1. Pricing Strategies

2. Pricing and Profits
$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
Price 10 8
The entire consumer surplus could be captured with Price Discrimination (charging different P for different quantities or in different markets) 6 4 2 MC
P = Q
Quantity
MR = Q

3. 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 consumer purchase 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.
Zero cost example

4. 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)

5. Two-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 (sports clubs, utilities, etc.).
Quantity D 10 8 6 4 2 MC
Fixed Fee = Profits = $16
Price
Per Unit
Charge
1. Set price at marginal cost.
2. Compute consumer surplus and charge a fixed-fee equal to consumer surplus of buyer with the lowest demand.

6. 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 = Q and TC = 2Q
Optimal package size: MC = 2 = Q = P => Q* = 4
Optimal package price is the entire value to consumer: both cost and consumer surplus P Q D 10 8 6 4 2
MC = AC
Consumer’s valuation
.5(8)(4) + (2)(4) = $24 = P
Profit = $16
Costs = $8

7. 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.

8. 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=mMC
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=2MC [-3/(1-3)]MC=1.5MC
PA (PB) is twice (one and half times) MC or 100% (50%) m.

9. 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

10. 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

11. TR Maximization With Price Discrimination
Firm produces for domestic QD = PD & foreign market QF = PF using TC = – 30QT (where QT=QD+QF). To max T set MR in each market equal to MC of total output Japanese market Foreign market
QD = PD QF = PF
PD = QD PF = QF
MRD = QD = 30 = MC MRF = QF = 30 = MC
QD = 550 & PD = $ QF = 900 & PF = $75 EP = -10(85/550) = EP = -20(75/900) =
TR = 85x x900 = $114,250 (/1450=$78.793=avg. P)

12. TR Maximization With No Price Discrimination
P is inverse Total Demand not sum of individual Inverse Demands QT = QD + QF = PD PF = P
P = QT
MRT = QT = 30 = MCT
QT = 1450, P = $ and EP = -30(78.33/1450) = -1.62
QD = PD = (78.33) = = 617
QF = PF = (78.33) = = 833
TR = 78.33x1450 = $113, TR (& T) is $ lower without discrimination.

13. 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

14. Peak-Load Pricing
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
Quantity
Price MC
MRL PL QL QH DH
MRH DL PH
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)

15. 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

16. Joint Product
Product 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 are produced 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*.

17. Transfer Product Pricing
For 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

18. Single Firm
Factory makes blades & then assembles fanes for MC = Q
Fane Demand: QF = PF
=> PF = QF
MRF = QF = Q = MC
=> Q* = 10 & P* = 125
Profit contribution
= (P*-MC)Q*+[(MCQ*-MCQ=0)Q*]/2
= ( )10 + [(100-30)10]/2
= = 600
150
MC=MCF+MCT
PF*=125
100 30
MRF
DF=PF
QF*=10 30 60

19. Correct PT W/o External Market
Firm is broken into final (fan) & transfer (blade) division. One set of blades per fan, so QF = QT. (MCF = QF & MCT = QT).
To max firm’s  transfer acts as P taker:
PT = NMRF = MRF - MCF = 150-5QF - (20+4QF) = QF = QT = 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
= {( )10 + [(60-20)10]/2} + {(40-40)10 + [(40-10)10]/2}
= { } + {0+150} = 600 QT* (=QF*) consistent with max firm’s 
150
MC=MCF+MCT
130
PF*=125
NMCF=MC-MCF=MCT
PT*=40 30 10
MRF
DF=PF
QF*= QT*=10
14.4 30 60
NMRF=MRF-MCF=PT=MRT

20. Incorrect PT W/o External Market
Transferee disregarding firm’s  acts as monopoly & max its  where MRT (corresponding to DT = PT = NMRF = QF) = MCT: MRT = QT = QT = MCT One set of blades per fan: QT’=QF’ = PF’ = (5.71) = $ PT’ = NMRF = (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
= { }+{ } = For double marginalization (both mark up: PT’>PT* & PF’>PF* => QT’=QF’ < QT*=QF*) profit contribution lower than when QT*=QF*
150
MC=MCF+MCT
PF’=135.73
130
NMCF=MC-MCF=MCT
PT’=78.61 30 10
MRF
DF=PF
7.2
QF’=QT’=5.71
14.4 30 60
MRT
NMRF=MRF-MCF=PT

21. Transfer Pricing W/ External Market
With 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.

22. Transfer Pricing With External PM = 22
Finalist acts as monopolist: NMRF = QF = 22 = PM = MCT
=> QF = 12 & PF = (12) = 120
Transferee acts as price taker:
NMCF = MCT = QT = 22 = PM = PT
=> QT = 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
= { } + {0 + 24} = 672
150
MC=MCF+MCT
QF*= QT*=10
PF*=125
PT*=40
130
PF=120
NMCF=MC-MCF=MCT 30
22=PM=PT=MRT 10
MRF
DF=PF
QT= QF=12 30 60
NMRF=MRF-MCF=PT=MRT

23. Transfer Pricing With External PM = 49
Finalist: NMRF = QF = 49 = PM = MCT
=> QF = 9 & PF = (9) = 127.5
Transferee acts as price taker:
NMCF = MCT = QT = 49 = PM = PT
=> QT = 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
= { }+{ } = 790
150
MC=MCF+MCT
QF*= QT*=10
PF*=125
PT*=40
PF=127.5
NMCF=MC-MCF=MCT
49=PM=PT=MRT 30 10
MRF
DF=PF
QF=9 QT=13 30 60
NMRF=MRF-MCF=PT=MRT

24. 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

25. 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.