Pricing Strategies

Pricing and Profits

Price

Quantity

P = 10 - 2Q

10

8

6

4

2

1 2 3 4 5

MC

MR = 10 - 4Q

$8 = Standard Pricing Profit (homogeneous product, sold in one market, uniform P for all units) captures only half of the consumer surplus for the perfectly competitive industry

The entire consumer surplus could be captured with Price Discrimination (charging different P for different quantities or in different markets)

Zero cost example

Second Degree Price Discrimination

Use a discrete schedule of declining prices for additional blocks of quantities(e.g. Electric utilities: lower P for additional units).

For no cost case with single price set at $5 consumerpurchase 5 units for max profit of $25.

With a discount of $2 for additional purchases of up to 2 units, consumer purchases 7 units, increasing profit by $6.

First Degree or Perfect Price Discrimination

To extract all surplus from consumers charge each consumer the maximum amount he or she will pay for each incremental unit

In practice, transactions costs and information constraints make it difficult to implement perfectly (car dealers and some professionals come close).

Price discrimination won’t work if consumers can resell the good.

Zero cost example (consumer surplus for the first 4 units)

Two-Part Pricing

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

and charge a fixed-fee equal to consumer surplus of buyerwith the lowest demand.

Quantity

D

10

8

6

4

2

1 2 3 4 5

MC

Fixed Fee = Profits = $16

Price

Per UnitCharge

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 (sports clubs, utilities, etc.).

Block Pricing• Pack multiple units of the product and sell them as a block

(paper napkin roles, six-packs, etc.).

• Let consumer’s demand be P = 10 - 2Q and TC = 2Q

• Optimal package size: MC = 2 = 10 - 2Q = P => Q* = 4

• Optimal packageprice is the entire value to consumer: both cost andconsumer surplus

P

QD

10

8

6

4

2

1 2 3 4 5

MC = AC

Consumer’s valuation .5(8)(4) + (2)(4) = $24 = P

Profit = $16

Costs = $8

Markup Pricing• Percentage of cost (usually experience

based) is added to cost (e.g. $50) to obtain the selling price (e.g. $80):

• Markup is (80-50) / 50 = 60%

• Firm with many products to sell may need a simple pricing strategy.

• Way of dealing with uncertain demand.

A Simple Markup Rule• If the firm’s elasticity of demand is EF, then: MR=P[1+EF]/EF

• Set MR = MC and simplify => P=[EF/(1+EF)]MC=mMC

• This relationship holds only for elastic demand |EF|>1.

• The optimal ( maximizing) P is a m over the relevant costs!

• More elastic the demand, lower the m.

• The higher the relevant cost the higher the P.

• Example: Firms A and B have EA=-2 and EB=-3:

[-2/(1-2)]MC=2MC [-3/(1-3)]MC=1.5MC

PA (PB) is twice (one and half times) MC or 100% (50%) m.

Markup Rule for Cournot Oligopoly

• Homogeneous product Cournot oligopoly• N = total number of firms in the industry

• Market elasticity of demand EM

• Elasticity of individual firm’s demand is given by EF = N EM

• P = [EF/(1+ EF)] MC = [NEM/(1+ NEM)] MC

• The greater the number of firms, the lower the profit-maximizing markup factor

Third Degree Price Discrimination

• Separate market into segments with different demands and charge each groups of consumers different prices for the same product

• Examples include student & senior citizens discounts, airline tickets, regional & international pricing

• Set MR of each group equal to MC of total output.• For price discrimination to work:

• Different groups of customers must have different price elasticity of demand• Firms have to be able to identify customers from different groups• Customers from different groups cannot resell products across groups

TR Maximization With Price Discrimination

Firm produces for domestic QD = 1400 - 10PD & foreign market QF = 2400 - 20PF using TC = 18200 – 30QT (where QT=QD+QF). To max T set MR in each market equal to MC of total output

Japanese market Foreign market

QD = 1400 - 10PD QF = 2400 - 20PF

PD = 140 - 0.1QD PF = 120 - 0.05QF

MRD = 140-.2QD = 30 = MC MRF = 120-.1QF = 30 = MC

QD = 550 & PD = $85 QF = 900 & PF = $75 EP = -10(85/550) = -1.545 EP = -20(75/900) = -1.667

TR = 85x550 + 75x900 = $114,250 (/1450=$78.793=avg. P)

TR Maximization With No Price Discrimination

P is inverse Total Demand not sum of individual Inverse DemandsQT = QD + QF = 1400 - 10PD + 2400 - 20PF = 3800 - 30P

P = 126.67 - 0.0333QT

MRT = 126.67 - 0.0667QT = 30 = MCT

QT = 1450, P = $78.33 and EP = -30(78.33/1450) = -1.62

QD = 1400 - 10PD = 1400 - 10(78.33) = 616.7 = 617

QF = 2400 - 20PF = 2400 - 20(78.33) = 833.4 = 833TR = 78.33x1450 = $113,578.50

TR (& T) is $671.50 lower without discrimination.

Type of Customer

Prints

Photodisk

Max P for Separate Sale Bundle P

Type P

$7.50

$4.00 $4.00 $11.50

Type D

$5.50

$8.00 $5.50 $13.50

Max Sale P of Package

$9.50 $11.50

Commodity Bundling• Bundle products together & charge single price for package• Objectives:

• Discrimination: Increase sales & profits (inversely varying demands)• Leverage: use monopoly power from one market in another (Microsoft vs.

Netscape)

• Examples: Vacation packages

Computers and software

Film and developing

Peak-Load Pricing

• When demand during peak times is higher than the capacity of the firm, the firm engages in peak-load pricing.

• Charge a higher price (PH) during peak times (DH)

• Charge a lower price (PL) during off-peak times (DL) Quantity

PriceMC

MRL

PL

QL QH

DH

MRH

DL

PH

• A firm with high TFC relative to TVC produces a service that cannot be stored: phone services, hotels, theaters, airlines etc.

• Suppose demand shifts over the day or week or year

Cross-Subsidies

• Prices charged for one product are subsidized by the sale of another product

• May be profitable when there are significant demand complementarities effects

• Examples• Browser and server software• Drinks and meals at restaurants

Joint ProductProduct A and B are joint or by products (one cannot be produced without the other) with individual D and MR curves as shown.

Add only the positive portion of the MR curves to get the bent curve: MRJ = MRA + MRB

For marginal cost SMC, Qe of each product areproduced and sold at PA|Qe and PB|Qe

For marginal cost SMC’, Qe’ of both A and B are produced. Qe’ of A is sold at PA|Qe’. Only Q* of B is sold at PB|Qe*.

Transfer Product PricingFor econ of scale break huge firm into divisions.

W/o external competitive market for transfers, to max firm’s finalist acts as monopolist (firm’s MRE is finalist MRF firm’s MCE is

sum of transferee MCT & finalist’s MCF):

MRE = MRF = MCF + MCT = MCE,

& transferee as price taker (finalist net MR represents demand for transfer products):

NMRF = MRF – MCF = DT = PT = MCT.

Or subtract MCF from firm max MRF=MCE:

NMRF=MRF-MCF=PT=MCT=MCE-MCF=NMCF

Single FirmFactory makes blades & then assembles fanes for MC = 30 + 7Q

Fane Demand: QF = 60 - 0.4PF

=> PF = 150 - 2.5QF

MRF = 150 - 5QF = 30 + 7Q = MC

=> Q* = 10 & P* = 125

Profit contribution

= (P*-MC)Q*+[(MCQ*-MCQ=0)Q*]/2

= (125-100)10 + [(100-30)10]/2

= 250 + 350 = 600

QF*=10 30 60

150

MRFDF=PF

PF*=125

100

30

MC=MCF+MCT

Correct PT W/o External Market

QF*= QT*=10 30 60

150

MRFDF=PF

PF*=125

30

130

14.4

PT*=40

NMRF=MRF-MCF=PT=MRT

NMCF=MC-MCF=MCT

MC=MCF+MCT

10

Firm is broken into final (fan) & transfer (blade) division. One set of blades per fan, so QF = QT. (MCF = 20 + 4QF & MCT = 10 + 3QT).

To max firm’s transfer acts as P taker:

PT = NMRF = MRF - MCF = 150-5QF - (20+4QF) = 130 - 9QF = 10 + 3QT = MCT

=> QT* = 10 & $40 = PT

* = MCT

Profit contribution of finalist & transferee

= (PF*-PT

*-MCF*)Q*+[(MCF

*-MCQ=0)Q*]/2

+ (PT*-MCT

*)Q* +[(MCT*-MCQ=0)Q*]/2

= {(125-40-60)10 + [(60-20)10]/2}

+ {(40-40)10 + [(40-10)10]/2}

= {250+200} + {0+150} = 600

QT* (=QF

*) consistent with max firm’s

Incorrect PT W/o External Market

QF’=QT’=5.71 30 60

150

MRFDF=PF

PF’=135.73

30

130

14.4

PT’=78.61

NMRF=MRF-MCF=PT

NMCF=MC-MCF=MCT

MC=MCF+MCT

107.2

MRT

Transferee disregarding firm’s acts as monopoly & max its where MRT (corresponding to DT = PT = NMRF = 130 - 9QF) = MCT:

MRT = 130 - 18QT = 10 + 3QT = MCT

One set of blades per fan: QT’=QF’ = 5.71

PF’ = 150 - 2.5(5.71) = $135.73PT’ = NMRF = 130 - 9(5.71) = $78.61

Profit contribution of finalist & transferee

= (PF’-PT’-MCF’)Q’+[(MCF’-MCQ=0)Q’]/2

+ (PT’-MCT’)Q’ +[(MCT’-MCQ=0)Q’]/2

= {81.54+65.21}+{293.95+48.91} = 489.61

For double marginalization (both mark up:

PT’>PT* & PF’>PF

* => QT’=QF’ < QT*=QF

*)

profit contribution lower than when QT*=QF

*

Transfer Pricing W/ External MarketWith external competitive market finalist pays no more & transferee charges no less than market P (appropriate transfer P).

For firm’s max finalist acts as monopolist: NMRF = PM (appropriate MCT for finalist)

& transferee as price taker: PM = PT = MCT = NMCF.

If transferee is less (more) efficient than market PT

*>PM (PT*<PM) finalist buys (sells)

additional quantities of market transfers.

If transferee is not efficient as market (PT

* = PM) QF and QT are not equal.

30 60

150

MRFDF=PF

PF=120

30

130

NMRF=MRF-MCF=PT=MRT

NMCF=MC-MCF=MCT

MC=MCF+MCT

10

QT=4 QF=12

22=PM=PT=MRT

QF*= QT*=10

PF*=125

PT*=40

Transfer Pricing With External PM = 22Finalist acts as monopolist: NMRF = 130 - 9QF = 22 = PM = MCT

=> QF = 12 & PF = 150 - 2.5(12) = 120

Transferee acts as price taker:

NMCF = MCT = 10 + 3QT = 22 = PM = PT

=> QT = 4

Because transferee is less efficient than market(PT

* > PM) firm produces 4 & buys 8 blades

Profit contribution of finalist & transferee

= (PF-PT-MCF)QF +[(MCF-MCQ=0)QF]/2

+ (PT-MCT)QT

+[(MCT-MCQ=0)QT]/2

= {360 + 288} + {0 + 24} = 672

30 60

150

MRFDF=PF

PF=127.5

30

NMRF=MRF-MCF=PT=MRT

NMCF=MC-MCF=MCT

MC=MCF+MCT

10

49=PM=PT=MRT

QF*= QT*=10

PF*=125

PT*=40

Transfer Pricing With External PM = 49

QF=9 QT=13

Finalist: NMRF = 130 - 9QF = 49 = PM = MCT

=> QF = 9 & PF = 150 - 2.5(9) = 127.5

Transferee acts as price taker:

NMCF = MCT = 10 + 3QT = 49 = PM = PT

=> QT = 13

Because transferee is more efficient than market(PT

* < PM) firm produces 13 & sells 4 blades

Profit contribution of finalist & transferee

= (PF-PT-MCF)QF + [(MCF-MCQ=0)QF]/2

+ (PT-MCT)QF + [(MCT|QF-MCT|Q=0)QF]/2

+ (QT-QF)PT

= {202.5+162}+{108+121.5+196} = 790

Pricing in Markets with Intense Price Competition

Prevent customers to become informed about prices through:• Price Matching

• Advertising a price and a promise to match any lower price offered by a competitor.

• No firm has an incentive to lower their prices.• Each firm charges the monopoly price and shares the market.

• Randomized Pricing• A strategy of constantly changing prices.• Decreases consumers’ incentive to shop around as they cannot learn from

experience which firm charges the lowest price.• Reduces the ability of rival firms to undercut a firm’s prices.

• Build Brand Loyalty

Recap of Pricing Strategies

• First degree price discrimination, block pricing, and two part pricing permit a firm to extract all consumer surplus.

• Commodity bundling, second-degree and third degree price discrimination permit a firm to extract some (but not all) consumer surplus.

• Simple markup rules are the easiest to implement, but leave consumers with the most surplus and may result in double-marginalization.

• Different strategies require different information.