Lecture Notes for
Pindyck and Rubinfeld Chapter 11:
Pricing with Market Power
Example:
A Theater’s Profit Based on the Pricing Method Used
1
First Degree Price Discrimination or Perfect Price Discrimination
p, $ per unit
6
5
e
MC
4
3
Demand, Marginal revenue
MR1 = $6 MR2 = $5 MR 3= $4
2
1
0
1
2
3
4
5
6
Q, Units per day
With Perfect First Degree Price Discrimination, customers pay their
maximum willingness to pay. In this way, the monopolist captures all the
consumer surplus (and turns it into profit).
The “willingness to pay” is also referred to as the “reservation price.”
With first degree price discrimination, the MR curve is no longer relevant to
the monopolist’s decision. It’s the demand curve - representing willingness
to pay - that is relevant. (In other words, the MR is the demand curve for
the first degree price discriminator.)
It’s necessary for the firm to be able to identify a customer’s willingness to
pay.
2
In practice, perfect first degree price discrimination might not be possible,
so a firm may charge a number of different prices representing the
approximate reservation prices of consumers – capturing less than all the
consumer surplus, but more than a monopolist that charges a single price.
P
MC
P4
P3
P2
P1
D
Q
3
Competitive, Single-Price, and Perfect Discrimination Equilibria
p, $ per unit
p1
A
ps
B
p c =MCc
MC
es
C
ec
E
D
MCs
Demand,MR d
MC1
MR s
Qs Qc=Q d
Q , Units per day
The quantity produced by the first degree price discriminator is the
same as the perfect competition quantity, which is larger than the
quantity produced by the single price (i.e. non-discriminating)
monopolist. Therefore there is no deadweight loss with perfect price
discrimination. However, all the CS under competition is captured as
PS for the perfect price discriminator.
4
Second Degree Price Discrimination or Quantity Discrimination
The willingness to pay for the first few units of a good is high, then the
willingness to pay for additional units is less.
Second Degree Price Discrimination entails charging different prices for different
quantities of the good.
Examples: Quantity Discounts (generally) and Block Pricing (for electricity, for
example).
(a)
Second Degree or Quantity Discrimination
p1, $ per unit
90
A=
$200
70
C=
$200
50
B=
$1,200
D=
$200
30
mc
Demand
0
20
40
9
Q , Units per day
0
The first 20 units cost $70 each. The next 20 units cost $50 each.
5
(b)
Single-Price Monopoly
p
, $ per unit
2
90
E = $450
60
F = $900
G = $450
m
cmc
30
Demand
MR
0
30
90
Q , Units per day
This table compares the CS, PS, and deadweight loss between second degree
price discrimination (last slide) and single price monopoly (this slide) using the
same demand curve and MC.
The deadweight loss is less with quantity (or second degree price) discrimination
than with the single price (i.e. non-price discriminating monopoly. The second
degree price discriminator gets more PS than the single price monopolist. CS is
less when there is second degree price discrimination than with the single price
monopolist.
6
Third Degree Price Discrimination or Multi-market Pricing
Third Degree Price Discrimination entails charging different prices to
different groups of consumers – each group of consumers has a
different demand curve.
Examples: Discounts to students or seniors (because they have lower
willingness to pay).
Airfares: higher fares charged to business travelers than other travelers
(due to Saturday stay-over requirements for discounts).
Coupons: Only those persons willing to spend time cutting coupons
will use them, so not necessary to give everyone discounted price!
Need a way to distinguish groups of customers!
Let there be two groups of customers. Then two conditions must hold
for profit maximization:
1. MR1(Q1) = MR2(Q2) The MR received from each group of
customers must be equal. If MR1 > MR2, then the firm can lower p1
and raise p2 in order to increase Q1 and decrease Q2, thus raising
profits.
2. MR1(Q1) = MR2(Q2)= MC(Q1+ Q2)
If only a single price is charged to both groups of customers, then we
don’t have MR=MC in both markets. If we don’t have MR=MC in
both markets, then we’re not profit maximizing!
7
Third Degree Price Discrimination: Example
(a) Japan (MARKET ONE)
pJ, $ per unit
3,500
CSJ
pJ = 2,000
DJ
J
DWLJ
500
MC
MRJ
0
QJ = 3,000
7,000
QJ, Units per year
(b) United States (MARKET TWO)
p US, $ per unit
4,500
CSUS
pUS = 2,500
D
US
US
DWLUS
500
MC
MRUS
0
QUS = 2,000
4,500
Q , Units per year
US
8
Another way to look at the Third-Degree Price Discrimination
Problem:
MC
MR1
Q1
Q2
MR2
MRT
QT
Q
To find QT = Q1+ Q2, find the intersection of the MC curve with the
combined MRT curve. The MRT curve can be found by summing the
individual MR curves horizontally.
QT is the total amount of output sold, and Q1 and Q2 are the quantities sold
to customers is market/group 1 and 2 respectively.
9
Third Degree Price Discrimination (cont’d)
Recall from chapter 10 that:
MR = P(Q) + P'(Q)Q
= P + P(P'(Q)(Q/P)]
= P (1 + 1/ed) (where ed = elasticity of demand)
We can apply this to the third degree price discrimination model to see the
relationship between the prices charged in each market.
MR1 = P1(1+1/e1) for market 1 and
MR2= P2(1+1/e2) for market 2
Since MR1 = MR2, then P1(1+1/e1) = P2(1+1/e2), or
P1/P2 = (1+1/e2)/(1+1/e1).
Example: If e1 = -2 and e2 = - 3, then P1/P2 = 4/3 so that the price charged
in market 1 is 1.33 times the price charged in market 2.
Final note of caution: If MC rising fast (steep upward sloping) and one of
the markets is small (low demand), it may not be worth it to sell to the small
market.
10
Intertemporal Price Discrimination
Intertemporal price discrimination means that customers are separated into
different groups by charging different prices at different points in time.
This is intended to capture the consumer surplus of those people who want
the newest goods right away and are willing to pay high prices for them.
Example: newest models of electronic goods, computers, cell phones, etc.
are priced much higher than next to last model. New books come out
originally as hardbacks and sold at much higher prices than paperback
versions that are published a year or so later.
Those with demand D1 have a high willingness to pay for new goods as
soon as they come out.
D2
MR1
D1
MR2
11
Two-part Tariff
With a two-part tariff, you first pay an upfront entry fee (T), then you pay a
per unit usage fee (P).
Example: Club membership + fees for using facilities, razors and blades
sold separately, printers that need specialized ink cartridges, phone service
(connection fee + per minute charge).
Total revenue per customer (i) = T + PQi.
ONE CUSTOMER
If there’s only one customer (or one type of customer), profit maximizing
choice is to charge P = MC and T = entire CS.
p, $ per unit
100
D2
T = $4050
10
0
mc
90 100
q2, Units per day
12
Two-Part Tariff (cont’d)
Two customers
If there are two types of customers, you will charge P>MC and T = remaining CS
of the customer with the smaller demand.
(a) Consumer 1
p, $ per unit
80
D1
A 1 = $1,800
20
10
C1 = $50
B1 = $600
mc
0
60 70 80
q1, Units per day
(b) Consumer 2
p, $ per unit
100
D2
A2 = $3,200
20
10
0
C2 = $50
B2 = $800
mc
80 90 100
q2, Units per day
13
Two-Part Tariff (cont’d)
From the previous slide:
If you were to charge P = MC and T = 2450 (the whole CS of
consumer 1, the one with smaller demand), then
Profit = 2(2450) = $4950.
If you charge P = 20 > MC and T = 1800, then
Profit = 2(1800) + 60(10) + 80(10) = $5000. ******
THEREFORE, if there are two customers (or two types of customer), it is more
profitable to charge P>MC and T = remaining CS of the customer with the
smaller demand.
With many types of customers, one must consider the trade-off.
Lower T means more customers will join (because of the more
affordable “entry fee”) but lower entry fee revenue per customer.
More customers means more per unit sales for usage.
Comparing the one-customer to the two-customer case, we can make the
following generalizations:
a. When customers are similar (have similar demand curves), then charge a high
entry fee (T) and a per unit price (P) so that P is close to MC.
b. When customers’ demands curve are different, then charge a lower entry fee
(T) but a higher per unit price (P) so that P>MC.
 The two-part tariff works best when customers have similar demand
curves.
 If demand curves are very different, then it might be better to drop the
entry fee and set P as a single-price (i.e. non-discriminating) monopolist.
14
Two-Part Tariff (cont’d)
Let N be the number of customers who are willing to pay the entry fee,
then:
Profit = N(T)T + (P-MC)Q(N(T))
1. N(T)T is the revenue from the entry fee. The number of customers willing to
pay the entry fee falls as T rises. As T rises, N(T)T initially rises (because the fee
per customer rises), but then falls (as T becomes high, fewer and fewer customers
are willing to pay).
Think about this as similar to what happens to MR in the regular monopoly case
when we lower P.
d(N(T)T)/dT = N’(T)T + N(T)
(-)
(+)
 As T rises, the first term of the derivative is negative (because N’(T) negative
since raising T drives away customers). The second term is positive. Initially,
revenue rises as T rises because the second term (+) overpowers the first term (-).
Then after a certain T, revenue falls as T increases further, because the first term
of the derivative (-) overpowers the second term (+). This gives rises to an
inverse U curve for the entry fee revenue.
2. (P-MC)Q(N(T)) is the revenue from per unit sales. Holding P and MC
constant, the revenue from per unit sales falls as T rises. This is because higher
T means fewer customers (N) paying the entry fee. Fewer customers means
lower per unit sales (Q).
15
Two-Part Tariff (cont’d)
Reminder: In the graph below, P and MC are held constant.
Total Profit= entry fee + unit sales
Entry fee revenue
Unit sales profit
T
16
Bundling
Bundling means that two or more different goods are sold as a package.
 Bundling is used when customers have heterogeneous demands. See the two
numerical examples below:
Example 1:
Reservation Prices:
Person A
Person B
DVD1: “There’s Something
About Mary”
$10
$8
DVD2: “Meet the
Parents”
$5
$6
Reading the Table: According to the table above, person A has a maximum
willingness to pay of $10 for the DVD “There’s Something About Mary.”
Note: Person A has a higher willingness to pay than Person B for DVD1. But the
reverse is the case for DVD2.
Let MC = 0
Two Pricing Strategies:
1. Sell DVD1 and DVD2 individually:
Set p1 = $8 and p2=$5. These are the maximum prices that can be charged while
selling to both customers. Given that MC=0, you want to sell to both customers.
Profit = 2($8) + 2($5) = $26
2. Sell DVD1 and DVD2 as a bundle – the “Ben Stiller Special”:
Set the price of the bundle pb = $14. That’s the maximum that can be charged if
you want to sell to both customers.
Profit = 2($14) = $28 ***
 In Example 1, profit is higher when selling as a bundle.
17
Bundling (cont’d)
Example 2:
Reservation Prices:
Person A
Person B
DVD1: “There’s Something
About Mary”
$10
$8
DVD2: “Meet the
Parents”
$6
$5
In example 2, we’ve switched the willingness to pay for DVD2, but the numbers
in the table are otherwise the same.
Two Pricing Strategies:
1. Sell DVD1 and DVD2 individually:
Set p1 = $8 and p2=$5. These are the maximum prices that can be charged while
selling to both customers. Given that MC=0, you want to sell to both customers.
Profit = 2($8) + 2($5) = $26
2. Sell DVD1 and DVD2 as a bundle – the “Ben Stiller Special”:
Set the price of the bundle pb = $13. That’s the maximum that can be charged if
you want to sell to both customers.
Profit = 2($13) = $26
 In Example 2, profit is the same whether selling as a bundle or individually.
WHY?
18
Bundling (cont’d)
Why does bundling create higher profits in Example 1 but not in Example 2?
Answer: Because in Example 1 demands were negatively correlated, but in
example 2 demands were positively correlated. To see this, look at the two
graphs of the reservation prices.
In the graph below, if you draw a line through points A and B, it is negatively
sloped.
Example 1: Graphing Reservation Prices
Reservation
price for good 2
(r2)
B
6
5
A
1
Reservation price for good 1
(r1)
1 2 3 4 5 6 7 8 9 10
In the graph below, if you draw a line through points A and B, it is positively
sloped.
Example 2: Graphing Reservation Prices
Reservation
price for good 2
(r2)
6
5
A
B
1
1 2 3 4 5 6 7 8 9 10
Reservation price for good 1
(r1)
19
Bundling (cont’d)
If you only offer goods as a bundle, it’s called “pure bundling.” If you offer
goods individually or as a bundle, it’s called “mixed bundling.”
Mixed Bundling
Mixed bundling may lead to higher profits than pure bundling when either:
1. MC >0
2. Demands not perfectly negatively correlated.
Example 3: MC>0
Reservation Prices:
Person A
Person B
Person C
Person D
DVD1: “There’s Something
About Mary”
$10
$50
$60
$90
DVD2: “Meet the
Parents”
$90
$50
$40
$10
MC1 = 20, MC2 = 30.
If you graph the reservation prices of Persons A, B, C, and D, you will see
that they are perfectly negatively correlated because they’re all on the line r1
+ r2 = 100
Reservation
price for good 2
(r2)
Reservation price for good 1
(r1)
20
Mixed Bundling (cont’d)
Example 3 Pricing Strategies:
1. Sell DVDs individually:
Set p1 = 50 and p2 = 90.
Then Persons B, C, and D buy DVD1 and Person A buys DVD2.
Profit = 3(50-20) + (90-30) = $150.
(To see why p1 = 50 and p2 = 90 is the best individual prices, try p1 = 90
or 60 and p2 = 50 or 40 and calculate the profit.)
2. Pure Bundling:
Set pb = $100
Then all 4 customers buy the bundle.
Profit = 4(100) – 4(20) – 4(30) = $200.
3. Mixed Bundling:
p1 = p2 = $89.99
pb = $100
Person A buys DVD2 only (because they get Consumer Surplus = $0.01
from buying DVD2 but CS = 0 from the bundle). Person D buys DVD1
only (similar reasoning as Person A). Persons B and C buy bundle (CS =
0, so they’re indifferent between buying and not buying the bundle – we
assume they buy).
Profit = 200 + 2(89.99) – 3(20) – 3(30) = $229.98 ***
Why mixed bundling is better here: Recall MC1 = 20, MC2 = 30. Person A
had a very high reservation price for DVD2 but a very low reservation price
for DVD1, and with person D it was the opposite case. (Note that MC1 <
reservation price of A for DVD1 and MC2 < reservation price of D for
DVD2.) Therefore it’s better to give these two customers the incentive to
buy one DVD only – the one for which they have a very high reservation
price – and save on the manufacturing costs for the DVD that is not valued
very highly.
21
Mixed Bundling (cont’d)
Example 4: Demands not perfectly negatively correlated
Reservation Prices:
Person A
Person B
Person C
Person D
DVD1: “There’s Something
About Mary”
$10
$40
$80
$90
DVD2: “Meet the
Parents”
$90
$80
$40
$10
MC1 = MC2 = 0.
If you graph the reservation prices of Persons A, B, C, and D, you will see
that they NOT are perfectly negatively correlated because they’re not all on
a straight line.
Reservation
price for good 2
(r2)
Reservation price for good 1
(r1)
22
Example 4 Pricing Strategies:
1. Sell DVDs individually:
Set p1 = 80 and p2 = 80.
Then Persons C and D buy DVD1 and Persons A and B buy DVD2.
Profit = 4(80) = $320.
(To see why p1 = 80 and p2 = 80 is the best individual prices, try p1 = 90,
40, or 10 and p2 = 90, 40, or 10 and calculate the profit.)
2. Pure Bundling:
Set pb = $100
Then all 4 customers buy the bundle.
Profit = 4(100) = $400.
3. Mixed Bundling:
p1 = p2 = $90
pb = $120
Person A buys DVD2 only and Person D buys DVD1 only, because the
bundle is too expensive. Persons B and C buy the bundle.
Profit = 2(120) + 2(90) = $420 ***
Why mixed bundling is better here: Person A had a very high reservation
price for DVD2 but a very low reservation price for DVD1, and with person
D it was the opposite case. Persons B and C have a higher joint valuation
for the bundle ($120) than Persons A and D ($100). Therefore it’s better to
give A and B the incentive to buy one DVD only – the one for which they
have a very high reservation price – while charging a higher bundle price to
Persons B and C.
23
Example: Bundling of Tickets to Football Games
24