Download price discrimination

Chapter 12
Pricing and
Advertising
Everything is worth what its purchaser
will pay for it.
Publilius Syrus
(first century BC)
Chapter 12 Outline
Challenge: Sale Price
12.1 Conditions for Price Discrimination
12.2 Perfect Price Discrimination
12.3 Group Price Discrimination
12.4 Nonlinear Pricing α
12.5 Two-Part Pricing
12.6 Tie-In Sales
12.7 Advertising
Challenge Solution
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12-2
Challenge: Sale Price
• Background:
• Because many firms use sales—temporarily setting the
price below the usual price—some customers pay lower
prices than others over time.
• When Heinz ketchup goes on sale, switchers — ketchup
customers who normally buy whichever brand is least
expensive—purchase Heinz rather than the low price
generic ketchup.
• Questions:
• How can Heinz’s managers design a pattern of sales that
maximizes Heinz’s profit by obtaining extra sales from
switchers without losing substantial sums by selling to its
loyal customers at a discount price?
• Under what conditions does it pay for Heinz to have a
policy of periodic sales?
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12-3
12.0 Price vs. Quantity Decision
• Monopoly’s quantity decision:
¶p
= P(Q) + P¢(Q)Q - C¢(Q) = 0
Max p = P(Q)Q - C(Q) Þ
{Q}
¶Q
• Price decision: (Note Q’(P)=1/P’(Q))
Max p = PQ(P) - C(Q(P))
{P}
Þ
¶p
= Q(P) + PQ¢(P) - C¢(Q)Q¢(P) = 0 = P(Q) + P¢(Q)Q - C¢(Q)
¶P
• Quantity and price decision yield the same
outcome for the monopoly, but not for the
oligopoly.
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12-4
12.1 Conditions for Price
Discrimination
• Why does Disneyworld charge local residents
$369 for an annual pass and out-of-towners
$489?
• Why are airline fares less if you book in
advance?
• Why are computers and software bundled and
sold at a single price?
• Firms sometimes use nonuniform pricing,
where prices vary across customers, to earn a
higher profit.
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12-5
12.1 Conditions for Price
Discrimination
• A firm engages in price discrimination by charging
consumers different prices for the same good based on
• individual characteristics
• belonging to an indentifiable sub-group of consumers
• the quantity purchased
• Two reasons why a firm earns a higher profit from price
discrimination than uniform pricing:
1.Price-discriminating firms charge higher prices to
customers who are willing to pay more than the
uniform price.
2.Price-discriminating firms sell to some people who are
not willing to pay as much as the uniform price.
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12-6
12.1 Conditions for Price
Discrimination
• Necessary conditions for successful price discrimination:
1.A firm must have market power (otherwise it cannot
charge a price above the competitive price).
•
Examples: monopolist, oligopolist, monopolistically
competitive, cartel
2.A firm must be able to identify which consumers are
willing to pay relatively more and there must be
variation in consumers’ reservation price, the
maximum amount someone is willing to pay.
3.A firm must be able to prevent or limit resale from
customers who are charged a relatively low price to
those who are charged a relatively high price.
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12-7
12.1 Conditions for Price
Discrimination
• A firm’s inability to prevent resale is often the biggest
obstacle to successful price discrimination.
• Resale is difficult or impossible for services and when
transaction costs are high.
• Examples: haircuts, plumbing services, admission that
requires showing an ID
• Not all differential pricing is price discrimination.
• It is not price discrimination if the different prices
simply reflect differences in costs.
• Example: selling magazines at a newsstand for a higher
price than via direct mailing
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12-8
12.1 Types of Price Discrimination
1.
2.
3.
First-degree
•
Also known as perfect price discrimination
•
Each unit sold for each customer’s reservation price
Second-degree
•
Also known as nonlinear discrimination
•
Firm charges a different price for large quantities
than for small quantities
Third-degree
•
Also known as group price discrimination
•
Firm charges different groups of customers different
prices, but charges any one customer the same
price for all units sold
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12-9
12.2 Perfect Price Discrimination
• Under perfect price discrimination, the firm charges
each consumer a price that is exactly equal to the
maximum he/she is willing to pay.
• Thus, each consumer gets zero consumer surplus.
• Firm profit is increased by the amount of consumer
surplus that would exist in a competitive market; all CS
is transferred to the firm.
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12-10
12.2 Perfect Price Discrimination
• All consumer
surplus is
transformed into
firm profit.
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12-11
12.2 Perfect Price Discrimination
• If D(Q) is the inverse demand function for total output, Q,
and p = D(Q) is the reservation price charged of each
customer, the discriminating monopoly’s revenue is:
• This is equal to the area under the demand curve up to Q.
• Maximizing profit by choosing output:
• FOC:
• Result: produce where D(Q) equals MC.
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12-12
12.2 Perfect Price Discrimination
• Producing where
Demand = MC, all
consumer surplus
(A+B+C) is
transformed into
firm profit.
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12-13
12.2 Perfect Price Discrimination
• The perfect price discrimination result of
producing where demand equals MC means
that the competitive quantity of output gets
produced.
• This outcome is efficient:
• it maximizes total welfare
• no deadweight loss is generated
• But the outcome is harmful to consumers
because all surplus is producer surplus!
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12-14
12.3 Group Price Discrimination
• Firms divide potential customers into two or more
groups (based on some easily observable characteristic)
and set a different price for each group.
• Example: senior or student discounts
• The firm chooses quantities sold to each group, Q1 and
Q2, such that
• FOCs:
• Marginal revenue from each group should be the same
and equal to marginal cost:
• 𝑀𝑅1 𝑄1 = 𝑀𝐶 𝑄1 + 𝑄2 = 𝑀𝑅 2 𝑄2
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12-15
12.3 Group Price Discrimination
• The first-order conditions imply that marginal revenue
from each group should be the same and equal to
marginal cost:
• Because marginal revenue is a function of elasticity, we
can write:
•
• Thus, the higher price will be charged in the less elastic
market segment.
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12-16
12.3 Group Price Discrimination
• A higher price will be charged in the market
with the more price-inelastic demand.
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12-17
12.4 Multimarket Price
Discrimination
1
29
29(1  )  1   A  
 1.0357
A
28
1
39
39(1  )  1   B    1.0263
B
38
1 1
pB 39
A


 1.345
p A 29 1  1
B
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12-18
Solved Problem 12.2
• A monopoly drug producer with a constant marginal
cost of m = 1 sells in only two countries and faces
a linear demand curve of
– Q1 = 12 − 2p1 in Country 1 and
– Q2 = 9 − p2 in Country 2.
• A price-discriminating monopoly? What price does
the monopoly charge in each country with a ban
against shipments between the countries?
– MR1=6-Q1=MC=1Q1=5; P1=3.5; π1=12.5; CS1=6.25.
– MR2=9-2Q2=MC=1Q2=4; P2=5; π1=16; CS2=8
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12-19
Solved Problem 12.2
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12-20
Solved Problem 12.2
• A single-price monopoly? What price does the
monopoly charge in both countries without a ban
against shipments between the countries?
– Q(p)=Q1(p)+Q2(p)= 21 − 3p ;p=7-Q/3
– MR=7-2Q/3=MC=1Q=9; P=4; π=27<28.5
– Q1=12−2p=4π1=12<12.5; CS1=4<6.25;
π1+CS1=16<18.75
– Q2=9−p=5π2=15<16; CS2=12.5>8; π2+CS2=27.5>24
– π1+CS1=16<18.75;π2+CS2=27.5>24; π+CS=43.5>42.75
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12-21
Solved Problem 12.2
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12-22
12.3 Group Price Discrimination
• Welfare under multimarket price discrimination is lower
than it is under either competition or perfect price
discrimination.
• Under competition, more output is produced and CS is
greater
• The welfare effects relative to uniform price monopoly
are indeterminate.
• Both types of monopolies set price above marginal cost,
so output is lower than in competition.
• Welfare is likely to be lower with discrimination due to
consumption inefficiency and time wasted shopping.
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12-23
12.4 Nonlinear Price Discrimination
• Price varies only with the quantity purchased, but
each customer faces the same nonlinear pricing
schedule.
• Not all quantity discounts are price discrimination;
some reflect reductions in firm costs associated with
large-quantity sales.
• Many utilities use block-pricing schedules, by which
they charge one price for the first few units of usage
(block) and then a different price for subsequent blocks.
• Example: increasing-block pricing associated with
electricity; per KWH charge increases the more you use
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12-24
12.4 Nonlinear Price Discrimination
• Consider a firm that uses declining-block prices to
maximize profit.
• $70 is charged for 1 ≤ Q ≤ 20
• $50 is charged for Q > 20
• Thus, a consumer who buys 30 units pays $70 • 20 =
$1400 for the first block and $50 • 10 = $500 for the
second block, for a total of $1900.
• By contrast, under a non-discriminating monopoly, this
consumer would be charged a uniform price of $60 and
pay a total of $1,800 for 30 units.
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12-25
12.4 Nonlinear Price Discrimination
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12-26
12.4 Nonlinear Price Discrimination
• Designing block prices with p(Q)=90-Q and MC=30.
• $p1 is charged for 1 ≤ Q ≤ Q1
• $p2 is charged for Q > Q1
• p1=p(Q1); p2=p(Q2)
• π=p(Q1)Q1+p(Q2)(Q2-Q1)-30Q2=(90-Q1)Q1+(90Q2)(Q2-Q1)-30Q2
• dπ/dQ1=90-2Q1-(90-Q2)=0 Q2=2Q1;
• dπ/dQ2=90-2Q2+Q1-30=0 Q1=20; Q2=40;
• p1=p(Q1)=70; p2=p(Q2)=50;
• The more block prices the monopoly can set, the
closer the monopoly can get to perfect price
discrimination.
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12-27
12.5 Two-Part Pricing
• Another form of nonlinear pricing, a two-part tariff, is
when the firm charges a consumer a lump-sum fee for
the right to purchase (first tariff) and a per unit fee for
each unit actually purchased (second tariff).
• Think of the first tariff as an “access fee” and the
second as a “usage fee”.
• Examples:
• A country club charges a membership fee and greens fees to
play a round of golf
• The state fair charges an entrance fee and a per ticket fee for
rides
• Cell phone service providers charge a monthly service fee
and a fee per text message
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12-28
12.5 Two-Part Tariffs
• If all consumers are
identically competitive
buyers, the firm can
capture all CS by
setting charging a
lump-sum “access fee”
equal to CS (A1+B1+C1)
and a “usage fee”
equal to marginal cost
(m).
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12-29
12.5 Two-Part Tariffs
• Now assume that the monopoly has two customers.
• If the firm can treat customers differently, it can still
capture all consumer surplus as in the previous graph.
• If the firm has to charge all customers the same price,
it maximizes profit by:
• Setting the lump-sum “access fee” equal to the
potential CS of the consumer with the smaller demand
and a price that is above marginal cost.
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12-30
12.5 Two-Part Tariffs
• With different customers, firm charges lumpsum fee of A1 and per unit fee of $20.
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12-31
12.5 Two-Part Tariffs
• If the firm charges both customers T=A+pq, and each
consumer determines his/her own qi:
• The lump-sum fee, A, depends on p.
• The lump-sum fee, A, will be the lower total CS
of the two consumers, CS1 in the example.
• CS1(p)=(80-p)2/2; CS2(p)=(100-p)2/2
• π=2CS1+(p-m)[q1(p)+q2(p)]
• =(80-p)2+(p-10)[80-p+100-p]
• dπ/dp=-2(80-p)+(180-2p)-2(p-10)=0p=20>10
• A=CS1(p)=1,800; q1(p)=60; q2(p)=80;
π=5,000;
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12-32
12.5 Two-Part Tariffs
• If the firm charges both customers only the same
uniform price p.
• π=(p-m)[q1(p)+q2(p)]=(p-10)[80-p+100-p]
• dπ/dp=(180-2p)-2(p-10)=0p=50>20
• q1(p)=30; q2(p)=50; π=3,200<5,000;
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12-33
12.6 Tie-In Sales
• Another type of nonuniform pricing is a tie-in sale, in
which customers can buy one product only if they agree
to purchase another product as well.
• Requirement tie-in sale: customers who buy one
product from a firm are required to make all purchases
of related products from that firm
• Example: photocopying machine buyers must buy services
and supplies from same company
• Bundling: two goods are combined so that customers
cannot buy either good separately
• Example: Refrigerators are sold with shelves
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12-34
12.6 Tie-In Sales (Pure Bundling)
Negatively correlated
Word
Proce
ssor
Sprea
dshee
t
Bundl
e
Alisha
120
50
170
Bob
90
70
P*
90
Q*
2
Positively correlated
Word
Proce
ssor
Sprea
dshee
t
Bundl
e
Carol
100
90
190
160
Dmitri
90
40
130
50
160
P*
90
90
130
2
2
Q*
2
1
2
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12-35
12.6 Tie-In Sales(Mixed Bundling)
Word
Proce
ssor
Sprea
dshee
t
Bundl
e
Aaron
120
30
150
Brigitte
110
90
200
Charle
s
90
110
200
Doroth
y
30
120
150
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• Negatively
correlated
reservation prices
– Separate prices
• 540 max
– Pure bundling
• 600 max
– Mixed bundling
• 640 max
12-36
12.7 Advertising
• Monopoly firms don’t just decide on price and quantity,
they also make important decisions about how much to
advertise their products.
• Advertising may positively influence consumers’
preferences and thereby increase demand for the
product.
• Although higher demand increases gross profit, if the
cost of advertising is substantial, net profit may or may
not increase.
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12-37
12.7 Deciding Whether to Advertise
• Advertise if cost is less than additional gross
profit, area B.
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12-38
12.7 How Much to Advertise
• If a monopoly raises advertising expenditures by $1,
how much does its gross profit rise?
• Additional advertising pays when gross profit rises by
more than $1 following an additional dollar spent on
advertising.
• Thus, the profit-maximizing amount of advertising
equates the marginal benefit and marginal cost of
advertising.
• Mathematically:
• where R is revenue and is a function of output and
advertising cost
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12-39
12.7 How Much to Advertise
• Given the maximization problem:
• The profit-maximizing output and advertising levels are
the Q* and A* that simultaneously satisfy the FOCs:
• The monopoly advertises until the marginal benefit
from the last unit of advertising equals $1, the
marginal cost.
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12-40
12.7 How Much to Advertise
• Given the maximization problem:
• 𝑝(𝑄, 𝐴) == 100 − 𝑄 + 4𝐴0.5 ; MC=10
• 𝜋 = (100 − 𝑄 + 4𝐴0.5 )𝑄 − 10𝑄 − 𝐴
–
𝜕𝜋
𝜕𝑄
= 90 − 2𝑄 + 4𝐴0.5 = 0;
–
𝜕𝜋
𝜕𝐴
= 2𝐴−0.5 𝑄 − 1 = 0
• A=900; Q=105; P=115; ϖ=10125;
– If A=0; Q=45; P=55; ϖ=10125
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12-41