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Competitive Pricing Techniques
Finance 30210: Managerial Economics
Once production decisions have been made, a firm can be represented by it’s cost function
Q
MC
)(QTCTC
Total costs of production are a function of quantity produced
$1.50
56
MC
An increase in production from 55 to 56 increased total costs by $1.50
For pricing decisions, we focus on marginal cost
Q
TCMC
TCPQ
We will be assuming that pricing decisions are being made to maximize current period profits
Total Revenues equal price times quantity
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
As with any economic decision, profit maximization involves evaluating every potential sale at the margin
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)
Q
TC
Q
PQ
Q
Q
MRMC,
Q*
MC
As with any economic decision, profit maximization involves evaluating every potential sale at the margin
MR>MC: Profits are increasing
MR>MC: Profits are Decreasing
MR=MC: Profits are Maximized
Profit = Producer Surplus – Fixed Costs
Producer Surplus
MR
Recall that in a perfectly competitive world, price equals marginal revenue
The market determines the equilibrium price
Market
Dollars
0
P*
Demand
Supply
Q*
Dollars
0
P*
Firm Level
The prevailing price (treated as a constant by each firm) becomes that firms marginal revenue
MC
MR
Q
Producer Surplus
Producer Surplus
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
Can you think of situations where all these assumptions hold?
Market Structure Spectrum
Perfect CompetitionMonopoly
One Producer With 100% market share
The market is supplied by many producers – each with zero market share
Firm Level Demand DOES NOT equal industry demand
Firm Level Demand EQUALS industry demand
When making pricing decisions, you need to be aware of what your market structure is
Measuring Market Structure – Concentration Ratios
Suppose that we have the following three industries…
Industry A• 10 Firms in the
industry, each with an equal 10% market share
Industry B• 22 Firms in the
industry• The two largest
firms have 20% market share each
• The remaining 20 Firms have 3% market share each
Industry C• 8 Firms in the
industry• The 4 largest firms
have 15% market share each
• The remaining 4 Firms have 10% market share each
Which industry is the most competitive? Which is the least?
# of Firms
100
60
40
20
01 32 4 5 60 7 2210
80
Cumulative Market Share
8 9
Let’s plot out the three industries and take a look…
Concentration ratios look at the cumulative market share of the N largest firms
# of Firms
100
60
40
20
01 32 4 5 60 7 2210
80
Cumulative Market Share
8 9
2CR 4CR 8CR 10CR 22CR
20
40
30
40
46
60
80
58
100
100
64
100
100
100
100
Concentration Ratios in US manufacturing; 1947 - 1997
Year1947 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
100CR 200CR50CR
Aggregate manufacturing in the US hasn’t really changed since WWII
Industry CR(4)
Breakfast Cereals 83
Automobiles 80
Aircraft 80
Telephone Equipment 55
Women’s Footwear 50
Soft Drinks 47
Computers & Peripherals 37
Pharmaceuticals 32
Petroleum Refineries 28
Textile Mills 13
Concentration Ratios in US by Industry
Concentration ratios vary significantly by industry!!
Measuring Market Structure: The Herfindahl-Hirschman Index (HHI)
N
iisHHI
1
2
is = Market share of firm i
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
2is
HHI = 2,000
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
B HHI = 500
HHI = 1,000
The HHI index penalizes a small number of total firms
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
B
HHI = 500HHI = 555
The HHI index also penalizes an unequal distribution of firms
# of Firms
100
60
40
20
01 32 4 5 60 7 2210
80
Cumulative Market Share
8 9
N
iisHHI
1
2is = Market share of firm i
10001010 2 HHI
980320202 22 HHI
1300104154 22 HHI
HHI Index in For Selected Industries
Industry HHI
Breakfast Cereals 2446
Automobiles 2862
Aircraft 2562
Telephone Equipment 1061
Women’s Footwear 795
Soft Drinks 800
Computers & Peripherals 464
Pharmaceuticals 446
Petroleum Refineries 422
Textile Mills 94
In a monopolized market, the single firm in the market faces the industry demand curve
Given the chosen quantity, industry demand determines price
Market
Dollars
0
P
Demand
Q
Dollars
0
Individual
The single firm in the market has profit maximized based off of where MR = MC
MC
Q
MR
Producer Surplus
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):
PQ 2100 Total Sales
Your listed price
Q
P
60Q
20$P
D
60202100 Q
For example: If you were to set a price of $20, you can expect 60 sales
We could also talk about inverse demand (a relationship between quantity and price):
PQ 2100
Q
P
40Q
30$P
D
30
260
210040
P
P
P
For example: If you wanted to make 40 sales, you could set a $30 price
QP 5.50 A price that will hit that target
Your target for sales
Either way, if we know price and total sales, we can calculate revenues
Q
P
40Q
30$P
D
QP 5.50
Total Revenues =($30)(40) = $1200
Total Revenues = Price*Quantity
Can we increase revenues past $1200 and, if so, how?
Either way, if we know price and total sales, we can calculate revenues
Q
P
40Q
30$P
D
QP 5.50
Turns out lowering price was the right thing to do to raise revenues.
50Q30Q
35$P
Total Revenues =($35)(30) = $1050
Total Revenues =($25)(50) = $1250
25$P
Q
p
Q
p
D
Initially, you have chosen a price (P) to charge and are making Q sales.
Total Revenues = PQ
Suppose that you want to increase your sales. What do you need to do?
Q
p
D
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
This area represents the revenues that you gain from attracting a new customerp
Q
Q
p
D
Your demand curve will tell you how much you need to lower your price to reach one more customer
30$p
40Q
Revenues =($30)(40) = $1200
41Q
50.29$p($.50)(40) =$20
($29.50)(1) =$29.50
$29.50 From additional sale- $20 loss from lowering price$9.50 increase in revenues
Revenues =($29.50)(41) = $1209.50
QP 5.50
An elasticity of demand that is greater than 1 in absolute value indicates that lowering price will increase revenues
Q
P
40Q
30$P
D41Q
50.29$P
47.1
PQTR
Total Revenues =($29.50)(41) = $1209.5
Total Revenues =($30)(40) = $1200
% Change in revenues = .80%
QPTR %%%
7.1% P
5.2% Q
.80% -1.70% 2.5%
47.17.1
5.2
%
%
P
Q
An elasticity of demand that is less than 1 in absolute value indicates that raising price will increase revenues
Q
P
79Q
50.10$P
D80Q
00.10$P25.
PQTR
Total Revenues =($10)(80) = $800
Total Revenues =($10.50)(79) = $829.50
% Change in revenues = 3 .75%
QPTR %%%
5% P
25.1% Q
3.75% 5.00% -1.25%
25.0.5
25.1
%
%
P
Q
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
Elasticity
1 9 17 25 33 41 49 57 65 73 81 89 970
200
400
600
800
1000
1200
1400
Total Revenues
Revenues are maximized when the elasticity of demand equals -1
Max RevenuesQuantity = 50Price =$25Revenues = $1,250
Quantity = 50Price =$25Elasticity = -1
Elasticity is less than -1: raise price
Elasticity is greater than -1: lower price
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95100
-60
-40
-20
0
20
40
60
P = $30
MR = $9.50
Q = 40P = $30Revenues = ($30)(40) = $1200
Q = 41P = $29.50Revenues = ($29.50)(41) = $1209.50
Marginal Revenues = $9.50
Because you must lower your price to existing customers to attract new customers, marginal revenue will always be less than price
QP 5.50
QMR 50
25.50 QQPQTR
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95100
-60
-40
-20
0
20
40
60
0
200
400
600
800
1000
1200
1400
P
MR
P = $25
MR = MC = $0
Note that because we have ignored the cost side, we are assuming marginal costs are equal to zero!
Revenues = $1250
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
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69
-500
0
500
1000
1500
Total Revenue Total CostProfit
Slope = 20
Profits = $450
A profit maximizing price sets marginal revenue equal to marginal cost. Marginal revenue is the change in total revenue (i.e. the slope)
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69
-30
-20
-10
0
10
20
30
40
50
60
Price Marginal CostMarginal Revenue
P = $35
Profit = ($35-$20)*30 = $450
Price = $35Quantity = 30Elasticity = -2.36
A profit maximizing price sets marginal revenue equal to marginal cost
QP 5.50
QMR 50
25.50 QQPQTR
MCQMR 2050
30Q
Q
p
D
A profit maximizing strategy equates marginal revenues with marginal costs…
MCpQQ
P
Q
P
Q
1
p
Marginal Revenue
MCppp
Q
Q
P
MCpp
1
1MC
p
Firm’s will be charging a markup over marginal cost where the markup is related to the elasticity of demand
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69
-30
-20
-10
0
10
20
30
40
50
60
Price Marginal CostMarginal Revenue
P = $35
Profit = ($35-$20)*30 = $450
Price = $35Quantity = 30Elasticity = -2.36
42.35$
20$35$
P
MCP
42.36.2
11
A profit maximizing price sets marginal revenue equal to marginal cost
This is not a coincidence. A monopoly sets a markup that is inversely proportional to the elasticity of demand!
1
P
MCP
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…
433.P
MCP
3.2433.
1
So, a 1% increase in automobile prices will lower sales by 2.3%
1
1
MCp Perfectly competitive firms face demand curves that are
perfectly elastic (infinite elasticity. Hence, the markup (and profits) are zero)
i
iQ
ip
D
Firm Level
Q
p
D
Industry
Note: Industry elasticities in competitive industries are always less than 1 (industry profits could be increased by raising price!)
Q
p
Q
p
D
Loss from charging existing customers a lower price
Gain from attracting new customers
Is it possible to attract new customers without lowering your price to everybody?
You need to be able to identify customer types and prevent resale!!
Dollars
0
$40
40,000
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.
$120
$80
70,000 80,000
Alumni
Faculty
Students
If Notre Dame had to set one uniform price to everybody, what price would it set?
Dollars
0
$40
40,000
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.
$120
$80
70,000 80,000
Alumni
Faculty
Students
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
$20 MC
Dollars
0
$40
40,000
Now, suppose that Notre Dame can set up differential pricing.
$120
$80
70,000 80,000
Alumni
Faculty
Students
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
$20 MC
Pricing Schedule• Regular Price: $120• Faculty/Staff: $80• Student: $40
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.
Suppose that you are the pricing for the DVD release of Avatar
Your marginal costs are constant at $4 and you have the following demand curves:
PQUS 25.9 PQE 25.6
US Sales
European Sales+
PQ 5.15 Total Sales
Here is what our aggregate demand looks like
Quantity
D
Price
$24PQUS 25.9
$36
PQE 25.6
At a price above $24, Europeans aren’t buying. You only have the American market
At a price below $24, we now have both markets.
+
PQ 5.15
3
PQUS 25.9
Option #1: We could charge a common price to everyone…
Quantity
D
Price
$24
$36
3
QP 230
PQ 5.15 Solve for inverse demand
2230 QQPQTR
Calculate total revenues
MCQMR 4430
Equate marginal revenues to marginal costs
17$
5.6
P
Q
5.84$5.6417$ MC
$17
$4
6.5
Option #2: Why don’t we just charge them different prices?
Quantity
D
Price
$20
4Quantity
D
Price
$14
2.5
20$
4
4836
436
436
25.9
2
P
Q
QMR
QQTR
QP
PQ
USUS
USUS
America Europe
$36
$24$80,000
14$
5.2
4824
424
424
25.6
2
P
Q
QMR
QQTR
QP
PQ
EE
EE
MC
64$
MC$4
$4
25$
Why is movie theatre popcorn so expensive?
Dollars
0 200
$15
300
General Public
Senior Citizens
$8
This would be an easy price discrimination problem…
Pricing Schedule• Regular Price: $15• Senior Citizens: $8
Now, suppose that the identities are unknown? How can the theatre extract more money out of the avid moviegoer?
Dollars
0 200
$15
300
Avid Moviegoer
Occasional Moviegoer
$8
Ticket Price Popcorn Price Total
Option #1 $14 $1 $15
Option #2 $8 $7 $15
Option #3 $2 $13 $15
As long as the total price (popcorn + ticket) is $15 or less, avid moviegoers will still go
Which pricing option would you choose?
PQ 100100
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
Dollars
0
.50
Demand
50
Price (per ride) Quantity (rides)
$1 0
$.99 1
$.98 2
$0 100
PQ 100100
As a first pass, we could solve for a profit maximizing price per ride
Dollars
0
.51
Demand
49
Price (per ride)
Quantity (rides)
Total Revenues
MarginalRevenues
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 $.02MC
MR
.02
Profit = $24.01
PQ 100100
If all Disney does is charge a price per ride, they are leaving some money on the table
Dollars
0
.51
Demand
49
MC
MR
.02
Profit = $24.01
$1
CS = (1/2)($1-.51)*49 = $12.00
We are charging this person $24.01 for 49 rides when they would’ve $36.01!
PQ 100100
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.
Dollars
0
$P
Demand
Q
MC.02
Profit = (P-.02)*Q
$1 Fee = (1/2)($1-P)*Q
Price (per ride)
Quantity (rides)
Ride Revenue
Fee Revenue
Total Revenues
MarginalRevenues
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
Total Profit = $48.02
We are still looking to where marginal revenues equal marginal costs.
PQ 100100
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.
Dollars
0
Demand
98
MC.02
$1 Fee = (1/2)($1-.02)*98 = $48.02
Total Profit = $48.02
Pricing Schedule• Entry Fee: $48.02• Price Per Ride: $.02
Or, we could combine the two
Entry Fee: $48.02+ Ride Charges: $1.9698 Ride Package = $49.98Ride Revenue = .02*98 = $1.96
Dollars
0
.51
Demand
49
MC
MR
.02
Profit = $24.01
$1
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)
PQ 100100 Non-Seniors
Dollars
0
.41
Demand
39
MC
MR
.02
Profit = $15.21
$.80
PQ 10080 Seniors
Total Profit = $24.01 + $15.21 = $39.22
Alternatively, you set the cost of the rides at their marginal cost ($.02) for everybody and discriminate on the entry fee.
Entry Fee =$48.02 Young
$30.42 OldP = $.02/Ride
Dollars
0
Demand
98
MC.02
$1
0
Demand
78
MC.02
$.80
Total Profit = $48.02 + $30.42 = $78.44
Fee = (1/2)($1-.02)*98 = $48.02 Fee = (1/2)($.80-.02)*78 = $30.42
Ride Revenue = .02*98 = $1.96 Ride Revenue = .02*78 = $1.56
PQ 10080 Seniors
PQ 100100 Non-Seniors
Or, you could establish different package prices.
Pricing Schedule=Regular Admission (98 rides): $49.98
Senior Citizen Special (78 Rides): $31.98
Dollars
0
Demand
98
MC.02
$1
0
Demand
78
MC.02
$.80
Total Price = $48.02 + $1.96 = $49.98
Fee = (1/2)($1-.02)*98 = $48.02 Fee = (1/2)($.80-.02)*78 = $30.42
Ride Revenue = .02*98 = $1.96 Ride Revenue = .02*78 = $1.56
Total Price = $30.42 + $1.56 = $31.98
PQ 10080 Seniors
PQ 100100 Non-Seniors
Suppose that you couldn’t distinguish High value customers from low value customers: Would this work?
Dollars
0
Demand
98
MC.02
$1
0
Demand
78
MC.02
$.80Fee = (1/2)($1-.02)*98 = $48.02 Fee = (1/2)($.80-.02)*78 = $30.42
Ride Revenue = .02*98 = $1.96 Ride Revenue = .02*78 = $1.56
PQ 10080 PQ 100100
Pricing Schedule=Regular Admission (98 rides): $49.98
“Early Bird” Special (78 Rides): $31.98
p
78
.22
$1
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?
$30.42
$17.16
If the high value customer buys the 78 ride package, she keeps $15.60 of her surplus!
78 Ride Coupons: $31.98
Total Willingness to pay for 78 Rides: $47.58
$15.60
-
PQ 100100
D
p
98
$.02
$1.00
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)
$1.96
$48.02
Total Willingness = $49.98
- Required Surplus = $15.60
Package Price = $34.38
q
78 Ride Coupons: $31.98
98 Ride Coupons: $34.38
84.62$17602$.38.34$98.31$
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
P Q TR Profit
$450 1 $450 $350
$300 2 $600 $400
$250 3 $750 $450
$50 4 $200 -$200
P Q TR Profit
$450 1 $450 $300
$275 2 $550 $250
$220 3 $660 $210
$50 4 $200 -$400
Product 1 (MC = $100) Product 2 (MC = $150)
Profits = $450 + $300 = $750
Consumer Product 1 Product 2 Sum
A $50 $450 $500
B $250 $275 $525
C $300 $220 $520
D $450 $50 $500
Pure Bundling does not allow the products to be sold separately
Product 2 (MC = $150)
Product 1 (MC = $100)
With a bundled price of $500, all four consumers buy both goods:
Profits = 4($500 -$100 - $150) = $1,000
Consumer Product 1 Product 2 Sum
A $50 $450 $500
B $250 $275 $525
C $300 $220 $520
D $450 $50 $500
Mixed Bundling allows the products to be sold separately
Product 1 (MC = $100)
Product 2 (MC = $150)
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
Consumer Product 1 Product 2 Sum
A $50 $450 $500
B $250 $275 $525
C $300 $220 $520
D $450 $50 $500
Mixed Bundling allows the products to be sold separately
Product 1 (MC = $100)
Product 2 (MC = $150)
Price 1 = $450
Price 2 = $450
Bundle = $520
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)
Profit = $1,190
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)
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!?
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.
Dollars
0
$2
Demand
14
$16
PQ 16
Quantity of printed pages (000s)
Toner cartridge price
You can set the price of the printer equal to the customer’s consumer surplus ?
CS = ½*($16 - $2)(14) = $98
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?
Dollars
0
$9
Demand
7
$16
PQ 16
Quantity of printed pages (000s)
Toner cartridge price
CS = ½*($9 - $2)(7) = $24.50
MR
MC$2
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
We could make our money on the cartridges and sell the printers cheap…
Profit = $49 + $24.50 = $73.50
$49
Alternatively, we could do something like the amusement park. We maximize profits combining cartridge revenue AND printer revenue
Dollars
0
Demand
14
$16
PQ 16
Quantity of printed pages (000s)
Toner cartridge price
CS = ½*($16 - $2)(14) = $98
MR
MC$2
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
We are back to a low cartridge price and a high printer price
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.
Dollars
0
$9
Demand
7
$16CS = ½*($16 - $9)(7) = $24.50
MR
MC$2
Dollars
0
$7
Demand
5
$12CS = ½*($12 - $2)(5) = $12.50
MR
MC$2
PQ 12PQ 16
Profit = ($9-$2)7 +$24.50 = $73.50 Profit = ($7-$2)5 +$12.50 = $37.50
Total Profit = $111
Alternatively, we could essentially give the cartridges away and discriminate on the printer (like Disneyworld).
Dollars
0
Demand
14
$16CS = ½*($16 - $2)(14) = $98
MC$2
Dollars
0
Demand
10
$12CS = ½*($12 - $2)(10) = $50
MC$2
PQ 12PQ 16
Profit = $98 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
0
Demand
14
$16CS = ½*($16 - $2)(14) = $98
MC$2
Dollars
0
Demand
10
$12CS = ½*($12 - $2)(10) = $50
MC$2
PQ 12
14 Cartridge Package = $98 + $2*14 = $126
PQ 16
10 Cartridge Package = $50 + $2*10 = $70
We need to choose packages so that each demander chooses the “correct” package
Dollars
0
Demand
10
$16CS = ½*($16 - $9)(10) = $50
$60
$6
PQ 16
- 10 Cartridge Package = $70
Total Willingness to Pay = $110
Consumer Surplus = $40
14 Cartridge Package = $126
- required consumer surplus = $40
“Discounted Price” = $86
14 Cartridge Package = $8610 Cartridge Package = $70
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.
Dollars
0
Demand
12-P
$12CS = ½*($12 - $P)(12-P)
$P
PQ 12 Example: Cartridge Price: $3Consumer Surplus = ½*($12 - $3)(9) = $40.50
Charge $40.50 for the printer (Both customers will buy)
Low value customers buy 9 cartridges
High Value customers buy 13 cartridges
Profit = 2*$40.50 + ($3-$2)(21) = $103
We need to find the best cartridge price…
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 $103.93
PQ 16PQ 12
21 QQP
2125. QP CS*2 212$ QQ
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.
Dollars
0
Demand
8
$12CS = ½*($12 - $4)(8) = $32
$60
$4
PQ 12 Best Choice:
Charge $32 for the printer (Both customers will buy)
Charge $4 for cartridgesLow value customers buy 8
cartridges (Pay $64 total)High Value customers buy 12
cartridges (Pay $80 total)
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!)
BH PPQ 12
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)
PPQ H 102$12
Suppose that you knew that the buns were selling for $2, what should you charge?
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
You charge $5
But, if the bun guy sees you charging $5, he needs to react to that…
PPQ B 75$12
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
Bun Guy charge $4
But, if the bun guy is charging $4, you need to react to that…
PPQ B 84$12
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
You charge $4
Each firm must price their own product based on their expectation of the other firm
BHB QPP 12
Bun Company Hot Dog Company
HBH QPP 12
0212 BH QPMR 0212 HB QPMR
2
12 HB
PQ
2
12 BH
PQ
Complementary Goods
Each firm must price their own product based on their expectation of the other firm
Bun Company Hot Dog Company
2
12 HB
PQ
2
12 BH
PQ
Substitute these quantities back into the demand curve to get the associated prices. This gives us each firm’s reaction function.
2
12 HB
PP
2
12 BH
PP
Complementary Goods
Any equilibrium with the two firms must have each of them acting optimally in response to the other.
Bp
Hp
2
12 HB
PP
2
12 BH
PP
$4
$4
$12
$6 $12
$6
8$
4$
HB
HB
PP
PP
Bun Company
Hot Dog Company
Now, suppose that these companies merged into one monopoly
PPPQ HB 1212
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
You charge $6 for hot dog/bun
Now, suppose that these companies merged into one monopoly
QPP BH 12
0212 QMR
6$
6
BH PP
Q
Complementary Goods
HB PPQ 12
Look at what happened here…
Separate Hot Dog/Bun Suppliers
4$
4$
B
H
P
P
Consumer Pays $8 for a hot dog/bun pair
Single Hot Dog/Bun Suppliers
6$ BH PP
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?
Spatial Competition – Location Preferences
When you purchase a product, you pay more than just the dollar cost. The total purchase cost is called your opportunity cost
Consider two customers shopping for wine. One lives close to the store while the other lives far away.
20 miles
2 miles
The opportunity cost is higher for the consumer that is further away. Therefore, if both customers have the same demand for wine, the distant customer would require a lower price.
Spatial Competition – Location Preferences
Starbucks currently has 12,937 locations in the US
Gucci currently has 31 locations in the US
How can we explain this difference?
Consider a market with N identical consumers. Each has a demand given by
otherwise
VpD
,0
if ,1
We must include their travel time in the total price they pay for the product. The firm can’t distinguish consumers and, hence, can’t price discriminate.
txpp ~
Dollar Price
Distance to Store
Travel Costs
There is one street of length one. Suppose that you build one store in the middle. For simplicity, assume that MC = 0
X = 1
X = 1/2 X = 1/2
With a price
Vtxp ~ This is the “marginal customer”
t
pVx
~
p~ What fraction of the market will you capture?
To capture the whole market, set x = 1/2 2
~ tVp
Now, suppose you build two stores…
X = 1
X = 1/4 X = 1/4
With a price
t
pVx
~
p~ What fraction of the market will you capture?
To capture the whole market, set x = 1/4 4
~ tVp
X = 1/4 X = 1/4
Now, suppose you build three stores…
X = 1
X = 1/6 X = 1/6
With a price
t
pVx
~
p~ What fraction of the market will you capture?
To capture the whole market, set x = 1/6 6
~ tVp
X = 1/6 X = 1/6 X = 1/6X = 1/6
Do you see the pattern??
With ‘n’ stores, the price you can charge is
nFn
tVN
2
n
tVp
2~ As n gets arbitrarily large, p
approaches V
Further, profits are equal to
Total Sales Price
Total Costs
nF
n
tVN
n 2max
Maximizing Profits
F
tNn
2
Number of locations is based on:
• Size of the market (N)
• Fixed costs of establishing a new location (F)
• “Moving Costs” (t)
Horizontal Differentiation
Baskin Robbins has 31 Flavors…how did they decide on 31?
F
tNn
2
t = Consumer “Pickiness”
N = Market size
F = R&D costs of finding a new flavor
