Price Discrimination in Monopoly and Product Strategies

1
Chapter 3

• Price Discrimination in Monopoly and Product
  Strategies

2
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 monopolists
  ability to extract consumer surplus?

3
Two-Part Pricing as First Degree price
discrimination

Take an example
V
Jazz club
n identical consumers
Demand is P V - Q
Cost is C(Q) F cQ
c
Marginal Revenue is
MC
MR V - 2Q
MR
Marginal Cost is
V
Quantity
MC c
4
Two-Part Pricing
Charging an entry fee increases profit by (V -
c)2/8 per consumer
What if the seller can charge an entry fee?

With a uniform price profit is maximized by
setting marginal revenue equal to marginal cost
V
The maximum entry fee that each consumer will be
willing to pay is consumer surplus
(Vc)/2
V - 2Q c
c
MC
So Q (V - c)/2
MR
P V - Q
V
So P (V c)/2
(V-c)/2
Quantity
Profit to the monopolist is n(V - c)2/4 - F
Consumer surplus for each consumer is (V - c)2/8
5
Two-Part Pricing
Is this the best the seller can do?

V
This whole area is now profit from each consumer
(Vc)/2
Lower the unit price
c
MC
This increases consumer surplus and so
increases the entry charge
MR
V
(V-c)/2
Quantity
6
Two-Part Pricing
What is the best the seller can do?

V
The entry charge converts consumer surplus into
profit
Using two-part pricing
increases the monopolists profit
Set the unit price equal to marginal cost
c
MC
MR
This gives consumer surplus of (V - c)2/2
V
V - c
Quantity
Set the entry charge to (V - c)2/2
7
Two-part pricing with different consumers

• There is an alternative approach

So the seller can charge an entry fee of 72 t o
each older customer and 32 to each younger one
Younger Consumers
Older Consumers

• Offer older customers entry plus 12 units for
  120

Demand P 16 - Q
Demand P 12 - Q
This converts all consumer surplus into profit

• and younger customers entry plus 8 units for 64

And for the younger customers consumer surplus is
32
If unit price is set at 4 older customers each
buy 12 units
16
Assume that marginal cost is constant at 4 per
unit
Consumer surplus for the older customers is 72
And younger customers each buy 8 units
12
72
72
32
32
48
32
16
12
12
8
Quantity
Quantity
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?
• When consumers differ in types and that the
  monopolist can identify the types no problem

9
Caveats with perfect pricediscrimination

• Even though it leads to an efficient outcome,
  what is a fair distribution of wealth in the
  society?
• In practice, transactions costs and information
  constraints make it difficult to implement
  perfectly (but car dealers and some professionals
  try to come close).
• Price discrimination wont work if consumers can
  resell the good.
• Consumers may resist it
• Example Guardian Weekly, Oct 12-18, 2000

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 with diagram

11
An example
High-Demand Consumers
Low-Demand Consumers
Could the seller prevent this by limiting the
number of units that can be bought?
Demand P 16 - Q
Demand P 12 - Q
NO! If a high-demand consumer pays the lower fee
and gets the lower quantity he gets 32 of
consumer surplus
If a high-demand consumer pays the lower fee and
buys 12 units he gets 40 of consumer surplus


16
12
32
8
32
32
8
16
32
32
8
16
12
12
8
Quantity
Quantity
12
Second-Degree Price Discrimination

• A pricing scheme must be designed that makes
  buyers
• reveal their true types
• self-select the quantity/price package designed
  for them
• This is 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

13
The example again
High-Demand
Low-Demand
So any other package offered to
high-demand consumers must offer at least 32
consumer surplus
The low-demand consumers will be willing to buy
this (64, 8) package
So will the high- demand consumers because the
(64, 8) package gives them 32 consumer surplus
This is the incentive compatibility constraint
Low demand consumers will not buy the (88,
12) package since they are willing to pay only
72 for 12 drinks
These packages exhibit quantity discounting
high- demand pay 7.33 per unit and low-demand
pay 8
So they can be offered a package of (88, 12)
(since 120 - 32 88) and they will buy this
High demand consumers are willing to pay up to
120 for entry plus 12 drinks if no other package
is available


Offer the low-demand consumers a package of entry
plus 8 drinks for 64
Profit from each high- demand consumer is 40
(88 - 12 x 4)
And profit from each low-demand consumer is 32
(64 - 8x4)
16
12
32
8
32
32
32
40
64
8
24
16
32
32
8
8
16
12
12
8
Quantity
Quantity
14
The example again
The monopolist does better by reducing the number
of units offered to low-demand consumers since
this allows him to increase the charge to
high-demand consumers
Can the club- owner do even better than this?
A high-demand consumer will pay up to 87.50 for
entry and 7 drinks
High-Demand
Low-Demand
So buying the (59.50, 7) package gives him 28
consumer surplus
Suppose each low-demand consumer is offered 7
drinks
So entry plus 12 drinks can be sold for 92 (120
- 28 92)
Each consumer will pay up to 59.50 for entry and
7 drinks


Profit from each (92, 12) package is 44 an
increase of 4 per consumer
16
Yes! Reduce the number of units offered to
each low-demand consumer
Profit from each (59.50, 7) package is 31.50 a
reduction of 0.50 per consumer
12
28
87.50
31.50
44
59.50
92
28
28
48
16
12
12
8
7
7
Quantity
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
  high-demand
• high-class restaurants
• golf and country clubs
• Take our example again
• suppose that there are Nl low-income consumers
• and Nh high-income consumers

16
2nd price discrimination

• 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 gt 72xNh ? 31.50Nl gt
  28Nh

Nh
31.50
This requires that
lt
1.125
Nl
28
There should not be too high a proportion of
high-demand consumers
17
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
• 2nd price discrimination converts consumer
  surplus into profit less effectively than
  first-degree
• Some consumer surplus is left on the table to
  induce high-demand groups to buy large quantities

18
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
• International pricing
• early-bird specials

19
Third-degree price discrimination

• 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

20
Third-degree price discrimination

• 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

21
An example
Type 1 Demand P A1 - BQ1
Type 2 Demand P A2 - BQ2
Since A1 gt A2 Type 1 consumers are charged
a higher price than Type 2 consumers
MR1 A1 - 2BQ1
MR2 A2 - 2BQ2
MC c
MC c
? Q1 (A1 - c)/2B
? Q2 (A2 - c)/2B
? P1 (A1 c)/2
? P2 (A2 c)/2


A1
A2
(A1c)/2
(A2c)/2
MR2
MR1
A1/B
A2/B
(A1-c)/2B
(A2-c)/2B
Quantity
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

23
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 for prices less
than 16
Invert these to give Q as a function of MR
Q1 10 - MR/2
MC 2Q
Q2 4 - MR/4
The consumers with less elastic demand
are charged higher prices
MC MR ? 2Q 56/3 - 4Q/3
So aggregate marginal revenue is
? Q 5.6
Q Q1 Q2 14 - 3MR/4
? MR 11.20
Invert this to give marginal revenue
? Q1 4.4 and Q2 1.2
MR 56/3 - 4Q/3 for MR lt 16
? P1 15.60 and P2 13.60
MR 20 - 2Q for MR gt 16
24
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
• so MR1 MR2
• ? P1(1 - 1/ ?1) P2(1 - 1/ ?2)

Prices are always higher in markets where demand
is inelastic
P1
(1 - 1/ ?2)
?

P2
(1 - 1/ ?1)
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

26
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
• but this requires that the consumer recognizes
  quality
• also some are willing to pay more than others for
  quality

27
Demand and Quality

• We might think of individual demand as being of
  the form
• Qi 1 if Pi lt 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

28
Demand and quality (cont.)
Begin with a particular demand curve for a good
of quality Z1
Price
Suppose that an increase in quality increases
the willingness to pay of inframarginal
consumers more than that of the marginal consumer
Then an increase in product quality from Z1 to Z2
rotates the demand curve around the quantity axis
as follows
R1(Z2)
P(Q, Z2)
If the price is P1 and the product quality is Z1
then all consumers with reservation prices
greater than P1 will buy the good
P2
R1(Z1)
Quantity Q1 can now be sold for the higher price
P2
This is the marginal consumer
These are the inframarginal consumers
P1
P(Q, Z1)
Quantity
Q1
29
Demand and quality (cont.)
Suppose instead that an increase in quality
increases the willingness to pay of
marginal consumers more than that of the
inframarginal consumers
Price
Then an increase in product quality from Z1 to Z2
rotates the demand curve around the price axis as
follows
R1(Z1)
Once again quantity Q1 can now be sold for a
higher price P2
P2
P1
P(Q, Z2)
P(Q, Z1)
Quantity
Q1
30
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
31
Demand and quality an example
P Z(q - Q)
Assume that marginal cost of output is zero
MC(Q) 0
Cost of quality is D(Z) aZ2
This means that quality is costly and
becomes increasingly costly
Marginal cost of quality dD(Z)/d(Z)
2aZ
The firms profit is
p(Q, Z) P.Q - D(Z)
Z(q - Q)Q - aZ2
The firm chooses Q and Z to maximize profit.
Take the choice of quantity first this is
easiest.
Zq - 2ZQ
Marginal revenue MR
MR MC ?
Zq - 2ZQ 0 ?
Q q/2
? P Zq/2
32
The example continued
Total revenue PQ
(Zq/2)x(q/2)
Zq2/4
So marginal revenue from increased quality is
MR(Z) q2/4
Marginal cost of quality is
MC(Z) 2aZ
Equating MR(Z) MC(Z) then gives
Z q2/8a
Does the monopolist produce too high or too low
quality?
Is it possible that quality is too high?
Only in particular constrained circumstances.
33
Demand and quality (cont.)
Price
Z2q
P(Q, Z2)
When quality is Z2 price is Z2q/2
How does increased quality affect demand?
MR(Z2)
When quality is Z1 price is Z1q/2
Z1q
P2 Z2q/2
P1 Z1q/2
MR(Z1)
P(Q,Z1)
q
q/2
Quantity
Q
34
Demand and quality (cont.)
Price
So an increase in quality from Z1 to Z2
increases surplus by this area minus the increase
in quality costs
Z2q
The increase in total surplus is greater than
the increase in profit. The monopolist may
produce too little quality
An increase in quality from Z1 to Z2
increases revenue by this area
Z1q
P2 Z2q/2
P1 Z1q/2
q
q/2
Quantity
Q