Transcript Pricing Strategies

Pricing Strategies
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
MC
2
P = 10 - 2Q
1
2
3
4
5
MR = 10 - 4Q
Quantity
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
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
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.).
Price
8
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
Fixed Fee = Profits = $16
10
Per Unit
Charge
4
MC
2
D
1
2
3
4
5
Quantity
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 package
price is the entire
value to consumer:
both cost and
consumer surplus
P
Consumer’s valuation
.5(8)(4) + (2)(4) = $24 = P
10
8
Profit = $16
6
4
Costs = $8
2
MC = AC
1
2
3
4
D
5 Q
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=mMC
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•
•
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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.
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
QD = 1400 - 10PD
PD = 140 - 0.1QD
MRD = 140-.2QD = 30 = MC
QD = 550 & PD = $85
EP = -10(85/550) = -1.545
Foreign market
QF = 2400 - 20PF
PF = 120 - 0.05QF
MRF = 120-.1QF = 30 = MC
QF = 900 & PF = $75
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 Demands
QT = 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 = 833
TR = 78.33x1450 = $113,578.50
TR (& T) is $671.50 lower without discrimination.
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
Type of Customer
Prints
Photodisk
Max P for
Separate Sale Bundle P
Type P
$7.50
$4.00
$4.00
$11.50
Type D
Max Sale P
of Package
$5.50
$8.00
$5.50
$13.50
$9.50
$11.50
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
• 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)
Price
MC
PH
DH
PL
MRH
MRL
QL
DL
QH Quantity
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 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*.
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
Single Firm
Factory makes blades & then assembles fanes for MC = 30 + 7Q
150
Fane Demand: QF = 60 - 0.4PF
=> PF = 150 - 2.5QF
MRF = 150 - 5QF = 30 + 7Q = MC
=> Q* = 10 & P* = 125
MC=MCF+MCT
PF*=125
100
Profit contribution
= (P*-MC)Q*+[(MCQ*-MCQ=0)Q*]/2
= (125-100)10 + [(100-30)10]/2
30
= 250 + 350 = 600
MRF
QF*=10
30
DF=PF
60
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 = 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 
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
Incorrect PT W/o External Market
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
150
MC=MCF+MCT
PF’=135.73
130
PF’ = 150 - 2.5(5.71)
= $135.73
PT’ = 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*
NMCF=MC-MCF=MCT
PT’=78.61
30
10
7.2
MRF
DF=PF
QF’=QT’=5.71
14.4 30
60
MRT NMR =MR -MC =P
F
F
F
T
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.
Transfer Pricing With External PM = 22
Finalist 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
150
MC=MCF+MCT
QF*= QT*=10
PF*=125
PT*=40
130
PF=120
NMCF=MC-MCF=MCT
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
22=PM=PT=MRT
10
MRF
DF=PF
QT=4
30
60
QF=12 NMR =MR -MC =P =MR
F
F
F
T
T
Transfer Pricing With External PM = 49
Finalist: NMRF = 130 - 9QF = 49 = PM = MCT
=> QF = 9 & PF = 150 - 2.5(9) = 127.5
150
MC=MCF+MCT
QF*= QT*=10
PF*=125
Transferee acts as price taker:
NMCF = MCT = 10 + 3QT = 49 = PM = PT
=> QT = 13
PT*=40
PF=127.5
NMCF=MC-MCF=MCT
Because transferee is more efficient than market
(PT* < PM) firm produces 13 & sells 4 blades
49=PM=PT=MRT
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
30
10
MRF
QF=9
QT=13
DF=PF
30
60
NMRF=MRF-MCF=PT=MRT
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.