Transcript price discriminates

Chapter 12
Capturing
Surplus
1
Chapter Twelve Overview
1. Introduction: Airline Tickets
2. Price Discrimination
• First Degree
• Second Degree
• Third Degree
3. Tie-in Sales
• Requirements Tie-ins
• Package Tie-ins (Bundling)
Chapter Twelve
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Uniform Price Vs. Price Discrimination
Definition: A monopolist charges a uniform price if it
sets the same price for every unit of output sold.
While the monopolist captures profits due to an
optimal uniform pricing policy, it does not receive
the consumer surplus or dead-weight loss associated
with this policy.
The monopolist can overcome this by charging more
than one price for its product.
Definition: A monopolist price discriminates if it
charges more than one price for the same good or
service.
Chapter Twelve
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Forms of Price Discrimination
Definition: A policy of first degree (or perfect) price
discrimination prices each unit sold at the consumer's
maximum willingness to pay. This willingness to pay is directly
observable by the monopolist.
Definition: A policy of second degree price discrimination
allows the monopolist to offer consumers a quantity discount.
Definition: A policy of third degree price discrimination offers a
different price for each segment of the market (or each
consumer group) when membership in a segment can be
observed.
Chapter Twelve
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“Willingness to Pay” Curve
Definition: The consumer's maximum
willingness to pay is called the consumer's reservation
price.
Think of the demand curve as a "willingness to pay" curve. If
the monopolist can observe the willingness to pay of each
customer (based on, for example, residence, education,
"look", etc), then the monopolist can observe demand
perfectly and can "perfectly" price discriminate.
Chapter Twelve
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Forms of Price Discrimination
Definition: A policy of first degree (or perfect) price
discrimination prices each unit sold at the
consumer's maximum willingness to pay. This
willingness to pay is directly observable by the
monopolist.
Chapter Twelve
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Uniform Price Vs. Price Discrimination
Uniform Price Monopoly 1st Degree P.D. Monopoly
Price
CS: E+F
0
PS: G+H+K+L
E+F+G+H+J+K+L+N
TS: E+F+G+H+K+L E+F+G+H+J+K+L+N
DWL: J+N
0
PU E F
H
G
P1
K
MC
J
N
L
MR
D
Quantity
Chapter Twelve
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Is it Reasonable?
The monopolist will continue selling units until the
reservation price exactly equals marginal cost.
Therefore, a perfectly price discriminating
monopolist will produce and sell the efficient
quantity of output.
Note: Only if the monopolist can prevent resale
can the monopolist capture the entire surplus.
Chapter Twelve
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Pricing Surplus – Monopoly
MC = 2
P = 20 - Q
What is producer surplus if uniform pricing is followed?
MR = P + (P/Q)Q = 20 - Q - Q = 20 - 2Q
MR = MC => 20 - 2Q = 2 =>
Q* = 9
P* = 11
PS= Revenue-TVC = PQ-2Q = 11(9)-2(9) = 81
Chapter Twelve
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Pricing Surplus – Monopoly
What will producer surplus be if the
monopolist perfectly price discriminates?
P = MC => 20 - Q = 2 =>Q* = 18
Revenue - TVC = [18(20-2)(1/2) + 18(2)]18(2) = 162
This is a gain in captured surplus of 81!
Chapter Twelve
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First Degree Price Discrimination
Price
What is the marginal revenue curve for a
perfectly price discriminating monopolist?
20
When the monopolist sells an additional unit,
it does not have to reduce the price on the
other units it is selling. Therefore, MR = P. (i.e.,
the marginal revenue curve equals the
demand curve.)
11
MC
2
9
18
D
20
Quantity
MR (uniform pricing)
Chapter Twelve
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Second Degree Price Discrimination
Definition: A policy of second degree price
discrimination allows the monopolist to
charge a different price to different
consumers. While different consumers pay
different prices, the reservation price of any
one consumer cannot be directly observed.
Chapter Twelve
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Two Part Tariff
Definition: A monopolist charges a two part
tariff if it charges a per unit fee, r, plus a lump
sum fee (paid whether or not a positive number
of units is consumed), F.
This, effectively, charges demanders of a low
quantity a different average price than
demanders of a high quantity.
Example: hook-up charge plus usage fee for a
telephone, club membership, or the like.
Chapter Twelve
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Two Part Tariff
P
10
0
Example:
All customers are identical and have demand
• P = 100 - Q
• MC = AC = 10
4050
10
90 100
Chapter Twelve
Q
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Two Part Tariff
What is the optimal two-part tariff?
Two steps:
(1) maximize the benefits to the consumers by
charging r = MC = 10.
(2) capture this benefit by setting F = consumer
benefits = 4050.
Chapter Twelve
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Two Part Tariff
Any higher usage charge would result in a deadweight loss that could not be captured by the
monopolist. Any lower usage charge would
result in selling at less than marginal cost.
In essence, the monopolist maximizes the size of
the "pie", then sets the lump sum fee so as to
capture the entire "pie" for itself.
The total surplus captured is the same as in the
case of perfect price discrimination.
Chapter Twelve
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Block Tariff
Definition: If a consumer pays
one price for one block of
output and another price for
another block of output, the
consumer faces a block tariff
Chapter Twelve
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Block Tariff
• P = 100 - Q
• MC = AC = 10
Let Q1 be the largest quantity for which the first
block rate applies so that p1(Q1) = 100 - Q1.
Let Q2 be the largest quantity purchased (so that
the second block rate will apply between Q1 and Q2)
so that p2(Q2) = 100 - Q2
Chapter Twelve
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Block Tariff
Then:
 = p1(Q1)Q1 + p2(Q2)(Q2-Q1) - TC(Q2)
= (100 - Q1)Q1 + (100 - Q2)(Q2-Q1) - 10Q2
and we must choose Q1 and Q2 to maximize this profit…
MR1 = (100 - Q1) - Q1 - (100 - Q2) = 0
MR2 = (100 - Q2) - Q2 + Q1 = MC = 10
Chapter Twelve
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Key Equations
These are two equations in two
unknowns that can be solved to obtain:
• Q1* = 30
• Q2* = 60
• P1* = 70
• P2* = 40 (a quantity discount)
Chapter Twelve
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Block Pricing
P
100
P
100
Demand
Demand
450
70
1012.5
55
450
40
2700
450
10
0
30
2025
60
100 Q
0
Chapter Twelve
1012.5
45 MR
MC
100
Q
21
Block Pricing
If the monopolist could set a
different block price for each
customer, it would capture the
same amount of surplus as a
perfectly
price
discriminating
monopolist.
Chapter Twelve
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Utility Pricing
D - small
D - large
MC
Chapter Twelve
Q
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Utility Pricing
D - small
D - large
Additional CS
P1
Additional PS
P2
MC
Q1s
Q1L Q2L
Chapter Twelve
Q
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Third Degree Price Discrimination
Definition: A policy of third degree price
discrimination offers a different price for each
segment of the market (or each consumer
group) when membership in a segment can be
observed.
Example: Movie ticket sales to older people or
students at discount
• Suppose that marginal costs for the two
markets are the same. How does a monopolist
maximize profit with this type of price
discrimination?
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Optimal Pricing
Set the marginal revenue in each market equal to marginal
cost. (i.e., the monopolist maximizes total profits by
maximizing profits from each group individually.)
This implies that MR1 = MC = MR2 at the optimum.
Otherwise, the monopolist could raise revenues by
switching sales from the low MR group to the high MR
group.
MC = AC = 20
Example
P1 = 100 - Q1
P2 = 80 - 2Q2
Chapter Twelve
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Optimal Pricing
MR1 = 100 - 2Q1 = MC = 20
MR2 = 80 - 4Q2 = MC = 20
Q1* = 40
Q2* = 15
Example
P1* = 60
P2* = 50
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Third Degree Price Discrimination
P
Market 1
P
100
Demand 1
80
60
Market 2
Demand 2
50
20
0
MR1
100
Q
0
Chapter Twelve
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40
MR2
Q
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Tie-in Sales – Requirements
Definition: A tie-in sale occurs if customer can
buy one product only if they agree to purchase
another product as well.
• Requirements tie-in sales occur when a firm
requires customers who buy one product from
the firm to buy another product from the firm.
A requirements tie-in sale may be used in place
of price discrimination when the firm cannot
observe the relative willingness to pay of
different customers.
Chapter Twelve
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Tie-in Sales – Bundling
• Package tie-in sales (or bundling) occur
when goods are combined so that customers
cannot buy either good separately.
Bundling may be used in place of price
discrimination to increase producer surplus
when consumers have different willingness to
pay for the goods sold in the bundle.
But bundling does not always pay…
Chapter Twelve
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Tie-in Sales – Bundling
Reservation Price
Computer
Monitor
Customer 1
$1,200
$600
Customer 2
$1,500
$400
Marginal Cost $1,000
$300
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Tie-in Sales – Bundling
Optimal Pricing Policy
Without bundling: pc = $1500 pm = $600
• Profit cm = $800
With bundling: pb = $1800
• Profit b = $1000
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Tie-in Sales – Bundling
Reservation Price
Computer
Monitor
Customer 1
$1,200
$400
Customer 2
$1,500
$600
Marginal Cost $1,000
$300
Chapter Twelve
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Tie-in Sales – Bundling
Optimal Pricing Policy
Without bundling: pc = $1500 pm = $600
• Profit cm = $800
With bundling: pb = $2100
• Profit b = $800
In general, bundling a pair of goods only pays if their
demands are negatively correlated (customers who
are willing to pay relatively more for good A are not
willing to pay as much for good B).
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Reservation Price
The reason is that the price is
determined by the purchaser with
the lowest reservation price.
If reservation prices for the two
goods are negatively correlated,
bundling reduces the dispersion of
reservation prices and so raises the
price at which additional units can be
sold.
Chapter Twelve
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Advertising
The firm can capture surplus using nonprice strategies such as
advertising.
Chapter Twelve
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