Transcript PowerpointPriceDiscrimination

Price Discrimination
(when there is no
strategic interaction)
1
Profit Maximization when setting a
Single Price
CONSUMER SURPLUS
Profits are maximized
at Q=4 and P=6.
Profits=TR-TC=
6*4-4.5*4=
24-18=6
Or
Profits=P*Q-ATC*Q
=(P-ATC)*Q
=(6-4.5)*4=6

9
PROFITS
MC
8
7
ATC
6
5
AVC
4
3
2
D
1
12
11
10
9
8
7
6
5
4
3
2
1
0
0
• Consumer Surplus the value consumers
get from a good but
do not have to pay for.
10
Q
MR
2
Definition of Price Discrimination
 The
practice of charging different
prices to consumers for the same
good or service (and the price
differences do not reflect cost
differences)
3
Three Conditions Required for
Price Discrimination to Occur
1.
2.
3.
Seller must exercise some “price control”
(i.e. face a downward sloping demand)
Seller must be able to distinguish among
customers who are willing to pay
different prices.
It must be impossible or too costly for
one buyer to resell the good to other
buyers (i.e., buyers cannot arbitrage).
4
Strategic Behavior By Firms
What actions do firms take to prevent resale
or make resale more “costly”?
1.
2.
Warranty becomes invalid if item is
resold.
Software firms do not provide support
services if software is resold.
Any others you can think of?
5
Types of Price Discrimination
1.
First-Degree (Perfect) Price Discrimination Occurs when the seller charges the highest
price each consumer would be willing to pay
for the product (consumer's reservation values)
rather than go without it.

2.
Universities, Car Dealers, Contractors, Flea Market
(at least they all try)
Third-Degree Price Discrimination - Occurs
when the seller charges different prices in
different markets, or charges a different price
to different segments of the buying population.

Movies, Soda, Computers, prescription drugs,
textbooks, safety gates, airlines, dry cleaning,
haircuts, …
6
Types of Price Discrimination
3.
Second-Degree Price Discrimination - Occurs
when the seller charges a uniform price per
unit for one specific quantity, a lower price for
an additional quantity, and so on. QUANTITY
DISCOUNTS (2-part Pricing is a type of
quantity discount)

4.
Electric Utilities, Country Clubs, Michigan Athletic
Club, Disneyland (in old days), Grocery Stores,
Espresso Royale, …
Peak Load Pricing – the practice of charging
higher prices during “peak hours” (i.e. high
demand times) than during off-peak hours.

Hotels, Ski Resorts, Airlines, Stadiums,
Restaurants, Toll roads, Bridges, …
7
Types of Price Discrimination
5.
Bundling – the practice of bundling several
different products together and selling them at
a single “bundle price”.

6.
Happy Meals, Restaurants, Stereos, Cars with
Options, Celebrity Endorsements, Movies (years
ago),…
Screening- the practice of requiring consumers
to “jump over a hurdle” to obtain a lower price.

Coupons, Warranties, Rebates, Outlet malls,
Saturday Night Stayovers for airlines,….
8
No Price Discrimination

Profits are
maximized at
Q=20 and P=30.
50
D
45
40
MC
35
30
25
ATC
AVC
20
15
10
5
60
55
50
45
40
35
30
25
20
15
10
5
0
0
Profits=TR-TC
=P*Q-ATC*Q
=30*20-14*20=320
MR
9
First-Degree (Perfect) Price
Discrimination
Definition:
Occurs when the seller charges the
highest price each consumer would
be willing to pay for the product
(consumer's reservation values)
rather than go without it.

Universities, Car Dealers, Contractors, Flea Market
(at least they all try)
10
1st-Degree Price Discrimination
50
D
45
40
MC
35
30
25
ATC
AVC
20
15
10
5
11
60
55
50
45
40
35
30
25
20
15
10
5
0
0
Charge Every
Consumer the
maximum he/she is
willing to pay. The
demand curve is
based on what
consumers are willing
to pay.
Market Demand is Obtained from
Adding Individual Demand Curves
12
Suppose Market Demand is Obtained
from Individual Demands Below
13
1st-Degree Price Discrimination
D
45
TR
40
MC
35
30
25
ATC
AVC
20
15
10
TC
5
60
55
50
45
40
35
30
25
20
15
0
10
Q=30
 What would be the firm’s total
revenue?
TR=.5*(50-20)*30+20*30
=1050
 What would be the firm’s TC at
an output of 30?
TC=ATC*Q=15*30=450
 Profits=1050-450=600
50
5
What output would the
firm produce to maximize
profits if it could 1stdegree price
discriminate?
0

Marginal Revenue is the Demand Curve
14
1st Degree Price Discrimination
MaxQ Profits = MaxQ TR(Q)-TC(Q)
Q
= MaxQ
-TC(Q)
P
(
x
)

x

x 0
Fundamental
Theorem of
Calculus

So,
=P(Q)-MC=0 and P(Q)=MC
Q
MR
Certain Degrees Now Cost More at Universities
The New York Times, July 29, 2007
16
Expensive Lesson: Colleges Manipulate Financial Aid Offers
The Wall Street Journal, April 4, 1996
17
Expensive Lesson: Colleges Manipulate Financial Aid Offers
The Wall Street Journal, April 4, 1996
18
Expensive Lesson: Colleges Manipulate Financial Aid Offers
The Wall Street Journal, April 4, 1996
19
Reckonings; What Price Fairness?
The New York Times, October 4, 2000
20
Third-Degree Price Discrimination
Definition:
Occurs when the seller charges
different prices in different markets,
or charges a different price to
different segments of the buying
population.

Movies, Soda, Computers, prescription drugs,
textbooks, safety gates, airlines, …
21
Movie Theater with 300 seats that price discriminates based on
age by offering different prices to senior citizens and non-senior
citizens. Assume (Daily) Fixed Costs of $1,000 and constant
Marginal Cost of $2.
Senior Citizen
Non-Senior Citizen
200
180
160
140
400
360
320
280
240
200
160
120
80
40
0
0
MC
120
2
100
MC
80
4
Dns
60
Ds
40
6
20
8
20
18
16
14
12
10
8
6
4
2
0
0
10
MRs
MRns
Set a price of $6 for Senior Citizens and have 160 buy tickets. Set a price of $11 for
Non-Senior Citizens and have 90 buy tickets.
22
Daily Profits would then be 6*160+11*90-2*160-2*90-1000 = 450.
3rd Degree Price Discrimination
MaxQ1,Q2 TR1(Q1)+TR2(Q2)-TC(Q1+Q2)

So,
= MR1-MC=0 so MR1=MC
Q1

So,
= MR2-MC=0 so MR2=MC
Q2
3rd Degree Price Discrimination
Max
Qs,Qns
So,

Q s
So,
(10-.025Qs)Qs +(20-.1Qns)Qns-2(Qs+Qns)-1000
=10-.05Qs -2=0 so Qs=160

=20-.2Q
-2=0
ns
Qns
so Qns=90
Lower Rates for Women Are Ruled Unfair
New York Times, August 13, 2008
25
Insurance ‘eggheads” Make Women Pay
Los Angeles Times, June 22, 2008
26
Second-Degree Price Discrimination
Definition:
Second-Degree Price Discrimination - Occurs
when the seller charges a uniform price per
unit for one specific quantity, a lower price for
an additional quantity, and so on. QUANTITY
DISCOUNTS (2-part Pricing is a type of
quantity discount).

Electric Utilities, Country Clubs, Michigan Athletic
Club, Disneyland (in old days), Espresso Royale, …
http://www.seasonticketrights.com/TeamSeats.aspx?lid=21
27
2-Part Pricing
50
D
45
40
MC
35
30
25
ATC
AVC
20
15
10
5
Q
60
55
50
45
40
35
30
25
20
15
10
5
0
0
Suppose the graph to
the right depicts the
demand and cost
curves for a country
club where quantity
(Q) represents the
number of rounds of
golf.
28
29
Suppose the country club sets the price per
round of golf at $20. What membership fee
(fixed fee) should the country club set?
3
•What is the maximum
membership fee Individual A
will pay given the price per
round is $20?
Individual A
50
45
40
35
Maximum
membership fee
Individual A is
willing to pay.
DA
30
25
20
15
10
5
qA
10
9
8
7
6
5
4
3
2
1
0
0
.5*(50-20)*3=45
11
•If the price per round is $20
and the membership fee isn’t
too high, how many rounds of
golf will Individual A play?
30
Suppose the country club sets the price per
round of golf at $20. What membership fee
(fixed fee) should the country club set?
DB
35
30
25
20
15
10
5
10
9
8
7
6
5
4
11
qB
0
3
.5*(50-20)*6=90
Maximum
membership fee
Individual B is
willing to pay.
40
2
•What is the maximum
membership fee Individual B
will pay given the price per
round is $20?
45
1
6
Individual B
50
0
•If the price per round is $20
and the membership fee isn’t
too high, how many rounds of
golf will Individual B play?
31
Suppose the country club sets the price per
round of golf at $20. What membership fee
(fixed fee) should the country club set?

Given the cost of each round is $20, the country club should charge
a membership fee of either $45 or $90.
Profits if membership fee is $45
Both types of individuals join with Type A golfing 3
rounds each and Type B golfing 6 rounds.
45*9+20*(8*3+1*6)-15*30= 555
 Profits if membership fee is $90
Only Type B joins and Type B golfs 6 rounds.
90*1+20*(1*6)-35*6= 0
SET MEMBERSHIP FEE AT $45

32
2-Part Pricing
D
45
40
MC
35
30
25
ATC
AVC
20
15
10
5
Q
60
55
50
45
40
35
30
25
20
15
10
0
5
•If membership fee is
$90, total number of
rounds golfed is
1*6=60. At
Q=6, ATC=35 so
TC=ATC*Q=35*6=210.
50
0
•If membership fee is
$45, total number of
rounds golfed is
8*3+1*6=30. At
Q=30, ATC=15 so
TC=ATC*Q=15*30=450
.
33
Peak Load Pricing

Definition
The practice of charging higher prices
during “peak hours” (i.e. high demand
times) than during off-peak hours.
 Hotels,
Ski Resorts, Airlines, Stadiums,
Restaurants, …
http://panynj.info/bridges-tunnels/tolls.html
34
Demands at a Restaurant for Lunch and Dinner
35
Suppose Restaurant’s Capacity is 45 seats,
Fixed Costs are $1800 per day and Marginal
Cost of a meal is constant at $20
DD
DL
MC=AVC
90
80
70
60
MRD
100
MRL
50
40
30
qL,qD
20
What are the
Restaurant’s daily
profits?
TR-TC=TR-TVC-TFC=
35*15+60*4020*(15+40)-1800= 25
100
95
90
85
80
75
70
65
PD=60
55
50
45
40
PL= 35
30
25
20
15
10
5
0
-5
-10
10

What prices will the
Restaurant charge for
lunch and dinner?
PL=$35 and PD=$60
0

36
Peak Load Profit Maximization
MaxQ ,Q
L
D
(50-QL)QL+ (100-QD)QD -20(QL+QD) -1800
s.t. QL< 45 , QD< 45
So,
So,

QL

QD
= 50-2QL -20=0 so QL=15
= 100-2Qb-20=0 so QD=40
Suppose Restaurant’s Capacity is 30 seats,
Fixed Costs are $1200 per day and Marginal
Cost of a meal is constant at $20
DD
DL
MC=AVC
90
80
70
60
MRD
100
MRL
50
40
30
qL,qD
20
What are the
Restaurant’s daily
profits?
TR-TC=TR-TVC-TFC=
35*15+70*3020*(15+30)-1200= 525
100
95
90
85
80
75
PD= 70
65
60
55
50
45
40
PL= 35
30
25
20
15
10
5
0
-5
-10
10

What prices will the
Restaurant charge for
lunch and dinner?
PL=$35 and PD=$70
0

38
Bundling

Definition
The practice of bundling several different
products together and selling them at a
single “bundle price”.
 Happy
Meals, Restaurants, Stereos, Cars with
Options, Celebrity Endorsements, Movies
(years ago),…
What are possible explanations as to why firms
do this?
39
Quote from Lebron James
(article in November 28, 2007 Fortune)
So in 2006, James founded LRMR Marketing, so named for
the initials of the four buddies: Lebron, Randy Mims,
Maverick Carter, and Richard Paul.
While James is LRMR's core business, the goal is to
diversify by representing other athletes. Right now they
have only one other client. In August the company
signed a contract with Ted Ginn Jr., the Ohio State star
and a rookie wide receiver on the Miami Dolphins. …
"He should be looking at multiyear deals with a vested
interest," says Doug Shabelman, the president of Burns
Entertainment & Sports Marketing. "He'll probably be in a
position to take some ownership stakes." Shabelman
added that if LRMR develops a stable of athletes, it
could package them in deals for marketers. In other
words, if you want LeBron, you gotta take the others.
40
Bundling – Example 1

Assume there are 10
Type I individuals and
10 Type II individuals
and that each
individual only
demands one
appetizer and one
entrée. For simplicity,
assume costs are
zero.
Willingness
to Pay
Appetizer
Entrée
Type I Type II
10
8
12
15
41
Bundling – Example 1



Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. For
simplicity, assume costs are
zero.
No Bundling
PA=8, PE=12
Profits= 8*20+12*20=400
Bundling
PAE=22
Profits = 22*20 = 440
Willingness
to Pay
Appetizer
Entrée
Type I Type II
10
8
12
15
42
Bundling – Example 1



Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. For
simplicity, assume costs are
zero.
No Bundling
PA=8, PE=12
Profits= 8*20+12*20=400
Bundling
PAE=22
Profits = 22*20 = 440
Willingness
to Pay
Appetizer
Type I Type II
10
8
Entrée
12
15
For Both
22
23
43
Bundling – Example 2



Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. For
simplicity, assume costs are
zero.
No Bundling
PA=8, PE=12
Profits= 8*20+12*20=400
Bundling
PAE=20
Profits = 20*20 = 400
Willingness
to Pay
Appetizer
Entrée
Type I Type II
8
10
12
15
44
Bundling – Example 2



Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. For
simplicity, assume costs are
zero.
No Bundling
PA=8, PE=12
Profits= 8*20+12*20=400
Bundling
PAE=20
Profits = 20*20 = 400
Willingness
to Pay
Appetizer
Type I Type II
8
10
Entrée
12
15
For Both
20
25
45
Bundling – Example 3



Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. For
simplicity, assume costs are
zero.
No Bundling
PA=10, PE=12
Profits= 10*10+12*20=340
Bundling
PAE=17
Profits = 17*20 = 340
Willingness
to Pay
Appetizer
Entrée
Type I Type II
10
2
12
15
46
Bundling – Example 3




Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. For
simplicity, assume costs are
zero.
No Bundling
PA=10, PE=12
Profits= 10*10+12*20=340
Bundling
PAE=17
Profits = 17*20 = 340
Mixed Bundling
PE=15, PAE=22
Profits= 15*10+22*10=370
Willingness
to Pay
Appetizer
Type I Type II
10
2
Entrée
12
15
For Both
22
17
47
Bundling – Example 4



Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. For
simplicity, assume costs are
zero.
No Bundling
PA=10, PE=12
Profits= 10*10+12*20=340
Bundling
PAE=14
Profits = 14*20 = 280
Willingness
to Pay
Appetizer
Entrée
Type I Type II
2
10
12
15
48
Bundling – Example 4




Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. For
simplicity, assume costs are
zero.
No Bundling
PA=10, PE=12
Profits= 10*10+12*20=340
Bundling
PAE=14
Profits = 14*20 = 280
Mixed Bundling
PE=12, PAE=25 ?
WRONG BECAUSE TYPE II
WILL BUY ONLY ENTRÉE
Willingness
to Pay
Appetizer
Type I Type II
2
10
Entrée
12
15
For Both
14
25
49
Bundling – Example 4




Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. For
simplicity, assume costs are
zero.
No Bundling
PA=10, PE=12
Profits= 10*10+12*20=340
Bundling
PAE=14
Profits = 14*20 = 280
Mixed Bundling
PE=12, PAE=22
Profits= 12*10+22*10=340
Willingness
to Pay
Appetizer
Type I Type II
2
10
Entrée
12
15
For Both
14
25
Assume that Type II buys bundle even though indifferent between buying
bundle and just entrée. If you don’t like this assumption, just set PAE=21.99. 50
Bundling – Example 5

Assume there are 10
Type I individuals and
10 Type II individuals
and that each
individual only
demands one
appetizer and one
entrée. Assume
marginal cost of an
appetizer is $5 and
marginal cost of an
entrée is $10 .
Willingness
to Pay
Appetizer
Entrée
Type I Type II
10
8
12
15
51
Bundling – Example 5
Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée.
Assume marginal cost of an
appetizer is $5 and marginal
cost of an entrée is $10 .
 No Bundling
PA=8, PE=15
Profits= (8-5)*20+(15-10)*10=110
 Bundling
PAE=22
Profits = (22-15)*20 = 140

Willingness
to Pay
Appetizer
Entrée
Type I Type II
10
8
12
15
52
Bundling – Example 5
Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée.
Assume marginal cost of an
appetizer is $5 and marginal
cost of an entrée is $10 .
 No Bundling
PA=8, PE=15
Profits= (8-5)*20+(15-10)*10=110
 Bundling
PAE=22
Profits = (22-15)*20 = 140

Willingness
to Pay
Appetizer
Type I Type II
10
8
Entrée
12
15
For Both
22
23
53
Bundling – Example 5
Assume there are 10 Type I
individuals and 10 Type II
individuals and that each
individual only demands one
appetizer and one entrée. Assume Willingness
marginal cost of an appetizer is $5
to Pay
and marginal cost of an entrée is
Appetizer
$10 .
 No Bundling
PA=8, PE=15 Profits= 110
 Bundling
Entrée
PAE=22 Profits = 140
 Mixed Bundling
PA=10, PAE=23
For Both
Profits= (10-5)10+(23-15)10=130
OR
PE=14, PAE=22
Profits= (14-10)10+(22-15)10=110

Type I Type II
10
8
12
15
22
23
54
Screening

The practice of requiring consumers
to “jump over a hurdle” to obtain a
lower price.
Coupons, Warranties, Rebates, Outlet
malls, Saturday Night Stayovers for
airlines,….
http://maps.google.com/maps?ie=UTF-8&oe=UTF-8&q=car+wash&near=Okemos,+MI&fb=1&cid=42682926,84430200,9316045653265795993&li=lmd&z=14&t=m
55
Coupon for Box of Cereal –
Assume MC of a box is constant at $.50 and TFC=15
56
Suppose Don’t Issue a Coupon
Set Price at $2 or $3 to maximize
profits.

If Set Price=$2
Profits = 30*2-30*.5-15= 30

If Set Price=$3
Profits = 10*3-10*.5-15= 10
57
Suppose the opportunity cost of cutting a
coupon is $0 for Type A individuals and
$1.50 for Type B individuals.

What Price and Coupon Value Maximizes
Profits?
Price=$3 and Coupon Value=$1
Type A cuts coupon and Type B does not.
TR=3*10+(3-1)*20 = 70
TC=.5*30+15=30
Profits= 70-30=40
58
Suppose the opportunity cost of cutting a
coupon is $0.25 for Type A individuals and
$1.50 for Type B individuals.

What Price and Coupon Value Maximizes
Profits?
Price=$3 and Coupon Value=$1.25
Type A cuts coupon and Type B does not.
TR=3*10+(3-1.25)*20 = 65
TC=.5*30+15=30
Profits= 65-30=35
59
Suppose the opportunity cost of cutting a
coupon is $0.75 for Type A individuals and
$1.50 for Type B individuals.

What Price and Coupon Value Maximizes Profits?
Price=$2.75 and Coupon Value=$1.50
Type A cuts coupon and Type B does not.
TR=2.75*10+(2.75-1.50)*20 = 52.50
TC=.5*30+15=30
Profits= 52.50 -30=22.50
Better off just charging a price of $2 and not using
coupon.
60
Suppose the opportunity cost of cutting a
coupon is $0.75 for Type A individuals and
$1.50 for Type B individuals.

What Price and Coupon Value Maximizes
Profits?
Price=$2.75 and Coupon Value=$1.50
TR=2.75*10+(2.75-1.50)*20 = 52.50
TC=.5*30+15=30
Profits= 52.50 -30=22.50
You could make Price=$2.74 and Coupon
Value=$1.49 if you want to make Type B strictly
prefer to not cut the coupon.
61
Intuition
There are two types of consumers. One with a high
willingness to pay and one with a low willingness to
pay. The cost of “jumping over the hurdle” is greater
for the high willingness to pay type.
You want the low willingness to pay type to jump
over the hurdle and then pay the maximum he/she is
willing to pay. You then want to charge the high
willingness to pay the maximum possible without
providing him/her the incentive to “jump over the
hurdle” or to not buy.
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“Shopper Alert: Price May Drop for You Alone”,
New York Times 2012
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iPhone Buyer Sues
The Times (London), October 3, 2007
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Reckonings; What Price Fairness?
The New York Times, October 4, 2000
65
Price Discrimination on the Internet
Online Pricing: Economist, June 2012
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