Price Discrimination and
Monopoly
Chapter 5: Price Discrimination and
Monopoly
1
Introduction
• Prescription drugs are cheaper in Canada than the
United States
• Textbooks are generally cheaper in Britain than the
United States
• Examples of price discrimination
– presumably profitable
– should affect market efficiency: not necessarily adversely
– is price discrimination necessarily bad – even if not seen as
“fair”?
Chapter 5: Price Discrimination and
Monopoly
2
Feasibility of price discrimination
• 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
Chapter 5: Price Discrimination and
Monopoly
3
Introduction to First-Degree Price Discrimination
• 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
Chapter 5: Price Discrimination and
Monopoly
4
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
Chapter 5: Price Discrimination and
Monopoly
5
First-degree price discrimination 3
• Suppose that you own five antique cars
• Market research shows there are collectors of different types
– keenest is willing to pay $10,000 for a car, second keenest $8,000,
third keenest $6,000, fourth keenest $4,000, fifth keenest $2,000
– sell the first car at $10,000
– sell the second car at $8,000
– sell the third car to at $6,000 and so on
– total revenue $30,000
• Contrast with linear pricing: all cars sold at the same price
– set a price of $6,000
– sell three cars
– total revenue $18,000
Chapter 5: Price Discrimination and
Monopoly
6
First-degree price discrimination 4
• 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
Chapter 5: Price Discrimination and
Monopoly
7
First-degree price discrimination 5
• The information requirements appear to be
insurmountable
– but not in particular cases
• tax accountants, doctors, students applying to private universities
• No arbitrage is less restrictive but potentially a
problem
• 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
Chapter 5: Price Discrimination and
Monopoly
8
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
Chapter 5: Price Discrimination and
Monopoly
9
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
Chapter 5: Price Discrimination and
Monopoly
10
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
Chapter 5: Price Discrimination and
Monopoly
11
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
Chapter 5: Price Discrimination and
Monopoly
12
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
Chapter 5: Price Discrimination and
Monopoly
13
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
Chapter 5: Price Discrimination and
Monopoly
14
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:
Chapter 5: Price Discrimination and
Monopoly
15
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
Chapter 5: Price Discrimination and
Monopoly
16
Block pricing 3
• How to implement this policy?
– card at the door
– give customers the requisite number of
tokens that are exchanged for drinks
Chapter 5: Price Discrimination and
Monopoly
17
A final comment
• One final point
– average price that is paid by an Old customer = (Vo2 – c2)/2(Vo
– c) = (Vo + c)/2
– average price paid by a Young customer = (Vy2 – c2)/2(Vo – c) =
(Vy + c)/2
– identical to the third-degree price discrimination (linear)
prices
– but the profit outcome is much better with first-degree price
discrimination. Why?
• consumer equates MC of last unit bought with marginal benefit
• with linear pricing MC = AC (= average price)
• with first-degree price discrimination MC of last unit bought is less
than AC (= average price) so more is bought
Chapter 5: Price Discrimination and
Monopoly
18
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
Chapter 5: Price Discrimination and
Monopoly
19
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
Chapter 5: Price Discrimination and
Monopoly
20
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
Chapter 5: Price Discrimination and
Monopoly
21
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
Chapter 5: Price Discrimination and
Monopoly
22
The example (npd 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
Chapter 5: Price Discrimination and
Monopoly
23
The example (npd 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
Chapter 5: Price Discrimination and
Monopoly
24
The example (npd 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
Chapter 5: Price Discrimination and
Monopoly
25
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
Chapter 5: Price Discrimination and
Monopoly
26
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
Chapter 5: Price Discrimination and
Monopoly
MC
9
Quantity
27
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
Chapter 5: Price Discrimination and
Monopoly
MC
6
Quantity
28
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
Chapter 5: Price Discrimination and
Monopoly
29
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
Chapter 5: Price Discrimination and
Monopoly
30
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
D
20
17
DE
MR
10
MRU
10
10
MC
MRE
0
0
4.75 5
Quantity
10
0
0
0
1.75
5
10
0
5 6.5
Quantity
Chapter 5: Price Discrimination and
Monopoly
10
15
20
Quantity
31
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
Chapter 5: Price Discrimination and
Monopoly
32
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
10
0
5 6.5
Quantity
Chapter 5: Price Discrimination and
Monopoly
10
15
20
Quantity
33
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
Chapter 5: Price Discrimination and
Monopoly
34
Price discrimination and elasticity
• Suppose that there are two markets with the same MC
• MR in market i is given by MRi = Pi(1 – 1/hi)
– where hi is (absolute value of) elasticity of demand
• From rule 1 (above)
– MR1 = MR2
– so P1(1 – 1/h1) = P2(1 – 1/h2) which gives
P1
P2
=
(1 – 1/h2)
(1 – 1/h1)
Price is lower in the
market with the higher
demand elasticity
h1h2 – h1
= h h – h
1 2
2
Chapter 5: Price Discrimination and
Monopoly
35
Third-degree price 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
Chapter 5: Price Discrimination and
Monopoly
36
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 P
U
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
Chapter 5: Price Discrimination and
Monopoly
MC
ΔQ2 Quantity
37
Price discrimination and welfare
Price
D1
Price discrimination
cannot increase
surplus unless it
increases aggregate
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)
Chapter 5: Price Discrimination and
Monopoly
38
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
Chapter 5: Price Discrimination and
Monopoly
39
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
Chapter 5: Price Discrimination and
Monopoly
Quantity
40
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
Chapter 5: Price Discrimination and
Monopoly
Quantity
41
New Markets: the example 3
Aggregate
Now consider the impact of a
reduction in 
Aggregate demand changes
Marginal revenue changes
It is no longer the case that both
markets are served
$/unit
PN
Demand
MC
The South market is dropped
Price in North is the monopoly
price for that market
Chapter 5: Price Discrimination and
Monopoly
MR
MR'
D'
Quantity
42
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
PN
At Q2 both markets are served
at the uniform price PU
PU
Switch from Q1 to Q2:
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
Demand
MC
MR
Q1 Q2
Chapter 5: Price Discrimination and
Monopoly
Quantity
43
Price discrimination and welfare Again
In this case only North is
served with uniform pricing
But MC is less than the
reservation price PR in South
So price discrimination will
lead to South being supplied
$/unit
Aggregate
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
Chapter 5: Price Discrimination and
Monopoly
Demand
MC
MR
Quantity
44
Price discrimination and welfare One more time
• Suppose only North is served with a uniform price
• Also assume that South will be served with price
discrimination
– Welfare in North is unaffected
– Consumer surplus is created in South: opening of a new market
– Profit is generated in South: otherwise the market is not opened
• As a result price discrimination increases welfare.
Chapter 5: Price Discrimination and
Monopoly
45
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
Chapter 5: Price Discrimination and
Monopoly
46
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
Chapter 5: Price Discrimination and
Monopoly
47
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
Chapter 5: Price Discrimination and
Monopoly
48
Low income
Second degree price discrimination
4
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
Chapter 5: Price Discrimination and
Monopoly
$8
8
12
Quantity
49
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
Chapter 5: Price Discrimination and
Monopoly
7 8 12
Quantity
50
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
Chapter 5: Price Discrimination and
Monopoly
51
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
Chapter 5: Price Discrimination and
Monopoly
52
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
Chapter 5: Price Discrimination and
Monopoly
53
Non-linear pricing and welfare
• Non-linear price discrimination
raises profit
• Does it increase social welfare?
– suppose that inverse demand of
consumer group i is P = Pi(Q)
– marginal cost is constant at MC – c
– suppose quantity offered to
consumer group i is Qi
– total surplus – consumer surplus
plus profit –is the area between the
inverse demand and marginal cost
up to quantity Qi
Price
Demand
Total
Surplus
c
MC
Qi
Chapter 5: Price Discrimination and
Monopoly
Qi(c) Quantity
54
Non-linear pricing and welfare 2
• 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
Chapter 5: Price Discrimination and
Monopoly
55
Non-linear pricing and welfare 3
• 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
Price
Demand
Total
Surplus
c
MC
Qi
Chapter 5: Price Discrimination and
Monopoly
Qi(c) Quantity
56
Non-linear pricing and welfare 4
• Menu pricing is less straightforward
Low demand
offered less than
the socially
optimal quantity
Price
– suppose that there are two markets
• low demand
• high demand
PU
• Uniform price is PU
• Menu pricing gives quantities Q1s,
s
Q
• 2Welfare loss is greater than L
• Welfare gain is less than G
L
MC
Qls QlU
Quantity
Price
High demand
offered the
socially optimal
quantity
PU
G
QhU Qhs
Chapter 5: Price Discrimination and
Monopoly
MC
Quantity
57
Non-linear pricing and welfare 5
Price
• It follows that
ΔW < G – L
= (PU – MC)ΔQ1 + (PU – MC)ΔQ2
= (PU – MC)(ΔQ1 + ΔQ2)
PU
• 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 PU
is more likely to increase output
L
MC
Qls QlU
Quantity
G
QhU Qhs
Chapter 5: Price Discrimination and
Monopoly
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
– piece rates in factories have to be accompanied by strict quality
inspection
– encouragement to buy in bulk must offer a price discount
Chapter 5: Price Discrimination and
Monopoly
59