pricing strategy. marginal revenue and selling costs l there is usually a cost to increasing sales l...

Pricing Strategy

Quantity

$

0 5 10 15 20

100

150

200

300

400

50

R

Profits = R - C

t

t'

c

c’

Example of Profit Maximization

C

Slope of R curve is MR

Slope of C curve is MC

Profit (Q) = Revenue - Cost = R(Q) - C(Q)

Maximum when = 0, i.e., =

Here:

= MR = marginal revenue

= MC = marginal cost

ddQ

dR dCdQ dQ

dR dQ

dC dQ

Profit Maximization

So profits are maximized at the price/output level at which

marginal revenue = marginal cost

P1

Q1

Lostprofit from loweroutput

MC

AC

Quantity

$ perunit ofoutput

D = AR

MR

P*

Q*

Maximizing Profit When Marginal Revenue Equals Marginal Cost

P2

Q2

Monopoly

An Example

QQ

CMC

QQCCost

2

50)( 2

The Monopolist’s Output DecisionThe Monopolist’s Output Decision

Note – here fixed cost = 50

Monopoly

An Example

QQ

RMR

QQQQPQR

QQPDemand

240

40)()(

40)(2


Monopoly

An Example

30 10,When

10

2240

P Q

Q

QQorMCMR


Monopoly

An Example By setting marginal revenue equal to marginal

cost, profit is maximized at P = $30 and Q = 10. This can be seen graphically:


Quantity

$

0 5 10 15 20

100

150

200

300

400

50

R

Profits

t

t'

c

c’


C

Fixed cost is $50. Changing fixed cost changes the intercept only.

All costs above $50 are variable.

Question – how does a change in fixed costs affect the best price?


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

Quantity

$

0 5 10 15 20

100

150

200

300

400

50

R

C

Profits

t

t'

c

c

Profit

AR

MR

MC

AC

Illustration of Profit Maximization

Quantity

$/Q

0 5 10 15 20

10

20

30

40

15

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

Quantity

$/Q

0 5 10 15 20

10

20

30

40

15

MC

AR

MR

ACProfit

Markup Rules

Two models of pricing – Markup over costs and What the market will bear. In fact they come together in a demand-

based approach to markup pricing. How should price relate to cost to maximize

profits?

PED = Ep =

Revenue = R = P(Q)Q

Marginal Revenue = MR = = [P(Q)Q]MR = Q + P

MR = P [ + 1]

MR = P [ + 1]

dQ PdP Q

dR dQ

d dQ

dP dQ

dP QdQ P

1 Ep

For maximum profits, MR = MC so

P + P = MC

Or

1 Ep

P - MC = - 1 P 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 p/MC

- 1

- 2 2

- 3 3/2

- 4 4/3

- 5 5/4

- 6 6/5

1

Elasticity of Demand and Price Markup

$/Q $/Q

Quantity Quantity

AR

MR

MR

AR

MC MC

Q* Q*

P*

P*

P*-MC

The more elastic isdemand, the less the

markup.

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 #: Will Pay: Revenue: Price:1 10 10 102 9 18 93 8 24 84 7 28 75 6 30 66 5 30 57 4 28 48 3 24 39 2 18 2

10 1 10 1

Total 55

Revenue:

0

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9 10

Price

Reve

nue

Revenue:

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.

W-T-P, $

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10

# of unit

W-T-P, $

Demand curve Area under D curve here is about 55, = total willingness to pay.

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.

W-T-P, $

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10

# of unit

W-T-P, $

Demand curve Area under D curve here is about 55, = total willingness to pay.

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

Quantity

D2 = AR2

MR2

$/Q

D1 = AR1MR1

Consumers are divided intotwo groups, with separate

demand curves for each group.

MRT = MR1 + MR2


Quantity

D2 = AR2

MR2

$/Q

D1 = AR1MR1

MC

Q2

P2

QT=Q1+Q2

•QT: MC = MRT

•Group 1: P1Q1 ; more elastic•Group 2: P2Q2; more inelastic•MR1 = MR2 = MC•QT control MC

Q1

P1

MC = MR1 at Q1 and P1

MR


Quantity

MR2

$/Q

MR1

MC

Q1 Q2 QT=Q1+Q2

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

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 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

Price Elasticity

Product Nonusers Users

Price Elasticities of Demand for Users Versus Nonusers of Coupons

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

Airlines

PED for Business Class = -1.25

PED for Economy in range -1.5 to -5 depending on category

Demand

# passengers

0

10

20

30

40

50

60

Price

# passengers

Passengers and fares on UAL # 815

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)

Pricing

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

Price Net Price # Lines Net Rev Lost to ATT From ATT Net ATT Rev from W. County Profit

$215 $175 24,250 $4,243,750 $5,600,000 $3,000,000 -$2,600,000 $3,500,000 $5,143,750$230 $190 23,000 $4,370,000 $5,200,000 $3,000,000 -$2,200,000 $3,800,000 $5,970,000$245 $205 19,950 $4,089,750 $4,400,000 $2,700,000 -$1,700,000 $4,100,000 $6,489,750$260 $220 16,250 $3,575,000 $3,200,000 $2,100,000 -$1,100,000 $4,400,000 $6,875,000$275 $235 11,500 $2,702,500 $2,000,000 $1,400,000 -$600,000 $4,700,000 $6,802,500$290 $250 8,500 $2,125,000 $0 $0 $0 $5,000,000 $7,125,000$305 $265 5,500 $1,457,500 $0 $0 $0 $5,300,000 $6,757,500

NYNEX profits & Revenues

-4000000

-2000000

0

2000000

4000000

6000000

8000000

$215 $230 $245 $260 $275 $290 $305

Price

$$

Operating Rev

Net ATT

Rev from W. County

Profit

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

User price P* is set atMC. Entry price T*

is equal to the entire consumer surplus.

T*

Two-Part Tariff with a Single Type of Consumer

Quantity

$/Q

MCP*

D

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.

D2 = consumer 2

D1 = consumer 1

Q1Q2

The price, P*, will be greater than MC. Set T* at the surplus value of D2.

T*

Two-Part Tariff with Two Types of Consumers

Quantity

$/Q

MC

A

BC

ABC e than twicmore

)()(2 21**

QQxMCPT

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

Selling several goods in one bundle

Hardware and software

Software suites

Auto accessories

Bundling

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.

A & B are individuals described by the amounts they are willing to pay for each good.

Consumption Decisions WhenProducts are Sold Separately

r2

r1

P2

II

Consumers buyonly good 2

22

11

PR

PR

P1

Consumers fall intofour categories basedon their reservation

price.I

Consumers buyboth goods

22

11

PR

PR

III

Consumers buyneither good

22

11

PR

PR

IV

Consumers buyonly Good 1

22

11

PR

PR

R = reservation price = willingness to pay

Consumption DecisionsWhen Products are Bundled

r2

r1

Consumers buy the bundlewhen r1 + r2 > PB

(PB = bundle price).PB = r1 + r2 or r2 = PB - r1

Region 1: r > PB

Region 2: r < PB

r2 = PB - r1

I

II

Consumersbuy bundle

(r > PB)

Consumers donot buy bundle

(r < PB)

Reservation Pricesr2

r1

P2

P1

If the demands are perfectly positivelycorrelated, the firm

will not gain by bundling.It would earn the same

profit by selling the goods separately.

Reservation Pricesr2

r1

If the demands are perfectly negatively

correlated bundling is the ideal strategy--all the

consumer surplus canbe extracted and a higher

profit results.

Mixed Versus Pure Bundlingr2

r110 20 30 40 50 60 70 80 90 100

10

20

30

40

50

60

70

80

90

100

C2 = MC2

C2 = 30

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.

A

B

D

C

C1 = MC1

C1 = 20 With positive marginalcosts, mixed bundling may be more profitable

than pure bundling.

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 $2002. Costs 2 x 30 + 2 x 20 = $1003. 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 $1502. Costs are $603. Profit is $90

A buys 2

1. Revenue is $902. Cost $303. Profit $60

Total for separate sales is $150

Mixed Bundlingwith Zero Marginal Costs

r2

r120 40 60 80 100

20

40

60

80

100

120

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.

C

10 90

10

90A

B

D

Sell separately $80 $80 ---- $320

Pure bundling ---- ---- $100 $400

Mixed bundling $90 $90 $120 $420

P1 P2 PB Profit

Mixed Bundlingwith Zero Marginal Costs

Bundling by Pricing

Willing to pay: Word Processor SpreadsheetJack $120 $100Jill $100 $120

In this case, try the following: $120 for thefirst application, and $100 for the second.

Pricing Cell-Phones

A mix of discrimination, bundling and two-part 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

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.

Different two-part tariffs

Cost of extra minute

# of minutes400 600 1000

0.50

0.25

0.20

$40/month

$60/month

$100/month

Supply curves under alternative tariffs.

“Free” minutes

These are the supply curves of cell-phone minutes you face as consumers. Each targets a different market segment.

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.

Demand curve.

Consumer surplus if service provided free.Charge this as fixed charge.

Maximum use if service free.Give this number of “free” minutes.

0

A

B

A TYPICAL MARKET SEGMENT

Cost of extra minute

# of minutes600 1000

0.50

0.25

0.20

$40/month

$60/month

$100/month

Different market segments

400

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

400 minutes

20 cents

10 cents

200 minutes

400 minutes for $40 produces revenue of $40 and appropriates all consumer surplus. Selling @ $0.10/minute sells 200 minutes forrevenue of $20.

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.

400 minutes

20 cents

10 cents

200 minutes

At 10 cents consumer gets first 200 units at lessthan she values them at. She has a positive consumer surplus on these.

At 10 cents consumer has negative CS on last 200 units.

Negative CS on last 200 units just offset by positive CS on first 200.

Bundling early and late minutes

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).

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


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


Examples of Illegal CombinationsExamples 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.


Examples of Illegal CombinationsExamples of Illegal Combinations

Sherman Act (1890) Section 2

– Makes it illegal to monopolize or attempt to monopolize a market and prohibits conspiracies that result in monopolization.


Clayton Act (1914)

1) Makes it unlawful to require a buyer or lessor not to buy from a competitor

2) Prohibits predatory pricing


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.


Robinson-Patman Act (1936) Prohibits price discrimination if it is likely to

injure the competition Also new case on Acuvue Contact Lenses 2002


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


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



2) Federal Trade Commission– Enforces through voluntary understanding or

formal commission order



3) Private Proceedings– Lawsuits for damages– Plaintiff can receive treble damages


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,

pricing strategy. marginal revenue and selling costs l there is usually a cost to increasing sales l...

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