Price Discrimination
1
Introduction
• Price Discrimination describes strategies used by firms
to extract surplus from customers
• Examples of price discrimination
– presumably profitable
– should affect market efficiency: not necessarily adversely
– is price discrimination necessarily bad – even if not seen as
“fair”?
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
• easier in some markets than others: e.g tax consultants, doctors
– arbitrage: prevent consumers who are charged a low price from
reselling to consumers who are charged a high price
• prevent re-importation of prescription drugs to the United States
• 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
• the number of different economy fares charged can be very large
indeed!
– early-bird specials; first-runs of movies
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
Aggregate these demands
Q = QU + QE = 9 – P/4 for $36 < P <
At these prices
only the US
market is active
Now both
markets are
$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
MR
10
10
MRU
4
4
0
4
MRE
0
0
0
5
Quantity
10
MC
0
1.75
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
Product differentiation and price discrimination
• Suppose that demand in each submarket is Pi = Ai – BiQi
• Assume that marginal cost in each submarket is MCi = ci
• Finally, suppose that consumers in submarket i do not
purchase from submarket j
• Equate marginal revenue with marginalItcost
inunlikely
eachthat the
is highly
difference in prices will equal
submarket
the difference in marginal
costs
Ai – 2BiQi = ci  Qi = (Ai – ci)/2Bi  Pi = (Ai + ci)/2
 Pi – Pj = (Ai – Aj)/2 + (ci – cj)/2
22
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
23
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
24
Third-degree rice discrimination and welfare
• Does third-degree price discrimination reduce welfare?
– not the same as being “fair”
– relates solely to efficiency
– so consider impact on total surplus
25
Price discrimination and welfare
Suppose that there are two markets: “weak” and “strong”
The discriminatory
price in the weak
market is P1
Price
D1
The maximum
The uniform
gain in surplus
price in both
in the weak
market is PU
market is G
PU
The discriminatory
price in the strong
market is P2
Price
D2
The minimum
loss of surplus in
the strong
market is L
MR2
P2
PU
P1
MR1
G
L
MC
ΔQ1
Quantity
MC
ΔQ2 Quantity
26
Price discrimination and welfare
Price
D1
Price
Pricediscrimination
discrimination
cannot
cannotincrease
increase
surplus
surplusunless
unlessitit
increases
increasesaggregate
aggregate
output
output
PU
Price
D2
MR2
P2
PU
P1
G
MR1
L
MC
ΔQ1
Quantity
MC
ΔQ2 Quantity
It follows that ΔW < G – L = (PU – MC)ΔQ1 + (PU – MC)ΔQ2
= (PU – MC)(ΔQ1 + ΔQ2)
27
Price discrimination and welfare 2
• Previous analysis assumes that the same markets are
served with and without price discrimination
• This may not be true
– uniform price is affected by demand in “weak” markets
– firm may then prefer not to serve such markets without price
discrimination
– price discrimination may open up weak markets
• The result can be an increase in aggregate output and
an increase in welfare
28
New markets: an example
Demand in “North” is PN = 100 – QN ; in “South” is PS = 100 - QS
Marginal cost to supply either market is $20
North
South
$/unit
Aggregate
$/unit
$/unit
100
100
Demand
MC
MC
MC
MR
Quantity
Quantity
Quantity
29
New Markets: the example 2
Aggregate demand is P = (1 + )50 – Q/2
provided that both markets are served $/unit
Aggregate
Equate MR and MC to get equilibrium
output QA = (1 + )50 - 20
Get equilibrium price from
aggregate demand P = 35 + 25
P
Demand
MC
MR
QA
Quantity
30
New Markets: the example 3
Aggregate
Now consider the impact of a
reduction in 
Aggregate demand changes
$/unit
Marginal revenue changes
It is no longer the case that both
markets are served
PN
Demand
MC
The South market is dropped
Price in North is the monopoly
price for that market
MR
MR'
D'
Quantity
31
The example again
Aggregate
Previous illustration is too extreme
$/unit
MC cuts MR at two points
So there are potentially two
equilibria with uniform pricing
At Q1 only North is served at the
monopoly price in North
At Q2 both markets are served
at the uniform price PU
PN
PU
Demand
Switch from Q1 to Q2:
MC
decreases profit by the red area
increases profit by the blue area
If South demand is “low enough” or
MC “high enough” serve only North
MR
Q1 Q2
Quantity
32
Price discrimination and welfare Again
$/unit
In this case only North is
served with uniform pricing
Aggregate
But MC is less than the
reservation price PR in South
So price discrimination will
lead to South being supplied
PN
PR
Price discrimination leaves
surplus unchanged in North
But price discrimination generates
profit and consumer surplus in South
Q1
So price discrimination increases welfare
Demand
MC
MR
Quantity
33
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
34
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
35
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
36
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
37
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
38
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
39
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 + V y
Linear pricing leaves each type of consumer with consumer surplus
40
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
41
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
42
Two-Part Pricing
$/unit
Vi
Set
Setthe
theunit
unitprice
priceequal
equal
totomarginal
marginalcost
cost
This
Thisgives
givesconsumer
consumer
2
surplus
surplusof
of(V
(Vi --c)c)2/2/2
i
Set
Setthe
theentry
entrycharge
charge
2
toto(V
(Vi --c)c)2/2/2
i
The entry charge
Using
converts consumer
Usingtwo-part
two-part
pricing
increases
intothe
profit
pricingsurplus
increases
the
monopolist’s
monopolist’s
profit
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
43
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:
44
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
45
Block pricing 3
• How to implement this policy?
46
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
47
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
48
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
– allows deception by buyers
• Use quantity discounting
49
Second degree price discrimination 4
Low
Lowincome
income
consumers
consumerswill
willnot
not
buy
($88,
buythe
theLow-Income
($88,12)
12)
High-income
package
since
These
package
packages
sincethey
they
exhibit
This is the incentive
are
willing
totopay
quantity
are
willing
discounting:
pay highSo
any
other
package
So
will
the
highSo
any
other
package
So will the highThe
low-demand
consumers
will
only
for
12
compatibility
constraint
The$72
low-demand
consumers
willbe
be
income
only
pay
$72
$7.33
for
per
12
unit
and
income
consumers:
offered
to
high-income
income
consumers:
willing
totobuy
drinks
offered
to
high-income
willing
buythis
this($64,
($64,8)
8)package
package
So
they
can
be
offered
a
package
low-income
drinks
pay
$8
So
they
can
be
offered
a
package
because
the
($64,
8)
because
the
($64,
8) $120
$ - 32
consumers
must
offer
at
High
income
consumers
are
consumers
must
offer
atAnd profit from
Profit
of
from
($88,
each
12)
(since
high=
88)
High
income
consumers
are
Profit
of
from
($88,
each
12)
(since
high$120
32
=
88)
package
gives
them
$32
And profit from
package
gives
them
$32 up
willing
to
pay
to
$120
for
least
$32
consumer
surplus
income
consumer
and
they
is
will
buy
this
willing
toconsumer
pay up
$120
for each
least
$32
surplus
income
consumer
and
they
is
will
buytothis
low-income
consumer
surplus
Offer
the
low-income
each
low-income
consumer
surplus
Offer
the
low-income
12
entry
plus
12
drinks
if
no
other
$40
--12
xx$4)
entry
$40($88
($88
12plus
$4)12 drinks if no other consumers
consumer
ais
consumer
consumers
aispackage
packageof
of
package
is
available
package
is
available
$32
($64
8x$4)
$32
entry
plus
drinks
$32
entry($64
plus-888x$4)
drinksfor
for$64
$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
50
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
number of units
gives him $28
consumerthe
surplus
consumer is offered 7 drinks
offered
to low-income
consumers
Can
the
So entry plus
12 drinks
can
beclubsold
Can
the
clubEach consumer will pay up to
Low-Income
for
$92
($120
28
=
$92)
since
this
him to increase
owner
do
$59.50 for entry and 7 drinks
Profit from each
($92,
12) allows
owner
do$even
even
$
16
package is $44: an increase
of $4
the
charge
to this?
high-income
Yes!
Reduce
the
Profit
from each
($59.50,
better
than
Yes!
Reduce
thenumber
number 7)
better
than
this?
12
per consumer
package
isoffered
$31.50:
reduction
of
totoaeach
consumers
ofunits
unitsoffered
each
of $0.50 per
consumer
low-income
consumer
$28
low-income consumer
$87.50
$44$92
4
$31.50
$59.50
MC
$28
$48
4
MC
$28
7
12
Quantity
16
7 8 12
Quantity
51
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
52
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
53
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
• 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
54
Non-linear pricing and welfare 1
•
Pricing policy affects
– distribution of surplus
– output of the firm
•
•
•
•
First is welfare neutral
Second affects welfare
Does it increase social welfare?
Price discrimination increases
social welfare of group i if it
increases quantity supplied to
group i
Price
Demand
Total
Surplus
c
MC
Qi Q’i Qi(c) Quantity
55
Non-linear pricing and welfare 2
•
First-degree price
discrimination always
increases social welfare
– extracts all consumer surplus
– but generates socially
optimal output
– output to group i is Qi(c)
– this exceeds output with
uniform (nondiscriminatory) pricing
56
Non-linear pricing and welfare 3
•
Menu pricing is less straightforward
– suppose that there are two markets
• low demand
• high demand
• Uniform price is PU
• Menu pricing gives quantities Q1s, Q2s
• Welfare loss is greater than L
• Welfare gain is less than G
57
Non-linear pricing and welfare 4
•
It follows that
Price
ΔW < G – L
= (PU – MC)ΔQ1 + (PU – MC)ΔQ2
= (PU – MC)(ΔQ1 + ΔQ2)
•
•
•
PU
L
A necessary condition for seconddegree price discrimination to
Price
increase social welfare is that it
increases total output
“Like” third-degree price discrimination
But second-degree price discrimination
is more likely to increase output
MC
Qls QlU
Quantity
PU
G
QhU Qhs
MC
Quantity
58
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
– encouragement to buy in bulk must offer a price discount
59
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?
60
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”
61