price discrimination overheads

Price Discrimination

Overheads

Price discrimination is the selling of two varieties ofa product to two different buyers at different netprices, where the net price is the price paid by thebuyer, adjusted for any cost of product differentiation

Price discrimination occurs when a firm chargesdifferent prices to different customers for reasonsother than differences in production costs

Requirements for Price Discrimination

There must be a downwards slopingdemand curve for the firm's output

The firm must be able to raise pricewithout losing all its customers

The firm must be able to identify consumerswho are willing to pay more for the product

The firm must know who will pay the higher price

Auctions

Airlines

The firm must be able to prevent low-pricecustomers from reselling to high-price customers

Arbitrage is the purchase of products at alow price in order sell them at a high price

Ways to identify customerslong term relationships

age

sex

type of job

other commonly bought items

place of residence

insurance agent

jeweler

doctor

Prevention of Arbitrage

Customer specific products

haircuts

house plans

dental filling

gall bladder operation

Use of product predicated on specific characteristics

student discount card

senior citizen discount

air travel with weekend stay

summer use of condominium at ski resort

Product is hard to resell because of distanceor transactions costs

purchase of feeder cattle

purchase of corn silage

purchase of custom made shoes

First-degree (perfect) price discrimination

A firm practices first-degree or perfect price discrimination

Specifically, perfect price discrimination involves the sellercharging a different price for each unit of the goodin such a way that the price charged for each unit is equalto the maximum willingness to pay for that unit

if it is able to charge the maximum priceeach consumer is willing to pay for each unit sold

Example of Grandpa Jones

5 Spoker D tractors

Marginal value of zero to Grandpa Jones

2 identical interested buyers

Tractors Price

First $16,000Second $12,000

Third $8,000

Fourth $6,000Fifth $4,000

Value (demand) schedule for each buyer

$

Tractors2 4 6 8 101 3 5 7 9

2468

10121416

Price and Demand

Price (Demand) Total Revenue

> $16,000 0 0

$12,000 3 36,000$16,000 2 32,000

$12,000 4 48,000$8,000 5 40,000

$8,000 6 48,000$6,000 7 42,000$6,000 8 48,000

$4,000 9 36,000

$16,000 1 16,000

Uniform pricing

$4,000 10 40,000

To sell all 5 tractors the uniform price must be

$8,000

Total revenue = $40,000

Can Grandpa Jones do better?

How about $12,000 a piece for 4 tractors?

Total revenue = $48,000

Grandpa Jones ends up with a tractorof no value to him

An individual willing to pay $8,000 for a tractor is shut out of the market

But revenue is higher than when sellingall 5 at a uniform price of $8,000

First Degree Price Discrimination

Charge the maximum priceeach consumer is willing to payfor each unit sold

Sell the first tractor for $16,000

First Degree Price Discrimination

Sell the second tractor for $16,000

Sell the third tractor for $12,000

Sell the fourth tractor for $12,000

Sell the fifth tractor for $8,000

Total Revenue = $64,000

How does Grandpa Jones do it?

Offer a bundle of two tractors for $28,000

Each consumer will buy one bundle

Total revenue is $56,000

$48,000 < $56,000 < $64,000

Offer a bundle of two tractors for $28,000

Even better

With an option to bid on a third

Each consumer will buy one bundle

The auction for the remaining tractor will yield $8,000

Total revenue = $64,000

Or an option to buy a third for $8,000

Either one guy buys or the other guy buys and Grandpa Jones is left with two tractors

Offer a three unit bundle for $36,000

Offer a two unit bundle for $28,000

Either one guy buys or the other guy buys and Grandpa Jones is left with no tractors

Total profit = $64,000

Another way

Offer a bundle of five tractors for $46,000

Why not offer all five units

One buyer will purchase all five of them

All the tractors are gone and Grandpa Jones’s profits are only $46,000

But first buyer can then sell two tractors for $28,000 to the other buyer

First buyer has profits of $18,000

Total profits are $64,000

But poor Grandpa only gets $46,000 of them

A simple example of discriminating monopolist

p = 20 - 2Q

Q = 10 - 1/2p

Cost = MC = $4.00

Uniform pricing first

TR MR MC ProfitQ Price UNF UNF Cost Exact

1 18 18 18 4 4 14.002 16 32 14 8 4 24.003 14 42 10 12 4 30.004 12 48 6 16 4 32.005 10 50 2 20 4 30.006 8 48 -2 24 4 24.007 6 42 -6 28 4 14.008 4 32 -1 32 4 0.009 2 18 -1 36 4 -18.0010 0 0 -1 40 4 -40.00

0 20 0 --- 0 4 0.00

Revenue

Profit Max for Uniform Price Monopolist

0

2

4

6

8

10

12

14

16

18

20

22

0 1 2 3 4 5 6 7 8 9 10 11 12

Output

$

Price

MR

MC

PU

QU

Cost

Profit

ResultsUniform Price Monopolist

Q = 4

TR = 48

TC = 16

Profit = 32

Now consider a price discriminating monopolist

Each unit receives a different price

MC TR MR ProfitQ Price Cost Exact DSC DSC DSC0 20 0 4 0.00 01 18 4 4 18.00 18 14.002 16 8 4 34.00 16 26.003 14 12 4 48.00 14 36.004 12 16 4 60.00 12 44.005 10 20 4 70.00 10 50.006 8 24 4 78.00 8 54.007 6 28 4 84.00 6 56.008 4 32 4 88.00 4 56.00

9 2 36 4 90.00 2 54.0010 0 40 4 90.00 0 50.00

Profit Max for Discriminating Monopolist

0

2

4

6

8

10

12

14

16

18

20

22

0 1 2 3 4 5 6 7 8 9 10 11 12

Output

$

Price

MR

PU

QU

MC

Profit Max for Discriminating Monopolist

0

2

4

6

8

10

12

14

16

18

20

22

0 1 2 3 4 5 6 7 8 9 10 11 12

Output

$

Price

PU

QU

MC

Q = 8

TR = 88

TC = 32

Profit = 56

DiscriminatingMonopolist

Uniform PriceMonopolist

Q = 4

TR = 48

TC = 16

Profit = 32

Results

Monopoly and Competition

The perfectly discriminating monopolistwill produce the same amount as acompetitive industry with the same cost structure

Consumers much prefer competition

They pay much less for the same quantity

Competitive Equilibrium

0

2

4

6

8

10

12

14

16

18

20

22

0 1 2 3 4 5 6 7 8 9 10 11 12

Output

$

Price

MC

Cost/ Revenue

Non-integer quantities (sales)

If the monopolist can charge for and sellpartial quantities, then the maximum thatcan be charged is

the total area under the demand curveto the left of a given quantity

Profit Max for Discriminating Monopolist

0

2

4

6

8

10

12

14

16

18

20

22

0 1 2 3 4 5 6 7 8 9 10 11 12

Output

$

Price

MC

Cost

Profit

DiscriminatingMonopolist

Q = 8

TR = 88

TC = 32

Profit = 56

PerfectlyDiscriminatingMonopolist

Q = 8

TR = 96

TC = 32

Profit = 64

Results

Segregating Markets

Identify Consumers

Prevent Arbitrage

Airline Example

0

80

100

120

160

0 10 30 40

Number of Round-tripTickets

$

Demand

MR

MC

H

E

Revenue

Cost

Profit

Uniform Price Monopoly

Total Profit = $1200

0

80

100

120

160

0 10 30 40

Number of Round-tripTickets

$

Demand

MR

MC

H

E

Charge $160 for No Restriction Ticket

ProfitGain Total Profit = $1600

AC

Revenue

Cost

0

80

100

120

160

0 10 30 40

Number of Round-tripTickets

$

Demand

MR

MC

H

Charge $100 for Student Tickets

P > MC

0

80

100

120

160

0 10 30 40

Number of Round-tripTickets

$

Demand

MC

Charge $100 for Student Tickets

P > MC

0

80

100

120

160

0 10 30 40

Number of Round-tripTickets

$

Demand

MC

Charge $100 for Student Tickets

P > MC

0

80

100

120

160

0 10 30 40

Number of Round-tripTickets

$

Demand

Charge $100 for Student Tickets

MC

Additional Cost

Additional Revenue

0

80

100

120

160

0 10 30 40

Number of Round-tripTickets

$

DemandH

Charge $100 for Student Tickets

MC

Additional Cost

Additional Profit

0

80

100

120

160

0 10 30 40

Number of Round-tripTickets

$

DemandH

Overall Gain from Price Discrimination

GainMC

The End

MC TR MR ProfitQ Price Cost Exact DSC DSC DSC0 20 0 4 01 18 4 4 18.00 18 14.002 16 8 4 34.00 16 26.003 14 12 4 48.00 14 36.004 12 16 4 60.00 12 44.005 10 20 4 70.00 10 50.006 8 24 4 78.00 8 54.007 6 28 4 84.00 6 56.008 4 32 4 88.00 4 56.009 2 36 4 90.00 2 54.0010 0 40 4 90.00 0 50.00

TR MR Profit MR TR MR ProfitQ Price UNF UNF Cost MC UNF DSC DSC DSC

0 20 0 0 4 0.00 20.00 01 18 18 18 4 4 14.00 16.00 18.00 18 14.002 16 32 14 8 4 24.00 12.00 34.00 16 26.003 14 42 10 12 4 30.00 8.00 48.00 14 36.004 12 48 6 16 4 32.00 4.00 60.00 12 44.005 10 50 2 20 4 30.00 0.00 70.00 10 50.006 8 48 -2 24 4 24.00 -4.00 78.00 8 54.007 6 42 -6 28 4 14.00 -8.00 84.00 6 56.008 4 32 -1 32 4 0.00 -12.00 88.00 4 56.009 2 18 -1 36 4 -18.00 -16.00 90.00 2 54.0010 0 0 -1 40 4 -40.00 -20.00 90.00 0 50.00

0

80

100

120

160

0 10 30 40Number of Round-tripTickets

$

FE

H

G