Transcript Economics of the Firm - University of Notre Dame

Economics of the Firm
Competitive Pricing Techniques
When making pricing decisions, you need to be aware of what your market
structure is
Market Structure Spectrum
Perfect Competition
The market is supplied by many
producers – each with zero market
share
Firm Level Demand DOES
NOT equal industry demand
Monopoly
One Producer With 100%
market share
Firm Level Demand
EQUALS industry
demand
Recall the characteristics we laid out for a competitive market
#1: Many buyers and sellers
– no individual buyer/firm has
any real market power
#2: Homogeneous products
– no variation in product
across firms
#3: No barriers to entry – it’s
costless for new firms to
enter the marketplace
#4: Perfect information –
prices and quality of products
are assumed to be known to
all producers/consumers
#5: No Externalities –ALL
costs/benefits of the product
are absorbed by the
consumer
#6: Transactions are costless
– buyers and sellers incur no
costs in an exchange
Can you think of situations where all these assumptions hold?
Measuring Market Structure – Concentration Ratios
Suppose that we take all the firms in an industry and ranked them by
size. Then calculate the cumulative market share of the n largest firms.
Cumulative Market
Share
100
A
C
80
B
40
20
0
01
# of
Firms
2
3
4
5
6
7
10
20
Measuring Market Structure – Concentration Ratios
Cumulative Market
Share
100
A
C
80
B
40
20
0
01
# of
Firms
2
3
4
5
6
7
10
20
CR4 Measures the cumulative market share of the top four firms
Concentration Ratios in US manufacturing; 1947 - 1997
Year
CR50
CR100
CR200
1947
17
23
30
1958
23
30
38
1967
25
33
42
1977
24
33
44
1987
25
33
43
1992
24
32
42
1997
24
32
40
Aggregate manufacturing in the US hasn’t really changed since WWII
Measuring Market Structure: The Herfindahl-Hirschman
Index (HHI)
N
HHI   s
i 1
2
i
si = Market share of firm i
s 2i
Rank
Market Share
1
25
625
2
25
625
3
25
625
4
5
25
5
5
25
6
5
25
7
5
25
8
5
25
HHI = 2,000
The HHI index penalizes a small number of total firms
Cumulative Market
Share
100
A
HHI = 500
80
B
HHI = 1,000
40
20
0
01
2
3
4
5
6
7
10
20
The HHI index also penalizes an unequal distribution of firms
Cumulative Market
Share
100
80
HHI = 500
HHI = 555
A
40
B
20
0
01
2
3
4
5
6
7
10
20
Concentration Ratios in For Selected Industries
Industry
CR(4)
HHI
Breakfast Cereals
83
2446
Automobiles
80
2862
Aircraft
80
2562
Telephone Equipment
55
1061
Women’s Footwear
50
795
Soft Drinks
47
800
Computers & Peripherals 37
464
Pharmaceuticals
32
446
Petroleum Refineries
28
422
Textile Mills
13
94
Recall that in a perfectly competitive world, price equals marginal
revenue
Individual
Market
Dollars
Dollars
Supply
MC
MR
1.44*
$1.44*
Demand
0
0
400
400,000*
The market determines the
equilibrium price of $1.44 and 400,000
fish sold by the 1,000 fishermen
At the prevailing market price of
$1.44, each fisherman supplies 400
fish
In a monopolized market, the single firm in the market faces the
industry demand curve
Individual
Market
Dollars
Dollars
MC
1.44*
$1.44*
Demand
Demand
0
0
400,000
400,000*
400,000 fish are sold at a market price
of $1.44
The single firm in the market has
chosen that price of $1.44 based off of
industry demand
We will be assuming that pricing decisions are being made to maximize
current period profits
Total Costs (note that total costs
here are economic costs. That is,
we have already included a
reasonable rate of return on
invested capital given the risk in
the industry)
Profits
  PQ  TC
Total Revenues
equal price times
quantity
As with any economic decision, profit maximization involves evaluating every
potential sale at the margin
  PQ  TC
How do my profits
change if I
increase my sales
by 1?
How do my
revenues change if
I increase my
sales by 1?
(Marginal
Revenues)
How do my costs
change if I
increase my sales
by 1? (Marginal
Costs)
In a world where firms have market power, they control their level of sales by setting their price.
Suppose that you have the following demand curve (A relationship between price and quantity):
Q  100  2 P
Your listed price
Total
Sales
P
For example: If you were to set a
price of $20, you can expect 60
sales
P  $20
Q  100  220  60
D
Q  60
Q
We could also talk about inverse demand (a relationship between quantity and price):
Q  100  2 P
P  50  .5Q
A price
that will hit
that target
Your target for sales
P
For example: If you wanted to
make 40 sales, you could set a $30
price
40  100  2 P
60  2 P
P  $30
P  30
D
Q  40
Q
Either way, if we know price and total sales, we can calculate revenues
P  50  .5Q
P
Total Revenues = Price*Quantity
P  $30
Total Revenues
=($30)(40)
= $1200
Q  40
D
Q
Can we increase revenues past
$1200 and, if so, how?
Either way, if we know price and total sales, we can calculate revenues
P  50  .5Q
P
Total Revenues =($35)(30) = $1050
P  $35
Total Revenues =($25)(50) = $1250
P  $30
P  $25
D
Q  30 Q  40 Q  50
Q
Turns out lowering price was the
right thing to do to raise revenues.
Initially, you have chosen a price (P)
to charge and are making Q sales.
p
p
Total Revenues = PQ
D
Q
Q
Suppose that you want to increase your sales.
What do you need to do?
Your demand curve will tell you how much you need to lower your price to reach
one more customer
This area represents the revenues
that you lose because you have to
lower your price to existing customers
p
This area represents
the revenues that you
gain from attracting a
new customer
p
D
Q
Q
Your demand curve will tell you how much you need to lower your price to reach
one more customer
P  50  .5Q
p
Revenues =($30)(40) = $1200
$29.50 From additional sale
-$20 loss from lowering price
$9.50 increase in revenues
p  $30
p  $29.50
($.50)(40) =$20
Revenues =($29.50)(41) = $1209.50
($29.50)(1)
=$29.50
D
Q  40 Q  41
Q
Demand curves slope downwards – this reflects the negative relationship between price
and quantity. Elasticity of Demand measures this effect quantitatively
%QD  20
D 

 2
%P
10
Price
 2.75  2.50 

 *100  10%
2.50 

$2.75
$2.50
DI  $50,000
Quantity
4
5
 45

 *100  20%
5


Note that elasticities vary along a linear demand curve
 D  2.3
Price
 D  .61
$35
Q  100  2 P
P
Q
$35
30
$34
32
$20
60
$19
62
% Change in
Q
% Change
in P
Elasticity
6.7
-2.9
-2.3
$20
D
3.3
-5
-.61
30
0
$10
80
$9
82
-1
2.5
-10
-.255
-2
-3
-4
-5
-6
-7
-8
-9
-10
12
20
28
80
60
36
44
52
60
68
76
84
Quantity
92
100
Let’s calculate the elasticity of demand at a quantity of 40 (a.k.a. a price of $30)
P  50  .5Q
P

%P  1.7
%Q
2.5

 1.47
%P  1.7
At a quantity of 40, the
elasticity of demand is
bigger that 1 in absolute
value
P  $30
P  $29.50
D
Q  40 Q  41
%Q  2.5
Q
Let’s calculate the elasticity of demand at a quantity of 40 (a.k.a. a price of $30)
P  50  .5Q
TR  PQ
If I want to increase my sales
target, I need to lower my price
to all my existing customers
P
Total Revenues
=($30)(40) = $1200
  1.47
P  $30
Total Revenues
=($29.50)(41) = $1209.5
P  $29.50
% Change in revenues = .80%
D
Q  40 Q  41
Q
An elasticity of demand that is greater
than 1 in absolute value indicates that
lowering price will increase revenues
TR  PQ
%TR  %P  %Q
.80%
-1.70%

P
2.5%
%Q
2.5

 1.47
%P  1.7
Total Revenues =($30)(40) = $1200
  1.47
%P  1.7
P  $30
Total Revenues
=($29.50)(41) = $1209.5
P  $29.50
% Change in revenues = .80%
D
Q  40 Q  41
%Q  2.5
Q
An elasticity of demand that is less than
1 in absolute value indicates that raising
price will increase revenues
TR  PQ
%TR  %P  %Q
3.75%
5.00%

P
%Q  1.25

 .25
%P
5.0
% Change in revenues = 3 .75%
Total Revenues =($10.50)(79) = $829.50
%P  5
P  $10.50
Total Revenues =($10)(80)
= $800
P  $10.00
  .25
D
Q  79 Q  80
%Q  1.25
Q
-1.25%
Revenues are maximized when the elasticity of demand equals -1
Total Revenues
1400
Elasticity
0
-1
1200
10
20
30
40
50
60
70
80
-2
1000
-3
-4
800
-5
600
-6
400
Elasticity is less
than -1: raise price
Elasticity is greater
than -1: lower price
-7
-8
200
-9
1
8
15
22
29
36
43
50
57
64
71
78
85
92
99
0
Max Revenues
Quantity = 50
Price =$25
Revenues = $1,250
-10
Quantity = 50
Price =$25
Elasticity = -1
90
Because you must lower your price to existing customers to attract new
customers, marginal revenue will always be less than price
Q = 40
P = $30
Revenues = ($30)(40) = $1200
60
Q = 41
P = $29.50
Revenues = ($29.50)(41) = $1209.50
40
P = $30
20
Marginal Revenues = $9.50
MR = $9.50
P
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
0
-20
-40
MR
-60
Note that because we have ignored the cost side, we are assuming marginal
costs are equal to zero!
60
1400
Revenues = $1250
1200
40
1000
P = $25
20
800
P
0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
MR = MC = $0
600
-20
400
-40
200
MR
-60
0
Now, let’s bring in the cost side. For simplicity, lets assume that you face a
constant marginal cost equal to $20 per unit.
Quantity
Price
Total
Revenue
Marginal
Revenue
Total
Cost
Marginal
Cost
Profit
1
$49.50
$49.50
$49.50
$20
$20
$29.50
2
$49
$98
$48.50
$40
$20
$58
3
$48.50
$145.50
$47.50
$60
$20
$85.50
4
$48
$192
$46.50
$80
$20
$112
5
$47.50
$237.50
$45.50
$100
$20
$137.50
6
$47
$282
$44.50
$120
$20
$162
7
$46.50
$325.50
$43.50
$140
$20
$185.50
Continuing on down…
29
$35.50
$1029.50
$21.50
$580
$20
$449.50
30
$35
$1050
$20.50
$600
$20
$450
31
$34.50
$1069.50
$19.50
$620
$20
$449.50
A profit maximizing price sets marginal revenue equal to marginal cost. Marginal
revenue is the change in total revenue (i.e. the slope)
1600
Slope = 20
1400
1200
1000
800
600
Profits = $450
400
200
0
1
6
11 16 21 26 31 36 41 46 51 56 61 66 71
-200
-400
-600
Total Revenue
Total Cost
Profit
A profit maximizing price sets
marginal revenue equal to marginal
cost
Price = $35
Quantity = 30
Elasticity = -2.36
60
50
P  MC $35  $20

 .42
P
$35
40
P = $35
30
Profit = ($35-$20)*30
= $450
20
1


1
 .42
2.36
10
0
1
6
11
16 21
26
31
36 41
46
51 56
61
66
-10
-20
-30
Price
Marginal Cost
Marginal Revenue
This is not a coincidence. A
monopoly sets a markup
that is inversely proportional
to the elasticity of demand!
Markups for Selected Industries
Industry
LI
Communication
.972
Paper & Allied Products
.930
Electric, Gas & Sanitary Services
.921
Food Products
.880
General Manufacturing
.777
Furniture
.731
Tobacco
.638
Apparel
.444
Motor Vehicles
.433
Machinery
.300
Suppose that we
assumed the
automobile
industry were
monopolized…
P  MC
 .433
P
 
So, a 1% increase in automobile prices will lower sales by 2.3%
1
 2.3
.433
Is it possible to attract new customers without lowering your price to
everybody?
p
Loss from charging
existing customers a
lower price
p
Gain from attracting new
customers
D
Q
Q
Let’s suppose that Notre dame has identified three different
consumer types for Notre Dame football tickets. Further,
assume that Notre Dame has a marginal cost of $20 per ticket.
Dollars
Alumni
$120
Faculty
$80
Students
$40
0
40,000
70,000
80,000
If Notre Dame had to
set one uniform price to
everybody, what price
would it set?
Let’s suppose that Notre dame has identified three different
consumer types for Notre Dame football tickets. Further,
assume that Notre Dame has a marginal cost of $20 per ticket.
Dollars
Alumni
$120
Price
Quantity
Total Revenue
Total Cost
Profit
$120
40,000
$4.8M
$800,000
$4.0M
$80
70,000
$5.6M
$1.4M
$4.2M
$40
80,000
$3.2M
$1.6M
$1.6M
Faculty
$80
Students
$40
$20
0
MC
40,000
70,000
80,000
Now, suppose that Notre Dame can set up differential pricing.
Pricing Schedule
•Regular Price: $120
•Faculty/Staff: $80
•Student: $40
Dollars
Alumni
$120
Price
Quantity
Total
Revenue
Total Cost
Profit
$120
40,000
$4.8M
$400,000
$4.4M
$80
30,000
$2.4M
$300,000
$2.1M
$40
10,000
$400,000
$200,000
$200,000
Total
80,000
$7.6M
$900,000
$6.7M
Faculty
$80
Students
$40
$20
0
MC
40,000
70,000
80,000
What would Notre Dame
need to do to accomplish
this?
Example: DVD codes are a digital rights management technique that allows film
distributors to control content, release date, and price according to region.
DVD coding allows for distributors to price discriminate by region.
Why is movie theatre popcorn so expensive?
Dollars
$15
General
Public
This would be an easy price
discrimination problem…
Senior
Citizens
$8
Pricing Schedule
•Regular Price: $15
•Senior Citizens: $8
0
200
300
Now, suppose that the identities are unknown? How
can the theatre extract more money out of the avid
moviegoer?
Ticket Price
Popcorn Price
Total
Option #1
$14
$1
$15
Option #2
$8
$7
$15
Option #3
$2
$13
$15
Dollars
$15
Avid
Moviegoer
Occasional
Moviegoer
$8
0
200
As long as the total
price (popcorn +
ticket) is $15 or less,
avid moviegoers will
still go
300
Which pricing option would you choose?
Suppose that Disneyworld knows something about the average
consumer’s demand for amusement park rides. Disneyworld has
a constant marginal cost of $.02 per ride
Q  100  100 P
Dollars
.50
Price (per ride)
Quantity (rides)
$1
0
$.99
1
$.98
2
$0
100
Demand
0
50
As a first pass, we could solve for a profit maximizing price per
ride
Q  100  100 P
Dollars
.51
Profit = $24.01
MC
Demand
.02
0
49
MR
Price (per
ride)
Quantity
(rides)
Total
Revenues
Marginal
Revenues
Marginal
Cost
$1
0
$0
$.99
1
$.99
$.99
$.02
$.98
2
$1.96
$.97
$.02
$.52
48
$24.96
$.05
$.02
$.51
49
$24.99
$.03
$.02
$.50
50
$25
$.01
$.02
If all Disney does is charge a price per ride, they are leaving
some money on the table
Q  100  100 P
Dollars
$1
CS = (1/2)($1-.51)*49 = $12.00
.51
Profit = $24.01
MC
Demand
.02
0
49
MR
We are charging this person
$24.01 for 49 rides when they
would’ve $36.01!
Like the movie theatre, Disney has two prices to play with. We have a
price per ride as well as an entry fee. For any price per ride, we can set
the entry fee equal to the consumer surplus generated.
Q  100  100 P
Dollars
Fee = (1/2)($1-P)*Q
$1
$P
Price
(per
ride)
Quantity
(rides)
Ride
Revenue
Fee
Revenue
Total
Revenues
Marginal
Revenues
Marginal
Cost
$1
0
$0
$0
$0
---
---
$.99
1
$.99
$.005
$.995
$.995
$.02
$.98
2
$1.96
$.02
$1.98
$.985
$.02
$.03
97
$2.91
$47.05
$49.96
$.03
$.02
$.02
98
$1.96
$48.02
$49.98
$.02
$.02
$.01
99
$.99
$49
$49.99
$.01
$.02
Profit = (P-.02)*Q
MC
Demand
.02
0
Q
Total Profit = $48.02
We are still looking to where
marginal revenues equal
marginal costs.
The optimal pricing scheme here is to set a price per ride equal
to marginal cost. We then set the entry fee equal to the
consumer surplus generated.
Q  100  100 P
Pricing Schedule
•Entry Fee: $48.02
•Price Per Ride: $.02
Dollars
Fee = (1/2)($1-.02)*98 = $48.02
$1
Or, we could
combine the two
MC
Demand
.02
Ride Revenue = .02*98 = $1.96
0
Total Profit = $48.02
98
Entry Fee: $48.02
+ Ride Charges: $1.96
98 Ride Package = $49.98
Now, suppose that we introduced two different clientele. Say, senior citizens and
Non-seniors. We could discriminate based on price per ride (assume there is one
of each type)
Non-Seniors
Seniors
Q  100  100 P
Q  80  100 P
Dollars
Dollars
$1
$.80
.51
.41
Profit = $24.01
Profit = $15.21
MC
Demand
.02
0
49
MC
Demand
.02
0
39
MR
Total Profit = $24.01 + $15.21 = $39.22
MR
Alternatively, you set the cost of the rides at their marginal cost ($.02) for
everybody and discriminate on the entry fee.
$48.02 Young
P = $.02/Ride
Entry Fee =
$30.42 Old
Dollars
Non-Seniors
Q  100  100 P
Seniors
Q  80  100 P
$1
$.80
Fee = (1/2)($.80-.02)*78 = $30.42
Fee = (1/2)($1-.02)*98 = $48.02
MC
Demand
.02
Ride Revenue = .02*98 = $1.96
0
98
MC
Demand
.02
Ride Revenue = .02*78 = $1.56
0
Total Profit = $48.02 + $30.42 = $78.44
78
Or, you could establish different package prices.
Regular Admission (98 rides): $49.98
Pricing Schedule=
Senior Citizen Special (78 Rides): $31.98
Dollars
Non-Seniors
Q  100  100 P
Seniors
Q  80  100 P
$1
$.80
Fee = (1/2)($.80-.02)*78 = $30.42
Fee = (1/2)($1-.02)*98 = $48.02
MC
Demand
.02
Ride Revenue = .02*98 = $1.96
0
98
Total Price = $48.02 + $1.96 = $49.98
MC
Demand
.02
Ride Revenue = .02*78 = $1.56
0
78
Total Price = $30.42 + $1.56 = $31.98
Suppose that you couldn’t distinguish High value customers from low value
customers: Would this work?
Dollars
Q  80  100 P
Q  100  100 P
$1
$.80
Fee = (1/2)($.80-.02)*78 = $30.42
Fee = (1/2)($1-.02)*98 = $48.02
MC
Demand
.02
Ride Revenue = .02*98 = $1.96
0
98
Ride Revenue = .02*78 = $1.56
0
Regular Admission (98 rides): $49.98
Pricing Schedule=
MC
Demand
.02
“Early Bird” Special (78 Rides): $31.98
78
We know that is the high value consumer buys 98 ticket package, all her surplus
is extracted by the amusement park. How about if she buys the 78 Ride
package?
p
Total Willingness to pay for 78 Rides: $47.58
- 78 Ride Coupons: $31.98
$100
$15.60
$30.42
If the high value customer buys
the 78 ride package, she keeps
$15.60 of her surplus!
$22
$17.16
Q  100  100 P
78
You need to set a price for the 98 ride package that is incentive compatible. That
is, you need to set a price that the high value customer will self select. (i.e., a
package that generates $15.60 of surplus)
p
Total Willingness = $49.98
$1.00
- Required Surplus = $15.60
Package Price
78 Ride Coupons: $31.98
98 Ride Coupons: $34.38
= $34.38
$48.02
$.02
$1.96
D
98
q
  $31.98  $34.38  $.02176  $62.84
Bundling
Suppose that you are selling two products. Marginal costs for these products
are $100 (Product 1) and $150 (Product 2). You have 4 potential consumers
that will either buy one unit or none of each product (they buy if the price is
below their reservation value)
Consumer Product 1 Product 2
Sum
A
$50
$450
$500
B
$250
$275
$525
C
$300
$220
$520
D
$450
$50
$500
If you sold each of these products separately, you would choose prices
as follows
Product 1 (MC = $100)
Product 2 (MC = $150)
P
Q
TR
Profit
P
Q
TR
Profit
$450
1
$450
$350
$450
1
$450
$300
$300
2
$600
$400
$275
2
$550
$250
$250
3
$750
$450
$220
3
$660
$210
$50
4
$200
-$200
$50
4
$200
-$400
Profits = $450 + $300 = $750
Pure Bundling does not allow the products to be sold separately
Product 1 (MC = $100)
Product 2 (MC = $150)
Consumer Product 1 Product 2
Sum
A
$50
$450
$500
B
$250
$275
$525
C
$300
$220
$520
D
$450
$50
$500
With a bundled price of $500, all four consumers buy
both goods:
Profits = 4($500 -$100 - $150) = $1,000
Mixed Bundling allows the products to be sold separately
Product 1 (MC = $100)
Product 2 (MC = $150)
Consumer Product 1 Product 2 Sum
A
$50
$450
$500
B
$250
$275
$525
C
$300
$220
$520
D
$450
$50
$500
Price 1 = $250
Price 2 = $450
Bundle = $500
Consumer A: Buys Product 2 (Profit = $300) or Bundle
(Profit = $250)
Consumer B: Buys Bundle (Profit = $250)
Consumer C: Buys Product 1 (Profit = $150)
Consumer D: Buys Only Product 1 (Profit = $150)
Profit = $850
or $800
Mixed Bundling allows the products to be sold separately
Product 1 (MC = $100)
Product 2 (MC = $150)
Consumer Product 1 Product 2 Sum
A
$50
$450
$500
B
$250
$275
$525
C
$300
$220
$520
D
$450
$50
$500
Consumer A: Buys Only Product 2 (Profit = $300)
Consumer B: Buys Bundle (Profit = $270)
Consumer C: Buys Bundle (Profit = $270)
Consumer D: Buys Only Product 1 (Profit = $350)
Price 1 = $450
Price 2 = $450
Bundle = $520
Profit = $1,190
Bundling is only Useful When there is variation over individual consumers
with respect to the individual goods, but little variation with respect to the
sum!?
Consumer Product 1 Product 2 Sum
A
$300
$200
$500
B
$300
$200
$500
C
$300
$200
$500
D
$300
$200
$500
Product 1 (MC = $100)
Product 2 (MC = $150)
Individually Priced: P1 = $300, P2 = $200, Profit = $1,000
Pure Bundling: PB = $500, Profit = $1,000
Mixed Bundling: P1 = $300, P2 = $200, PB = $500, Profit = $1,000
Suppose that you sell laser printers. To create printed pages, you need both a printer
and an ink cartridge. For now, assume that the toner cartridges are sold in a
competitive market and sell for $2 each. An ink cartridge is good for 1,000 printed
pages.
Q  16  P
Dollars
CS = ½*($16 - $2)(14) = $98
Quantity of
printed pages
(000s)
$16
Toner cartridge
price
$2
Demand
0
14
What price would you
sell the printer for?
Now, suppose that you design a printer that requires a special cartridge that
only you produce. What would you do if you could choose a printer price
and a cartridge price?
Q  16  P
Dollars
CS = ½*($9 - $2)(7) = $24.50
$16
Quantity of
printed pages
(000s)
Toner cartridge
price
$9
MC
$2
Demand
0
7
MR
We could make our money on the
cartridges and sell the printers
cheap…
Q
P
TR
TC
MR
MC
Profit
1
$15
$15
$2
$15
$2
$13
2
$14
$28
$4
$13
$2
$24
3
$13
$39
$6
$11
$2
$33
4
$12
$48
$8
$9
$2
$40
5
$11
$55
$10
$7
$2
$45
6
$10
$60
$12
$5
$2
$48
7
$9
$63
$14
$3
$2
$49
8
$8
$64
$16
$1
$2
$48
Alternatively, we could do something like the amusement park. We
maximize profits combining cartridge revenue AND printer revenue
Q  16  P
Dollars
CS = ½*($16 - $2)(14) = $98
$16
Quantity of
printed pages
(000s)
MC
$2
Demand
0
14
MR
We are back to a low
cartridge price and a high
printer price
Toner cartridge
price
Q
P
TR
CS
Total
TC
MR
MC
Profit
1
$15
$15
$.5
$15.5
$2
$15.5
$2
$13.5
2
$14
$28
$2
$30
$4
$14.5
$2
$26
3
$13
$39
$4.5
$43.5
$6
$13.5
$2
$37.5
4
$12
$48
$8
$56
$8
$12.5
$2
$48
5
$11
$55
$12.5
$67.5
$10
$11.5
$2
$57.5
13
$3
$39
$84.5
$123.5
$26
$3.5
$2
$97.5
14
$2
$28
$98
$126
$28
$2.5
$2
$98
15
$1
$15
$112.5
$127.5
$30
$1.50
$2
$97.5
Now, suppose that you have two customers. Call them high value and low value.
Suppose that you can easily identify them and prevent resale. We could
discriminate on both the printer price and the cartridge price.
Q  12  P
Q  16  P
Dollars
Dollars
CS = ½*($16 - $9)(7) = $24.50
$16
$9
CS = ½*($12 - $2)(5) = $12.50
$12
$7
MC
$2
MC
$2
Demand
0
7
Demand
0
MR
5
MR
Profit = ($9-$2)7 +$24.50 = $73.50
Total Profit = $111
Profit = ($7-$2)5 +$12.50 = $37.50
Alternatively, we could essentially give the cartridges away and discriminate on
the printer (like Disneyworld).
Dollars
Q  12  P
Q  16  P
Dollars
CS = ½*($16 - $2)(14) = $98
$16
MC
$2
CS = ½*($12 - $2)(10) = $50
$12
MC
$2
Demand
0
14
Demand
0
Profit = $98
10
Profit $50
Total Profit = $148
Suppose that you couldn’t explicitly price discriminate. Let’s say that you know
you have a high value and low value demander, but you don’t know who is who.
Let’s first try and do this like the amusement park
Dollars
Q  12  P
Q  16  P
Dollars
CS = ½*($16 - $2)(14) = $98
$16
MC
$2
CS = ½*($12 - $2)(10) = $50
$12
MC
$2
Demand
0
14
14 Cartridge Package = $98 + $2*14 = $126
Demand
0
10
10 Cartridge Package = $50 + $2*10 = $70
Suppose that you couldn’t explicitly price discriminate. Let’s say that you know
you have a high value and low value demander, but you don’t know who is who.
Let’s first try and do this like the amusement park
Q  16  P
Dollars
14 Cartridge Package = $126
- required consumer surplus = $40
CS = ½*($16 - $9)(10) = $50
$16
“Discounted Price” = $86
14 Cartridge Package = $86
10 Cartridge Package = $70
$6
$60
Demand
0
10
Total Willingness to Pay = $110
- 10 Cartridge Package = $70
Consumer Surplus = $40
Profit = $86 + $70 - $2*24 = $108
Let’s try a different strategy. Suppose that you charge a markup on the cartridges
and then charge a common price for the printer to each. We would set the price
of the printer equal to the consumer surplus of the lower value demander of
insure that both groups buy the printer.
Q  12  P
Example:
Cartridge Price: $3
Consumer Surplus = ½*($12 - $3)(9) = $40.50
Dollars
CS = ½*($12 - $P)(12-P)
$12
Charge $40.50 for the printer
(Both customers will buy)
Low value customers buy 9
cartridges
High Value customers buy 13
cartridges
$P
$60
Demand
0
12-P
Profit = 2*$40.50 + ($3-$2)(21) = $103
We need to find the best cartridge price…
PQ1  Q2 
Q  16  P
.512  PQ2
Q  12  P
$2Q1  Q2 
2 * CS
Price
Quantity 1
Quantity
2
Total
Revenue
Consumer
Surplus
Printer
Revenue
Total Revenue
Total Cost
Profit
$0
16
12
$0
$72
$144
$144
$56
$88
$.25
15.75
11.75
$6.875
$69.03
$138.06
$144.93
$55
$89.93
$.50
15.5
11.5
$13.50
$66.135
$132.25
$145.75
$54
$91.75
$3
13
9
$66
$40.5
$81
$147
$44
$103
$4
12
8
$80
$32
$64
$144
$40
$104
$4.25
11.75
7.75
$82.875
$30.03
$60.06
$142.93
$39
$103.93
Let’s try a different strategy. Suppose that you charge a market on the cartridges
and then charge a common price for the printer to each. We would set the price
of the printer equal to the consumer surplus of the lower value demander of
insure that both groups buy the printer.
Q  12  P
Best Choice:
Dollars
CS = ½*($12 - $4)(8) = $32
$12
$4
Charge $32 for the printer
(Both customers will buy)
Charge $4 for cartridges
Low value customers buy 8
cartridges
High Value customers buy 12
cartridges
$60
Demand
0
8
Profit = 2*$32 + ($4-$2)(20) = $104
One last example. Consider the market for hot dogs.
Most people require a bun for each hot dog they eat
(with the exception of the Atkins diet people!)
Q 12  PH  PB 
Price of a Hot Dog
Price of a Hot Dog Bun
Hot Dogs and Buns are made by separate companies – each
has a monopoly in its own industry. For simplicity, assume
that the marginal cost of production for each equals zero.
For simplicity I will assume that marginal costs are zero
(i.e. we are maximizing revenues)
Suppose that you knew that the buns were selling for $2,
what should you charge?
Q  12  PH  $2  10  P
You
charge $5
Quantity
Price
Total Revenue Marginal
Revenue
1
$9
$9
$9
2
$8
$16
$7
3
$7
$21
$5
4
$6
$24
$3
5
$5
$25
$1
6
$4
$24
-$1
But, if the bun guy sees you charging $5, he needs to
react to that…
Q  12  PB  $5  7  P
Bun Guy
charge $4
Quantity
Price
Total Revenue Marginal
Revenue
1
$6
$6
$6
2
$5
$10
$4
3
$4
$12
$2
4
$3
$12
$0
5
$2
$10
-$2
6
$1
$6
-$4
But, if the bun guy is charging $4, you need to react to that…
Q  12  PB  $4  8  P
You
charge $4
Quantity
Price
Total Revenue Marginal
Revenue
1
$7
$7
$7
2
$6
$12
$5
3
$5
$15
$3
4
$4
$16
$1
5
$3
$15
-$1
6
$2
$12
-$3
Now, suppose that these companies merged into
one monopoly
Q  12  PB  PH   8  P
You
charge $6
for hot
dog/bun
Quantity
Combined
Price
Total Revenue Marginal
Revenue
1
$11
$11
$11
2
$10
$20
$9
3
$9
$27
$7
4
$8
$32
$5
5
$7
$35
-$3
6
$6
$36
-$1
7
$5
$35
-$1
8
$4
$32
-$3
9
$3
$27
-$5
Look at what happened here…
Q 12  PB  PH 
Separate Hot Dog/Bun Suppliers
PH  $4
PB  $4
Consumer Pays $8 for a
hot dog/bun pair
Single Hot Dog/Bun Suppliers
PH  PB  $6
Consumer Pays $6 for a
hot dog/bun pair
Eliminating a company benefits consumers!!!
Example: Microsoft vs. Netscape
The argument against Microsoft was using its monopoly power in
the operating system market to force its way into the browser
market by “bundling” Internet Explorer with Windows 95.
To prove its claim, the government needed to show:
•Microsoft did, in fact, possess monopoly power
•The browser and the operating system were, in fact, two
distinct products that did not need to be integrated
•Microsoft’s behavior was an abuse of power that hurt
consumers
What should Microsoft’s defense be?