ECON-115 Lecture 05 - Kids in Prison Program · Disaggregating the Daytime Demand function, we see...

ECON 115

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


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.


• 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


• 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


• 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” )


• 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


• 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


• 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


• 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


• 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


• 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


• 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


• Nonlinear Price Discrimination (1st

and 2nd Degree Price Discrimination)

18


• 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


• 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


• 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


• 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


• 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


• 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


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.


• 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


• 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


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


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


• 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


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


• 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


• 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


• 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


• 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


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


40


$

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


41


$

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)


42


$

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


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


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


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


• 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


• 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


• 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


• 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

ECON-115 Lecture 05 - Kids in Prison Program · Disaggregating the Daytime Demand function, we see...

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