### A.10 Monopolistic Pricing

```Readings
Baye 6th edition or 7th edition, Chapter 11
BA 445 Lesson A.10 Monopoly Pricing
1
Overview
Overview
BA 445 Lesson A.10 Monopoly Pricing
2
Overview
Uniform Pricing for a monopolized good determine price equal marginal cost
times a decreasing function of own price elasticity of demand. — So, Apple has
high markup since Apple demand has low elasticity.
Price Discrimination captures consumer surplus by charging prices equal to
willingness to pay for initial units rather than one price equal to the (lower)
willingness to pay for the last unit.
Block Pricing captures consumer surplus by packaging goods into a block, and
charging an average price per unit equal to the average willingness to pay. — So,
36-packs become profitable.
Bundle Pricing captures consumer surplus like block pricing, but the bundle
contains different types of goods. — So, Medieval Times bundles Valentine’s
photos with the Museum of Torture.
Two Part Pricing works like perfect price discrimination but consumer surplus is
captured by charging an entry fee. — So, Disneyland’s entry fee leaves no
surplus fun or magic, Disney gets it all.
Group Pricing applies uniform pricing rules for groups like seniors, students, and
kids. — So, Knott’s Berry Farm discounts to seniors since seniors cannot survive
Knott’s distinctive thrill rides.
BA 445 Lesson A.10 Monopoly Pricing
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Markup Rules
Markup Rules
BA 445 Lesson A.10 Monopoly Pricing
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Markup Rules
Overview
Markup Rules for a monopolized good determine price
equal marginal cost times a decreasing function of own
price elasticity of demand. — So, Apple has high markup
since Apple demand has low elasticity.
BA 445 Lesson A.10 Monopoly Pricing
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Markup Rules
A Linear Example of Uniform Pricing
• As a benchmark for this lesson, consider a firm with
linear demand and cost
 P = 10 - 2Q
 C(Q) = 2Q
• If the firm must charge the same price per unit to all
consumers, find the profit-maximizing quantity by setting
MR(Q) = MC(Q)
 10 - 4Q = 2, so Q* = 2
• Then, find price from demand, P* = 10 - 2(2) = 6
• Profits = (6)(2) - 2(2) = \$8.
BA 445 Lesson A.10 Monopoly Pricing
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Markup Rules
Graphing Uniform Pricing
Price
Profits from uniform pricing = \$8
10
8
6
4
MC
2
P = 10 - 2Q
1
2
3
4
5
Quantity
MR = 10 - 4Q
BA 445 Lesson A.10 Monopoly Pricing
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Markup Rules
Potential Non-Standard Profits
Price
Consumer surplus that might be captured = \$4
10
Profits from uniform pricing = \$8
8
6
captured = \$4
4
MC
2
P = 10 - 2Q
1
2
3
4
5
Quantity
MR = 10 - 4Q
BA 445 Lesson A.10 Monopoly Pricing
8
Markup Rules
The Standard Markup Rule for Non-Linear Demand
• Let E denote the own price elasticity of demand for a
firm’s product.
• Since MR = P[1 + E]/ E, setting MR = MC and simplifying
yields the standard markup rule:
P = [E/(1+ E)]  MC.
• The optimal price is a proportional markup over marginal
cost.
BA 445 Lesson A.10 Monopoly Pricing
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Markup Rules
An Example
• Elasticity of demand for Kodak film is -2.
• P = [E/(1+ E)]  MC
• P = [-2/(1 - 2)]  MC
• P = 2  MC
• Price is twice marginal cost.
• Fifty percent of Kodak’s price is margin above
manufacturing costs (marginal cost).
BA 445 Lesson A.10 Monopoly Pricing
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Markup Rules
Markup Rule and Market Power
• Market Power for any firm is inversely related to the
magnitude of own-price elasticity. So, according to the
markup rule, higher market power means higher price.
 For Apple computers elasticity is lower, say E = -2, so
P = [E/(1+E)]MC = 2MC
 For HP computers elasticity is higher, say E = -4, so
P = [E/(1+E)]MC = (4/3)MC
• For a perfectly competition, the own-price elasticity E = ∞, so the rule
P = [E/(1+ E)]  MC = [1-(1/(1+ E))]  MC
is
P = [1-(1/(1-∞))]  MC = 1  MC
or
P = MC.
BA 445 Lesson A.10 Monopoly Pricing
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Perfect Price Discrimination
Perfect Price Discrimination
BA 445 Lesson A.10 Monopoly Pricing
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Perfect Price Discrimination
Overview
Perfect Price Discrimination yields maximum possible profit
(capturing all consumer surplus and recovering and
capturing all deadweight loss) by charging higher prices
equal to willingness to pay for initial units rather than a
uniform price equal to willingness to pay for the marginal
unit. Perfect price discrimination requires perfect
knowledge of willingness to pay for each unit and for each
consumer. --- Peter may be charged \$4 for his first unit
and \$2 for his second unit, and Paul may be charged \$6 for
his first unit and \$1 for his second unit.
BA 445 Lesson A.10 Monopoly Pricing
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Perfect Price Discrimination
Example from CNN.com:
• According to a recent study, many consumers are unaware that
price discrimination occurs over the Internet.
• The Internet allows shoppers to easily compare prices across
thousands of stores. But it also enables businesses to collect
preferences, and financial resources -- and to set prices accordingly.
• So when you buy an airplane ticket or a DVD online, you may pay a
higher -- or lower -- price than another customer buying the very
same item from the very same site.
• Why? Because the information the site has compiled on you
suggests that you may be willing to pay more -- or less -- than others
for that item.
• (Another reason for price discrimination is to measure demand. The
company my be conducting random price tests to figure out what is
the ideal price point for its product.)
BA 445 Lesson A.10 Monopoly Pricing
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Perfect Price Discrimination
• Until now, all models involved a single optimum price.
• But there is more profit in charging different prices.
• Price discrimination is the practice of charging different
prices to consumers for the same good.
• Price discrimination can be perfect or imperfect.
 Perfect price discrimination achieves maximum
profits, leaving no surplus for consumers.
 Imperfect price discrimination achieves less than
maximum profits, and leaves some surplus for
consumers.
BA 445 Lesson A.10 Monopoly Pricing
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Perfect Price Discrimination
Perfect Price Discrimination
• Practice of charging each consumer the maximum
amount he or she will pay for each incremental unit (the
height of the demand curve).
• Permits a firm to extract all surplus from consumers and
BA 445 Lesson A.10 Monopoly Pricing
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Perfect Price Discrimination
Perfect Price Discrimination
Price
Profits*:
.5(4-0)(10 - 2)
= \$16
10
8
6
4
Total Cost* = \$8
2
MC
D
1
2
3
4
5
Quantity
* Assuming no fixed costs
BA 445 Lesson A.10 Monopoly Pricing
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Perfect Price Discrimination
Example:
• A Pepperdine professor visiting Mexico paid \$15 for a chess set
(about equal to the maximum he was willing to pay).
• When he returned to the same store, he was offered a lower price
on a second set. After refusing the offer, the price continued to
lower as the manager read his posture and tried to figure out the
maximum amount he would be willing to pay.
• Some say perfect price discrimination won’t work if consumers can
resell the good. It does get harder, but it is still possible:

Suppose a Pepperdine student is only willing to pay \$10 for a
chess set for himself, but that student could resell the set to the
professor for \$15.

How much would the student be charged for the first set?

For the second set? (the one he keeps for himself)
BA 445 Lesson A.10 Monopoly Pricing
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Perfect Price Discrimination
Caveat:
• Information constraints make perfect price discrimination
difficult (it is difficult to know how much someone is
willing to pay).
• The information constraints are especially difficult if
consumers can resell the good.
 The manager cannot just appraise the maximum price
the customer before him would pay for the good if he
were buying it for himself, but also how much that
customer could get by reselling the good.
BA 445 Lesson A.10 Monopoly Pricing
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Block Pricing
Block Pricing
BA 445 Lesson A.10 Monopoly Pricing
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Block Pricing
Overview
Block Pricing packages goods into a block. Block pricing
yields maximum possible profit from each consumer (just
like Perfect Price Discrimination) when the block price
results in an average price per unit equal to the average
willingness to pay. Knowing the profit-maximizing block
price for each consumer requires perfect knowledge of
willingness to pay for each unit. --- Peter may be charged
\$6 for a bag of 6 cookies, and Paul may be charged \$3 for
BA 445 Lesson A.10 Monopoly Pricing
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Block Pricing
Block Pricing
• When consumers can not resell the good and when the
firm has unlimited information, block pricing generates
the same maximum profit as perfect price discrimination.
• The practice of packaging multiple units of an identical
product together and selling them as one package.
• Examples
 Paper.
 Six-packs of soda.
 Different sized of cans of green beans.
BA 445 Lesson A.10 Monopoly Pricing
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Block Pricing
An Algebraic Example
• Typical consumer’s demand is P = 10 - 2Q
• C(Q) = 2Q
• Optimal number of units in a package?
• Optimal package price?
BA 445 Lesson A.10 Monopoly Pricing
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Block Pricing
Optimal Quantity To Package: 4 Units
Price
10
8
6
4
MC = AC
2
D
1
2
3
4
5
BA 445 Lesson A.10 Monopoly Pricing
Quantity
24
Block Pricing
Optimal Price for the Package: \$24
Consumer’s valuation of 4
units = .5(8)(4) + (2)(4) = \$24
Therefore, set P = \$24.
Price
10
8
6
4
MC = AC
2
D
1
2
3
4
5
BA 445 Lesson A.10 Monopoly Pricing
Quantity
25
Block Pricing
Costs and Profits with Block Pricing
Price
10
Profits* = [.5(8)(4) + (2)(4)] – (2)(4)
= \$16
8
6
4
Costs = (2)(4) = \$8
2
D
1
2
3
4
5
MC = AC
Quantity
* Assuming no fixed costs
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Commodity Bundling
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Overview
Commodity Bundling packages non-identical goods into a
block or bundle. Commodity bundling can yield more profit
than uniform pricing (but not maximum possible profit) by
charging an average price per unit equal to the average
willingness to pay. Commodity bundling may yield more
profit than block pricing when the seller does not know the
profit-maximizing block price for each consumer.
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Commodity Bundling
• The practice of bundling two or more differentiated products together
and charging one price for the bundle.
• Examples

Vacation packages.

Computers and software.

Film and developing.
• Commodity bundling is always possible because there are no
information constraints (unlike first-order price discrimination).
• Commodity bundling is sometimes profitable, sometimes not.

Let’s see an example of each.

Examples hint at a rule for when bundling is profitable.
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Example of unprofitable bundling
• Two products (combs and head wax), zero production cost.
• Two consumers (Fabio and Bruce Willis)

Fabio would pay \$1 for a comb and \$0 for head wax.

Bruce would pay \$0 for a comb and \$3 for head wax.
• If the goods are sold separately, compute the optimum nondiscriminating prices?

\$1 per comb, \$3 for head wax. Profit = \$4.
• If the goods are bundled, compute the optimum price for the bundle
of 1 comb and 1 jar of head wax?

Fabio would pay \$1 for the bundle (tossing the wax).

Bruce would pay \$3 for the bundle (tossing the comb).

Optimum price is \$3. Profit = \$3.
• It was better to keep the products unbundled.
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Example of profitable bundling: The Kodak Moment
• Total market size for film and developing is 4 million
consumers.
• Four types of consumers
 25% will use only Kodak film (F).
 25% will use only Kodak developing (D).
 25% will use only Kodak film and use only Kodak
developing (FD).
 25% have no preference (N).
• Zero costs (for simplicity).
• Maximum price each type of consumer will pay is as
follows:
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Reservation Prices (maximum consumers are willing to
pay) for Kodak Film and Developing by Type of Consumer:
Consumer
Type
Film Price
Developing
Price
F
FD
D
\$8
\$8
\$4
\$3
\$4
\$6
N
\$3
\$2
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Optimal Film Price?
• Assume no production cost.
• Optimal Price is \$8; only types F and FD buy, resulting in
profit of \$8 x 2 million = \$16 Million.
• At a price of \$4, only types F, FD, and D will buy, profits
= \$12 Million.
• At a price of \$3, all will types will buy, profit = \$12 Million.
Consumer
Type
Film Price
Developing
Price
F
FD
D
\$8
\$8
\$4
\$3
\$4
\$6
N
\$3
\$2
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Optimal Developing Price?
• Assume no production cost.
• At a price of \$6, only “D” type buys, profit = \$6 Million.
• At a price of \$4, “D” and “FD” buy, profit = \$8 Million.
• Optimal price \$3, only types “F”, “FD”, and “D” buy,
profits = \$9 Million.
• At a price of \$2, all will types will buy, profit = \$8 Million.
Consumer
Type
Film Price
Developing
Price
F
FD
D
\$8
\$8
\$4
\$3
\$4
\$6
N
\$3
\$2
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Total Profits by Pricing Each Item Separately.
• Assume no production cost.
• Total Profit = Film Profits + Development Profits
• Total Profit = \$16 Million + \$9 Million = \$25 Million.
• The firm can earn even greater profits by bundling.
Consumer
Type
Film Price
Developing
Price
F
FD
D
\$8
\$8
\$4
\$3
\$4
\$6
N
\$3
\$2
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Consumer valuation of a “Bundle” of Film and Developing
• Assume no production cost.
• Do not allow consumers to separately buy Film and
Developing.
Consumer
Type
Film Price
Developing
Price
Bundle
Price
F
FD
D
\$8
\$8
\$4
\$3
\$4
\$6
\$11
\$12
\$10
N
\$3
\$2
\$5
BA 445 Lesson A.10 Monopoly Pricing
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Commodity Bundling
Optimal Bundle Price?
• Assume no production cost.
• At a price of \$12, only “FD” type buys, profit = \$12 Million.
• At a price of \$11, “F” and “FD” buy, profit = \$22 Million.
• Optimal price \$10, only types “F”, “FD”, and “D” buy, profits = \$30
Million.
• At a price of \$5, all will types will buy, profit = \$20 Million.
Consumer
Type
Film Price
Developing
Price
Bundle
Price
F
FD
D
\$8
\$8
\$4
\$3
\$4
\$6
\$11
\$12
\$10
N
\$3
\$2
\$5
BA 445 Lesson A.10 Monopoly Pricing
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Two-Part Pricing
Two-Part Pricing
BA 445 Lesson A.10 Monopoly Pricing
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Two-Part Pricing
Overview
Two Part Pricing charges both a customer fee and a
uniform price per unit. Two-part pricing yields maximum
possible profit from each consumer (just like Perfect Price
Discrimination) when the uniform price equals marginal
cost and the customer fee equals consumer surplus, and
when customers cannot buy then resell to other customers.
Knowing the profit-maximizing two-part price for each
consumer requires perfect knowledge of consumer surplus.
--- Peter may be charged \$36 for admission to Disneyland
and a price of \$0 (= marginal cost) per ride, and Paul may
be charged \$13 and a price of \$0 per ride.
BA 445 Lesson A.10 Monopoly Pricing
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Two-Part Pricing
Two-Part Pricing
• When consumers can not resell the good and when the
firm has unlimited information, two-part pricing generates
the same maximum profit as perfect price discrimination.
• Two-part pricing consists of a fee and a per unit charge.
• Examples:
 Disneyland with admission fee and zero per ride.
 \$2 cokes with free-refills (\$2 fee and zero per refill).
 Athletic club memberships.
 Netflix with monthly fee and free movie streaming.
 Spotify with monthly fee and free music streaming.
 Other examples?
BA 445 Lesson A.10 Monopoly Pricing
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Two-Part Pricing
How Two-Part Pricing Works
1. Set price at marginal cost (to maximize
total surplus).
2. Compute consumer surplus.
3. Charge a fixed-fee equal to consumer
surplus (to capture all surplus as profit).
Price
10
8
6
Fixed Fee = Profits* = \$16
Per Unit
Charge
4
MC
2
D
1
2
3
4
5
* Assuming no fixed costs
Quantity
41
Group Pricing
Group Pricing
BA 445 Lesson A.10 Monopoly Pricing
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Group Pricing
Overview
Group Pricing applies markup rules for groups like seniors,
students, and kids. Group pricing yields more profit than
uniform pricing but less than maximum profits. Group
pricing does not require perfect knowledge of each
consumer. — So, Knott’s Berry Farm discounts to seniors
because seniors cannot survive Knott’s distinctive thrill
rides.
BA 445 Lesson A.10 Monopoly Pricing
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Group Pricing
Imperfect Price Discrimination
• Third-degree price discrimination: The practice of
charging different groups of consumers different prices
for the same product.
• Group must have observable characteristics for thirddegree price discrimination to work.
• Examples:
 Student discounts
 Child discounts
 Poverty discounts (like when poor people clip
coupons)
 Senior citizen’s discounts
 Regional and international pricing.
BA 445 Lesson A.10 Monopoly Pricing
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Group Pricing
Implementing Third-Degree Price Discrimination
• Suppose the total demand for a product is comprised of
two groups with different elasticities, E1 < E2 < - 1
• Notice that group 1 is more price sensitive than group 2.
• Profit-maximizing prices?
• P1 = [E1/(1+ E1)]  MC < [E2/(1+ E2)]  MC = P2
Qualitative Examples
• Why are seniors charged less than others at Disneyland
and at restaurants? Higher elasticity (more substitutes).
 They shop at Disneyland, like they shop at the mall.
 They eat plain food at restaurants, like they eat at
home.
BA 445 Lesson A.10 Monopoly Pricing
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Group Pricing
A Numerical Example
• Suppose the elasticity of demand for Kodak film in the
US is EU = -1.5, and the elasticity of demand in Japan is
EJ = -2.5.
• Marginal cost of manufacturing film is \$3.
• PU = [EU/(1+ EU)]  MC = [-1.5/(1 - 1.5)]  \$3 = \$9
• PJ = [EJ/(1+ EJ)]  MC = [-2.5/(1 - 2.5)]  \$3 = \$5
• Kodak’s optimal third-degree pricing strategy is to charge
a higher price in the US, where demand is less elastic.
BA 445 Lesson A.10 Monopoly Pricing
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Summary
Summary
BA 445 Lesson A.10 Monopoly Pricing
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Summary
Summary
• Consider a monopolist with demand Q = 100 – 0.1P and
constant unit cost of 500.
 The Lesson covered three levels (orders) of price
discrimination:
 Perfect discrimination, including two-part pricing and
block pricing.
 Commodity bundling and imperfect discrimination.
 No price discrimination.
BA 445 Lesson A.10 Monopoly Pricing
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Summary
• No price discrimination
 Q = 100 – 0.1P implies P = 1,000 – 10Q
 MR = 1,000 – 20Q
 MC = 500
 MR = MC implies 1,000 – 20Q = 500, or Q = 25.
 P = 1,000 – 10(25) = 750
 P = (P-MC)Q - FC = (750-500)(25) – 10,000 = -3,750
BA 445 Lesson A.10 Monopoly Pricing
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Summary
• Perfect price discrimination: Two-part price.
 P(Q) = 1,000 – 10Q
 P(Q) = MC implies 1,000 – 10Q = 500, and Q = 50.
 Firm breaks even on P = MC per unit profit.
 Consumer surplus triangle = .5(1,000-500)(25) =
12,500.
 Fee = Consumer surplus = 12,500.
 Profit = 12,500 – 10,000 = 2,500.
BA 445 Lesson A.10 Monopoly Pricing
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Summary
Conclusion
• First-degree price discrimination, two part pricing, and
block pricing and permit a firm to maximize profit and
extract all consumer surplus.
• Commodity bundling and imperfect price discrimination
permit a firm to extract some (but not all) consumer
surplus.
• Markup rules are the simplest to implement, but leave
consumers with surplus.
• Different pricing strategies require different information.
BA 445 Lesson A.10 Monopoly Pricing
51
Review Questions
Review Questions
 You should try to answer some of the review
questions (see the online syllabus) before the next
class.
request to discuss their answers to begin the next class.
 Your upcoming Exam 1 and cumulative Final Exam
will contain some similar questions, so you should
eventually consider every review question before taking