Transcript MANAGERIAL ECONOMICS 11th Edition

Pricing Practices
Chapter 15
Chapter 15
OVERVIEW
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Pricing Rules-of-thumb
Markup Pricing And Profit Maximization
Price Discrimination
Price Discrimination Example
Two-part Pricing
Multiple-product Pricing
Joint Products
Joint Product Pricing Example
Pricing Rules-of-thumb
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Competitive Markets
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Profit maximization always requires setting
MR=MC, to maximize profits.
In competitive markets, P=MR, so profit
maximization requires setting P=MR= MC.
Imperfectly Competitive Markets
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With imperfect competition, P > MR, so profit
maximization requires setting MR=MC.
MR = P[1 + (1/εP)]
Optimal P* = MC/[1 + (1/εP)]
Pricing Rules-of-thumb
Imperfectly Competitive Markets
𝑑𝑇𝑅 𝑑 𝑃 ∙ 𝑄
𝜕𝑃
𝑀𝑅 = −
=
=𝑃+𝑄∙
𝑑𝑄
𝑑𝑄
𝜕𝑄
𝜕𝑃 𝑃
𝑄 𝜕𝑃
𝑀𝑅 = 𝑃 + 𝑄 ∙
∙ =𝑃+𝑃
∙
𝜕𝑄 𝑃
𝑃 𝜕𝑄
1
1
𝑀𝑅 = 𝑃 + 𝑃
=𝑃 1+
𝜀𝑃
𝜀𝑃
Pricing Rules-of-thumb
Imperfectly Competitive Markets
at Profit Maximization
𝑀𝑅 = 𝑀𝐶
1
𝑃 1+
𝜀𝑃
𝑀𝐶
𝑃=
1
1+
𝜀𝑃
= 𝑀𝐶
Markup Pricing
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Optimal Markup on Cost
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Markup pricing is an efficient means for
achieving profit maximization.
Markup on cost uses cost as a basis.
Optimal markup on cost = -1/(εP + 1).
Optimal Markup on Price
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Markup on price uses price as a basis.
Optimal markup on price = -1/εP
Optimal Markup of Cost
𝑃 − 𝑀𝐶
𝑚𝑎𝑟𝑘𝑢𝑝 𝑜𝑛 𝑐𝑜𝑠𝑡 =
𝑀𝐶
𝑃 = 𝑀𝐶(1 + 𝑚𝑎𝑟𝑘𝑢𝑝 𝑜𝑛 𝑐𝑜𝑠𝑡)
𝑀𝐶
𝑀𝐶 1 + 𝑚𝑎𝑟𝑘𝑢𝑝 𝑜𝑛 𝑐𝑜𝑠𝑡 =
1
1+
𝜀𝑃
−1
𝑚𝑎𝑟𝑘𝑢𝑝 𝑜𝑛 𝑐𝑜𝑠𝑡 =
𝜀𝑃 + 1
−1
𝑚𝑎𝑟𝑘𝑢𝑝 𝑜𝑛 𝑐𝑜𝑠𝑡 =
= 2 𝑜𝑟 200%
−1.5 + 1
Optimal Markup of Price
𝑃 − 𝑀𝐶
𝑚𝑎𝑟𝑘𝑢𝑝 𝑜𝑛 𝑝𝑟𝑖𝑐𝑒 =
𝑃
1
𝑃 1+
= 𝑀𝐶
𝜀𝑃
𝑃
𝑃+
= 𝑀𝐶
𝜀𝑃
−𝑃
𝑃 − 𝑀𝐶 =
𝜀𝑃
𝑃 − 𝑀𝐶
−1
−1
=
=
= 66.7% 𝑚𝑎𝑟𝑘𝑢𝑝 𝑜𝑛 𝑝𝑟𝑖𝑐𝑒
𝑃
𝜀𝑃
−1.5
Price Discrimination
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Profit-Making Criteria
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Price elasticity of demand must differ in submarkets.
Must have ability to prevent reselling.
Price discrimination exists if P1/P2 ≠ MC1/MC2.
Degrees of Price Discrimination
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First degree creates different prices for each
customer (maximum profits).
Second degree gives quantity discounts.
Third degree assigns different prices by customer
age, sex, income, etc. (most common).
Price Discrimination
Gas
Price
Market Supply
Willing to Pay
$5
($4) P*
Market Demand
Q*
Quantity
Price Discrimination
Gas
Price
Market Supply
Consumer
Surplus
P*
Producer
Surplus
Market Demand
Q*
Quantity
Price Discrimination
Sweater
Price
Market Supply
Lord and Taylor
Macy’s
Venture
Market Demand
Qlt
Qm
Qv
Quantity
Price Discrimination Example
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Price – Output Determination
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To maximize profits, set MR=MC in each
market.
One-price Alternative
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Without price discrimination, MR=MC for all
customers as a group.
With price discrimination, MR=MC for each
customer or customer group.
Profitable price discrimination benefits sellers
at the expense of some customers.
Price Discrimination Example
Public Demand
Student Demand
𝑃𝑝 = $850 − $0.01𝑄𝑝
𝑃𝑠 = $200 − $0.0025𝑄𝑠
𝑀𝑅𝑝 = $850 − $0.02𝑄𝑝
𝑀𝑅𝑠 = $200 − $0.005𝑄𝑠
𝑇𝐶 = $15,000,000 + $50𝑄
𝑀𝐶 = $50
Price Discrimination Example
Public Demand
Student Demand
𝑀𝑅𝑝 = 𝑀𝐶
𝑀𝑅𝑠 = 𝑀𝐶
$850 − $0.02𝑄𝑝 = $50
$200 − $0.005𝑄𝑠 = $50
$0.02𝑄𝑝 = $800
800
𝑄𝑝 =
= 40,000
0.02
$0.005𝑄𝑠 = $150
150
𝑄𝑠 =
= 30,000
0.005
𝑃𝑝 = $850 − $0.01(40,000)
𝑃𝑠 = $200 − $0.0025(30,000)
𝑃𝑝 = $450
𝑃𝑠 = $125
𝐸𝑝 = 0.17778
𝐸𝑠 = 1.2
Price Discrimination Example
Profit
𝜋 = 𝑇𝑅𝑝 + 𝑇𝑅𝑠 − 𝑇𝐶
𝜋 = $450 ∙ 40,000 + $125 ∙ 30,000 − 15,000,000 − $50 ∙ 70,000
𝜋 = 3,250,000
Price Discrimination Example
One Price Solution
𝑄𝑝 = 85,000 − 100𝑃𝑝
𝑄𝑠 = 80,000 − 400𝑃𝑠
𝑄 = 𝑄𝑝 + 𝑄𝑠 = 85,000 − 100𝑃𝑝 + 80,000 − 400𝑃𝑠
𝑄 = 165,000 − 500𝑃
𝑃 = $330 − $0.002𝑄
𝑀𝑅 = $330 − $0.004𝑄
Price Discrimination Example
One Price Solution
𝑀𝑅 = 𝑀𝐶
$330 − $0.004𝑄 = $50
$0.004𝑄 = $280
280
𝑄=
= 70,000
0.004
𝑃 = $330 − $0.002 70,000 = $190
Price Discrimination Example
One Price Solution
Public Demand
Student Demand
𝑄𝑝 = 85,000 − 100($190)
𝑄𝑠 = 80,000 − 400($190)
𝑄𝑝 = 66,000
𝑄𝑆 = 4,000
𝜋 = 𝑇𝑅 − 𝑇𝐶
𝜋 = $190 ∙ 70,000 − 15,000,000 − $50 ∙ 70,000
𝜋 = −5,200,000
Two-Part Pricing
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One-price Policy and Consumer Surplus
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A single price policy creates bargains for avid buyers;
they enjoy consumer surplus.
Consumer surplus reflects unpaid benefit.
Capturing Consumer Surplus With Two-part
Pricing
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Lump-sum prices plus user fees capture consumer
surplus for producers, e.g., club memberships.
Two-Part Pricing
Golf Fees
Price
Consumer Surplus=$800
Profits=$1,600
Demand (P=$100 - $1Q)
$60
MC=$20
40
Quantity
MR = $100 - $2Q
Two-Part Pricing
𝑃 = $100 − $1𝑄
𝑀𝑅 = $100 − $2𝑄
𝑇𝐶 = $20𝑄
𝑀𝐶 = $20
𝑀𝑅 = 𝑀𝑅
$100 − $2𝑄 = $20
𝑄 = 40
𝑃 = $100 − $1 ∙ 40 = $60
𝜋 = 𝑇𝑅 − 𝑇𝐶 = $60 ∙ 40 − $20 ∙ 40 = $1,600
𝐶𝑆 = 0.5 40 ∙ ($100 − $60) = $800
Two-Part Pricing
Golf Fees
Price
Profits = $3,200
Demand
$20
MC = $20
80 Quantity
Two-Part Pricing
𝑃 = $100 − $1𝑄
𝑀𝐶 = $20
𝑃 = 𝑀𝐶
$100 − $1𝑄 = $20
𝑄 = 80
𝐶𝑆 = 0.5 80 ∙ ($100 − $20) = $3,200
Consumer Surplus of $3,200 represents the maximum annual membership
free a golfer will pay to play 80 rounds of golf per year
𝑇𝑅 = $3,200 + $20 ∙ 80 = $4,800
𝜋 = $4,800 − $20 ∙ 80 = $3,200 Profit for each golfer per
Two-Part Pricing
• Consumer Surplus and Bundle Pricing
• When significant consumer surplus exists, profits
can be enhanced if products are purchased
together.
Multiple-product Pricing
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Demand Interrelations

Cross-marginal revenue terms indicate how
product revenues are related to another.
𝜕𝑇𝑅 𝜕𝑇𝑅𝐴 𝜕𝑇𝑅𝐵
𝑀𝑅𝐴 =
=
+
𝜕𝑄𝐴
𝜕𝑄𝐴
𝜕𝑄𝐴
𝜕𝑇𝑅 𝜕𝑇𝑅𝐵 𝜕𝑇𝑅𝐴
𝑀𝑅𝐵 =
=
+
𝜕𝑄𝐵
𝜕𝑄𝐵
𝜕𝑄𝐵
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Could be substitute or complimentary
products
Multiple-product Pricing
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Production Interrelations
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Joint products may compete for resources or
be complementary.
A by-product is any output customarily
produced as a direct result of an increase in
the production of some other output.
Joint Products
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Joint Products in Variable Proportions
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If products are produced in variable proportions, they
are distinct outputs.
For joint products produced in variable proportions,
set
𝑀𝑅𝐴 = 𝑀𝐶𝐴 and 𝑀𝑅𝐵 = 𝑀𝐶𝐵

Allocation of common costs is wrong and arbitrary.
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Joint Products in Fixed Proportions
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Some products are produced in a fixed ratio.
𝑄 = 𝑄𝐴 +𝑄𝐵
𝑀𝑅𝑄 = 𝑀𝑅𝐴 + 𝑀𝑅𝐵 = 𝑀𝐶𝑄
Joint Product Pricing Example
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Joint Products Without Excess By-product
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Profit-maximization requires setting MRQ= MRA+MRB = MCQ
Marginal revenue from each byproduct makes a contribution
toward covering MCQ
Newsprint
Packaging Material
𝑃𝐴 = $400 − $0.01𝑄𝐴
𝑃𝐵 = $350 − $0.015𝑄𝐵
𝑀𝑅𝐴 = $400 − $0.02𝑄𝐴
𝑀𝑅𝐵 = $350 − $0.03𝑄𝐵
𝑇𝐶 = $2,000,000 + $50𝑄 + $0.01𝑄2
𝑀𝐶 = $50 + $0.02𝑄
Joint Product Pricing Example
𝑇𝑅 = 𝑇𝑅𝐴 + 𝑇𝑅𝐵
𝑇𝑅 = 𝑃𝐴 𝑄𝐴 + 𝑃𝐵 𝑄𝐵
𝑇𝑅 = $400 − $0.01𝑄𝐴 𝑄𝐴 + $350 − $0.015𝑄𝐵 𝑄𝐵
𝑇𝑅 = $400𝑄𝐴 − $0.01𝑄𝐴2 + $350𝑄𝐵 − $0.015𝑄𝐵2
𝑇𝑅 = $750Q − $0.025𝑄2
𝑀𝑅 = $750 − $0.05𝑄
𝑀𝑅 = 𝑀𝐶
$750 − $0.05𝑄 = $50 + $0.02𝑄
$0.07𝑄 = 700
𝑄 = 10,000
Joint Product Pricing Example
𝑀𝑅𝐴 = $400 − $0.02𝑄𝐴
𝑀𝑅𝐵 = $350 − $0.03𝑄𝐵
𝑀𝑅𝐴 = $400 − $0.02(10,000)
𝑀𝑅𝐵 = $350 − $0.03(10,000)
𝑀𝑅𝐴 = $200
𝑀𝑅𝐵 = $50
𝑀𝐶 = $50 + $0.02𝑄
𝑀𝐶 = $50 + $0.02(10,000)
𝑀𝐶 = $250
𝑃𝐴 = $400 − $0.01𝑄𝐴 = $400 − $0.01 10,000 = $300
𝑃𝐵 = $350 − $0.015𝑄𝐵 = $350 − $0.015 10,000 = $200
Joint Product Pricing Example
𝜋 = 𝑃𝐴 𝑄𝐴 + 𝑃𝐵 𝑄𝐵 − 𝑇𝐶
𝜋 = $300 ∙ 10,000 + $200 ∙ 10,000
−2,000,000 − $50 ∙ 10,000 − $0.01 ∙ 10,0002
𝜋 = $1,500,000
Joint Product Pricing Example
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Joint Production With Excess By-product (Dumping)
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Profit-maximization requires setting MRQ= MRA+MRB= MCQ
Primary product marginal revenue covers MCQ
By product: MR=MC=0
𝑃𝐵′ + $290 − $0.02𝑄𝐵
𝑀𝑅𝐵′ + $290 − $0.04𝑄𝐵
𝑀𝑅 = 𝑀𝑅𝐴 + 𝑀𝑅𝐵′
𝑀𝑅 = $400 − $0.02𝑄𝐴 + $290 − $0.04𝑄𝐵
𝑀𝑅 = $690 − $0.06𝑄
Joint Product Pricing Example
𝑀𝑅 = 𝑀𝐶
$690 − $0.06𝑄 = $50 + $0.02𝑄
$0.08𝑄 = $640
𝑄 = 8,000
𝑀𝑅 = 𝑀𝐶 = $210
𝑤ℎ𝑒𝑛 𝑄 = 8,000
𝑀𝑅𝐴 = $400 − $0.02𝑄𝐴
𝑀𝑅𝐵′ = $290 − $0.04𝑄𝐵
𝑀𝑅𝐴 = $400 − $0.02(8,000)
𝑀𝑅𝐵′ = $290 − $0.04(8,000)
𝑀𝑅𝐴 = $240
𝑀𝑅𝐵′ = −$30
Joint Product Pricing Example
𝑀𝑅𝐴 = 𝑀𝐶
𝑀𝑅𝐵′ = 𝑀𝐶𝐵
$400 − $0.02𝑄 = $50 + $0.02𝑄
$0.04𝑄 = $350
$290 − $0.04𝑄 = $0
$0.04𝑄 = $290
𝑄 = 8,750
𝑄 = 7,250
𝑃𝐴 = $400 − $0.01𝑄𝐴 = $400 − $0.01 8,750 = $312,50
𝑃𝐵′ = $350 − $0.015𝑄𝐵 = $350 − $0.015 7,250 = $145
𝜋 = 𝑃𝐴 𝑄𝐴 + 𝑃𝐵′ 𝑄𝐵 − 𝑇𝐶
𝜋 = $312.50 ∙ 8,750 + $145 ∙ 7,250
−2,000,000 − $50 ∙ 8,750 − $0.01 ∙ 8,7502 = $582,500