Transcript EC 170: Industrial Organization

Price Discrimination
1
Introduction
• Price Discrimination describes strategies used by firms
to extract surplus from customers
2
Mechanisms for Capturing Surplus
• Market segmentation
• Non-linear pricing
– Two-part pricing
– Block pricing
• Tying and bundling
• Quality discrimination
3
Feasibility of price discrimination
• Market power
• Two problems confront a firm wishing to price
discriminate
– identification: the firm is able to identify demands of different
types of consumer or in separate markets
– arbitrage: prevent consumers who are charged a low price from
reselling to consumers who are charged a high price
• The firm then must choose the type of price
discrimination
– first-degree or personalized pricing
– second-degree or menu pricing
– third-degree or group pricing
4
Third-degree price discrimination
• Consumers differ by some observable characteristic(s)
• A uniform price is charged to all consumers in a
particular group – linear price
• Different uniform prices are charged to different groups
– “kids are free”
– subscriptions to professional journals e.g. American Economic
Review
– Airlines
– early-bird specials
5
Third-degree price discrimination 2
• 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
6
Third degree price discrimination: example
• Harry Potter volume sold in the United States and Europe
• Demand:
– United States: PU = 36 – 4QU
– Europe: PE = 24 – 4QE
• Marginal cost constant in each market
– MC = $4
7
The example: no price discrimination
• Suppose that the same price is charged in both markets
• Use the following procedure:
– calculate aggregate demand in the two markets
– identify marginal revenue for that aggregate demand
– equate marginal revenue with marginal cost to identify the
profit maximizing quantity
– identify the market clearing price from the aggregate demand
– calculate demands in the individual markets from the
individual market demand curves and the equilibrium price
8
The example (cont.)
United States: PU = 36 – 4QU Invert this:
QU = 9 – P/4 for P < $36
Europe: PU = 24 – 4QE Invert
QE = 6 – P/4 for P < $24
At these prices
only the US
market is active
Aggregate these demands
Now both
markets are
Q = QU + QE = 9 – P/4 for $36 ≥ P ≥ $24
active
Q = QU + QE = 15 – P/2 for P < $24
9
The example (cont.)
Invert the direct demands
P = 36 – 4Q for Q < 3
P = 30 – 2Q for Q > 3
Marginal revenue is
MR = 36 – 8Q for Q < 3
MR = 30 – 4Q for Q < 3
Set MR = MC
Q = 6.5
$/unit
36
30
17
Demand
MR
MC
6.5
Quantity
15
Price from the demand curve P = $17
10
The example (cont.)
Substitute price into the individual market demand curves:
QU = 9 – P/4 = 9 – 17/4 = 4.75 million
QE = 6 – P/4 = 6 – 17/4 = 1.75 million
Aggregate profit = (17 – 4)x6.5 = $84.5 million
11
The example: price discrimination
• The firm can improve on this outcome
• Check that MR is not equal to MC in both markets
– MR > MC in Europe
– MR < MC in the US
– the firms should transfer some books from the US to Europe
• This requires that different prices be charged in the
two markets
• Procedure:
– take each market separately
– identify equilibrium quantity in each market by equating MR
and MC
– identify the price in each market from market demand
12
The example: price discrimination 2
$/unit
Demand in the US:
PU = 36 – 4QU
Marginal revenue:
MR = 36 – 8QU
36
20
Demand
MR
MC = 4
4
Equate MR and MC
4
QU = 4
Price from the demand curve PU = $20
MC
9
Quantity
13
The example: price discrimination 3
$/unit
Demand in the Europe:
PE = 24 – 4QU
Marginal revenue:
MR = 24 – 8QU
24
14
Demand
MR
MC = 4
4
Equate MR and MC
2.5
QE = 2.5
Price from the demand curve PE = $14
MC
6
Quantity
14
The example: price discrimination 4
• Aggregate sales are 6.5 million books
– the same as without price discrimination
• Aggregate profit is (20 – 4)x4 + (14 – 4)x2.5 =
$89 million
– $4.5 million greater than without price discrimination
15
No price discrimination: non-constant cost
• The example assumes constant marginal cost
• How is this affected if MC is non-constant?
– Suppose MC is increasing
• No price discrimination procedure
–
–
–
–
–
Calculate aggregate demand
Calculate the associated MR
Equate MR with MC to give aggregate output
Identify price from aggregate demand
Identify market demands from individual demand curves
16
The example again
Applying this procedure assuming that MC =
0.75 + Q/2 gives:
(a) United States
Price
40
30
DU
(c) Aggregate
(b) Europe
Price
40
Price
40
30
30
24
20
17
20
17
20
17
DE
D
MR
10
MRU
10
10
MC
MRE
0
0
4.75 5
Quantity
10
0
0
0
1.75
5
Quantity
10
0
5 6.5
10
15
20
Quantity
17
Price discrimination: non-constant cost
• With price discrimination the procedure is
– Identify marginal revenue in each market
– Aggregate these marginal revenues to give aggregate marginal
revenue
– Equate this MR with MC to give aggregate output
– Identify equilibrium MR from the aggregate MR curve
– Equate this MR with MC in each market to give individual
market quantities
– Identify equilibrium prices from individual market demands
18
The example again
Applying this procedure assuming that MC = 0.75 +
Q/2 gives:
(a) United States
Price
40
30
DU
(c) Aggregate
(b) Europe
Price
40
Price
40
30
30
24
20
20
20
17
DE
14
10
4
0
4
0
MR
10
10
MRU
0
5
Quantity
10
4
MRE
0
0
1.75
MC
5
Quantity
10
0
5 6.5
10
15
20
Quantity
19
Some additional comments
• Suppose that demands are linear
– price discrimination results in the same aggregate
output as no price discrimination
– price discrimination increases profit
• For any demand specifications two rules apply
– marginal revenue must be equalized in each market
– marginal revenue must equal aggregate marginal
cost
20
Third-degree price discrimination 2
• 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
21
Other mechanisms for price discrimination
• Impose restrictions on use to control arbitrage
–
–
–
–
Saturday night stay
no changes/alterations
personal use only (academic journals)
time of purchase (movies, restaurants)
• Damaged goods
• Discrimination by location
22
Discrimination by location
• Suppose demand in two distinct markets is identical
– Pi = A = BQi
• But suppose that there are different marginal costs in
supplying the two markets
– cj = ci + t
• Profit maximizing rule:
–
–
–
–
equate MR with MC in each market as before
 Pi = (A + ci)/2; Pj = (A + ci + t)/2
 Pj – Pi = t/2  cj – ci
difference in prices is not the same as the difference in costs
23
Introduction to Nonlinear Pricing
• Annual subscriptions generally cost less in total than one-off
purchases
• Buying in bulk usually offers a price discount
– these are price discrimination reflecting quantity discounts
– prices are nonlinear, with the unit price dependent upon the quantity
bought
– allows pricing nearer to willingness to pay
– so should be more profitable than third-degree price discrimination
• How to design such pricing schemes?
– depends upon the information available to the seller about buyers
– distinguish first-degree (personalized) and second-degree (menu)
pricing
24
First-degree price discrimination 2
• Monopolist can charge maximum price that each
consumer is willing to pay
• Extracts all consumer surplus
• Since profit is now total surplus, find that first-degree
price discrimination is efficient
25
First-degree price discrimination 3
• First-degree price discrimination is 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
– no value-creating exchanges are missed
26
First-degree price discrimination 4
• The information requirements appear to be
insurmountable
– but not in particular cases
• tax accountants, doctors, students applying to private universities
• But there are pricing schemes that will achieve the
same outcome
– non-linear prices
– two-part pricing as a particular example of non-linear prices
• charge a quantity-independent fee (membership?) plus a per unit
usage charge
– block pricing is another
• bundle total charge and quantity in a package
27
Two-part pricing
• Jazz club serves two types of customer
– Old: demand for entry plus Qo drinks is P = Vo – Qo
– Young: demand for entry plus Qy drinks is P = Vy –
Qy
– Equal numbers of each type
– Assume that Vo > Vy: Old are willing to pay more
than Young
– Cost of operating the jazz club C(Q) = F + cQ
• Demand and costs are all in daily units
28
Two-part pricing 2
• Suppose that the jazz club owner applies “traditional”
linear pricing: free entry and a set price for drinks
–
–
–
–
–
–
–
–
–
–
aggregate demand is Q = Qo + Qy = (Vo + Vy) – 2P
invert to give: P = (Vo + Vy)/2 – Q/2
MR is then MR = (Vo + Vy)/2 – Q
equate MR and MC, where MC = c and solve for Q to give
QU = (Vo + Vy)/2 – c
substitute into aggregate demand to give the equilibrium price
PU = (Vo + Vy)/4 + c/2
each Old consumer buys Qo = (3Vo – Vy)/4 – c/2 drinks
each Young consumer buys Qy = (3Vy – Vo)/4 – c/2 drinks
profit from each pair of Old and Young is
U = (Vo + Vy – 2c)2 / 8
29
Two part pricing 3
This example can be illustrated as follows:
(a) Old Customers
Price
Vo
(b) Young Customers
Price
Price
Vo
a
V
d
(c) Old/Young Pair of Customers
y
b
e
f
g
Vo+V y + c h
4
2
i
c k
j
MC
MR
Quantity
Vo
Quantity
Vy
Vo+V y
2
-c
Quantity
Vo + Vy
Linear pricing leaves each type of consumer with consumer surplus
30
Two part pricing 4
• Jazz club owner can do better than this
• Consumer surplus at the uniform linear price is:
– Old: CSo = (Vo – PU).Qo/2 = (Qo)2/2
– Young: CSy = (Vy – PU).Qy/2 = (Qy)2/2
• So charge an entry fee (just less than):
– Eo = CSo to each Old customer and Ey = CSy to each Young
customer
• check IDs to implement this policy
– each type will still be willing to frequent the club and buy the
equilibrium number of drinks
• So this increases profit by Eo for each Old and Ey for
each Young customer
31
Two part pricing 5
• The jazz club can do even better
– reduce the price per drink
– this increases consumer surplus
– but the additional consumer surplus can be extracted through
a higher entry fee
• Consider the best that the jazz club owner can do with
respect to each type of consumer
32
Two-Part Pricing
$/unit
Vi
Set the unit price equal
to marginal cost
This gives consumer
surplus of (Vi - c)2/2
Set the entry charge
to (Vi - c)2/2
The entry charge
Using two-part
converts consumer
pricing surplus
increases
intothe
profit
monopolist’s
profit
c
MC
MR
Vi - c
Vi
Quantity
Profit from each pair of Old and Young now d = [(Vo – c)2 + (Vy – c)2]/2
33
Block pricing
• There is another pricing method that the club owner
can apply
– offer a package of “Entry plus X drinks for $Y”
• To maximize profit apply two rules
– set the quantity offered to each consumer type equal to the
amount that type would buy at price equal to marginal cost
– set the total charge for each consumer type to the total
willingness to pay for the relevant quantity
• Return to the example:
34
Block pricing 2
$
Vo
Old
$
Willingness to
pay of each
Old customer
Quantity
supplied to
each Old
customer
c
MC
Qo
Quantity
Vy
Young
Willingness to
pay of each
Young customer
Quantity
supplied to
each Young
customer
c
Vo
MC
Qy
Vy
Quantity
WTPo = (Vo – c)2/2 + (Vo – c)c = (Vo2 – c2)/2
WTPy = (Vy – c)2/2 + (Vy – c)c = (Vy2 – c2)/2
35
Block pricing 3
• How to implement this policy?
36
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
• Take a specific example
– Ph = 16 – Qh
– Pl = 12 – Ql
– MC = 4
37
Second-degree price discrimination 2
• First-degree price discrimination requires:
– High Income: entry fee $72 and $4 per drink or entry plus 12
drinks for a total charge of $120
– Low Income: entry fee $32 and $4 per drink or entry plus 8
drinks for total charge of $64
• This will not work
– high income types get no consumer surplus from the package
designed for them but get consumer surplus from the other
package
– so they will pretend to be low income even if this limits the
number of drinks they can buy
• Need to design a “menu” of offerings targeted at the
two types
38
Second-degree price discrimination 3
• The seller has to compromise
• Design a pricing scheme that makes buyers
– reveal their true types
– self-select the quantity/price package designed for them
• 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
• Use quantity discounting
39
Second degree price discrimination 4
Low income
consumers will not
buy the ($88, 12)
High-income
Low-Income
package
since they
These
packages
exhibit
This is the incentive
are willing
to pay highquantity
discounting:
So
any
other
package
So
will
the
highThe
low-demand
will be
only
$72
forper
12 unitconsumers
compatibility constraint
income
pay
$7.33
and
income consumers:
offered
to
high-income
willing
to buy
this
($64, 8) package
drinks
So
they
can
be
offered
a
package
low-income
pay
$8
because the
($64, 8) must
$ - 32
consumers
offer
at
High
income
consumers
are
Profit
of
from
($88,
each
12)
(since
high$120
=
88)
And profit from
package gives them $32
willing
to
pay
up
to
$120
for
least
$32
income
consumer
and
theyconsumer
is
will buy thissurplus
each
low-income
consumer
surplus
Offer
the low-income
12
entry
plus
12
drinks
if
no
other
$40 ($88 - 12 x $4)
consumeraispackage of
consumers
package
is
available
$32
$32
entry($64
plus- 88x$4)
drinks for $64
$
16
8
4
$32
$40
$64
$32
$8
$24
$32
$32
MC
$16
8 12
Quantity
4
MC
$32
16
$8
8
12
Quantity
40
Second degree price discrimination 5
A high-income consumer will pay
High-Income
up to $87.50 for entry and 7
The
monopolist does better by
drinks
So buying the ($59.50, 7) package
Suppose each low-income
reducing
the
number
of
units
gives him $28 consumer surplus
consumer is offered 7 drinks
offered
to low-income
consumers
Can
thebeclubSo entry plus
12 drinks
can
sold
Each consumer will pay up to
Low-Income
for each
$92
($120
-12)
28 allows
= $92)
since
this
him to increase
owner
do $even
$59.50 for entry and 7 drinks
Profit from
($92,
$
16
package is $44: an increase
of $4
the
charge
to this?
high-income
Yes!
Reduce
the number
Profit
from each
($59.50, 7)
better
than
12
per consumer
package
is $31.50:
reduction
of
units offered
toaeach
consumers
of $0.50 per
consumer
low-income
consumer
$28
$87.50
$44$92
4
$31.50
$59.50
MC
$28$48
4
MC
$28
7
12
Quantity
16
7 8 12
Quantity
41
Second-degree price discrimination 6
• Will the monopolist always want to supply both types
of consumer?
• There are cases where it is better to supply only highdemand types
– high-class restaurants
– golf and country clubs
• Take our example again
– suppose that there are Nl low-income consumers
– and Nh high-income consumers
42
Second-degree price discrimination 7
• Suppose both types of consumer are served
– two packages are offered ($57.50, 7) aimed at low-income and
($92, 12) aimed at high-income
– profit is $31.50xNl + $44xNh
• Now suppose only high-income 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
< 31.50 = 1.125
Nl
28
There should not be “too high” a fraction of high-demand consumers
43
Second-degree price discrimination 8
• Characteristics of second-degree price discrimination
– extract all consumer surplus from the lowest-demand group
– leave some consumer surplus for other groups
– 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
44
Tying
• Tying is a seller’s conditioning the purchase of
one product on the purchase of another
– Technological ties
• Printer cartridges
– Contractual ties
• Car dealer and car parts
• Why tying?
45
Quality Discrimination
• Why is Quality Discrimination a form of Price
Discrimination?
– First / business class airfare vs economy class
• Reduction in quality of the lower-quality good to
reduce the incentive of people with high
willingness to pay to switch from the high-quality
good when the firm increases its price
– “Damaged goods”
46