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Economics of the Firm
Competitive Pricing Techniques
Every business has a goal. What’s the goal of your
business?
Maximize Profits
Maximize return on
investment
“To Make Money!!!”
Increase Market
Share
Maximize
Shareholder Value
To be a leader in
technology
To be “Green”
Optimal decision making (for example, pricing) depends crucially
on what your goal is!
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)
Lets take this piece by
piece
We will treat costs as a given. Every firm has a total cost function.
TC  TC (Q )
Total costs of production are a function of quantity
produced
TC
TC
TC  10
For pricing decisions,
we focus on marginal
cost
TC 10
MC 
  10
Q
1
$310
$300
56
57
Q  1
Q
Next, we need to know something about the consumer the firm faces.
Every firm should have an estimated demand curve. We can think about a
demand curve in one of two ways
For every price I could charge, my demand curve
tells me what my sales will be.
Q  Q(P)
P
For any sales goal that I set, my demand curve will
tell me what price I can charge to obtain that goal
P  P(Q)
P
D
Q
Q
So, we can get firm revenues one of two ways:
I select a
sales target
Q
T
I select a
price
target
P
T
My demand curve
will tell me the price
I can charge to hit
that target
P  P(Q )
T
My demand curve
will tell me the
sales I will achieve
at that target
Q  Q( P )
T
Revenues equal
price times
quantity
TR  PQT
Revenues equal
price times
quantity
TR  PT Q
In either case, higher sales will be associated with a lower price
TR  PQT
TR  PT Q
OR
If I want to increase
my sales target, I
need to lower my
price to all my existing
customers
I need to drop my
target price if I want to
reach new customers
Initially, you have chosen a price (P)
to charge and are making Q sales.
p
Total Revenues = PQ
p
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
P
Q
Q
p
This area represents the revenues
that you lose because you have to
lower your price to existing customers
Q
P
Q
This area represents
the revenues that you
gain from attracting a
new customer
p
p
p
D
Q
Q
1
P
MR 
Q p
Q
If we are maximizing profits, we want marginal revenues to equal marginal
costs:
MR  MC
P
Q  p  MC
Q
P Q
P  p  MC
Q P
p

 p  MC
Firm’s will be charging a markup over
marginal cost where the markup is
related to the elasticity of demand
MC
p
1
1

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 Supplies
the entire Market
Firm Level Demand
EQUALS industry
demand
Suppose there is a monopolist that faces the following demand
Q  100  2 P
Further, the monopoly has a linear cost function
TC  10Q
p
  4020  1020  600
$40
Can this firm do better?
D
20
Q
First, to increase sales by one, by how much does this firm have to lower it’s
price?
Q  100  2 P
P  50  .5Q
A $0.50 price drop would
increase sales by one
p
-$.50*20 = -$10
Again, this is a loss because we lowered our
price to our existing customers!
(1)($39.50)
$40
$39.50
The additional sale!
MR = $29.50
MC = $10
D
20 21
Q
We should lower
price!
P  50  .5Q
P  50  .5Q
P
Q  p  MC
Q
p
TC  10Q
30
10
MC=$10
 .5Q  50  .5Q  10
50  Q  10
Q  40
P  30
D
40
Q
MR = 50-Q
  3040  1040  800
P  50  .5Q
Let’s check…
p
  30.5039  1039  799.50
$30.50
  29.5041  1041  799.50
30
$29.50
10
MC=$10
D
39 40 41
Q
Q  100  2 P
The markup formula works!
p
 Q  P 
 30 
 
   2   1.5
 P  Q 
 40 
30
10
MC
D
40
Q
MR
10
p
 30
1
1
1.5
Now, suppose this market is serviced by a large
number of identical firms – each with marginal
costs equal to $10
P
Firm Level
Industry
Q  100  2 P
Pi
~
P
D
D
Q
Qi
~
  PQ  TC
Qi
Lowest price among
firm i’s competitors
~
Is it possible for P  MC
P
Industry
Firm Level
Q  100  2 P
Pi
Profit > 0
~
P
D
$10
D
Q
Qi
Qi
As long as price is above marginal cost, there is an incentive for each
firm to undercut its rivals. This incentive disappears when price equals
marginal cost.
Competitive Market
equilibrium
P
Industry
Firm Level
Q  100  2 P
$10
Pi
Profit = 0
~
P  $10
S
D
D
Q
80
Qi
Qi
As long as price is above marginal cost, there is an incentive for each
firm to undercut its rivals. This incentive disappears when price equals
marginal cost.
MC
p
 1
1  
 
Perfectly competitive firms face demand curves that
are perfectly elastic (infinite elasticity. Hence, the
markup (and profits) are zero)
p
Firm Level
Pi
$10
Industry
 i  
  .25
D
$10
Qi
MC
D
Qi
80
Q
Note: Industry elasticities in competitive industries are always less than 1
(industry profits could be increased by raising price!)
Measuring Market Structure – Concentration Ratios
Suppose that we take all the firms in an industry and raked 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
Size
Rank
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
Size
Rank
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
Another way to measure competition is by the outcome.
P  MC
LI 
P
Perfect Competition
p  MC
LI  0
The Lerner index measures the percentage of a
product’s price that is due to the markup
Monopoly
MC
p
 1
1  
 
LI 
1

Lerner index in 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
P  MC
LI 
P
An industry’s cost structure will influence an industry’s competitive nature
Costs
AC
MC
Q
If market size is small, this industry
experiences decreasing costs (big
firms have an advantage over small
firms)
However, if the industry gets big
enough, costs start to increase and
the size advantage becomes a
disadvantage!
Industries with globally scale economies tend to develop as natural
monopolies (the market should – and will – be serviced by one producer).
This can happen if production exhibits increasing marginal productivity, or
if there are large fixed costs.
Costs
Costs
AC
MC
AC
MC
Monopoly Market Characteristics
Small market size
Scale economies (Network Externalities, Learning
by Doing, Large Fixed Costs)
Government Policy (Protected Monopolies)
Any one of these characteristics suggest that the
market structure could be monopolistic.
Long Run Industry Dynamics
As an industry ages, three things happen….
p
p
Short Run
Long Run
  .25
  1.5
D
D
Q
As more alternatives become available, consumer
demand becomes much more price responsive
Q
Long Run Industry Dynamics
As an industry ages, three things happen….
p
p
Short Run
Long Run
MC
MC
Q
As production techniques become more flexible,
marginal costs drop and become much less sensitive
to input prices
Q
Long Run Industry Dynamics
As an industry ages, three things happen….
Market Structure Spectrum
Monopoly
(Short Run)
Perfect Competition
(Long Run)
As new firms enter the industry (i.e. no artificial or
natural barriers), the industry becomes more
competitive and markups fall
Most firms face the a downward sloping market demand and
therefore must lower its price to increase sales.
p
Loss from charging
existing customers a
lower price
p
Gain from attracting new
customers
D
Q
Q
Is it possible to attract
new customers without
lowering your price to
everybody?
Price Discrimination
p
If this monopolist could lower its price to the
21st customer while continuing to charge the
20th customer $15, it could increase profits.
Requirements:
Identification
$15
No Arbitrage
$12
D
20 21
Q
Price Discrimination (Group Pricing)
Suppose that you are the publisher for JK Rowling’s
newest book “Harry Potter and the Deathly Hallows”
Your marginal costs are constant at $4 per book and
you have the following demand curves:
QUS  9  .25P
US Sales
QE  6  .25P
European Sales
If you don’t have the ability to sell at different prices to the two markets,
then we need to aggregate these demands into a world demand.
European
Market
US Market
QUS  9  .25P
QE  6  .25P
p
p
Worldwide
 9  .25P, P  24
Q
15  .5P, P  24
p
$36
$36
$24
$24
$24
D
3
9
D
Q
6
D
Q
3
15
Q
 36  4Q, Q  3
P
30  2Q, Q  3
 9  .25P, P  24
Q
15  .5P, P  24
p
 36  8Q, Q  3
MR  
30  4Q, Q  3
$36
$24
$18
$12
MR
3
D
15
Q
Q  6. 5
P  $17
 36  8Q, Q  3 
MR  
  MC  4
30  4Q, Q  3
p
$36
  $176.5  $46.5  $84.5
$17
$4
MC
MR
3
6.5
D
15
Q
If you can distinguish between the two markets (and resale is not a
problem), then you can treat them separately.
US Market
QUS  9  .25P
p
PUS  36  4QUS
MRUS  36  8QUS  4  MC
$20
Q4
MC
MR
4
D
9
P  $20
If you can distinguish between the two markets (and resale is not a
problem), then you can treat them separately.
European
Market
QE  6  .25PE
p
PE  24  4QE
MRE  24  8QE  4  MC
$14
Q  2.5
MC
MR
2.5
D
6
P  $14
Price Discrimination (Group Pricing)
  $204  $14(2.5)  $46.5  $89
p
p
US Market
European
Market
$20
$14
MC
MR
4
MC
D
9
MR
2.5
D
6
Suppose you operate an amusement park. You know that you face two types
of customers (Young and Old). You have estimated their demands as follows:
Qo  80  PO
QY 100  PY
Old
Young
You have a a constant marginal cost of $2 per ride
Can you distinguish low demanders from high
demanders?
Can you prevent resale?
If you could distinguish each group and prevent resale,
you could charge different prices
QY 100  PY
p
Qo  80  PO
p
Young
Old
$100
$80
$51
$41
D
49
Q
D
39
Q
Two Part Pricing
First, lets calculate a uniform price for
both consumers
100  Q, Q  20
P
 90  .5Q, Q  20
p
100  2Q, Q  20
MR  
 90  Q, Q  20
$100
$80
$70
$60
MR
20
90
D
180
Q
100  2Q, Q  20
MR  
  MC  2
 90  Q, Q  20 
p
$100
$46
$2
MC
MR
88
D
180
Q
Q  88
P  $46
First, you set a price for everyone equal to $46. Young people choose
54 rides while old people choose 34 rides.
p
p
Young
Old
$100
$80
$46
$46
D
54
Q
D
34
Can we do better than this?
Q
Note that young consumer was willing to pay exactly $46 for the 54th ride.
However, she was willing to pay more than $46 for all the previous rides. We
call this consumer surplus.
p
QY 100  PY
$55
This consumer would have paid up to
$55 for the 45th ride. If the going market
price was $46, consumer surplus for the
45th ride would have been $9.
$46
D
45
54
Q
The young person paid a total of $2,484 for the 54 rides. However,
this consumer was willing to pay $3942.
QY 100  PY
p
CSY  (1/ 2)(54)$100  $46  $1,458
Sales  $4654  $2,484
$3,942
$100
$1,458
$46
How can we extract this
extra money?
$2,484
D
54
Q
Two Part pricing involves setting an “entry fee” as well as a per unit price. In
this case, you could set a common per ride fee of $46, but then extract any
remaining surplus from the consumers by setting the following entry fees.
$1458 Young
P = $46/Ride
Entry Fee =
$578 Old
p
p
Young
Old
$100
$1458
$80
$46
$578
$46
$1564
$2484
D
54
Q
D
34
Could you do better than this?
Q
Suppose that you set the cost of the rides at their marginal cost ($2). Both
old and young people would use more rides and, hence, have even more
surplus to extract via the fee.
$4802 Young
P = $2/Ride
Entry Fee =
$3042 Old
p
p
Young
Old
$100
$4802
$80
$3042
$2
$2
D
98
Q
D
78
Q
Block Pricing involves offering “packages”. For example:
p
p
Young
Old
$100
$4802
$80
$2
$2
D
D
98
$2(98) = $196
$3042
78
$2(78) = $156
“Geezer Pleaser”: Entry + 78 Ride Coupons (1 coupon per ride): $3198
($3042 +$156)
“Standard” Admission: Entry + 98 Ride Coupons (1 coupon per ride): $4998
($4802 +$196)
Suppose that you couldn’t distinguish High value customers from low value
customers: Would this work?
p
p
Young
Old
$100
$4802
$80
$3042
$2
$2
D
D
98
$2(98) = $196
1 Ticket Per Ride
78
$2(78) = $156
78 Ride Coupons: $3198
98 Ride Coupons: $4998
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: $4758
- 78 Ride Coupons: $3198
$100
$1560
$3042
If the high value customer buys
the 78 ride package, she keeps
$1560 of her surplus!
$22
$1716
QY 100  PY
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 $1560 of surplus)
p
Total Willingness = $4,998
$100
- Required Surplus = $1,560
Package Price
= $3,438
$4802
This is known as
Menu Pricing
$2
$196
D
98
q
Block Pricing: You can distinguish high demand and low demand
(1st Degree Price Discrimination)
78 Ride: $3198 ( $41/Ride)
1 Ticket Per Ride
98 Rides: $4998 ( $51/Ride)
Menu Pricing: You can’t distinguish high demand from low demand
(2nd Degree Price Discrimination)
78 Ride: $3198 ($41/Ride)
1 Ticket Per Ride
98 Rides: $3438 ($35/Ride)
Group Pricing: You can distinguish high demand from low demand
(3rd Degree Price Discrimination)
No Entry Fee
Low Demanders: $41/Ride
High Demanders: $51/Ride
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
Tie-in Sales
Suppose that you are the producer of laser printers. You face two types of
demanders (high and low). You can’t distinguish high from low.
p
$12
p
Q  12  P
Quantity of
printed pages (in
thousands)
D
12
$16
Q  16  P
Price for 1,000
printed pages
Q
D
Q
16
You have a monopoly in the printer market, but the toner cartridge market is
perfectly competitive. The price of cartridges is $2 (equal to MC) – a toner
cartridge is good for 1,000 printed pages.
Tie-in Sales
You have already built 1,000 printers (the production cost is sunk and
can be ignored). You are planning on leasing the printers. What price
should you charge?
Q  12  P
p
Q  16  P
p
$16
$12
$98
$50
$2
$2
D
10 12
D
Q
14
Q
16
A monthly fee of $50 will allow you to sell to both consumers. Can
you do better than this? Profit = $50*1000 = $50,000
Tie-in Sales
Suppose that you started producing toner cartridges and insisted that your
lessees used your cartridges. Your marginal cost for the cartridges is also
$2. How would you set up your pricing schedule?
28  2 pc
p
(Aggregate Demand)
   pc  2Q  12  pc 
2
$12
.512  Pc 
2
pc
D
12  pc
Q
pc  $4
Tie-in Sales
Q  12  P
p
Q  16  P
p
$16
$12
$72
$32
$4
$4
D
8 12
D
Q
12
Q
16
By forcing tie-in sales. You can charge $4 per cartridge and then a
monthly fee of $32.
Profit = ($4 - $2)*(8 + 12) + 2($32) = $104*500 = $52,000
Complementary Goods
Suppose that the demand for Hot Dogs is given as
follows:
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.
Complementary Goods
Each firm must price their own product based on
their expectation of the other firm
Bun Company
Hot Dog Company
PB  12  PH   QB
MR  12  PH   2QB  0
QB

12  PH 

2
PH  12  PB   QH
MR  12  PB   2QH  0
QH

12  PB 

2
Complementary Goods
Each firm must price their own product based on
their expectation of the other firm
Bun Company
QB
Hot Dog Company

12  PH 

2
QH

12  PB 

2
Substitute these quantities back into the demand curve to get the associated
prices. This gives us each firm’s reaction function.
PB

12  PH 

2
PH

12  PB 

2
Any equilibrium with the two firms must have each of them acting
optimally in response to the other.
PB
pB
$12

12  PH 

2
PH

12  PB 

2
Hot Dog Company
PB  PH  $4
PB  PH  $8
$6
$4
Bun Company
$4 $6
$12
pH
Complementary Goods
Now, suppose that these companies merged into
one monopoly
PH  PB   12  Q
MR  12  2Q  0
Q6
PH  PB   $6
Case Study: 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?
Case Study: Microsoft vs. Netscape
Suppose that the demand for browsers/operating systems is as
follows (look familiar?). Again, Assume MC=0
Q  12  POS  PB 
Case #1: Suppose that Microsoft never entered the browser
market – leaving Netscape as a monopolist.
POS  PB  $4
POS  PB   $8
Case Study: Microsoft vs. Netscape
Case #2: Now, suppose that Microsoft competes in the Browser
market
With competition (and no collusion) in the browser market,
Microsoft and Netscape continue to undercut one another
until the price of the browser equals MC ( =$0)
Given the browser’s price of zero, Microsoft will sell its
operating system for $6
POS  0  12  Q
MR  12  2Q  0
Q6
POS  $6