1 price discrimination. 2 introduction price discrimination describes strategies used by firms to...
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1
Price Discrimination
2
Introduction
• Price Discrimination describes strategies used by firms to extract surplus from customers
3
Mechanisms for Capturing Surplus
• Market segmentation• Non-linear pricing
– Two-part pricing
– Block pricing
• Tying and bundling• Quality discrimination
4
Feasibility of price discrimination
• Market power
• Two problems confront a firm wishing to price discriminate– identification: the firm is able to identify demands of different
types of consumer or in separate markets– arbitrage: prevent consumers who are charged a low price from
reselling to consumers who are charged a high price
• The firm then must choose the type of price discrimination– first-degree or personalized pricing– second-degree or menu pricing– third-degree or group pricing
5
Third-degree price discrimination
• Consumers differ by some observable characteristic(s)• A uniform price is charged to all consumers in a
particular group – linear price• Different uniform prices are charged to different groups
– “kids are free”– subscriptions to professional journals e.g. American Economic
Review– Airlines– early-bird specials
6
Third-degree price discrimination 2
• The pricing rule is very simple:– consumers with low elasticity of demand should be
charged a high price
– consumers with high elasticity of demand should be charged a low price
7
Third degree price discrimination: example
• Harry Potter volume sold in the United States and Europe
• Demand:– United States: PU = 36 – 4QU
– Europe: PE = 24 – 4QE
• Marginal cost constant in each market– MC = $4
8
The example: no price discrimination
• Suppose that the same price is charged in both markets
• Use the following procedure:– calculate aggregate demand in the two markets
– identify marginal revenue for that aggregate demand
– equate marginal revenue with marginal cost to identify the profit maximizing quantity
– identify the market clearing price from the aggregate demand
– calculate demands in the individual markets from the individual market demand curves and the equilibrium price
9
The example (cont.)
United States: PU = 36 – 4QU Invert this:
QU = 9 – P/4 for P < $36
Europe: PU = 24 – 4QE Invert
QE = 6 – P/4 for P < $24
Aggregate these demands
Q = QU + QE = 9 – P/4 for $36 ≥ P ≥ $24
At these prices only the US market is
active
Q = QU + QE = 15 – P/2 for P < $24
Now both markets are
active
10
The example (cont.)
Invert the direct demands
P = 36 – 4Q for Q < 3
P = 30 – 2Q for Q > 3
$/unit
Quantity15
36
30Marginal revenue is
MR = 36 – 8Q for Q < 3
MR = 30 – 4Q for Q < 3DemandMR
Set MR = MC MC
Q = 6.5
P = $17
6.5
17
Price from the demand curve
11
The example (cont.)
Substitute price into the individual market demand curves:
QU = 9 – P/4 = 9 – 17/4 = 4.75 million
QE = 6 – P/4 = 6 – 17/4 = 1.75 million
Aggregate profit = (17 – 4)x6.5 = $84.5 million
12
The example: price discrimination
• The firm can improve on this outcome• Check that MR is not equal to MC in both markets
– MR > MC in Europe– MR < MC in the US– the firms should transfer some books from the US to Europe
• This requires that different prices be charged in the two markets
• Procedure:– take each market separately– identify equilibrium quantity in each market by equating MR
and MC– identify the price in each market from market demand
13
The example: price discrimination 2
Demand in the US: PU = 36 – 4QU
$/unit
Quantity
Demand
Marginal revenue:
MR = 36 – 8QU
36
9
MR
MC = 4 MC4
Equate MR and MC
QU = 4Price from the demand curve PU = $20
4
20
14
The example: price discrimination 3
Demand in the Europe: PE = 24 – 4QU
$/unit
Quantity
Demand
Marginal revenue:
MR = 24 – 8QU
24
6
MR
MC = 4 MC4
Equate MR and MC
QE = 2.5Price from the demand curve PE = $14
2.5
14
15
The example: price discrimination 4
• Aggregate sales are 6.5 million books– the same as without price discrimination
• Aggregate profit is (20 – 4)x4 + (14 – 4)x2.5 = $89 million– $4.5 million greater than without price discrimination
16
No price discrimination: non-constant cost
• The example assumes constant marginal cost
• How is this affected if MC is non-constant?– Suppose MC is increasing
• No price discrimination procedure– Calculate aggregate demand
– Calculate the associated MR
– Equate MR with MC to give aggregate output
– Identify price from aggregate demand
– Identify market demands from individual demand curves
17
The example again
Applying this procedure assuming that MC = 0.75 + Q/2 gives:
0 5 100
10
20
30
40
DU
MRU
17
4.75
Price
(a) United States
Quantity
0 5 100
10
20
30
40
DE
MRE
1.75
17
Price
(b) Europe
Quantity
0 5 10 15 200
10
20
30
40
D
MR
MC
24
6.5
17
Price
(c) Aggregate
Quantity
18
Price discrimination: non-constant cost
• With price discrimination the procedure is– Identify marginal revenue in each market
– Aggregate these marginal revenues to give aggregate marginal revenue
– Equate this MR with MC to give aggregate output
– Identify equilibrium MR from the aggregate MR curve
– Equate this MR with MC in each market to give individual market quantities
– Identify equilibrium prices from individual market demands
19
The example again
Applying this procedure assuming that MC = 0.75 + Q/2 gives:
Price
(a) United States
Quantity
0 5 100
10
20
30
40
DU
MRU
4
Price
(b) Europe
Quantity
4
0 5 100
10
20
30
40
DE
MRE
1.75
14
Price
(c) Aggregate
Quantity
0 5 10 15 200
10
20
30
40
MR
MC
24
6.5
17
4
20
Some additional comments
• Suppose that demands are linear – price discrimination results in the same aggregate
output as no price discrimination
– price discrimination increases profit
• For any demand specifications two rules apply– marginal revenue must be equalized in each market
– marginal revenue must equal aggregate marginal cost
21
Third-degree price discrimination 2• Often arises when firms sell differentiated products
– hard-back versus paper back books– first-class versus economy airfare
• Price discrimination exists in these cases when:– “two varieties of a commodity are sold by the same seller to
two buyers at different net prices, the net price being the price paid by the buyer corrected for the cost associated with the product differentiation.” (Phlips)
• The seller needs an easily observable characteristic that signals willingness to pay
• The seller must be able to prevent arbitrage– e.g. require a Saturday night stay for a cheap flight
22
Other mechanisms for price discrimination
• Impose restrictions on use to control arbitrage– Saturday night stay
– no changes/alterations
– personal use only (academic journals)
– time of purchase (movies, restaurants)
• Damaged goods
• Discrimination by location
23
Discrimination by location
• Suppose demand in two distinct markets is identical – Pi = A = BQi
• But suppose that there are different marginal costs in supplying the two markets– cj = ci + t
• Profit maximizing rule:– equate MR with MC in each market as before Pi = (A + ci)/2; Pj = (A + ci + t)/2 Pj – Pi = t/2 cj – ci
– difference in prices is not the same as the difference in costs
24
Introduction to Nonlinear Pricing
• Annual subscriptions generally cost less in total than one-off purchases
• Buying in bulk usually offers a price discount– these are price discrimination reflecting quantity discounts– prices are nonlinear, with the unit price dependent upon the quantity
bought– allows pricing nearer to willingness to pay– so should be more profitable than third-degree price discrimination
• How to design such pricing schemes?– depends upon the information available to the seller about buyers– distinguish first-degree (personalized) and second-degree (menu)
pricing
25
First-degree price discrimination 2
• Monopolist can charge maximum price that each consumer is willing to pay
• Extracts all consumer surplus
• Since profit is now total surplus, find that first-degree price discrimination is efficient
26
First-degree price discrimination 3
• First-degree price discrimination is highly profitable but requires– detailed information
– ability to avoid arbitrage
• Leads to the efficient choice of output: since price equals marginal revenue and MR = MC– no value-creating exchanges are missed
27
First-degree price discrimination 4
• The information requirements appear to be insurmountable– but not in particular cases
• tax accountants, doctors, students applying to private universities
• But there are pricing schemes that will achieve the same outcome– non-linear prices
– two-part pricing as a particular example of non-linear prices• charge a quantity-independent fee (membership?) plus a per unit
usage charge
– block pricing is another• bundle total charge and quantity in a package
28
Two-part pricing
• Jazz club serves two types of customer– Old: demand for entry plus Qo drinks is P = Vo – Qo
– Young: demand for entry plus Qy drinks is P = Vy – Qy
– Equal numbers of each type– Assume that Vo > Vy: Old are willing to pay more
than Young– Cost of operating the jazz club C(Q) = F + cQ
• Demand and costs are all in daily units
29
Two-part pricing 2
• Suppose that the jazz club owner applies “traditional” linear pricing: free entry and a set price for drinks– aggregate demand is Q = Qo + Qy = (Vo + Vy) – 2P– invert to give: P = (Vo + Vy)/2 – Q/2– MR is then MR = (Vo + Vy)/2 – Q– equate MR and MC, where MC = c and solve for Q to give– QU = (Vo + Vy)/2 – c– substitute into aggregate demand to give the equilibrium price– PU = (Vo + Vy)/4 + c/2– each Old consumer buys Qo = (3Vo – Vy)/4 – c/2 drinks– each Young consumer buys Qy = (3Vy – Vo)/4 – c/2 drinks– profit from each pair of Old and Young is
U = (Vo + Vy – 2c)2 / 8
30
Two part pricing 3
This example can be illustrated as follows:
Price
Quantity
Vo
Vo
Price
Quantity
Vy
Vy
Price
Quantity
Vo
Vo + Vy
MC
MR
(a) Old Customers (b) Young Customers (c) Old/Young Pair of Customers
Vo+Vy
2- c
c
Vo+Vy
4 + c2h i
jk
a
bd
e
fg
Linear pricing leaves each type of consumer with consumer surplus
31
Two part pricing 4
• Jazz club owner can do better than this• Consumer surplus at the uniform linear price is:
– Old: CSo = (Vo – PU).Qo/2 = (Qo)2/2– Young: CSy = (Vy – PU).Qy/2 = (Qy)2/2
• So charge an entry fee (just less than):– Eo = CSo to each Old customer and Ey = CSy to each Young
customer• check IDs to implement this policy
– each type will still be willing to frequent the club and buy the equilibrium number of drinks
• So this increases profit by Eo for each Old and Ey for each Young customer
32
Two part pricing 5
• The jazz club can do even better– reduce the price per drink
– this increases consumer surplus
– but the additional consumer surplus can be extracted through a higher entry fee
• Consider the best that the jazz club owner can do with respect to each type of consumer
33
Two-Part Pricing
$/unit
Quantity
Vi
Vi
MR
MCc
Set the unit price equalto marginal cost
Set the unit price equalto marginal cost
This gives consumer surplus of (Vi - c)2/2
This gives consumer surplus of (Vi - c)2/2
The entry chargeconverts consumersurplus into profit
Vi - cSet the entry charge
to (Vi - c)2/2
Set the entry chargeto (Vi - c)2/2
Profit from each pair of Old and Young now d = [(Vo – c)2 + (Vy – c)2]/2
Using two-part
pricing increases themonopolist’s
profit
34
Block pricing
• There is another pricing method that the club owner can apply– offer a package of “Entry plus X drinks for $Y”
• To maximize profit apply two rules– set the quantity offered to each consumer type equal to the
amount that type would buy at price equal to marginal cost
– set the total charge for each consumer type to the total willingness to pay for the relevant quantity
• Return to the example:
35
Block pricing 2
Old$
Quantity
Vo
Vo
Young$
Quantity
Vy
Vy
MC MCc c
Quantity supplied to each Old customer
Quantity supplied to each Young
customer
Qo Qy
Willingness to pay of each
Old customer
Willingness to pay of each
Young customer
WTPo = (Vo – c)2/2 + (Vo – c)c = (Vo2 – c2)/2
WTPy = (Vy – c)2/2 + (Vy – c)c = (Vy2 – c2)/2
36
Block pricing 3
• How to implement this policy?
37
Second-degree price discrimination
• What if the seller cannot distinguish between buyers?– perhaps they differ in income (unobservable)
• Then the type of price discrimination just discussed is impossible
• High-income buyer will pretend to be a low-income buyer – to avoid the high entry price– to pay the smaller total charge
• Take a specific example– Ph = 16 – Qh
– Pl = 12 – Ql
– MC = 4
38
Second-degree price discrimination 2
• First-degree price discrimination requires:– High Income: entry fee $72 and $4 per drink or entry plus 12
drinks for a total charge of $120– Low Income: entry fee $32 and $4 per drink or entry plus 8
drinks for total charge of $64
• This will not work– high income types get no consumer surplus from the package
designed for them but get consumer surplus from the other package
– so they will pretend to be low income even if this limits the number of drinks they can buy
• Need to design a “menu” of offerings targeted at the two types
39
Second-degree price discrimination 3
• The seller has to compromise• Design a pricing scheme that makes buyers
– reveal their true types– self-select the quantity/price package designed for them
• Essence of second-degree price discrimination• It is “like” first-degree price discrimination
– the seller knows that there are buyers of different types– but the seller is not able to identify the different types
• A two-part tariff is ineffective• Use quantity discounting
40
Second degree price discrimination 4
High-income Low-Income
$
Quantity Quantity
16
16
12
12
4 MC 4 MC
12 88
$328
$16$32
$
Offer the low-incomeconsumers a package of
entry plus 8 drinks for $64
Offer the low-incomeconsumers a package of
entry plus 8 drinks for $64
$32
$32
The low-demand consumers will bewilling to buy this ($64, 8) package
The low-demand consumers will bewilling to buy this ($64, 8) package
So will the high-income consumers:because the ($64, 8)
package gives them $32consumer surplus
So will the high-income consumers:because the ($64, 8)
package gives them $32consumer surplus
$64
$32
$8
So any other packageoffered to high-income
consumers must offer atleast $32 consumer surplus
So any other packageoffered to high-income
consumers must offer atleast $32 consumer surplus
This is the incentivecompatibility constraint
High income consumers arewilling to pay up to $120 for
entry plus 12 drinks if no otherpackage is available
High income consumers arewilling to pay up to $120 for
entry plus 12 drinks if no otherpackage is available
So they can be offered a packageof ($88, 12) (since $120 - 32 = 88)
and they will buy this
So they can be offered a packageof ($88, 12) (since $120 - 32 = 88)
and they will buy this
$24
Low income consumers will notbuy the ($88, 12)
package since theyare willing to payonly $72 for 12
drinks
Low income consumers will notbuy the ($88, 12)
package since theyare willing to payonly $72 for 12
drinks
$8
Profit from each high-income consumer is$40 ($88 - 12 x $4)
Profit from each high-income consumer is$40 ($88 - 12 x $4)
$40
And profit fromeach low-income
consumer is$32 ($64 - 8x$4)
And profit fromeach low-income
consumer is$32 ($64 - 8x$4)
$32
These packages exhibitquantity discounting: high-
income pay $7.33 per unit andlow-income pay $8
41
Second degree price discrimination 5
High-Income
Low-Income$
Quantity Quantity
16
16
12
12
4 MC 4 MC
12
$Can the club-
owner do even better than this?
Can the club-owner do even
better than this?
8
Yes! Reduce the numberof units offered to eachlow-income consumer
Yes! Reduce the numberof units offered to eachlow-income consumer
Suppose each low-income consumer is offered 7 drinks
7
Each consumer will pay up to $59.50 for entry and 7 drinks
$59.50
Profit from each ($59.50, 7) package is $31.50: a reduction
of $0.50 per consumer
$31.50
A high-income consumer will pay up to $87.50 for entry and 7
drinks
7
$87.50
$28
So buying the ($59.50, 7) package gives him $28 consumer surplus
$28
So entry plus 12 drinks can be sold for $92 ($120 - 28 = $92)
$92
$28
Profit from each ($92, 12) package is $44: an increase of $4
per consumer
$44
$48
The monopolist does better byreducing the number of units
offered to low-income consumerssince this allows him to increase
the charge to high-incomeconsumers
42
Second-degree price discrimination 6
• Will the monopolist always want to supply both types of consumer?
• There are cases where it is better to supply only high-demand types– high-class restaurants
– golf and country clubs
• Take our example again– suppose that there are Nl low-income consumers
– and Nh high-income consumers
43
Second-degree price discrimination 7
• Suppose both types of consumer are served– two packages are offered ($57.50, 7) aimed at low-income and
($92, 12) aimed at high-income– profit is $31.50xNl + $44xNh
• Now suppose only high-income consumers are served– then a ($120, 12) package can be offered– profit is $72xNh
• Is it profitable to serve both types?– Only if $31.50xNl + $44xNh > $72xNh 31.50Nl > 28Nh
This requires that Nh
Nl
< 31.5028
= 1.125
There should not be “too high” a fraction of high-demand consumers
44
Second-degree price discrimination 8
• Characteristics of second-degree price discrimination– extract all consumer surplus from the lowest-demand group– leave some consumer surplus for other groups– offer less than the socially efficient quantity to all groups other
than the highest-demand group– offer quantity-discounting
• Second-degree price discrimination converts consumer surplus into profit less effectively than first-degree
• Some consumer surplus is left “on the table” in order to induce high-demand groups to buy large quantities
45
Tying
• Tying is a seller’s conditioning the purchase of one product on the purchase of another – Technological ties
• Printer cartridges
– Contractual ties• Car dealer and car parts
• Why tying?
46
Quality Discrimination
• Why is Quality Discrimination a form of Price Discrimination?– First / business class airfare vs economy class
• Reduction in quality of the lower-quality good to reduce the incentive of people with high willingness to pay to switch from the high-quality good when the firm increases its price– “Damaged goods”