A.10 Monopolistic Pricing
Review Questions
Lesson Topics
Uniform Pricing (3) 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 (2) 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 (4) 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 (7) 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 (3) applies markup 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.
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A.10 Monopolistic Pricing
Review Questions
Uniform Pricing
Question. An analyst for Coke estimates the
aggregate demand for Coke to be
ln(Qc) = 5.5 – 3.2 ln(Pc) + 3.8 ln(Pd) + 2.3 ln(Ac)
where Qc is the bottles demanded for Coke, Pc is the
price of Coke, Pd is the price of Dr. Pepper, and Ac is the dollars spent
advertising Coke. Last year, Coke sold 10 million bottles and spent $2
million on advertising on national T.V. Its plant lease is $4 million, and that
includes utilities. Capital depreciated from age, at a cost of $5 million.
Payments to employees (all on salary) cost $1.75 million. Finally,
carbonated water, sugar, phosphoric acid, fructose, corn syrup, caramel,
color, natural flavors, and caffeine cost a combined $5 million, which were
purchased in competitive input markets.
Assume market conditions only allow the firm to charge a uniform price for
all units and for all customers.
What price should Coke charge per bottle?
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A.10 Monopolistic Pricing
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Answer to Question: The only relevant costs in this problem are the costs
of carbonated water, sugar, phosphoric acid, fructose, corn syrup, caramel,
color, natural flavors, and caffeine. All other costs are fixed costs and
irrelevant for decision making purposes. The average unit cost of these
items is $0.50 per bottle, which is found by dividing the $5 million in
relevant costs by 10 million bottles of Coke. This approximates Coke’s
relevant marginal cost. Since the own-price elasticity of demand for Coke is
-3.2, the profit-maximizing price for a bottle is
  3.2 
P
$0.50  $0.72727 ,
 1  3.2 
or about $0.73 per bottle. This estimate does
not adjust the elasticity to account for the existence of rivals, since the
elasticity of demand estimate is for the firm, not for the market.
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A.10 Monopolistic Pricing
Review Questions
Uniform Pricing
Question. An analyst for Nikon estimates the
aggregate demand for its Coolpix Camera to be
ln(Qc) = 400 – 5 ln(Pc) + 8 ln(Ps) + 3 ln(Ac)
where Qc is the number of Nikon Coolpix cameras
demanded, Pc is the price of Coolpix cameras, Ps is the price of the Sony
Cyber-shot camera, and Ac is the dollars spent advertising Nikon Coolpix
cameras.
Last year, Nikon produced 1 million Coolpix cameras and spent $2 million
on advertising on national T.V. Its plant lease is $40 million, and that
includes utilities. Capital depreciated from age, at a cost of $50 million.
Payments to employees (all on salary) cost $17.50 million. Finally, metal
and plastic components of the Coolpix cameras cost a combined $50
million, which were purchased in competitive input markets.
Assume market conditions only allow the firm to charge a uniform price for
all units and for all customers.
What price should Nikon charge per Coolpix camera?
How are Nikon Coolpix cameras related to Sony Cyber-shot cameras?
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A.10 Monopolistic Pricing
Review Questions
Answer to Question: The only relevant costs in this problem are metal
and plastic components of the Coolpix cameras. All other costs are fixed
costs and irrelevant for decision making purposes. The average unit cost of
these items is $50 million/1 million = $50 per camera, which is found by
dividing the $50 million in relevant costs by 1 million cameras produced.
This approximates Nikon’s relevant marginal cost. Since the own-price
elasticity of demand for Coolpix cameras is -5, the profit-maximizing price is
P = (-5/(1-5)) ( $50) = (5/4)($50) = $62.50 per camera.
That estimate does not adjust the elasticity to account for the existence of
rivals, since the elasticity of demand estimate is for the firm, not for the
market.
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A.10 Monopolistic Pricing
Review Questions
Uniform Pricing
Question. 20th Century Fox is producing a film
adaptation of Abraham Lincoln: Vampire Hunter. An
analyst for Fox estimates the aggregate demand for
copies of this movie on DVD to be
ln(QA) = 400 + 1.5 ln(PT) – 1.2 ln(PA) – 3.0 ln(S)
where QA is the number of DVD copies of Abraham Lincoln: Vampire
Hunter demanded, PT is the price of DVD copies of the movie Twilight, PA
is the price of of DVD copies of Abraham Lincoln: Vampire Hunter, and S
is the level of the Standard & Poor's 500 Stock Index.
Benjamin Walker and the other the stars of Abraham Lincoln: Vampire
Hunter were paid a combined total of $40 million to make the film. It is
estimate that each copy of the DVD will require $0.60 in advertising, $1.20
to copy the DVD, and $2.00 for shipping and handling.
Assume market conditions only allow the firm to charge a uniform price for
all units and for all customers.
What price should Fox charge per Abraham Lincoln: Vampire Hunter DVD?
How is Abraham Lincoln: Vampire Hunter related to the movie Twilight?
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A.10 Monopolistic Pricing
Review Questions
Answer to Question: The only relevant costs in this problem are $0.60 in
advertising, $1.20 to copy the DVD, and $2.00 for shipping and handling.
All other costs are fixed costs and irrelevant for decision making. The
marginal unit cost of those items is $3.80. Since the own-price elasticity of
demand for Abraham Lincoln: Vampire Hunter DVDs is -1.2, the profitmaximizing price is
P = (-1.2/(1-1.2)) ( $3.80) = 6($3.80) = $22.80 per DVD.
That estimate does not adjust the elasticity to account for the existence of
rivals, since the elasticity of demand estimate is for the firm, not for the
market.
Abraham Lincoln: Vampire Hunter is a gross substitute for the movie
Twilight since the cross-price elasticity of demand is 1.5, which is positive.
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A.10 Monopolistic Pricing
Review Questions
Block Pricing
Question. Suppose typical consumer’s demand for
cans of Mountain Dew is estimated to be Q = 9 –
(0.5)P, and the cost of producing Q cans is C(Q) =
2Q.
Assume market conditions allow the firm to package units sold to each
customer so that customers do not share their packages.
Compute the optimal number of cans in a package of Mountain Dew. And
compute the optimal package price, and optimal profit.
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A.10 Monopolistic Pricing
Review Questions
Answer to Question: Selling cans in a package, rather than individually,
is block pricing. Optimal block pricing is just like optimal perfect price
discrimination or optimal two-part pricing.
First, determine optimal quantity by setting price equal to marginal cost.
P = 18 – 2Q = MC = 2,
so Q = 16/2 = 8 cans per package.
Second, the optimal package price is the consumer valuation of the optimal
quantity, which is (1/2)16x8+2x8 = $80
18
2
8
Finally, optimal profit equals package price minus production cost,
which is $80-$16 = $64
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A.10 Monopolistic Pricing
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Block Pricing
Question. Suppose typical consumer’s demand for
liters of Samotok Bijeli wine is estimated to be
Q = 10 – 5P, and the cost of producing Q liters is C(Q)
= Q.
Assume market conditions allow the firm to package units sold to each
customer so that customers do not share their packages.
Compute the optimal number of liters in a box of Samotok Bijeli wine. And
compute the optimal box price, and optimal profit.
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A.10 Monopolistic Pricing
Review Questions
Answer to Question: Selling liters in a box, rather than individually, is
block pricing. Optimal block pricing is just like optimal perfect price
discrimination or optimal two-part pricing.
First, determine optimal quantity by setting price equal to marginal cost.
Solve Q = 10 – 5P, for P = 2-(1/5)Q.
Set P = 2-(1/5)Q = MC = 1,
so Q = 5 liters per box.
Second, the optimal box price is the consumer valuation of at the optimal
quantity, which is (1/2)5x1+1x5 = $7.50
2
1
5
Finally, optimal profit equals package price minus production cost,
which is $7.50-$5 = $2.50
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A.10 Monopolistic Pricing
Review Questions
Bundle Pricing
Question. Apple Records is a record label founded
by The Beatles in 1968. Apple has to decide whether
to sell the first four Beatles albums (Album 1, Album 2,
Album 3, Album 4) separately or sell all four as a box
set. Apple has divided its potential customers into 3 equal-sized groups
(Group A, Group B, Group C) and collected internet data to estimate the
maximum price each type of consumer will pay for each album:
Consumer\Album
Album 1
Album 2
Album 3
Album 4
Group A
$10
$15
$20
$15
Group B
$15
$20
$15
$10
Group C
$40
$11
$11
$10
To keep the problem simple, assume there are zero marginal costs of
selling to any of those consumers.
Assume market conditions allow the firm to bundle units sold to each
customer so that customers do not share their bundles.
What are the optimal prices of each album if each is sold separately?
What is the optimal price per box set if all four albums are sold as a box
set? Is it better to sell the four albums separately? Or better to sell as a
box set?
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A.10 Monopolistic Pricing
Review Questions
Answer to Question: Let G = number of people in each group.
Optimal Album 1 Price? Optimal Profit?
• At a price of $40, only Group C buys, profit = $40xG
• At a price of $15, B and C buy, profit = $15x2xG
• At a price of $10, all three buy, profit = $10x3xG
Optimal profit is $40xG, with price $40.
Optimal Album 2 Price? Optimal Profit?
• At a price of $20, only Group B buys, profit = $20xG
• At a price of $15, A and B buy, profit = $15x2xG
• At a price of $11, all three buy, profit = $11x3xG
Optimal profit is $33xG, with price $11.
Optimal Album 3 Price? Optimal Profit?
• At a price of $20, only Group A buys, profit = $20xG
• At a price of $15, A and B buy, profit = $15x2xG
• At a price of $11, all three buy, profit = $11x3xG
Optimal profit is $33xG, with price $11.
Optimal Album 4 Price? Optimal Profit?
• At a price of $15, only Group A buys, profit = $15xG
• At a price of $10, all three buy, profit = $10x3xG
Optimal profit is $30xG, with price $10.
Given the maximum price each type of consumer will pay for each album,
we can compute the maximum price each type of consumer will pay for the
box set of all four albums: Group A would pay $60=$10+15+20+15; B, $60;
C, $72.
Optimal Box Set Price? Optimal Profit?
• At a price of $72, only Group C buys, profit = $72xG
• At a price of $60, all three buy, profit = $60x3xG
Optimal profit is $180xG, with price $60.
If they sell the four products separately, total profit is
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A.10 Monopolistic Pricing
Review Questions
$136xG, which is lower than total profit $180xG the four products are sold
as a bundle. So, sell as a bundle.
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A.10 Monopolistic Pricing
Review Questions
Bundle Pricing
Question. Apple Records is a record label founded
by The Beatles in 1968. Apple has to decide whether
to sell the first four Beatles albums on Vinyl (Album 1,
Album 2, Album 3, Album 4) separately or sell all four
as a box set. Apple has divided its potential customers into 4 equal-sized
groups (Baby Boom, Generation X, Generation Y, Generation Z) and
collected internet data to estimate the maximum price each type of
consumer will pay for each album:
Consumer\Album
Album 1
Album 2
Album 3
Album 4
Baby Boom
$20
$20
$25
$20
Generation X
$15
$10
$25
$25
Generation Y
$25
$20
$15
$10
Generation Z
$15
$20
$30
$40
To keep the problem simple, assume there are zero marginal costs of
selling to any of those consumers.
Assume market conditions allow the firm to bundle units sold to each
customer so that customers do not share their bundles. But assume that
the price of a bundle must be the same to all consumers.
What are the optimal prices of each album if each is sold separately?
What is the optimal price per box set if all four albums are sold as a box
set? Is it better to sell the four albums separately? Or better to sell as a
box set?
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A.10 Monopolistic Pricing
Review Questions
Answer to Question: Let G = number of people in each group.
Optimal Album 1 Price? Optimal Profit?
• At a price of $25, only Group 3 buys, profit = $25x1xG
• At a price of $20, Groups 1 and 3 buy, profit = $20x2xG
• At a price of $10, all four buy, profit = $15x4xG
Optimal profit is $60xG, with price $15.
Optimal Album 2 Price? Optimal Profit?
• At a price of $20, three groups buy, profit = $20x3xG
• At a price of $10, all four buy, profit = $10x4xG
Optimal profit is $60xG, with price $20.
Optimal Album 3 Price? Optimal Profit?
• At a price of $30, one group buys, profit = $30x1xG
• At a price of $25, three groups buy, profit = $25x3xG
• At a price of $15, all four buy, profit = $15x4xG
Optimal profit is $75xG, with price $25.
Optimal Album 4 Price? Optimal Profit?
• At a price of $40, one group buys, profit = $40x1xG
• At a price of $25, two groups buy, profit = $25x2xG
• At a price of $20, three groups buy, profit = $20x3xG
• At a price of $10, all four buy, profit = $10x4xG
Optimal profit is $60xG, with price $20.
Given the maximum price each type of consumer will pay for each album,
we can compute the maximum price each type of consumer will pay for the
box set of all four albums: Group 1 would pay $85=$20+20+25+20; B, $75;
C, $70; D, $105.
Optimal Box Set Price? Optimal Profit?
• At a price of $105, one group buys, profit = $105x1xG
• At a price of $85, two groups buy, profit = $85x2xG
• At a price of $75, three groups buy, profit = $75x3xG
• At a price of $70, all four buy, profit = $70x4xG
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A.10 Monopolistic Pricing
Review Questions
Optimal profit is $280xG, with price $70.
If they sell the four products separately, total profit is
$255xG, which is lower than total profit $280xG when the four products are
sold as a bundle. So, sell as a bundle.
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A.10 Monopolistic Pricing
Review Questions
Bundle Pricing
Question. Block booking is a system of selling
multiple films to a theater as a unit. Block booking was
the prevailing practice among Hollywood's major
studios from the turn of the 1930s until it was
outlawed by the U.S. Supreme Court's decision in United States v.
Paramount Pictures, Inc. (1948). Under block booking, theater owners
were forced to license large numbers of a studio's pictures as a bundle.
For example, suppose Paramount Pictures has to decide whether to
license its five biggest movies to theaters separately or sell all five as a
block. Paramount has divided all theaters into 4 groups (West Coast,
Midwest, South, East Coast) and collected internet data to estimate the
maximum price each type of theater will pay to license each movie:
Group\Movie
West Coast
Midwest
South
East Coast
Movie 1
$8
$6
$7
$4
Movie 2
$3
$6
$7
$5
Movie 3
$3
$8
$9
$7
Movie 4
$2
$3
$8
$9
Movie 5
$5
$6
$3
$8
To keep the problem simple, assume there are zero marginal costs of
licensing to any of those theaters, and there are 210 theaters in each
group.
Assume market conditions allow the firm to bundle units licensed to each
theater so that theaters do not share their bundles. But assume that the
price to license a bundle must be the same to all theaters in all groups.
What are the optimal prices of licensing each movie if each is licensed
separately? What is the optimal price per block if all five movies are
licensed as a block? Is it better to license the five movies separately? Or
better to license as a block? Or is it the same?
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A.10 Monopolistic Pricing
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Answer to Question: Let G = number of theaters in each group.
Optimal Movie 1 Price? Optimal Profit?
• At a price of $8, only Group 1 buys license, profit = $8x1xG
• At a price of $7, only Groups 1 and 3 buy, profit = $7x2xG
• At a price of $6, all but Group 4 buys, profit = $6x3xG
• At a price of $4, all four buy, profit = $4x4xG
Optimal profit is $18xG, with price $6
Optimal Movie 2 Price? Optimal Profit?
• At a price of $7, one group buys, profit = $7x1xG
• At a price of $6, two groups buy, profit = $6x2xG
• At a price of $5, three groups buy, profit = $5x3xG
• At a price of $3, four groups buy, profit = $3x4xG
Optimal profit is $15xG, with price $5
Optimal Movie 3 Price? Optimal Profit?
• At a price of $9, one group buys, profit = $9x1xG
• At a price of $8, two groups buy, profit = $8x2xG
• At a price of $7, three groups buy, profit = $7x3xG
• At a price of $3, four groups buy, profit = $3x4xG
Optimal profit is $21xG, with price $7
Optimal Movie 4 Price? Optimal Profit?
• At a price of $9, one group buys, profit = $9x1xG
• At a price of $8, two groups buy, profit = $8x2xG
• At a price of $4, three groups buy, profit = $4x3xG
• At a price of $2, four groups buy, profit = $2x4xG
Optimal profit is $16xG, with price $8
Optimal Movie 5 Price? Optimal Profit?
• At a price of $8, one group buys, profit = $8x1xG
• At a price of $6, two groups buy, profit = $6x2xG
• At a price of $5, three groups buy, profit = $5x3xG
• At a price of $3, four groups buy, profit = $3x4xG
Optimal profit is $15xG, with price $5
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A.10 Monopolistic Pricing
Review Questions
Given the maximum price each type of theater will pay to license each
movie, we can compute the maximum price each type of theater will pay for
the block of all five movies: Group 1 would pay $21=$8+3+3+2+5; Group 2,
$29; Group 3, $34; Group 4, $33.
Optimal Box Set Price? Optimal Profit?
• At a price of $34, one group buys, profit = $34x1xG
• At a price of $33, two groups buy, profit = $33x2xG
• At a price of $29, three groups buy, profit = $29x3xG
• At a price of $21, four groups buy, profit = $21x4xG
Optimal profit is $87xG, with price $29
If they license all five movies separately, total profit is
$85xG, which is lower than total profit $87xG when the five products are
licensed as a block. So, license as a block.
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A.10 Monopolistic Pricing
Review Questions
Bundle Pricing
Question. Block booking is a system of selling
multiple films to a theater as a unit. Block booking was
the prevailing practice among Hollywood's major
studios from the turn of the 1930s until it was outlawed
by the U.S. Supreme Court's decision in United States v. Paramount
Pictures, Inc. (1948). Under block booking, theater owners were forced to
license large numbers of a studio's pictures as a bundle.
For example, suppose Paramount Pictures has to decide whether to
license its five biggest movies to theaters separately or sell all five as a
block. Paramount has divided all theaters into 4 groups (West Coast,
Midwest, South, East Coast) and collected internet data to estimate the
maximum price each type of theater will pay to license each movie:
Group\Movie
West Coast
Midwest
South
East Coast
Movie 1
$8
$6
$7
$4
Movie 2
$4
$6
$8
$7
Movie 3
$3
$8
$9
$7
Movie 4
$3
$6
$9
$2
Movie 5
$5
$6
$3
$8
To keep the problem simple, assume there are zero marginal costs of
licensing to any of those theaters, and there are 312 theaters in each
group.
Assume market conditions allow the firm to bundle units licensed to each
theater so that theaters do not share their bundles. But assume that the
price to license a bundle must be the same to all theaters in all groups.
What are the optimal prices of licensing each movie if each is licensed
separately? What is the optimal price per block if all five movies are
licensed as a block? Is it better to license the five movies separately? Or
better to license as a block? Or is it the same?
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A.10 Monopolistic Pricing
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Answer to Question: Let G = number of theaters in each group.
Optimal Movie 1 Price? Optimal Profit?
• At a price of $8, only Group 1 buys license, profit = $8x1xG
• At a price of $7, only Groups 1 and 3 buy, profit = $7x2xG
• At a price of $6, all but Group 4 buys, profit = $6x3xG
• At a price of $4, all four buy, profit = $4x4xG
Optimal profit is $18xG, with price $6
Optimal Movie 2 Price? Optimal Profit?
• At a price of $8, one group buys, profit = $8x1xG
• At a price of $7, two groups buy, profit = $7x2xG
• At a price of $6, three groups buy, profit = $6x3xG
• At a price of $4, four groups buy, profit = $4x4xG
Optimal profit is $18xG, with price $6
Optimal Movie 3 Price? Optimal Profit?
• At a price of $9, one group buys, profit = $9x1xG
• At a price of $8, two groups buy, profit = $8x2xG
• At a price of $7, three groups buy, profit = $7x3xG
• At a price of $3, four groups buy, profit = $3x4xG
Optimal profit is $21xG, with price $7
Optimal Movie 4 Price? Optimal Profit?
• At a price of $9, one group buys, profit = $9x1xG
• At a price of $6, two groups buy, profit = $6x2xG
• At a price of $3, three groups buy, profit = $3x3xG
• At a price of $2, four groups buy, profit = $2x4xG
Optimal profit is $12xG, with price $6
Optimal Movie 5 Price? Optimal Profit?
• At a price of $8, one group buys, profit = $8x1xG
• At a price of $6, two groups buy, profit = $6x2xG
• At a price of $5, three groups buy, profit = $5x3xG
• At a price of $3, four groups buy, profit = $3x4xG
Optimal profit is $15xG, with price $5
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Given the maximum price each type of theater will pay to license each
movie, we can compute the maximum price each type of theater will pay for
the block of all five movies: Group 1 would pay $23=$8+4+3+3+5; Group 2,
$32; Group 3, $36; Group 4, $28.
Optimal Block Price? Optimal Profit?
• At a price of $36, one group buys, profit = $36x1xG
• At a price of $32, two groups buy, profit = $32x2xG
• At a price of $28, three groups buy, profit = $28x3xG
• At a price of $23, four groups buy, profit = $23x4xG
Optimal profit is $92xG, with price $28
If they license all five movies separately, total profit is
$84xG, which is worse than the total profit $92xG when the five products
are licensed as a block. So, license as a block.
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Two Part Pricing
Question. Suppose typical consumer’s demand for
rides at Disneyland is estimated to be P = 9 - 2Q, and
Disney’s cost of providing Q rides is C(Q) = Q.
(Naturally, assume market conditions allow the firm to charge a fee to each
customer to have the right to buy individual units (rides) from the firm, and
that customers do not resell individual units to other customers.)
Compute the optimal price for Disneyland to charge for each ride, and the
optimal fee for Disneyland to charge for each consumer to enter the park.
Finally, compute optimal profit.
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Answer to Question: Optimal two-part pricing sets price to marginal cost
(to maximize total surplus), then charges a fixed fee equal to consumer
surplus.
First, set price equal to the marginal cost of 1.
Second, the optimal fee equals the consumer surplus of (1/2)8x4 = 16.
9
1
4
Finally, optimal profit equals the optimal fee of $16 per consumer.
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Two Part Pricing
Question. Suppose typical consumer’s demand for
rides at Disneyland is estimated to be Q = 10 – (1/2)P,
and Disney’s cost of providing Q rides is C(Q) = Q.
(Naturally, assume market conditions allow the firm to charge a fee to each
customer to have the right to buy individual units (rides) from the firm, and
that customers do not resell individual units to other customers.)
Compute the optimal price for Disneyland to charge for each ride, and the
optimal fee for Disneyland to charge for each consumer to enter the park.
Finally, compute optimal profit.
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Answer to Question: Optimal two-part pricing sets price to marginal cost
(to maximize total surplus), then charges a fixed fee equal to consumer
surplus.
First, set price P = 20 - 2Q (from Q = 10 – (1/2)P) equal to the marginal
cost of 1.
Second, the optimal fee equals the consumer surplus of (1/2)19x(9.5) =
90.25
.
20
1
9.5
Finally, optimal profit equals the optimal fee of $90.25 per consumer.
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Two Part Pricing
Question. Netflix is an American provider of ondemand Internet streaming media. Suppose typical
consumer’s demand for streaming movies is
estimated to be Q = 10 – 5P per month, and Netflix’s
cost of providing Q movies is zero.
Assume market conditions allow the firm to charge a fee to each customer
to have the right to buy individual units (streaming movies) from the firm,
and that customers do not resell individual units to other customers.
Compute the optimal price for Netflix to charge for each streaming movie,
and the optimal monthly membership fee to charge for each consumer to
be able to buy streaming movies. Finally, compute optimal profit from each
customer.
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Answer to Question: Optimal two-part pricing sets price to marginal cost
(to maximize total surplus), then charges a fixed fee equal to consumer
surplus.
First, set price P = 2 – (1/5)Q (from Q = 10 – 5P) equal to the marginal cost
of 0.
Second, the optimal fee equals the consumer surplus of (1/2)2x10 = 10
2
0
10
Finally, optimal profit equals the optimal fee of $10 per consumer.
31
A.10 Monopolistic Pricing
Review Questions
Two Part Pricing
Question. Netflix is an American provider of ondemand Internet streaming media. Suppose typical
consumer’s demand for streaming movies is
estimated to be Q = 8 – 2P per month, and Netflix’s
cost of providing Q movies is zero. Consider three alternative sets of
market conditions:
1. Uniform pricing: Assume market conditions only allow the firm to
charge a uniform price for each steaming movie. Compute the
optimal price for Netflix to charge for each streaming movie. Finally,
compute optimal profit from each customer.
2. Block pricing: Assume market conditions allow the firm to package
streaming movies rented by each customer so that customers do not
share their packages. Compute the optimal number of streaming
movies in a package. And compute the optimal package price, and
optimal profit.
3. Two-part pricing: Assume market conditions allow the firm to charge
a fee to each customer to have the right to buy individual units
(streaming movies) from the firm, and that customers do not resell
individual units to other customers. Compute the optimal price for
Netflix to charge for each streaming movie, and the optimal monthly
membership fee to charge for each consumer to be able to buy
streaming movies. Finally, compute optimal profit from each
customer.
32
A.10 Monopolistic Pricing
Review Questions
Answer to Question:
Alternative 1: Optimal uniform pricing sets marginal revenue to marginal
cost.
First, determine inverse demand
P = 4 – (1/2)Q (from Q = 8 – 2P),
then marginal revenue by doubling the slope,
MR = 4 – Q (P = 4 – (1/2)Q).
Then set MR equal to the marginal cost of 0 to determine Q = 4 streaming
movies.
Second, use inverse demand to determine price P = 4 – (1/2)(4) = $2.
Fnally, optimal profit equals PQ – C(Q) = 2(4) – 0 = $8.
33
A.10 Monopolistic Pricing
Review Questions
Alternative 2: Optimal block pricing sets price to marginal cost to determine
optimal output, then charges a price for all of that output sold as one
package.
First, determine optimal quantity by setting price equal to marginal cost.
Set price P = 4 – (1/2)Q (from Q = 8 – 2P) equal to the marginal cost of 0 to
determine Q = 8 streaming movies in a package.
Second, the optimal package price is the consumer valuation of the optimal
quantity, which is (1/2)4x8 = $16
4
0
8
Finally, optimal profit equals the optimal package price of $16 per
consumer.
34
A.10 Monopolistic Pricing
Review Questions
Alternative 3: Optimal two-part pricing sets price to marginal cost (to
maximize total surplus), then charges a fixed fee equal to consumer
surplus.
First, set price P = 4 – (1/2)Q (from Q = 8 – 2P) per streaming movie equal
to the marginal cost of 0.
Second, the optimal fee equals the consumer surplus of (1/2)4x8 = $16
4
0
8
Finally, optimal profit equals the optimal fee of $16 per consumer.
35
A.10 Monopolistic Pricing
Review Questions
Two Part Pricing
Question. Netflix is an American provider of ondemand Internet streaming media. Suppose typical
consumer’s demand for streaming movies is
estimated to be Q = 18 – 6P per month, and Netflix’s
cost of providing Q movies is zero. Consider three alternative sets of
market conditions:
1. Uniform pricing: Assume market conditions only allow the firm to
charge a uniform price for each steaming movie. Compute the
optimal price for Netflix to charge for each streaming movie. Finally,
compute optimal profit from each customer.
2. Block pricing: Assume market conditions allow the firm to package
streaming movies rented by each customer so that customers do not
share their packages. Compute the optimal number of streaming
movies in a package. And compute the optimal package price, and
optimal profit.
3. Two-part pricing: Assume market conditions allow the firm to charge
a fee to each customer to have the right to buy individual units
(streaming movies) from the firm, and that customers do not resell
individual units to other customers. Compute the optimal price for
Netflix to charge for each streaming movie, and the optimal monthly
membership fee to charge for each consumer to be able to buy
streaming movies. Finally, compute optimal profit from each
customer.
36
A.10 Monopolistic Pricing
Review Questions
Answer to Question:
Alternative 1: Optimal uniform pricing sets marginal revenue to marginal
cost.
First, determine inverse demand
P = 3 – (1/6)Q (from Q = 18 – 6P),
then marginal revenue by doubling the slope,
MR = 3 – (1/3)Q (P = 3 – (1/6)Q).
Then set MR equal to the marginal cost of 0 to determine Q = 9 streaming
movies.
Second, use inverse demand to determine price P = 3 – (1/6)(9) = $1.50
Fnally, optimal profit equals PQ – C(Q) = 1.50(9) – 0 = $13.50
37
A.10 Monopolistic Pricing
Review Questions
Alternative 2: Optimal block pricing sets price to marginal cost to determine
optimal output, then charges a price for all of that output sold as one
package.
First, determine optimal quantity by setting price equal to marginal cost.
Set price P = 3 – (1/6)Q (from Q = 18 – 6P) equal to the marginal cost of 0
to determine Q = 18 streaming movies in a package.
Second, the optimal package price is the consumer valuation of the optimal
quantity, which is (1/2)3x18 = $27
3
0
18
Finally, optimal profit equals the optimal package price of $27 per
consumer.
38
A.10 Monopolistic Pricing
Review Questions
Alternative 3: Optimal two-part pricing sets price to marginal cost (to
maximize total surplus), then charges a fixed fee equal to consumer
surplus.
First, set price P = 3 – (1/6)Q (from Q = 18 – 6P) per streaming movie
equal to the marginal cost of 0.
Second, the optimal fee equals the consumer surplus of (1/2)3x18 = $27
3
0
18
Finally, optimal profit equals the optimal fee of $27 per consumer.
39
A.10 Monopolistic Pricing
Review Questions
Two Part Pricing
Question. DirecTV, LLC, is an American direct
broadcast satellite service provider. Suppose typical
consumer’s demand to watch NFL games is estimated
to be Q = 9.5 – 0.5 P per season, and DirecTV’s cost
of providing games is $3 per game per customer. Consider three
alternative sets of market conditions:
1. Uniform pricing: Assume market conditions only allow the firm to
charge a uniform price for a customer to watch each game. Compute
the optimal price for each game. Finally, compute optimal profit from
each customer.
2. Block pricing: Assume market conditions allow the firm to package
games watched by each customer so that customers do not share
their packages. Compute the optimal number of games in a package.
And compute the optimal package price, and optimal profit.
3. Two-part pricing: Assume market conditions allow the firm to charge
a membership fee to each customer to have the right to pay to watch
individual games, and that customers do not share their
memberships. Compute the optimal price membership fee and the
optimal to charge for each game. Finally, compute optimal profit from
each customer.
40
A.10 Monopolistic Pricing
Review Questions
Answer to Question:
Alternative 1: Optimal uniform pricing sets marginal revenue to marginal
cost.
First, determine inverse demand
P = 19 – 2Q (from Q = 9.5 – 0.5 P),
then marginal revenue by doubling the slope,
MR = 19 – 4Q (P = 18 – 2Q).
Then set MR equal to the marginal cost of 3 to determine Q = 4 games.
Second, use inverse demand to determine price P = 19 – 2(4) = $11
Fnally, optimal profit equals PQ – C(Q) = 11(4) – 3(4) = $32
41
A.10 Monopolistic Pricing
Review Questions
Alternative 2: Optimal block pricing sets price to marginal cost to determine
optimal output, then charges a price for all of that output sold as one
package.
First, determine optimal quantity by setting price equal to marginal cost.
Set price P = 19 – 2Q (from Q = 9.5 – 0.5 P) equal to the marginal cost of 3
to determine Q = 8 games in a package.
Second, the optimal package price is the consumer valuation of the optimal
quantity, which is (1/2)16x8+3x8 = $88
19
3
8
Finally, optimal profit per consumer equals the optimal package price of
$88 minus the cost of $3x8, which is $64 per consumer.
42
A.10 Monopolistic Pricing
Review Questions
Alternative 3: Optimal two-part pricing sets price to marginal cost (to
maximize total surplus), then charges a fixed fee equal to consumer
surplus.
First, set price 19 – 2Q (from Q = 9.5 – 0.5 P) per game equal to the
marginal cost of 3.
Second, the optimal fee equals the consumer surplus of (1/2)16x8 = $64
19
3
8
Finally, optimal profit equals the optimal fee of $64 per consumer.
43
A.10 Monopolistic Pricing
Review Questions
Two Part Pricing
Question. The Yellowstone Club is a private golf
community set on 14,000 acres in Big Sky, Montana,
which counts Microsoft founder Bill Gates as a
member.
Suppose typical consumer’s demand for a game (round) of golf at the
Yellowstone Club is estimated to be Q = 2000 – 2 P per year, and
Yellowstone’s cost of providing games is $100 per game per customer.
Consider three alternative sets of market conditions:
1. Block pricing: Assume market conditions allow the firm to package
games played by each customer so that customers do not share their
packages. Compute the optimal number of games in a package.
And compute the optimal package price, and optimal profit.
2. Uniform pricing: Assume market conditions only allow the firm to
charge a uniform price for a customer to play each game. Compute
the optimal price for each game. Finally, compute optimal profit from
each customer.
3. Two-part pricing: Assume market conditions allow the firm to charge
a membership fee to each customer to have the right to pay to play
individual games, and that customers do not share their
memberships. Compute the optimal price membership fee and the
optimal to charge for each game. Finally, compute optimal profit from
each customer.
44
A.10 Monopolistic Pricing
Review Questions
Answer to Question:
Alternative 2: Optimal uniform pricing sets marginal revenue to marginal
cost.
First, determine inverse demand
P = 1000 – 0.5 Q (from Q = 2000 – 2 P),
then marginal revenue by doubling the slope,
MR = 1000 – Q (P = 1000 – 0.5 Q).
Then set MR equal to the marginal cost of 100 to determine Q = 900
games.
Second, use inverse demand to determine price P = 1000 – 0.5 (900) =
$550
Fnally, optimal profit equals PQ – C(Q) = 550(900) – 100(900) = $40,5000
45
A.10 Monopolistic Pricing
Review Questions
Alternative 1: Optimal block pricing sets price to marginal cost to determine
optimal output, then charges a price for all of that output sold as one
package.
First, determine optimal quantity by setting price equal to marginal cost.
Set price P = 1000 – 0.5 Q (from Q = 2000 – 2 P) equal to the marginal
cost of 100 to determine Q = 1800 games.
Second, the optimal package price is the consumer valuation of the optimal
quantity, which is (1/2)900x1800+100x1800 = $990,000
1000
100
1800
Finally, optimal profit per consumer equals the optimal package price of
$99000 minus the cost of $100x1800, which is $810,000 per consumer.
46
A.10 Monopolistic Pricing
Review Questions
Alternative 3: Optimal two-part pricing sets price to marginal cost (to
maximize total surplus), then charges a fixed fee equal to consumer
surplus.
First, set price P = 1000 – 0.5 Q (from Q = 2000 – 2 P) equal to the
marginal cost of 100 to determine Q = 1800 games.
Second, the optimal fee equals the consumer surplus of (1/2)900x1800 =
$810,000
1000
100
1800
Finally, optimal profit equals the optimal fee of $810,000 per consumer.
47
A.10 Monopolistic Pricing
Review Questions
Two Part Pricing
Question. The Sports Club is an upscale fitness
center in Los Angeles. Suppose typical consumer’s
demand for fitness classes at The Sports Club is
estimated to be Q = 800 – 4 P per year, and The
Sports Club’s cost of providing classes is $5 per class per customer.
Consider three alternative sets of market conditions:
1. Two-part pricing: Assume market conditions allow the firm to charge
a membership fee to each customer to have the right to buy individual
classes, and that customers do not share their memberships.
Compute the optimal price membership fee and the optimal to charge
for each class. Finally, compute optimal profit from each customer.
2. Uniform pricing: Assume market conditions only allow the firm to
charge a uniform price for a customer to take a class. Compute the
optimal price for each class. Finally, compute optimal profit from
each customer.
3. Block pricing: Assume market conditions allow the firm to package
classes taken by each customer so that customers do not share their
packages. Compute the optimal number of classes in a package.
And compute the optimal package price, and optimal profit.
48
A.10 Monopolistic Pricing
Review Questions
Answer to Question:
Alternative 2: Optimal uniform pricing sets marginal revenue to marginal
cost.
First, determine inverse demand
P = 200 – 0.25 Q (from Q = 800 – 4 P),
then marginal revenue by doubling the slope,
MR = 200 – 0.5 Q (P = 200 – 0.25 Q).
Then set MR equal to the marginal cost of 5 to determine Q = 390 classes.
Second, use inverse demand to determine price P = 200 – 0.25(390) =
$102.50
Fnally, optimal profit equals PQ – C(Q) = 102.50(390) – 5(390) = $38025
49
A.10 Monopolistic Pricing
Review Questions
Alternative 3: Optimal block pricing sets price to marginal cost to determine
optimal output, then charges a price for all of that output sold as one
package.
First, determine optimal quantity by setting price equal to marginal cost.
Set price P = 200 – 0.25 Q (from Q = 800 – 4 P) equal to the marginal cost
of 5 to determine Q = 780 classes in a package.
Second, the optimal package price is the consumer valuation of the optimal
quantity, which is (1/2)195x780+5x780 = $79950
200
5
780
Finally, optimal profit per consumer equals the optimal package price of
$79950 minus the cost of $5x780, which is $76050 per consumer.
50
A.10 Monopolistic Pricing
Review Questions
Alternative 1: Optimal two-part pricing sets price to marginal cost (to
maximize total surplus), then charges a fixed fee equal to consumer
surplus.
First, set P = 200 – 0.25 Q (from Q = 800 – 4 P) equal to the marginal cost
of 5 to determine Q = 780 classes in a package.
Second, the optimal fee equals the consumer surplus of (1/2)195x780 =
$76050
200
5
780
Finally, optimal profit equals the optimal fee of $76050 per consumer.
51
A.10 Monopolistic Pricing
Review Questions
Two Part Pricing
Question. Netflix is an American provider of ondemand Internet streaming media. Suppose typical
consumer’s demand for streaming movies is
estimated to be Q = 12 – 4P per month, and Netflix’s
cost of providing Q movies is zero. Consider three alternative sets of
market conditions:
1. Uniform pricing: Assume market conditions only allow the firm to
charge a uniform price for each steaming movie. Compute the
optimal price for Netflix to charge for each streaming movie. Finally,
compute optimal profit from each customer.
2. Block pricing: Assume market conditions allow the firm to package
streaming movies rented by each customer so that customers do not
share their packages. Compute the optimal number of streaming
movies in a package. And compute the optimal package price, and
optimal profit.
3. Two-part pricing: Assume market conditions allow the firm to charge
a fee to each customer to have the right to buy individual units
(streaming movies) from the firm, and that customers do not resell
individual units to other customers. Compute the optimal price for
Netflix to charge for each streaming movie, and the optimal monthly
membership fee to charge for each consumer to be able to buy
streaming movies. Finally, compute optimal profit from each
customer.
.
52
A.10 Monopolistic Pricing
Review Questions
Answer to Question:
Alternative 1: Optimal uniform pricing sets marginal revenue to marginal
cost.
First, determine inverse demand
P = 3 – (1/4)Q (from Q = 12 – 4P),
then marginal revenue by doubling the slope of inverse demand,
MR = 3 – (1/2)Q.
Then set MR equal to the marginal cost of 0 to determine Q = 6 streaming
movies.
Second, use inverse demand to determine price P = 3 – (1/4)(6) = $1.50
Fnally, optimal profit equals PQ – C(Q) = 1.5(6) – 0 = $9.
53
A.10 Monopolistic Pricing
Review Questions
Alternative 2: Optimal block pricing sets price to marginal cost to determine
optimal output, then charges a price for all of that output sold as one
package.
First, determine optimal quantity by setting price equal to marginal cost.
Set price P = 3 – (1/4)Q (from Q = 12 – 4P) equal to the marginal cost of 0
to determine Q = 12 streaming movies in a package.
Second, the optimal package price is the consumer valuation of the optimal
quantity, which is (1/2)3x12 = $18
3
0
12
Finally, optimal profit equals the optimal package price of $18 per
consumer.
54
A.10 Monopolistic Pricing
Review Questions
Alternative 3: Optimal two-part pricing sets price to marginal cost (to
maximize total surplus), then charges a fixed fee equal to consumer
surplus.
First, set price P = 3 – (1/4)Q (from Q = 12 – 4P) per streaming movie
equal to the marginal cost of 0.
Second, the optimal fee equals the consumer surplus of (1/2)3x12 = $18
3
0
12
Finally, optimal profit equals the optimal fee of $18 per consumer.
55
A.10 Monopolistic Pricing
Review Questions
Group Pricing
Each of the following review questions apply the
theory of Group Pricing to the managerial decision of
how best to set prices to take advantage of customers
with different demand elasticities.
56
A.10 Monopolistic Pricing
Review Questions
Group Pricing
Question. Since the Marie Callender’s closed in
Thousand Oaks shortly after Dr. Burke moved into the
area, your Marie Callender’s in Camarillo is the only
Marie Callender’s in a 50 mile radius. You have
noticed that senior citizens (age 65 and older) are more sensitive to price
changes for your food than young adults. Specifically, you have found
senior citizens have an own price elasticity of demand of -4 for your food
and young adults have an own price elasticity of -3. How can you use that
difference in elasticities to your advantage? What do you think accounts
for that difference in elasticities?
Assume market conditions do not allow customers to resell individual units
(food) to other customers.
57
A.10 Monopolistic Pricing
Review Questions
Answer to Question: Since the two groups of people have different
demand elasticity, you should charge them different prices for the same
food to maximize profits.
For senior citizens, which have -4 as demand elasticity, you should follow
the rule
and set PF = -4/(1-4)MC = 1.33MC.
For young adults, which have -3 as demand elasticity, you should follow the
rule
and set PF = -3/(1-3)MC = 1.50MC.
That is, you should charge senior citizens a price that is 1.33 times your
marginal cost, and young adults the higher price of 1.50 times marginal
cost.
The higher elasticity by the senior citizens is because they have more
substitutes for your food, including eating at home. This is because
• senior citizens have lower wages and so do not need to save time
eating out;
• senior citizens eat similar food in restaurants and at home.
58
A.10 Monopolistic Pricing
Review Questions
Group Pricing
Question. Two attractions that make Knotts Berry
Farm different from other amusement parks are its
shows and its roller coaster rides. After Knotts Berry
Farm took out some of its shows and added more
roller coaster rides, they noticed that demand for admission by senior
citizens (age 65 and older) is more sensitive to price changes than demand
for admission by young adults. Specifically, they found senior citizens have
an own price elasticity of demand of -6 for admission and young adults
have an own price elasticity of -2. How can Knotts Berry Farm use that
difference in elasticities to its advantage? What do you think accounts for
that difference in elasticities?
(Naturally, assume market conditions do not allow customers to resell
individual units (park admissions) to other customers.)
59
A.10 Monopolistic Pricing
Review Questions
Answer to Question: Since the two groups of people have different
demand elasticity, Knotts should charge them different prices for admission
to maximize profits.
For senior citizens, which have -6 as demand elasticity, Knotts should
follow the rule
and set PF = -6/(1-6)MC = 1.2MC.
For young adults, which have -2 as demand elasticity, Knotts should follow
the rule
and set PF = -2/(1-2)MC = 2MC.
That is, Knotts should charge senior citizens a price that is 1.2 times
marginal cost, and young adults the higher price of 2 times marginal cost.
The higher elasticity by the senior citizens is because they have more
substitutes for admission to the park. This is because
• senior citizens cannot go on the roller coasters that make Knotts
special;
• senior citizens have fewer shows to attend, which used to make
Knotts special.
60
A.10 Monopolistic Pricing
Review Questions
Group Pricing
Question. Cipla Limited is a prominent Indian
pharmaceutical company. It is the world's largest
manufacturer of antiretroviral drugs (ARVs) to
fight HIV/AIDS. An analyst for Cipla estimates the
demand for ARVs by customers in the United States to be
ln(Qa) = 5.5 – 1.1 ln(Pa) - 3.8 ln(Pf) - 2.3 ln(Pc)
where Qa is the units demanded for ARVs, Pa is the price of ARVs, Pf is the
price of food, and Pc is the price of clothing. That analyst also estimates
the demand for ARVs by customers in Africa to be
ln(Qa) = 1.7 - 5 ln(Pa) - 0.8 ln(Pf) - 1.3 ln(Pc)
How can Cipla use that difference in demand to its advantage?
Assume market conditions do not allow customers to resell individual units
(drugs) to other customers.
61
A.10 Monopolistic Pricing
Review Questions
Answer to Question: Since the two groups of people have different
demand elasticities, Cipla should charge them different prices to maximize
profits.
For customers in the United States, which have -1.1 as demand elasticity,
Cipla should follow the rule
and set PF = -1.1/(1-1.1)MC = (1.1/.1)MC = 11MC.
For customers in Africa, which have -5 as demand elasticity, Cipla should
follow the rule
and set PF = -5/(1-5)MC = (5/4)MC = 1.25MC.
That is, Cipla should charge customers in the United States a price that is
11 times marginal cost, and customers in Africa the lower price of 1.25
times marginal cost.
62