PRICING WITH PRICING WITH MARKET POWER-IIMARKET POWER-II

PRICING WITH PRICING WITH MARKET POWER-IIMARKET POWER-II

ME, SESSION 13ME, SESSION 13

1313thth August, 2012 August, 2012

PROF. SAMAR K. DATTAPROF. SAMAR K. DATTA

Checklist for Checklist for studentsstudents

•Two-part tariff•Advertising•Pricing of Joint Products

•Bundling & tying

Two-Part PricingTwo-Part Pricing• When it isn’t feasible to charge

different prices for different units sold, but demand information is known, two-part pricing may permit you to extract all surplus from consumers.

• Two-part pricing consists of a fixed fee and a per unit charge.– Example: Athletic club memberships.

How Two-Part Pricing How Two-Part Pricing WorksWorks

1. Set price at marginal cost.2. Compute consumer

surplus.3. Charge a fixed-fee equal

to consumer surplus.

Quantity

D

10

8

6

4

2

1 2 3 4 5

MC

Fixed Fee = Profits* = $16

Price

Per UnitCharge

* Assuming no fixed costs

Meaning of Two-Part Meaning of Two-Part TariffTariff

• The purchase of some products and services can be separated into two decisions, and therefore, two prices. Examples

1) Amusement Park• Pay to enter• Pay for rides and food within the park

2) Tennis Club• Pay to join• Pay to play

• Pricing decision is setting the entry fee (T) and the usage fee (P), thus choosing the trade-off between free-entry and high use prices, or high-entry and zero use prices

Usage price P* is set whereMC = D. Entry price T*

is equal to the entire consumer surplus.

T*

Two-Part Tariff with a Two-Part Tariff with a Single ConsumerSingle Consumer

Quantity

$/Q

MCP*

D

D2 = consumer 2

D1 = consumer 1

Two-Part Tariff with Two Two-Part Tariff with Two ConsumersConsumers

Quantity

$/Q

MC

Q1Q2

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

P*

Thus there is a trade-off between high entry fee & high user price

A

C

Π=2T*+(P*-MC).(Q1+Q2)>2ΔABC

B

The Two-Part Tariff with The Two-Part Tariff with Many ConsumersMany 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.

• To find optimum combination, choose several combinations of P and T

• Choose the combination that maximizes profit

• Rule of Thumb– Similar demand: Choose P close to MC and high

T– Dissimilar demand: Choose high P and low T.

Two-Part Tariff With A TwistTwo-Part Tariff With A Twist

• Suppose, 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

AdvertisingAdvertising

• Assumptions– Firm sets only one price– Firm knows Q(P,A)

• How quantity demanded depends on price and advertising

Q0

0

P0

Q1

1

P1

AR

MR

AR and MR are averageand marginal revenue whenthe firm doesn’t advertise.

MC

If the firm advertises, its average and marginalrevenue curves shift to

the right -- average costsrise, but marginal cost

does not.

AR’

MR’

AC’

Effects of AdvertisingEffects of Advertising

Quantity

$/Q

AC

AdvertisingAdvertising• Choosing Price and Advertising

Expenditure

• A Rule of Thumb for Advertising

adv. of MC full1

)(),(

A

QMC

A

QPMR

AQCAPPQ

Ads

ratio sales toAdv.

1)(

pricingfor /1/)(

PQ

A

A

Q

Q

A

P

MCP

A

QP-MC

EPMCP P

AdvertisingAdvertising• A Rule of Thumb for Advertising

• To maximize profit, the firm’s advertising-to-sales ratio should be equal to minus the ratio of the advertising and price elasticities of demand

Thumb of Rule

demand of elasticity Adv.

P

)(

1)(

))((

PA

A

EEPQA

EPMCP

EAQQA

Advertising – An ExampleAdvertising – An Example• R(Q) = $1 million/yr• $10,000 budget for A (advertising--1% of

revenues)• EA = 0.2 (increase budget $20,000, sales

increase by 20%• EP = -4 (markup price over MC is substantial)

• Should the firm increase advertising?

• YES– A/PQ = -(0.2/-4) = 5%– Increase budget to $50,000

Meaning of Joint ProductsMeaning of Joint Products

• Goods jointly produced in fixed proportions:– Interdependence in production– Single marginal cost curve for both

products or product package; e.g., beef & hides

• However, demand curves & MR curves are independent

• Pricing decision must recognize inter-dependence in production– Marginal revenue of product package is

vertical sum of two MR curves;

Pricing of Joint Products w/o Pricing of Joint Products w/o Excess production of Hides Excess production of Hides (case 1: (case 1:

MR>0 for both products at equilibrium)MR>0 for both products at equilibrium)

PH

PB

DB

MRT

DH

MRT

MRB

MRH

MRH MRB

Prices etc.

QuantityX*

MC

As MR for B<0 at Q1, (Q1-Q0) amount of product B ought to be kept off the

market for maximization of profit

Tangency of iso-product curves to the highest possible iso-revenue curves

provides the optimal points in figure

Case 3: Unlike in the two earlierCases, outputs A & B are nowproduced under flexible proportions,giving rise to concave to origin product transformation curves at constant costs.

BundlingBundling

• Bundling is packaging two or more products to gain a pricing advantage.

• Conditions necessary for bundling– Heterogeneous customers– Price discrimination is not possible– Demands must be negatively correlated

Bundling Example With Bundling Example With Two ConsumersTwo Consumers

Spiderman Spaceballs

Theater A $12,000 $3,000

Theater B $10,000 $4,000

• Renting the movies separately would result in each theater paying the lowest reservation price for each movie

– Total Revenue = $26,000

• If the movies are bundled and if each were charged the lower of the two prices

– Total revenue will be $28,000.

Reservation Price

Bundling Example With Two Bundling Example With Two Consumers – Importance of Negative Consumers – Importance of Negative

Correlation of DemandsCorrelation of Demands• If the demands were positively correlated

(Theater A would pay more for both films as shown), bundling would not result in an increase in revenue.

Gone with the Wind Getting Gertie’s Garter

Theater A $12,000 $4,000

Theater B $10,000 $3,000

If the movies are bundled and if each were charged the lower of the two prices, total revenue will be $26,000, the same as by selling the films, separately.

Bundling Example With Two Bundling Example With Two Heterogeneous Goods and Many Heterogeneous Goods and Many

ConsumersConsumersr2

(reservationprice Good 2)

r1 (reservation price Good 1)

$5

$10

$5 $10

$6

$3.25 $8.25

$3.25

ConsumerA

ConsumerC

ConsumerB

Consumer A is willing to pay up to

$3.25 for good 1 andup to $6 for good 2.

Consumption Decisions Consumption Decisions WhenWhen

Products are Sold Products are Sold SeparatelySeparately

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

Consumption DecisionsConsumption DecisionsWhen Products are When Products are

BundledBundledr2

r1

r2 = PB - r1

I

II

Consumersbuy bundle

(r > PB)

Consumers donot buy bundle

(r < PB)

Consumers compare the sum of their reservation prices, r1 + r2, with the bundle price PB. They buy the bundle only if r1 + r2 is at least as large as PB.

Consumption DecisionsConsumption DecisionsWhen Products are BundledWhen Products are Bundled

Depending on the prices, some of the consumers in regions II and IV might have bought one of the goods if they were sold separately. These customers are lost to the firm.

However, the other customers in regions II and IV now buy both goods where they formerly bought only one.

The firm then, must decide whether it can do better by bundling.

Buyers who buy neither good

Buyers of good 1 lost to the firm

Buyers of good 1 who now buy good 2 also

Buyers of good 2 lost to the firm

Buyers of good 2 who now buy good 1 also

Buyers who buy both the goods

Efficiency of Bundling Depends Efficiency of Bundling Depends on the Degree of Negative on the Degree of Negative

CorrelationCorrelation

r2

r1

Bundling pays due to negative correlation

(Spaceballs)

(Spiderman)

5,000 14,00010,000

5,000

10,000

12,000

4,000

3,000

B

A

Mixed Versus Pure BundlingMixed Versus Pure Bundling

r2

r110 20 30 40 50 60 70 80 90 100

10

20

30

40

50

60

70

80

90

100

C2 = MC2 = 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 = 20With positive marginalcosts, mixed bundling may be more profitable

than pure bundling.

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

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

Mixed bundling $90 $90 $120$420

P1 P2 PB Profit

Mixed BundlingMixed Bundlingwith Zero Marginal Costswith Zero Marginal Costs

Mixed BundlingMixed Bundlingwith Zero Marginal Costswith 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

Mixed Bundling in PracticeMixed Bundling in Practice

• Use of market surveys to determine reservation prices

• Design a pricing strategy from the survey results

• Mixed bundling allows the customer to get maximum utility from a given expenditure by allowing a greater number of choices.

TyingTying• Practice of requiring a customer to

purchase one good in order to purchase another.

• Allows the seller to meter the customer and use a two-part tariff to discriminate against the heavy user

• Examples– Xerox machines and the paper

– IBM mainframe and computer cards