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Lecture 5: Price
Discrimination
AEM 4160: Strategic Pricing
Prof. Jura Liaukonyte
Lecture Plan

1
HW1
Second degree price discrimination


2
Designing pricing plans for consumers to self-select
themselves
Examples
Third degree price discrimination


Market segmenting
Examples
Second Degree PRICE
DISCRIMINATION
Price Discrimination Based on SelfSelection

Often firms cannot distinguish between groups of consumers based
on observable characteristics
Price Discrimination may still be
possible


Offer a menu of alternatives to let customers self-select
 If properly designed, customers with different willingness to pay
will choose different alternatives
Examples: supermarket discounts for shoppers who clip coupons,
wireless phone companies with multiple calling plans
Second-degree price discrimination
principles



Induce customers to select into high and low price
groups themselves.
Key constraint: you can’t make the inexpensive version
too attractive to those willing to pay more.
If there aren’t many customers in the low-valuation
group, you may want to ignore this group, since selling to
it forces you to lower the price to the high valuation
group.
Example: Coupons
Coupons
Grocery Trends (2009)
Coupons
Distributed
+12%
Coupons Redeemed
+19%
Internet Coupons
+83%
75% of coupon users say coupon
had at least some influence on their
decision to purchase a new product
Coupons


A form of second-degree
price discrimination
Enables retailers to attract
informed customers by
discounting
Coupon Overview
Coupon Usage Distribution
Coupons and Income



Trends relating to newspaper readership provide
some explanation for this imbalance.
According to Scarborough Research, better
educated and higher income households buy and
read the newspaper more than others and
newspapers remain a key vehicle for delivering
coupons.
Additionally, promotions are generally targeted in
areas with more affluent consumers.
In essence, the better educated and more affluent
consumers are much better at looking for deals as
they recognize the value of money.
Two-Part Tariffs
More types of second degree price
discrimination

Multiple two-part tariffs


Examples of two-part tariffs: cell phone plans with monthly and
per minute fees.
Idea: separate between low volume users and high volume
users.

A two-part tariff is a lump-sum fee, p1, plus a price p2 for each
unit of product purchased.

Thus the cost of buying x units of product is p1 + p2x.

Q: What is the largest that p1 can be?
Two-Part Tariffs




p1 + p2x
Q: What is the largest that p1 can be?
A: p1 is the “entrance fee” so the largest it can be is
the surplus the buyer gains from entering the market.
Set p1 = CS and now ask what should be p2?
The monopolist maximizes its profit when using a two-part tariff by
setting its per unit price p2 at marginal cost and setting its lumpsum fee p1 equal to Consumers’ Surplus.
Profit with a Two-Part Tariff




Per-unit charge equals
marginal cost
Fixed fee is the consumer’s
surplus at that per-unit
price
Maximizes aggregate
surplus
Leaves the consumer no
surplus
18-16
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
Two-Part Pricing
$
Vi
The entry charge
converts consumer
surplus into profit
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
c
MC
MR
Vi - c
Vi
Quantity
Profit from each pair of Old and Young is now d = [(Vo – c)2 + (Vy – c)2]/2
Clearvoice Wireless Example


Clearvoice is a wireless telephone monopolist in a rural area
Two types of consumers: high-demand and low-demand

Distinct monthly demand curves for wireless minutes for each
group
Clearvoice Wireless Example

If we could observe consumer characteristics, we would offer
two-part tariff with 10-cent per-minute price
Low Demand

Fixed fee: $8 =(40*.4)/2
High Demand

Fixed fee : $40.50 = (90*.9)/2
Profit-Maximizing Two-Part Tariff
Suppose Clearvoice wants to offer a single two-part tariff
High
Demand




Low
Demand
Question
Per-minute price of 10 cents and monthly fee of $40.50
Per-minute price of 10 cents and monthly fee of $8



High-demand customers …
Low-demand customers …
High-demand customers …
Low-demand customers …
Q: Which plan is better?

A:
Profit-Maximizing Two-Part Tariff
Suppose Clearvoice wants to offer a single two-part tariff
High
Demand
Low
Demand
Question

Per-minute price of 10 cents and monthly fee of $40.50



Per-minute price of 10 cents and monthly fee of $8


High-demand customers accept
Low-demand customers reject
All consumers accept
Q: Which plan is better?

A: If there are a large number of low-demand customers, $8
monthly fee is better
Profit-Maximizing Two-Part Tariff

If the monopolist plans on selling to both types of consumers it is
always profitable to raise the per-unit price at least a little above
marginal cost
 Regardless of the types’ relative proportions

Extract some of high-demand consumers’ surplus without
changing surplus of low-demand consumer (already zero)
 Raise per-unit price to get more surplus from high-demand
consumers
 Adjust fixed fee so low-demand consumers’ surplus is
unchanged

The smaller the fraction of low-demand consumer, the more
worthwhile it is to raise the per-unit price
Max Profits
Intuition
Conclusion
Benefits of Raising the Per-Minute Charge
Using Menus to Increase Profit


Even better by offering a menu of two-part tariffs, each
designed to attract a specific type of consumer
Intuition:

Extract more surplus from high-demand consumers by making
the low-demand plan less attractive to high-demand customers
High-Demand Consumers
Suppose Clearvoice offers a pair of two-part tariffs
Low
Demand

First Option for low-demand consumers:


High
Demand
Second option intended to attract high-demand
customers:


Effects

Per-minute price of 20 cents, fixed fee of $4.50
Per-minute price of 10 cents, equal to Clearvoice’s marginal
cost
Fixed fee should be set as high as possible without causing
high-demand consumer to choose the other plan
With menu of plans:


Firm profits are higher from high-demand consumers
Profits from low-demand consumers are the same
Menu of Two-Part Tariffs
18-27
Making the Low-Demand Plan Less
Attractive

Can increase profit even more by making the low-demand
plan less attractive to high-demand consumers



That plan determines the fixed fee the firm can charge a highdemand consumer
It is the level that makes the high-demand consumer indifferent
between the two plans
Limit the number of minutes a consumer can purchase in the
20-cent-per-minute plan




Set the limit equal to the number low-demand consumers want
Will have no effect on value a low-demand consumer derives
Make the plan less attractive to high-demand customers
Will increase the fixed fee Clearvoice can charge high-demand
consumers for the 10-cent-per-minute plan
Capping Minutes
Menu of Two-Part Tariffs

A firm can often profit by offering a menu of choices


To maximize its profits, firm should try to make each plan
attractive to one group only


Designed for different types of consumers
And unattractive to other consumer groups
Firm benefits from setting the per-unit price in the plan
intended for consumers with the highest willingness to
pay equal to the marginal cost