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ECON 115
Industrial Organization
Industrial Organization
1. Review the Quiz
2. Reprise 3rd Degree Price
Discrimination
3. A problem and its implications
4. Introduction to non-linear (1st &
2nd Degree) Price Discrimination
Industrial Organization
First Hour
• Review of the quiz.
• Review third-degree
price discrimination
– MR = MR = MC
• 3rd Degree Price
Discrimination Problem
• Analyzing the Problem
Second Hour
• First-Degree Price
Discrimination.
• Two-tiered pricing
• Bundling
• Introduction to Second-
Degree Price
Discrimination.
Industrial Organization
• Two issues confront a firm wishing to price discriminate:
1. Identification: can the firm identify demands of
different types of consumer or in separate markets
• easier in some markets than others: e.g tax
consultants, doctors
2. Arbitrage: can the firm prevent consumers charged a
low price from reselling to consumers charged a high
price
• prevent re-importation of prescription drugs to the
United States
Industrial Organization
• 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
Industrial Organization
• There are three types of price discrimination:
Type Name Example
First Degree Personalized
Pricing
Maximum price charged to each
consumer
Second Degree Menu Pricing Quantity discounts
Third Degree Group Pricing Group discounts (“early bird special”
“senior discount” )
Industrial Organization
• Third-degree price discrimination: Group pricing.
• Consumers differ by some observable
characteristic(s). A uniform price is charged to
everyone in the group. This is “linear pricing.”
• Different uniform prices are charged to different
groups:
– “children under 12 are free”
– “senior discounts”
– high variety of airline ticket prices
– early-bird specials 7
Industrial Organization• RULE 1: If demands are linear –
– price discrimination results in the same aggregate output as
no price discrimination
– price discrimination increases profit because allocated more
profitably across two markets
• RULE 2 (Elasticity of Demand):
– consumers with low elasticity of demand are charged a high
price.
– consumers with high elasticity of demand are charged a low
price.
• RULE 3 (Marginal Revenue):
– marginal revenue must be equalized in each market.
– marginal revenue must equal aggregate marginal cost.8
Industrial Organization
• Exploring 3rd Degree Price
Discrimination Further:
disaggregating the demand
function.
9
Industrial Organization• From last week’s in-class problem:
– Aggregate Demand: P = 12 – Q/20
– Marginal Revenue: MR = 12 – Q/10
– MAX Profit (MR = MC): 3 = 12 – Q/10
– Q = 90 and P = $7.50
• Plugging these values back into the Daytime and
Evening demand curves:
– Daytime: P = 10 – Q/10; Q = 25
– Evening: P = 14 – Q/10; Q = 65
10
Industrial Organization
• Suppose that there are two markets with the same MC.
• MR in market i is given by MRi = Pi(1 – 1/hi)
– where hi is (absolute value of) elasticity of demand
• From Rule 3 (above)
– MR1 = MR2
– so P1(1 – 1/h1) = P2(1 – 1/h2)
– Therefore:
–𝑷𝟏
𝑷𝟐
= (𝟏−
𝟏
𝒉𝟐
)
(𝟏−𝟏
𝒉𝟏
)= 𝒉𝟏𝒉𝟐−𝒉
𝟏
𝒉𝟏𝒉𝟐−𝒉𝟐
11
Price is lower in
the market with
the higher
demand elasticity
Industrial Organization• Question 1: what are the elasticities of demand
of these two functions?
– Daytime: P = 10 – Q/10; Q = 25
– Evening: P = 14 – Q/10; Q = 65
• Therefore the we should be charging a higher
price for the evening customers.12
Industrial Organization• Question 2: what are the different MRs for
each demand function at P = $7.50?
– Daytime Demand: P = 10 – Q/10; Q = 25
– Daytime Marginal Revenue: MR = 10 – Q/5
– Plug in 25; MR = 5!!!!!
– Evening Demand: P = 14 – Q/19; Q = 65
– Evening Marginal Revenue: MR = 14 – Q/5
– Plug in 65; MR = 1!!!!!
• MRdaytime > MRevening
13
Industrial Organization
• Just like the situation between Europe and the
US in the bookselling example, here our
theater owner can improve on this outcome
by using more 3rd degree price discrimination.
• Note that MR ≠ MC in both markets:
– MR > MC for daytime customers
– MR < MC evening customers
– Therefore, the theater owner wants more
customers in the daytime than evening.
14
Industrial Organization
• The demand function for the daytime is P =
10 – Q/10.
• MRdaytime = 10 – Q/5 At MC = 3, Q = 35
and price = $6.50. Profits = $6.50 - $3.00
= $3.50/person x 35 persons = $122.50.
This superior result allowed us to grow our
overall profits from $405 to $425.
• Now let’s push this further . . .
15
Industrial Organization
• Suppose we could further disaggregate the
daytime demand function, P = 10 – Q/10.
• Let’s say there are two distinct groups of
customers who attend movies in the
afternoon: retired people and UC Merced
ECON students. Each group has a
different demand function:
• RETIRED: P = 12 – Q/5; MR = 12 – Q/2.5
• ECON: P = 8 – Q/5; MR = 8 – Q/2.516
Industrial Organization
• Both groups pay the $6.50 “price discrimination” charge.
Disaggregating the Daytime Demand function, we see
Qretired = 27.5 and QECON = 7.5. (27.5 + 7.5 = 35). But
the marginal revenue in each segment is now different:
• MRretired = $1 and MRECON = $5. Therefore, we should
further price discriminate with the goal of reducing the
retired customers and adding ECON customers.
• Equating the MRs to $3, we get Qretired = 22.5 and QECON
= 12.5. New prices are Pretired = $7.50 and PECON =
$5.50. New Profit = $132.50 > $122.50.
17
Industrial Organization
• Nonlinear Price Discrimination (1st
and 2nd Degree Price Discrimination)
18
Industrial Organization
• A nonlinear pricing strategy depends upon the information available to the seller. That determines whether to employ first-degree (personalized) or second-degree (menu) pricing.
• Under first-degree price discrimination, the
monopolist charges the maximum price that each
consumer is willing to pay.
– Extracts all consumer surplus
– Since profit equals the total surplus, first-degree price
discrimination is efficient. 19
Industrial Organization • Suppose you inherit five antique cars. Your research shows
there are 5 collectors each with different reservation prices.
• Revenue under standard monopoly pricing = $18,000
• Revenue under personalized pricing = $30,000
20
Each is willing to
pay:
Linear Pricing: Personalized
pricing
$10000 $6000 $10000
$8000 $6000 $8000
$6000 $6000 $6000
$4000 $6000 $4000
$2000 $6000 $2000
Industrial Organization
• First-degree price discrimination is very profitable,
• And it leads to the efficient choice of output,
since no value-creating exchanges are missed.
• However, it requires:
1. detailed customer information; and
2. the ability to avoid arbitrage.
• The information requirements appear insurmountable.– Solvable if personal information is available
(accounting services; university applicants) and prices can be set after the customer has agreed to the contract.
21
Industrial Organization
• Can a seller achieve a similar outcome if prices
must be announced in advance?
• Yes, with non-linear prices
• Two-part pricing is an example of common
non-linear pricing strategy.
– charge a quantity-independent fee
(membership?), plus a per unit usage charge
• Block pricing is a second example.
– bundle total charge and quantity in a package22
Industrial Organization
• Example of Two-part pricing.
• A jazz club serves two types of customer:
Old: demand for entry + Qo drinks is P = Vo – Qo
Young: demand for entry + Qy drinks is P = Vy – Qy
Cost of operating the jazz club C(Q) = F + cQ
Assumptions: Vo > Vy: Old will to pay more than Young
Demand and costs are all in daily units
Equal numbers of each type of customer.23
Industrial Organization
• Suppose that the jazz club owner applies “traditional”
linear pricing: free entry and a fixed price for drinks.
– Aggregate demand is Q = Qo + Qy = (Vo + Vy) – 2P
– Set the equation equal to price: P = (Vo + Vy)/2 – Q/2
– MR therefore is MR = (Vo + Vy)/2 – Q
– Maximize profits be equating MR and MC, where
MC = c and solve for Q:
QU = (Vo + Vy)/2 – c
– Substitute into aggregate demand to give the
equilibrium price:
PU = (Vo + Vy)/4 + c/2 24
Industrial Organization
• Under this linear pricing scheme:
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
25
Industrial Organization
26
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+ c
2h i
jk
a
bd
e
fg
Linear pricing leaves each type of consumer retaining the
consumer surplus.
Industrial Organization
• Jazz club owner can improve on this. Remember the 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
• He can charge an entry fee (just less than):
– Eo = CSo to each Old customer and Ey = CSy
to each Young customer;• The club checks IDs to implement this policy.
– Each type will still be willing to frequent the club and buy the equilibrium number of drinks.
• This increases profit by Eo for each Old and Ey for each Young customer.
27
Industrial Organization
• The jazz club can do better still! The club can
1. Reduce the price per drink; this increases
consumer surplus;
2. Then extract the additional consumer
surplus can through a higher entry fee.
• Let’s consider the best the jazz club owner
can do with respect to each type of consumer.
28
Industrial Organization
29
$/unit
Quantity
Vi
Vi
MR
MCc
Set the unit price equal
to marginal cost
This gives consumer
surplus of (Vi - c)2/2
The entry charge
converts consumer
surplus into profit
Vi - c
Set the entry charge
to (Vi - c)2/2
Profit from each pair of Old and Young now d =
[(Vo – c)2 + (Vy – c)2]/2
Industrial Organization
30
$/unit
Quantity
Vi
Vi
MR
MCc
Set the unit price equal
to marginal cost
This gives consumer
surplus of (Vi - c)2/2
The entry charge
converts consumer
surplus into profit
Vi - c
Set the entry charge
to (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 the
monopolist’s
profit
Industrial Organization
• There’s another pricing method the club owner
can use called Block Pricing: offer a package
“Entry plus X number of drinks for $Y.”
• Maximize profit by following these two rules:
1. Offer each consumer type an amount equal to
how much that type would buy if price equaled
marginal cost.
2. Set the total charge for each type equal to the
total willingness to pay for the that quantity.
31
Industrial Organization
32
Old$
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
Industrial Organization
• How to implement this block pricing
policy? Here are the simple rules:
1. Card everyone at the door.
2. Give customers the requisite number of
tokens that are exchanged for drinks.
33
Industrial Organization
• What if the seller cannot distinguish between buyers?
• For example, perhaps they don’t differ by age by rather by income, which is unobservable.
• Then the type of price discrimination just discussed is impossible. A high-income buyer will pretend to be a low-income buyer to avoid the high entry price and to pay the smaller total charge
34
Industrial Organization• Take a specific example:
– Ph = 16 – Qh
– Pl = 12 – Ql
– MC = 4
• To capture the consumer surplus using 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.
35
Industrial Organization
• This will not work.
– High-Income types get no consumer surplus from the package designed for them, but get consumer surplus from the low-income package.
– Therefore, they will pretend to be low-income even if this limits the number of drinks they can buy.
• To address this problem, the seller designs a “menu” of offerings targeted at the two types.
36
Industrial Organization
• This alternative offer must be what economists
call “incentive compatible.”
Any offer made to high-demand consumers
must provide as much consumer surplus as
they would get from an offer designed for low-
demand consumers.
37
Industrial Organization• In designing this pricing scheme, the seller
endeavors to make buyers:
1. Reveal their true types;
2. Self-select the quantity/price package
designed for them.
• This is the essence of second-degree price
discrimination.
• Without the ability to identify different types
of buyers, a two-part tariff is ineffective
because it allows deception by buyers.
• The best option is quantity discounting. 38
Industrial Organization
39
High-income Low-Income
$
Quantity Quantity
16
16
12
12
4 MC 4 MC
12 88
$32
8
$16$32
$
Offer the low-income
consumers a package of
entry plus 8 drinks for $64
$32
$32
The low-demand consumers will be
willing to buy this ($64, 8) package
So will the high-
income consumers:
because the ($64, 8)
package gives them $32
consumer surplus
$64
$32
$8$24
$8
$40 $32
Industrial Organization
40
High-income Low-Income
$
Quantity Quantity
16
16
12
12
4 MC 4 MC
12 88
$32
8
$16$32
$
$32
$32
$64
$32
$8
So any other package
offered to high-income
consumers must offer at
least $32 consumer surplus
This is the incentive
compatibility constraint
$24
$8
$40 $32
Industrial Organization
41
High-income Low-Income
$
Quantity Quantity
16
16
12
12
4 MC 4 MC
12 88
$32
8
$16$32
$
$32
$32
$64
$32
$8
High income consumers are
willing to pay up to $120 for
entry plus 12 drinks if no other
package is available
So they can be offered a package
of ($88, 12) (since $120 - 32 = 88)
and they will buy this
$24
Low income
consumers will not
buy the ($88, 12)
package since they
are willing to pay
only $72 for 12
drinks
$8
$40
And profit from
each low-income
consumer is
$32 ($64 - 8x$4)$32
Profit from each
high-income
consumer is
$40
($88 - 12 x $4)
Industrial Organization
42
High-income Low-Income
$
Quantity Quantity
16
16
12
12
4 MC 4 MC
12 88
$32
8
$16$32
$
$32
$32
$64
$32
$8$24
$8
$40 $32
These packages exhibit
quantity discounting: high-
income pay $7.33 per unit and
low-income pay $8
Industrial Organization
43
High-Income
Low-Income$
Quantity Quantity
16
16
12
12
4 MC 4 MC
12
$
Can the club-
owner do even
better than this?
8
Yes! Reduce the number
of units offered to each
low-income consumer
7
$59.50$31.50
7
$87.50
$28$28
$92
$28
$44
$48
Industrial Organization
44
High-Income
Low-Income$
Quantity Quantity
16
16
12
12
4 MC 4 MC
12
$
8
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
$48
Industrial Organization
45
High-Income
Low-Income$
Quantity Quantity
16
16
12
12
4 MC 4 MC
12
$
Can the club-
owner do even
better than this?
8
Yes! Reduce the number
of units offered to each
low-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 by
reducing the number of units
offered to low-income consumers
since this allows him to increase
the charge to high-income
consumers
Industrial Organization
• Reducing the number of units to each low-income
consumer begs the question: does the monopolist
always want to supply both types of consumer?
• There are cases where it is better to supply only
high-income types:
– high-end restaurants
– golf and country clubs
• To return to our example, suppose there are Nl
low-income and Nh high-income consumers.46
Industrial Organization
• 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
47
This requires thatNh
Nl
<31.50
28= 1.125
There should not be “too high” a fraction of high-demand
consumers. If the fraction is
Industrial Organization
• Summarizing second-degree price discrimination:
1. Extract all consumer surplus from the lowest-demand group.
2. Leave some consumer surplus for other groups . . .
• to satisfy the incentive compatibility constraint
3. Offer less than the socially efficient quantity to all groups other than the highest-demand group.
4. 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.
48
Industrial Organization
• Next Week:
• A reprise of 2nd Degree Price Discrimination
• A 2nd Degree Problem
• The welfare implications of price
discrimination
• A bonus lecture on Standard Oil
49