Lecture 6
2nd and 3rd Degree Price
Discrimination
AEM 4160: STRATEGIC PRICING
Prof. Jura Liaukonyte
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Two-Part Tariffs
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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?
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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.
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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
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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
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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
• Per-minute price of 10 cents and monthly fee of $40.50
– High-demand customers …
– Low-demand customers …
• Per-minute price of 10 cents and monthly fee of $8
– High-demand customers …
– Low-demand customers …
Question
• Q: Which plan is better?
– A:
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Profit-Maximizing Two-Part Tariff
Suppose Clearvoice wants to offer a single two-part tariff
High
Demand
Low
Demand
• Per-minute price of 10 cents and monthly fee of $40.50
– High-demand customers accept
– Low-demand customers reject
• Per-minute price of 10 cents and monthly fee of $8
– All consumers accept
Question
• Q: Which plan is better?
– A: If there are a large number of low-demand customers, $8
monthly fee is better
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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
Max Profits above marginal cost
– Regardless of the types’ relative proportions
Intuition
• 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
Conclusion worthwhile it is to raise the per-unit price
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Benefits of Raising the Per-Minute Charge
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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
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High-Demand Consumers
Suppose Clearvoice offers a pair of two-part tariffs
Low
Demand
• First Option for low-demand consumers:
– Per-minute price of 20 cents, fixed fee of $4.50
• Second option intended to attract high-demand customers:
High
Demand
– Per-minute price of 10 cents, equal to Clearvoice’s marginal cost
– Fixed fee should be set as high as possible without causing highdemand consumer to choose the other plan
• With menu of plans:
Effects
– Firm profits are higher from high-demand consumers
– Profits from low-demand consumers are the same
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Menu of Two-Part Tariffs
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18-13
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 high-demand
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
–
–
–
–
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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
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Capping Minutes
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Menu of Two-Part Tariffs
• A firm can often profit by offering a menu of choices
– Designed for different types of consumers
• To maximize its profits, firm should try to make each plan
attractive to one group only
– And unattractive to other consumer groups
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Third Degree Price Discrimination
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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
– Subscriptions to professional journals [library/student]
– Entry prices by age
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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
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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
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The Example: No Price Discrimination
• Suppose that the same price is charged in both markets
• What do we need to find out?
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The Example: No Price Discrimination
• Suppose that the same price is charged in both markets
• What do we need to find out?
• 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
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The Example
United States: PU = 36 – 4QU
QU = 9 – P/4 for P < $36
Europe: PU = 24 – 4QE
QE = 6 – P/4 for P < $24
Invert this:
Invert
At these prices
only the US
market is active
Aggregate these demands
Q = QU + QE = 9 – P/4 for $24 < P < $36
Q = QU + QE = 15 – P/2 for P < $24
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Now both
markets are
active
The Example
Invert the direct demands
P = 36 – 4Q for Q < 3
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P = 30 – 2Q for Q > 3
Marginal revenue is
MR = 36 – 8Q for Q < 3
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MR = 30 – 4Q for Q > 3
Set MR = MC
Q = 6.5
$/unit
Demand
MR
MC
6.5
Price from the demand curve P = $17
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Quantity
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The Example
• 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
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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
• 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
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The Example
$/unit
Demand in the US:
PU = 36 – 4QU
Marginal revenue:
36
20
MR = 36 – 8QU
MC = 4
4
Equate MR and MC
QU = 4
Price from the demand curve
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Demand
MR
MC
4
PU = $20
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Quantity
The Example:
$/unit
Demand in the Europe:
PE = 24 – 4QE
Marginal revenue:
24
14
MR = 24 – 8QE
MC = 4
4
Equate MR and MC
QE = 2.5
Price from the demand curve
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Deman
d
MR
MC
2.5
PE = $14
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Quantity
The Example
• 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
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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
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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/ηi)
– Where ηi is (absolute value of) elasticity of demand
• From rule 1 (above)
– MR1 = MR2
– So = P1(1 – 1/η1) = P2(1 – 1/η2) which gives
P1 1  1  2  1 2  1


.
P2 1  1 1  1 2   2
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Price is lower in the
market with the
higher demand
elasticity
Takeaways
– Firms would prefer to use perfect (aka first-degree) price
discrimination, but this may be impossible.
– Third-degree PD is one way to approximate perfect PD, but requires
that firms can separately identify members different groups.
– Second-degree PD induces customers to sort themselves into groups.
– Recall the no arbitrage constraint—consumers can’t resell to others.
– Price discrimination and other advanced pricing strategies are
powerful tools; you now have the economic models to understand
them.
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BUNDLING AND TYING
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Introduction
• Firms often bundle the goods that they offer
– Microsoft bundles Windows and Explorer
– Office bundles Word, Excel, PowerPoint, Access
• Bundled package is usually offered at a discount
• Bundling may increase market power
– GE merger with Honeywell
• Tie-in sales ties the sale of one product to the purchase of
another
• Tying may be contractual or technological
– IBM computer card machines and computer cards
– Kodak tie service to sales of large-scale photocopiers
– Tie computer printers and printer cartridges
• Why? To make money!
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More Examples of Bundling
• Telecommunications
– Firms bundle local, long-distance, and mobile telephone services,
• Banks
– Bundle checking, credit, and investment services
• Hospitals bundle an array of medical services
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Incentives to Bundle
• Bundling may arise in many contexts to sort consumers in
a manner similar to second-degree price discrimination.
• When consumers have heterogeneous tastes for several
products, a firm may bundle to reduce that heterogeneity,
earning greater profit than would be possible with
component (unbundled) prices.
• Bundling—like price discrimination—allows firms to design
product lines to extract maximum consumer surplus.
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Bundling Advantages
• Simplifies consumer choice (as in telecommunications and
financial services)
• Reduces costs from consolidated production of
complementary products
• Reduces consumer search costs and product or marketing
costs
• Bundling to extend market power and/or deter entry
– as witnessed by antitrust challenges to Microsoft’s bundling of software
applications (e.g. its Internet browser, media player) with its dominant
Windows operating system
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Cable TV
• Crawford’s (2001) empirical study of bundling decisions of
cable providers
• Bundle several networks into a basic bundle service, cable
provider increases its profit on average above unbundled
sales by 14%
• 13% less CS than from unbundled sales
• bundling together similar networks is less profitable than
bundling dissimilar ones
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Example: Cable and Satellite TV Industry
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Third Degree Price Discrimination
• Raw Data Analysis
– Collected the price of Comcast Xfinity’s basic cable in 11 cities
• Chose Comcast because it has the largest market share
– Plotted prices relative to geography
– Ran regressions against the number of competitors in the market
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Geographic Price Discrimination
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Price of Basic Cable ($)
20
15
Price of Basic Cable
10
5
0
Price vs. Number of Competitors in the Marketplace
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Price
25
Log. (Price)
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Price of Basic Cable ($)
Linear (Price)
y = -1.5295x + 27.735
R² = 0.5554
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R² = 0.6439
10
5
0
0
1
2
3
4
5
6
Number of Competitors
7
8
9
10
Computer Software Suites
• Microsoft and others bundle dissimilar programs—word
processors and spreadsheets—into a suite
• Gandal (2003):
– survey of home PC users: 43% use both programs;50% used only one;
7% used neither
– survey business PC users: 63% used both, 37% used only one
– A lot of users use only one (but not both) pieces of software
– consumers with a high value for spreadsheets had a low value for word
processors and vice versa: negative correlation in demand
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Tie-In Sales
• Generally considered to be an ‘extension of monopoly’ by
courts. In other words, courts believed it was an attempt to
use one monopoly to create a second.
• Frequently, tying good is sold very cheaply, while tied good
is very expensive. Famous cases: IBM and computer
cards, Xerox and toner, Canning machines and tin plate.
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Printers and Ink Cartridges
• High-intensity usage consumers => high willingness-topay
• Low-intensity usage consumers => print small volumes =>
a low willingness-to-pay
• Strategy: lower the price of the initial, one-time purchase
printer and raise the price of the aftermarket, repeat
purchase ink cartridge
• Ink cartridge becomes the mechanism by which
consumers' intensity of usage is metered:
– Inducing high-intensity users to pay a higher overall price
– Low-intensity users a lower overall price
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Examples cont’d
• This basic idea holds for a variety of other aftermarket
situations:
– Razors and razor blades
– Video game consoles and video games
– Etc.
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Anti-Trust and Bundling
• The Microsoft case is central
– Accusation that used power in operating system (OS) to gain
control of browser market by bundling browser into the OS
– Need to show
• Monopoly power in OS
• OS and browser are separate products that do not need
to be bundled
• Abuse of power to maintain or extend monopoly position
– Microsoft argued that technology required integration
– Further argued that it was not “acting badly”
• Consumers would benefit from lower price because of the
complementarity between OS and browser
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And now…
• This view gained more force and support in Europe
– Bundling of Media Player into Windows
– Competition Directorate found against Microsoft
• No on appeal
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Antitrust and tying arrangements
• Tying arrangements have been the subject of extensive
litigation
• Current policy
– Tie-in violates antitrust laws if
• There exists distinct products: tying product and tied one
• Firm tying the products has sufficient monopoly power in the tying
market to force purchase of the tied good
• Tying arrangement forecloses or has the potential to foreclose a
substantial volume of trade
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