1. Lecture 5 Monopoly Pricing
ECON 4100: Industrial Organization
Lecture 5 Monopoly Pricing

2. Introduction Tim Hartford https://www.youtube.com/watch?v=cuQUenY_dNg
Fair trade coffee
Bulgaria:

3. Introduction Monopoly pricing MR = MC
uniform versus non-uniform pricing
perfect price discrimination and the appropriation of surplus
types of price discrimination and conditions to implement them
first degree price discrimination
two-part tariffs and block pricing

4. Introduction A monopolist has the power to set prices
We assume that this power is used to maximize profits
Consider how the monopolist exercises this power
Focus first on a single-product monopolist:
MC=MR
Then charge the highest price

5. First-Degree Price Discrimination
First-degree price discrimination occurs when the seller is able to extract the entire consumer surplus
Highly profitable but requires:
detailed information
ability to avoid arbitrage
(The rural doctor can do it, local prostitutes…and of course the personal tax consultants!)
Some firms have made an art of price discrimination (real state agents, used car dealers, etc.)
Leads to the efficient choice of output (P=MC): since P=MR and MR = MC

6. 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

7. Two-Part Pricing $ Take an example: V Jazz club: n identical consumers
Demand is P = V - Q
Cost is C(Q) = F + cQ
Marginal Revenue is c MC
MR = V - 2Q MR
Marginal Cost is V
MC = c
Quantity

8. Two-Part Pricing What if the seller can charge an entry Charging an
entry fee increases
profit by
(V - c)2/8
per consumer
Two-Part Pricing
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
(V+c)/2
V - 2Q = c c MC
So Q = (V - c)/2 MR
P = V - Q
So P = (V + c)/2 V
(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

9. 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 MC
This increases consumer
Surplus, so it increases
the entry charge MR V
(V-c)/2
Quantity

10. Set the unit price equal
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
monopolist’s
profit
Set the unit price equal
to marginal cost c MC MR
This gives consumer
surplus of (V - c)2/2
V - c V
Quantity
Set the entry charge
to (V - c)2/2

11. 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 (or even lower than that…in fact sometimes free if exacting a price is costly, SODEXO does it!)
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

12. 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
Consumer surplus
for the older
customers is $72
Assume that
marginal cost is
constant at
$4 per unit
And younger
customers each
buy 8 units 12
$72
$72
$32
$32 4 MC 4 MC
$48
$32 12 16 8 12
Quantity
Quantity

13. Second degree price discrimination 4
Low income
consumers will not
buy the ($88, 12)
package since they
are willing to pay
only $72 for 12
drinks
Second degree price discrimination 4
These packages exhibit
quantity discounting: high-
income pay $7.33 per unit and
low-income pay $8
This is the incentive
compatibility constraint
High-income
Low-Income
So any other package
offered to high-income
consumers must offer at
least $32 consumer surplus
So will the high-
income consumers:
because the ($64, 8)
package gives them $32
consumer surplus
The low-demand consumers will be
willing to buy this ($64, 8) package
So they can be offered a package
of ($88, 12) (since $ = 88)
and they will buy this $
High income consumers are
willing to pay up to $120 for
entry plus 12 drinks if no other
package is available
Profit from each high-
income consumer is
$40 ($88 – (12 x $4)) $
And profit from
each low-income
consumer is
$32 ($64 - 8x$4) 16
Offer the low-income
consumers a package of
entry plus 8 drinks for $64 12
$32 8
$32
$32
$40
$32
$64
$24 $8 4 MC 4 MC
$16
$32
$32 $8 8 12 16 8 12
Quantity
Quantity
Chapter 6: Price Discrimination: Nonlinear Pricing

14. But…
We can check people’s ages…but sometimes age is not what matters (e.g. jazziness is what counts if we have a jazz club )
But jazziness is not easily observable! what if there is no way for the monopolist to identify the type of customer?
The monopolist would like to design the pricing scheme in such a way that customers self-select themselves: if they identify themselves, the monopolist does not have to do it!
That is what second-degree price discrimination is about

15. Second-Degree Price Discrimination
What if the seller cannot distinguish between buyers?
perhaps they differ in income, or jazziness (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

16. The example again 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
If a high-demand
consumer pays the lower
fee and buys 12 units he
gets $40 ($(144/2)-$32)
of consumer surplus
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.
This is still $32 better than getting
$0 with the 12-drink deal! $ $ 16 12
$32 8
$32
$32 $8 4 MC 4 MC
$16
$32
$32 8 12 16 8 12
Quantity
Quantity

17. 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

18. The example again High-Demand Low-Demand So any other package
offered to high-demand
consumers must offer at
least $32 consumer surplus
So will the high-
demand consumers:
because the ($64, 8)
package gives them $32
consumer surplus
This is the incentive
compatibility constraint
The low-demand consumers will be
willing to buy this ($64, 8) package
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 $ = 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 $
Profit from each high-
demand consumer is
$40 ($ x $4) $
Offer the low-demand
consumers a package of
entry plus 8 drinks for $64
And profit from
each low-demand
consumer is
$32 ($64 - 8x$4) 16 12
$32 8
$32
$32
$40
$32
$64
$24 $8 4 MC 4 MC
$16
$32
$32 $8 8 12 16 8 12
Quantity
Quantity

19. 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 $92 ($ = $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
$44
$31.50
$92
$59.50 4 MC 4 MC
$28
$48
$28 7 12 16 7 8 12
Quantity
Quantity

20. 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 (try going to Raymond’s and asking for a small one of French fries with gravy
golf and country clubs
Take our example again
suppose that there are Nl low-income consumers
and Nh high-income consumers

21. Second-degree price discrimination (cont.)
This type of price discrimination is everywhere
Buy 2 litres of milk and get the 3rd one free
Buy the big pizza and we will give you a free drink
This is not generally because there are economies of scale when serving in bulk, as most people think!

22. 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 Nh
31.50
This requires that
<
= 1.125 Nl 28
There should not be “too high” a proportion of high-demand consumers

23. 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

24. 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 versus rented ones

25. 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

26. 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
We can illustrate with a simple example on the board
monopolist has constant marginal costs of c per unit
two identifiable types of consumers
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

27. Third-degree price discrimination (cont.)

28. Third-degree price discrimination with varying MC
Now consider an increasing MC (MC=2Q)
two identifiable types of consumers
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

29. The example Two markets Market 1: P = 20 - Q1 Market 2: P = 16 - 2Q2
Now calculate
aggregate marginal
revenue
MR1 = Q1
MR2 = Q2
Note that this applies
only for prices less than
$16 (there is a KINK)
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 = MR/4
 MR = $11.20
Invert this to give marginal revenue:
 Q1 = 4.4 and Q2 = 1.2
MR = 56/3 - 4Q/3 for MR < $16
 P1 = $15.60 and P2 = $13.60
MR = Q for MR > $16

30. 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)

31. Price discrimination and welfare Public Policy
Next
Price discrimination and welfare
Public Policy
The multiplant monopolist

32. Market 1 Market 2 Aggregate $ $ $ $20 $20 MC $16 $15.60 $16 $13.60
$11.20 D1
MR1+MR2
MR1 D2
MR2
4.4 10 20
1.2 4 8
5.6 14
Quantity
Quantity
Quantity

33. 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