a monopolist is
determined by its ability to generate profit
• Focus for the moment on a monopolist producing a single
good
– what quality should it have?
– determined by consumer attitudes to quality
•
•
•
•
prefer high to low quality
willing to pay more for high quality
but this requires that the consumer recognizes quality
also some are willing to pay more than others for quality
Industrial Organization: Chapter 3
28
Demand and Quality
• We might think of individual demand as being of the form
– Qi = 1 if Pi < Ri(Z) and = 0 otherwise for each consumer i
– Each consumer buys exactly one unit so long as price is less than
her reservation price
– the reservation price is affected by product quality Z
• Assume that consumers vary in their reservation prices
• Then aggregate demand is of the form P = P(Q, Z)
• An increase in product quality increases demand
Industrial Organization: Chapter 3
29
Demand and quality (cont.)
Begin with a particular demand curve
for a good of quality Z1
Price
Then an increase in product
R1(Z2)
Suppose that
an from
increase
quality
Z1 toinZ2 rotates
P(Q, Z2)
quality the
increases
demandthe
curve around
If the price is P1willingness
and the product
quality
to pay of
the quantity
axis as follows
is
Z
then
all
consumers
with
reservation
1
inframarginal consumers more
P2
prices greater than
than P
the good
1 will
that
of buy
the marginal
R1(Z1)
Quantity Q1 can now be
consumer
This
is
the
These are the
P1
sold for the higher
marginal
inframarginal
price P2
consumer
consumers
P(Q, Z1)
Q1
Quantity
Industrial Organization: Chapter 3
30
Demand and quality (cont.)
Price
R1(Z1)
P2
P1
P(Q, Z1)
Q1
Suppose instead that an
Then anin
increase in product
increase
fromthe
Z1 to Z2 rotates
qualityquality
increases
thepay
demand
curve around
willingness to
of marginal
the price
axis as follows
consumers
more
than that of the inframarginal
consumers
Once again quantity Q1
can now be sold for a
higher price P2
P(Q, Z2)
Quantity
Industrial Organization: Chapter 3
31
Demand and quality (cont.)
• The monopolist must choose both
– price (or quantity)
– quality
• Two profit-maximizing rules
– marginal revenue equals marginal cost on the last unit sold for a
given quality
– marginal revenue from increased quality equals marginal cost of
increased quality for a given quantity
• This can be illustrated with a simple example:
P = Z( - Q) where Z is an index of quality
Industrial Organization: Chapter 3
32
Demand and quality: an example
P = Z( - Q)
Assume that marginal cost of output is zero: MC(Q) = 0
Cost of quality is D(Z) = aZ2
Marginal cost of quality = dD(Z)/d(Z)
This means that quality is
= 2aZ
costly and becomes
The firm’s profit is:
increasingly costly
p(Q, Z) =P.Q - D(Z) = Z( - Q)Q - aZ2
The firm chooses Q and Z to maximize profit.
Take the choice of quantity first: this is easiest.
Marginal revenue = MR = Z - 2ZQ
MR = MC  Z - 2ZQ = 0  Q* = /2
 P* = Z/2
Industrial Organization: Chapter 3
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The example continued
Total revenue = P*Q* = (Z/2)x(/2) = Z2/4
So marginal revenue from increased quality is
MR(Z) = 2/4
Marginal cost of quality is MC(Z) = 2aZ
Equating MR(Z) = MC(Z) then gives Z* = 2/8a
Does the monopolist produce too high or too low quality?
Is it possible that quality is too high?
Only in particular constrained circumstances.
Industrial Organization: Chapter 3
34
The Multiplant Monopolist
• A monopolist rarely produces all output in one plant
– how should production be allocated across plants?
– this is especially important if different plants have different costs
• To maximize profit set MR = MC on the last unit produced
• But with several plants what is MC?
• First case:
– marginal costs constant within a plant but varying across plants
– each plant has a capacity constraint
Industrial Organization: Chapter 3
35
The multiplant monopolist (cont.)
Price
Plant 3 has marginal
Suppose
cost
MC3 that
and there are
three possible
capacity
q3 plants.
Plant 2 has marginal
Arrange
Maximize
profit
by them in order
MCcost
MC2 and
3
of their
marginal costs
equating
cost
Plant 1 has marginal
capacitymarginal
q2
and marginal revenue
cost
MC2 MC1 andProduce output Q* using plant
capacity q1 1 and plant 2. Plant 3 is not
operated (or introduced)
MC1
MR
q1 Q*
q1 + q2
Quantity
Industrial Organization: Chapter 3
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The multiplant monopolist (cont.)
• What happens if marginal costs are not constant?
• Output allocation
– operate plants such that marginal cost is equal on the last unit
produced in each plant
• Why?
– If not, then cost can be reduced by reallocating output between
plants
– For example: suppose MC1 = $10 and MC2 = $15
– Reducing output of plant 2 by one unit and increasing output of
plant 1 by one unit reduces total costs
Industrial Organization: Chapter 3
37
An Example
Suppose MC1 = aq1 and MC2 = bq2
$
q1 = MC/a ; q2 = MC/b
$
Allocate output
to the two plants
to equate
marginal costs
MC2 = bq2
 Q =q1 + q2 = MC(a + b)/ab
Maximize profit
 MCby
= Qab/
+ b)
setting(amarginal
revenue equal
to marginal cost
MC1 = aq1
MC1 + MC2
MR
q2*
q1*
Quantity
Industrial Organization: Chapter 3
Q*
Quantity
38
Industrial Organization: Chapter 3
39
Demand and quality (cont.)
Price
Z2 
P(Q, Z2)
When quality is Z2
price is
2/2
Howisdoes
WhenZquality
Z1 increased quality
price is affect demand?
Z1/2
MR(Z2)
Z1 
P2 = Z2/2
P1 = Z1/2
MR(Z1)
P(Q,Z1)
/2
Q*

Quantity
Industrial Organization: Chapter 3
40
Demand and quality (cont.)
Price
Z2 
Z1 
P2 = Z2/2
P1 = Z1/2
So an increase is quality from
Z1 to Z
surplus
2 increases
Social
surplus
at quality
Z2
area
minus
the
is by
thisthis
area
minus
quality
increase in
quality costs
costs
An increase in quality from
The increase is total
Z1 to Z2 increases
surplus
revenue
by this
area Zis greater than
Social
surplus
at quality
1
the
increase
in profit.
is this area minus quality
The monopolist produces
costs
too little quality
/2
Q*

Quantity
Industrial Organization: Chapter 3
41
Demand and quality: an alternative
Price
The increase in
social surplus
The increase in
Assume that an increase
is this area
quality increasesThe increase
in from
totalZ1 to
in quality
minus the cost of
profit by this area
less the
than
Z2is
rotates
demand
increased quality surplus
minus the cost of
function
as follows
the increase
in profit.
increased quality
The monopolist produces
assume that
too muchFurther
quality
the firm is constrained
to produce output Q
P(Q,Z2)
P(Q,Z
Exporters subject to quotas
1)
This may
arise as a result
tend to export high quality of an export quota or
Quantity
goodsQ
other restriction on
output
Industrial Organization: Chapter 3
42
Demand and quality
Derivation of aggregate demand
Order consumers by their reservation prices
Aggregate individual demand horizontally
Price
1 2 3 4 5 6 7 8
Quantity
Industrial Organization: Chapter 3
43
Market 1
Market 2
$
Aggregate
$
$
$20
$20
$16
$13.60
$15.60
MR1
4.4 10
Quantity
$16
$11.20
D1
MR2
20
MC
D2
1.2 4 8
Quantity
Industrial Organization: Chapter 3
MR1+MR2
5.6
14
Quantity
44
The incentive compatibility constraint
• Any offer made to high demand consumers must offer
them as much consumer surplus as they would get from
an offer designed for low-demand consumers.
• This is a common phenomenon
– performance bonuses must encourage effort
– insurance policies need large deductibles to deter cheating
– piece rates in factories have to be accompanied by strict quality
inspection
– encouragement to buy in bulk must offer a price discount
Industrial Organization: Chapter 3
45