Download B 7006 Pricing - Columbia Business School

Pricing Strategy
Example of Profit Maximization
$
400
C
Slope of R curve is MR
t'
R
300
c’
200
Slope of C curve is MC
t
Profits = R - C
150
100
50
0
c
5
10
15
20 Quantity
Profit Maximization
Profit  (Q) = Revenue - Cost = R(Q) - C(Q)
Maximum when
d
dQ
= 0,
dR
i.e.,dQ
Here:
dR
dQ
= MR = marginal revenue
dC
dQ
= MC = marginal cost
=
dC
dQ
So profits are maximized at the
price/output level at which
marginal revenue = marginal cost
Maximizing Profit When Marginal Revenue
Equals Marginal Cost
$ per
unit of
output
MC
P1
P*
AC
P2
Lost
profit
from lower
output
D = AR
MR
Q1
Q*
Q2
Quantity
Monopoly
The Monopolist’s Output Decision

An Example
Cost  C (Q )  50  Q
C
MC 
 2Q
Q
Note – here fixed cost = 50
2
Monopoly
The Monopolist’s Output Decision

An Example
Demand  P(Q)  40  Q
R(Q)  P(Q)Q  40Q  Q
R
MR 
 40  2Q
Q
2
Monopoly
The Monopolist’s Output Decision

An Example
MR  MC or 40  2Q  2Q
Q  10
When Q  10, P  30
Monopoly
The Monopolist’s Output Decision

An Example
By setting marginal revenue equal to marginal
cost, profit is maximized at P = $30 and Q = 10.
 This can be seen graphically:

Example of Profit Maximization
Question – how does a change in fixed costs affect the best price?
$
C
t'
400
300
c’
200
R
All costs above $50 are
variable.
t
Profits
150
100
50
0
c
5
10
15
Fixed cost is
$50. Changing fixed cost changes the intercept only.
20 Quantity
Example of Profit Maximization

Observations





Slope of rr’ = slope cc’
and they are parallel at 10
units
Profits are maximized at 10
units
P = $30, Q = 10,
TR = P x Q = $300
AC = $15, Q = 10,
TC = AC x Q = 150
Profit = TR - TC
– $150 = $300 - $150
C
$
t'
400
R
300
c
200
t
150
Profits
100
50
c
0
5
10
15
20
Quantity
Illustration of Profit Maximization
$/Q
40
MC
30
AC
Profit
20
AR
15
10
MR
0
5
10
15
20
Quantity
Illustration of Profit Maximization

Observations



AC = $15, Q = 10,
TC = AC x Q = 150
Profit = TR = TC = $300 $150 = $150 or
Profit = (P - AC) x Q =
($30 - $15)(10) = $150
$/Q
40
MC
30
AC
Profit
20
AR
15
MR
10
0
5
10
15
20
Quantity
Markup Rules





Two models of pricing –
Markup over costs and
What the market will bear.
In fact they come together in a demandbased approach to markup pricing.
How should price relate to cost to maximize
profits?
dQ P
dP Q

PED = Ep =

Revenue = R = P(Q)Q

Marginal Revenue = MR =
MR = dP Q + P
dQ
MR
dP
= P [ dQ
MR
=P[
Q+
P
1
+
Ep
1]
1]
dR
dQ
=
d
dQ[P(Q)Q]
For maximum profits, MR = MC so
P
1+
Ep
P = MC
Or
P - MC =
P
-
1
Ep
Another way of saying the same
thing:
P - MC = - P
Ep
Plot the ratio of price to marginal cost as a
function of the demand elasticity:
Ep
-1
-2
-3
-4
-5
-6

p/MC

2
3/2
4/3
5/4
6/5
1
Elasticity of Demand and Price Markup
$/Q
$/Q
The more elastic is
demand, the less the
markup.
P*
MC
MC
P*
AR
P*-MC
MR
AR
MR
Q*
Quantity
Q*
Quantity
Summary

This is a model of price setting as a markup
over costs with the markup reflecting what
the market will bear.
Switching costs ( “lock-in”)

These are the costs to consumers of switching from
one producer or brand to another

They make demand for the first brand less elastic less responsive to lower prices by competitors

Switching costs associated with your competitors’
brands make your selling costs higher
Examples of switching costs:



Frequent flier bonuses and other rewards for
loyalty
Emphasis on “relationships” rather than
“transactions”. Valid for banking, computer
systems (custom jobs vs. off-the-shelf
software), consulting, legal services
Emphasis on “uniqueness” of product
Examples of Switching Costs

IBM with mainframes

ATT with PBXs

Microsoft with Windows
Switching Costs

Can be high for widely-used software
because of need to retrain, modify file
formats, maintain links to other applications,
etc.

Hence incoming products will attempt to
maintain compatibility and reduce these
costs.

In general, a major role of marketing
strategy and image building is to increase
the costs of switching from your product, so
as to make demand less elastic.

Switching costs are reflected in the PED.

Being an industry standard raises
switching costs.
Consumer Surplus

With a downward sloping demand curve,
and uniform price for all buyers, some
buyers will be paying less than they are
willing to pay for the good (for example, the
buyers at the top left hand end of the
demand curve)

The difference between what a buyer is
willing to pay for the units of a good which
she buys, and the amount she actually
pays, is called the buyer’s consumer
surplus
One of the main aims of pricing strategy is to
find a way of charging for goods which brings
this consumer surplus to the seller. To quote
the marketing SVP of American Airlines, “Why
sell a seat for $200 to someone who is willing
to pay $500 for it?”
Buyer #:
1
2
3
4
5
6
7
8
9
10
Total
Will Pay: Revenue: Price:
10
10
10
9
18
9
8
24
8
7
28
7
6
30
6
5
30
5
4
28
4
3
24
3
2
18
2
1
10
1
55
Revenue:
35
Revenue
30
25
20
15
Revenue:
10
5
0
1
2
3
4
5
6
Price
7
8
9
10
Consumer surplus & demand
curve



Buyer’s consumer surplus is area beneath
her demand curve and above horizontal line
whose height is the price.
Example - buyer is willing to pay $10 for 1st
unit, $9 for 2nd, $8 for 3rd, $7 for 4th, etc.
Construct demand curve.
Area under D curve here is
about 55, = total willingness to pay.
Demand curve
W-T-P, $
12
10
8
6
W-T-P, $
4
2
0
1
2
3
4
5
6
# of unit
7
8
9
10
Consumer Surplus



Suppose price is zero. She will buy 10 units
and consumer surplus is $(10+9+8+7+6 … )
which is $55.
Area beneath demand curve and above P=0
is 1/2x10.5x10.5 which is 55.125.
Try second example: price is just less than
$6, so she buys 5 units. Pays $5x6 = $30.
Area under D curve here is
about 55, = total willingness to pay.
Demand curve
W-T-P, $
12
10
8
6
W-T-P, $
4
2
0
1
2
3
4
5
6
# of unit
7
8
9
10
Consumer surplus



Area beneath demand curve and above P=6
is 1/2x4.5x4.5 = 10.125.
Total value attributed to first 5 units is
$(10+9+8+7+6) = $40. Subtract payment of
$30 and consumer surplus is $10.
So - CS is area beneath D curve and above
horizontal line with vertical coordinate of
price.
Tools of pricing strategy
Three main tools:
Price discrimination, two-part pricing and
bundling
(1) Price discrimination: charging different prices for
essentially the same good to different buyers. Charge
each what they are willing to pay.
Different types of price discrimination



Charging a different price to every buyer. Examples:
Reuters Info Services, car sales
Segmenting the market. Airlines with business vs.
vacation travel, railroads with time-of-day pricing,
phone companies with time-of-day pricing, retail stores
pricing by location.
price discrimination over time: introduce a product at a
high price and reduce the price over time. Sell at a high
price to the aficionados - e.g. high fi systems, new and
more powerful computers
Two market segments, with demand curves
P1 = P1 (Q1) and P2 = (Q2)
Marginal cost curve is
MC = MC (Q1 + Q2)
Market Segmentation


Choose price, output so that MR same in
each segment
Common MR should equal MC
Third-Degree Price Discrimination
$/Q
Consumers are divided into
two groups, with separate
demand curves for each group.
MRT = MR1 + MR2
D2 = AR2
MR2
MR1
D1 = AR1
Quantity
Third-Degree Price Discrimination
$/Q
MC = MR1 at Q1 and P1
P1
•QT: MC = MRT
•Group 1: P1Q1 ; more elastic
•Group 2: P2Q2; more inelastic
•MR1 = MR2 = MC
•QT control MC
MC
P2
D2 = AR2
MR
MR2
D1 = AR1
MR1
Q1
Q2
QT=Q1+Q2
Quantity
Third-Degree Price Discrimination
$/Q
MC
MR2
MR1
Q1
Q2
QT=Q1+Q2
Quantity
Market Segmentation


Choose price, output so that MR same in
each segment
Common MR should equal MC
Sales, Coupons, Random
Discounts



All of these are frequently forms of price
discrimination.
People who won’t pay the full price wait for
sales.
Coupon users typically have low incomes.
Price Elasticities of Demand for Users Versus
Nonusers of Coupons
Price Elasticity
Product
Nonusers
Users
Toilet tissue
-0.60
-0.66
Stuffing/dressing
-0.71
-0.96
Shampoo
-0.84
-1.04
Cooking/salad oil
-1.22
-1.32
Dry mix dinner
-0.88
-1.09
Cake mix
-0.21
-0.43
Price Elasticities of Demand for Users Versus
Nonusers of Coupons
Price Elasticity
Product
Nonusers
Users
Cat food
-0.49
-1.13
Frozen entrée
-0.60
-0.95
Gelatin
-0.97
-1.25
Spaghetti sauce
-1.65
-1.81
Crème rinse/conditioner
-0.82
-1.12
Soup
-1.05
-1.22
Hot dogs
-0.59
-0.77
Airlines
Cost Structure
Consulting studies: costs are 12 cents/available
passenger mile (a.p.m.).
Is this AC or MC? Focus on AC vs. MC distinction
and on SR vs. LR MC
12 cents/a.p.m. is AC
LR MC is AC
SR MC is close to zero
Demand
PED for Business Class = -1.25
PED for Economy in range -1.5 to -5
depending on category
Passengers and fares on UAL # 815
# passengers
60
50
40
30
# passengers
20
10
Price
0
0
10
0
20
0
40
0
60
0
80
00
10
20
00
0
Pricing
Markup is PED/(1+PED)
Business: Markup = -1.25/(-.25) = 5
So price = 5 times MC
Should be LR MC
Take NY - SFO - NY round trip, about 5800 miles.
Price = 5800 x .12 x 5 = $3480. (actual $3628)
Economy:
Markup range -1.5/(-0.5) = 3 to -5/(-4) =
1.25
Price range: 5800 x .12 x 3 = $2088
to 5800 x .12 x 1.25 = $870
These are prices based on LR MC.(Actual
range $326 to $2344)
Actual prices go lower - may be based on
lower PED estimates, or on SR MC.
What about situations where SR MC applies?
Standby, bucket-shops, end-of-week specials.
Examples of “Yield Management” - see also
hotels, car rentals, etc.
Also adjust prices for “load factor”. If this is
75%, actual revenues will be only 75% of
that predicted by these prices so gross up
price to allow for this.
NYNEX Case
NYNEX profits & Revenues
Price
Net Price # Lines
$215
$230
$245
$260
$275
$290
$305
$175
$190
$205
$220
$235
$250
$265
24,250
23,000
19,950
16,250
11,500
8,500
5,500
Net Rev
$4,243,750
$4,370,000
$4,089,750
$3,575,000
$2,702,500
$2,125,000
$1,457,500
Lost to ATT From ATT Net ATT
$5,600,000
$5,200,000
$4,400,000
$3,200,000
$2,000,000
$0
$0
$3,000,000
$3,000,000
$2,700,000
$2,100,000
$1,400,000
$0
$0
-$2,600,000
-$2,200,000
-$1,700,000
-$1,100,000
-$600,000
$0
$0
Rev from W. County Profit
$3,500,000
$3,800,000
$4,100,000
$4,400,000
$4,700,000
$5,000,000
$5,300,000
$5,143,750
$5,970,000
$6,489,750
$6,875,000
$6,802,500
$7,125,000
$6,757,500
8000000
6000000
4000000
$$
Operating Rev
Net ATT
2000000
Rev from W. County
Profit
0
$215
$230
$245
$260
-2000000
-4000000
Price
$275
$290
$305
The Two-Part Tariff

The purchase of some products and services
can be separated into two decisions, and
therefore, two prices

Decision to enter market and decision about
how much to buy
The Two-Part Tariff

Examples
1) Amusement Park
– Pay to enter
– Pay for rides and food within the park
2) Tennis Club
– Pay to join
– Pay to play
The Two-Part Tariff

Examples
3) Rental of Mainframe Computers
– Flat Fee
– Processing Time
4) Safety Razor
– Pay for razor
– Pay for blades
The Two-Part Tariff

Examples
5) Polaroid Film
– Pay for the camera
– Pay for the film
The Two-Part Tariff

Pricing decision is setting the entry fee (T)
and the usage fee (P)

Choosing the trade-off between free-entry
and high user charges or high-entry and zero
user charges
Two-Part Tariff with a Single Type of
Consumer
$/Q
T*
P*
User price P* is set at
MC. Entry price T*
is equal to the entire
consumer surplus.
MC
D
Quantity
Two-part tariffs with varied consumers:


Consumer surplus of the lowest demand
curve limits what you can charge as the
fixed charge. If you charge more than this
you lose this group of consumers.
Try to devise ways of differentiating the
fixed charges- see below about cell phones.
Two-Part Tariff with Two Types of
Consumers
The price, P*, will be
greater than MC. Set T*
at the surplus value of D2.
$/Q
  2T *  ( P*  MC ) x(Q1  Q2 )
 more than twic e ABC
A
T*
MC
B
C
D1 = consumer 1
D2 = consumer 2
Q2
Q1
Quantity
The Two-Part Tariff

The Two-Part Tariff With Many Different
Consumers
No exact way to determine P* and T*.
 Must consider the trade-off between the entry
fee T* and the use fee P*.

– Low entry fee: High sales and falling profit with
lower price and more entrants.
The Two-Part Tariff

The Two-Part Tariff With Many Different
Consumers
To find optimum combination, choose several
combinations of P,T.
 Choose the combination that maximizes profit.

The Two-Part Tariff

Rule of Thumb
Similar demand: Choose P close to MC and
high T
 Dissimilar demand: Choose high P and low T.

The Two-Part Tariff

Two-Part Tariff With A Twist

Entry price (T) entitles the buyer to a certain
number of free units
– Gillette razors with several blades
– Amusement parks with some tokens
– On-line with free time
Bundling

Selling several goods in one bundle

Hardware and software

Software suites

Auto accessories
A & B are individuals
described by the amounts they
are willing to pay for each
good.
A will pay $9.25 for the bundle and B, $11.50. To sell 1 and 2 separately and get
both customers to buy both, cannot charge more than $3.25 for either good. Gives
revenue of 4x$3.25 = $13. Bundling gets $2x$9.25 = $18.50. Selling only to
customer willing to pay most gets $6 + $8.25 = $14.25. Selling 1 for $8.25 and 2
for $3.25 gets $8.25 + $6.50 = $14.75.
Consumption Decisions When
Products are Sold Separately
r2
R1  P1
R1  P1
R2  P2
R2  P2
II
I
Consumers buy
only good 2
P2
Consumers buy
both goods
Consumers fall into
four categories based
on their reservation
price.
R = reservation price =
willingness to pay
R1  P1
R1  P1
R2  P2
R2  P2
III
IV
Consumers buy
neither good
Consumers buy
only Good 1
P1
r1
Consumption Decisions
When Products are Bundled
r2
I
Consumers
buy bundle
(r > PB)
Consumers buy the bundle
when r1 + r2 > PB
(PB = bundle price).
PB = r1 + r2 or r2 = PB - r1
Region 1: r > PB
Region 2: r < PB
r2 = PB - r1
II
Consumers do
not buy bundle
(r < PB)
r1
Reservation Prices
If the demands are
perfectly positively
correlated, the firm
will not gain by bundling.
It would earn the same
profit by selling the
goods separately.
r2
P2
P1
r1
Reservation Prices
r2
If the demands are
perfectly negatively
correlated bundling is the
ideal strategy--all the
consumer surplus can
be extracted and a higher
profit results.
r1
Mixed Versus Pure Bundling
r2
100
C1 = MC1
C1 = 20
A
With positive marginal
costs, mixed bundling
may be more profitable
than pure bundling.
90
80
70
60
50
B
C
Consumer A, for example, has
a reservation price for good 1
that is below marginal cost c1.
With mixed bundling, consumer A
is induced to buy only good 2, while
consumer D is induced to buy only good 1,
reducing the firm’s cost.
40
30
20
D
C2 = MC2
C2 = 30
10
10 20 30 40 50 60 70 80 90 100
r1
Bundle at $100
A,B,C,D all buy
1. Revenue is $400
2. Costs are 4 x 30 + 4 x 20 = $200
3. Profits are $200
Mixed bundle at $100, $89, $89
B,C buy bundle
1. Revenue $200
2. Costs 2 x 30 + 2 x 20 = $100
3. Profits are $100
A buys 2: profit is $89 - $30 = $59
D buys 1: profit is $89 - $20 = $69
Total for mixed bundling is $100 + $59 + $69 = $228
Sell separately
Sell 1 at $50, 2 at $90
B, C, D all buy 1
1. Revenue is $150
2. Costs are $60
3. Profit is $90
A buys 2
1. Revenue is $90
2. Cost $30
3. Profit $60
Total for separate sales is $150
Mixed Bundling
with Zero Marginal Costs
r2
120
In this example, consumers B and C
are willing to pay $20 more for the bundle
than are consumers A and D. With
mixed bundling, the price of the bundle
can be increased to $120.
A & D can be charged $90 for a single good.
100
90
A
B
80
60
C
40
20
D
10
10 20
40
60
80 90 100
120
r1
Mixed Bundling
with Zero Marginal Costs
P1
P2
PB
Profit
Sell separately
$80
$80
----
$320
Pure bundling
----
----
$100
$400
Mixed bundling
$90
$90
$120
$420
Bundling by Pricing
Willing to pay: Word Processor
Jack
$120
Jill
$100
Spreadsheet
$100
$120
In this case, try the following: $120 for the
first application, and $100 for the second.
Pricing Cell-Phones



A mix of discrimination, bundling and twopart pricing
Buy the phone (connection/membership
charge) & pay for service - like Polaroid,
Gilette. Phones at different price points.
Then you have a choice between several
two-part tariffs
Different two-part tariffs



Typically $40 per month with 400 minutes
free and 40c/min additionally
or $60 per month with 600 minutes free and
30c/min additionally, etc.
Choice of two-part tariffs - intended to price
discriminate. Heavy users - willing to pay a
lot - will opt for high fixed charge to get the
lower per unit price, and vice versa.
Cost of
extra minute
These are the supply curves of cell-phone minutes you
face as consumers. Each targets a different market segment.
Supply curves under alternative tariffs.
0.50
$40/month
$60/month
0.25
$100/month
0.20
400
“Free” minutes
600
1000
# of minutes
Pricing policy

For each market segment try to estimate



Maximum consumption if marginal
consumption cost is zero.
Consumer surplus at this consumption level.
Use this surplus as a fixed monthly charge
and then have a steep fee for going over the
allotted number of minutes.
A TYPICAL MARKET SEGMENT
Demand curve.
A
Consumer surplus if service provided free.
Charge this as fixed charge.
Maximum use if service free.
Give this number of “free”
minutes.
0
B
Different market segments
Cost of
extra
minute
0.50
$40/month
$60/month
0.25
$100/month
0.20
400
600
1000
# of minutes
Key aspects of pricing policy

Compare



giving 400 minutes for $40 ($0.10 per minute on
average) with
charging $0.10 per minute for any number of
minutes.
If demand curve is as Verizon policy
implies, then selling at $0.10/minute will
sell 100 minutes (next slide) and give
revenue of $20, rather than $40
20 cents
400 minutes for $40 produces revenue of $40
and appropriates all consumer surplus.
Selling @ $0.10/minute sells 200 minutes for
revenue of $20.
10 cents
200 minutes
400 minutes
Key aspects



So selling 400 minutes for $40 is NOT the
same as selling each minute at the average
price, 40/400 = $0.10.
Selling the 400 minutes together is twice as
profitable as selling each minute at $0.10.
WHY?
Bundling earlier and later minutes together.
Bundling early and late minutes
20 cents
At 10 cents consumer gets first 200 units at less
than she values them at. She has a positive consumer
surplus on these.
10 cents
At 10 cents consumer has
negative CS on last 200 units.
200 minutes
400 minutes
Negative CS on last 200 units just offset by positive CS on first 200.
Conclusions



Key aspect of pricing here is bundling early
and late minutes. Positive CS on former
offsets negative CS on latter.
Prices seem to be low - probably
competition between different carriers and
between cell phones and normal phones.
Carriers see market share as critical in
growing market. Valued “per pop.”
Pricing of AIDS Drugs



Key issue – price discrimination by country
is natural as country is a proxy for income
and WTP.
Deal struck with SA and other poor
countries is no more than extension of this
principle.
Leads to situation where rich countries
naturally contribute more to R&D expenses
and so in effect subsidize others.
Pricing AIDS Drugs

May make economic sense to sell to poorest
markets at less than average cost as long as
price above marginal cost
Limiting Market Power:
The U.S. Antitrust Laws

Antitrust Laws:
Promote a competitive economy - competition
benefits consumers.
 Rules and regulations designed to promote a
competitive economy by:

– Prohibiting actions that restrain or are likely to
restrain competition
– Restricting the forms of market structures that are
allowable (e.g. excessive concentration).
Limiting Market Power:
The U.S. Antitrust Laws

Sherman Act (1890)

Section 1
– Prohibits contracts, combinations, or conspiracies in
restraint of trade
 Explicit agreement to restrict output or fix prices
 Implicit collusion through parallel conduct
Limiting Market Power:
The U.S. Antitrust Laws
Examples of Illegal Combinations

1983


Six companies and six executives indicted for
price of copper tubing
1996

Archer Daniels Midland (ADM) pleaded guilty
to price fixing for lysine -- three sentenced to
prison in 1999
Limiting Market Power:
The U.S. Antitrust Laws
Examples of Illegal Combinations

1999

Roche A.G., BASF A.G., Rhone-Poulenc and
Takeda pleaded guilty to price fixing of
vitamins -- fined more than $1 billion.
Limiting Market Power:
The U.S. Antitrust Laws

Sherman Act (1890)

Section 2
– Makes it illegal to monopolize or attempt to
monopolize a market and prohibits conspiracies
that result in monopolization.
Limiting Market Power:
The U.S. Antitrust Laws

Clayton Act (1914)
1) Makes it unlawful to require a buyer or
lessor not to buy from a competitor
2) Prohibits predatory pricing
Limiting Market Power:
The U.S. Antitrust Laws


Clayton Act (1914)
Prohibits mergers and acquisitions if they
“substantially lessen competition”or “tend to
create a monopoly”
Proposed mergers have to be approved by
the Justice Department.
Limiting Market Power:
The U.S. Antitrust Laws

Robinson-Patman Act (1936)
Prohibits price discrimination if it is likely to
injure the competition
 Also new case on Acuvue Contact Lenses 2002

Limiting Market Power:
The U.S. Antitrust Laws

Federal Trade Commission Act (1914,
amended 1938, 1973, 1975)
1) Created the Federal Trade
Commission (FTC)
2) Prohibitions against deceptive
advertising, labeling, agreements
with retailer to exclude competing
brands
Limiting Market Power:
The U.S. Antitrust Laws

Antitrust laws are enforced three ways:
1) Antitrust Division of the Department
of Justice
– A part of the executive branch--the
administration can influence enforcement
– Fines levied on businesses; fines and
imprisonment levied on individuals
Limiting Market Power:
The U.S. Antitrust Laws

Antitrust laws are enforced three ways:
2) Federal Trade Commission
– Enforces through voluntary understanding or
formal commission order
Limiting Market Power:
The U.S. Antitrust Laws

Antitrust laws are enforced three ways:
3) Private Proceedings
– Lawsuits for damages
– Plaintiff can receive treble damages
Limiting Market Power:
The U.S. Antitrust Laws

Two Examples


American Airlines -- Price fixing
Microsoft
– Monopoly power
– Predatory actions
– Collusion
Recent cases




GE and Honeywell
United Airlines and US Airways
Mergers blocked on grounds of restriction of
competition.
Bundling an issue for Microsoft – but
because of its anti-competitive implications,