Price Discrimination

1
Price Discrimination

• Kowloon Technical School
• Vincent Ng
• 6AT (22)

2
Definition

• When an identical good is sold to different
  customers at different prices at the same time
  but not for different cost

3
Necessary Conditions for Price Discrimination

• The seller is a price searcher, facing a downward
  sloping demand curve

• The seller is able to prevent resale of the
  commodity among buyer

4
Perfect Price Discrimination or First Degree
Price Discrimination
1. Given an individual demand curve
P()
A

• If a single price is charged, e.g. P and the
  customer is allowed to buy any quantities he
  desires, then he buys Q. He pays 0PBQ and enjoys
  PAB amount of consumer surplus.

B
P
D
0
Q
Quantity
5
Perfect Price Discrimination or First Degree
Price Discrimination

• Under perfect price discrimination, the custome
  is charged a price that equals to his MUV for
  each unit sold. If he buys Q units, he has to pay
  0ABQ and enjoys no consumer surplus. Only for the
  last unit bought, i.e. the 0Q unit, he pays 0P
  which equals his MUV for that unit.

P()
A
B
P
D
0
Q
Quantity
6
Perfect Price Discrimination or First Degree
Price Discrimination

• For perfect price discrimination, the seller
  charges the same customer different prices for
  different quantities of goods sold. The customer
  is charged the maximum amount he is willing to
  pay. This will leave him indifferent between
  buying and not buying. The seller is able to
  extract all consumer surplus form the customer.

P()
A
B
P
D
0
Q
Quantity
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Perfect Price Discrimination or First Degree
Price Discrimination
2. The profit-maximizing equilibrium output for
a perfect price discriminator
a. Under perfect price discrimination, the
demand curve facing the monopolist measures the
marginal revenue from selling the product, i.e. P
MUV MR. It is because the seller lowers the
price on the marginal units but not on the
infra-marginal units. Thus, the price charged for
an unit also measures it marginal revenue. The
demand curve is therefore the marginal revenue
curve.
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Perfect Price Discrimination or First Degree
Price Discrimination

• Give the demand curve, D and the cost function

P()
MC
A

• The perfect price discriminator maximize its
  profits by producing at Q where it marginal cost
  of production equals its marginal revenue (MC
  MR) and equals the price of the output unit sold
  at point B.
• Total revenue obtained is 0ABQ and equals the
  customers total use value for 0Q amount of the
  good. Consumer surplus is zero as the customers
  total payment (TEV) equals his total use value
  (TUV) for the good bought.

B
p
D MR
0
Quantity
Q
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Perfect Price Discrimination or First Degree
Price Discrimination
P()
MC
A
ii. For the last unit sold, the price charged is
P and the infra-marginal units, they are all sold
at prices higher than P.
B
p

• Production is efficient for a perfect price
  discriminator because at Q, P ( MUV) MC. It
  maximizes its profits and produces at an optimal
  or efficient level of output.

D MR
0
Quantity
Q
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Some Comments On Perfect Price Discrimination
1. The above tells what perfect price
discrimination is. In the real world,
perfect price discrimination is rarely found. It
assumes the sellers knows the demand curves of it
customers and their own production and cost
functions perfectly well.
In practice, perfect price discrimination is
never prefect. Information is costly to
obtain. As demand curve is downward sloping, the
seller simply discriminates by charging a lower
price for successively more units sold to an
individual customer. The price charged for each
unit may not equal the maximum amount that the
customer is willing to pay (i.e. his marginal use
value). This will leave him some consumer
surplus, the seller may not be able to extract
all consumer surplus from the customer.
An imperfect way to extract consumer surplus is
sometimes called the second degree price
discrimination. Quantity discounts, declining
rates, group rates, and multi-part pricing are
examples.
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Some Comments On Perfect Price Discrimination
2. Comparing to a simple monopoly, perfect price
discriminator can produce and sell more without
lowering the price for the previous units sold,
It produces a MC P and its output level is
allocatively efficient.
a. To be consistent with the axiom of
maximization, we then ask the question why a real
world monopolist does not always adopt perfect
price discrimination. What stops it from doing
so? Transaction costs. We know that using price
discrimination is costly, Thus only when costs
allow, then price discrimination is profitable.
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Some Comments On Perfect Price Discrimination
b. This , it is argued that a simple monopolist
may not be inefficient. There, the accusation
that a simple monopolist produces at P gt MC and
is inefficient may not be right.
A maximizing seller adopts single pricing and
leads to a dead-weight welfare loss may not be
inefficient if we consider the transaction costs
involved in using other alternative pricing
arrangements, The welfare loss associated with
single pricing may bit be a loss if we consider
the savings in transaction costs in adopting
other pricing arrangements
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Some Comments On Perfect Price Discrimination

• Perfect price discrimination may be a necessary
  pricing arrangement for a firm to cover costs and
  survive. There are two such possible situation.

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Some Comments On Perfect Price Discrimination

• The average cost curve is everywhere above the
  market demand curve. If a single price is
  charged, the seller always suffer loss and
  therefore will soon be out of business.

P()
AC
b
d
c
If it practises price discrimination, it
willcover its costs of production. The total
cost of producing 0Q is 0cbQ and the total
revenue under perfect price discrimination is
0deQ. As long as its total revenue is greater
than it total cost, i.e. TR gt TC, the firm can
survive and remain in business.
a
e
D MR
Quantity
0
Q
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Some Comments On Perfect Price Discrimination

• In the case of natural monopoly, perfect price
  discrimination will result in efficient
  production and the firm can cover costs and
  survive without demanding subsidies from the
  government.

P()
d
b
AC
c
a
MC
e
D MR
If the natural monopolist produces at 0Q,
charging a single price 0c, then it suffers a per
unit loss of be in this figure. If it practises
perfect price discrimination, it obtains a
revenue of 0deQ and is able to cover its total
cost of production 0cbQ.
Quantity
0
Q
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Third Degree Price Discrimination

• The third degree price discriminator charges
  different prices in different markets for the
  same good.

• The seller must be able to separate its customers
  into groups with different price elasticities
  of demand and keep the m separate at low cost.
  The differences in price elasticities among
  customers must be identfiable at low enough cost
  to make third degree discrimination profitable.
• A high price is charged in the market with
  less elastic demand and a low price is charged in
  the market with more elastic demand.

• It may discriminates according to age, income,
  location or sex.

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Third Degree Price Discrimination

• The profit-maximizing equilibrium output for a
  third degree price discriminator

Price

• The equi-marginal revenue principle If a seller
  is able to sell its output in different markets,
  then it should distribute and sell its output in
  each market in such a way that their marginal
  revenues are the same in all markets

30
D2
20
D1
MR2
MR1
Q
Q
25
100
0

• Suppose there are two markets of different demand
  curves with correspondingly different marginal
  revenue curves.

Market II
Market I
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Third Degree Price Discrimination
ii. Initially the seller produces 125 units and
it sells 25 units in Market II and 100 units in
Market I. The marginal revenue obtained for the
last unit in Market II is 30. The marginal
revenue obtained for the last unit in Market I is
20.
Price
30
D2
20
D1

• Since the marginal revenues in the two market
  differ, the seller can raise its total revenue by
  switching the sale of output from the market of
  low marginal revenue to the one of high revenue

MR2
MR1
Q
Q
25
100
0
Market II
Market I
The one-hundredth unit from Market I will be
transferred to Market II. Total output remains at
125 units but there is an increase in revenue of
about 10. Revenue falls by 20 in Market I but
rises by 30 in Market II.
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Third Degree Price Discrimination

• Suppose there are 2 different markets of
  different price elasticities of demand, ?1 and
  ?2. The costs in identifying the two market are
  low enough for the seller to practise third
  degree price discrimination.

• According to the equi-marginal revenue principle,
  the necessary condition for profit-maximization
  is

1
1
MR1 P1 (1 - )
MR2 P2 (1 - )
?1
?2
1
1
MR1 MR2
P1 (1 - ) P2 (1 - )
?1
?2
1
P1
(1 - )
?2

1
P2
(1 - )
?1
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Third Degree Price Discrimination

• To simply, assume a constant cost function and D1
  is more elastic than D2

Price
P2

• To maximize profits, the profit maximizing output
  for each market is given by the respective
  intersection of the marginal revenue curves with
  the common marginal cost curve.

P1
MC AC
D2
D1
MR2
MR1
Q
Q
0
Q2
Q1
Market II
Market I
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Third Degree Price Discrimination
ii. The third degree price discriminator will
produce Q1 for Market I and Q2 for Market II.
Price
P2
iii. It sells the same product to consumers with
a less elastic demand at a higher price than that
charged to the consumers with a more elastic
demand.
P1
MC AC
D2
D1
MR2
MR1
Q
Q
0
Q2
Q1
Market II
Market I
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Third Degree Price Discrimination

• Compared to a simple monopolist a third degree
  price discriminator will produce more output and
  supply goods to weak markets.

Price
P2
Since a third degree price discriminator can sell
the same good at different prices in markets of
different price elasticities, it supplies goods
in both the strong market and the weak
market. A simple monopolist will only sell in the
strong market. Charging a single price, P2,
result in zero quantity demanded in the weak
market.
P1
MC AC
D2
D1
MR2
MR1
Q
Q
0
Q2
Q1
Strong Market
Weak Market
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Price Discrimination and Information Costs

• The differences in prices between goods sold in
  the tourist and the non-tourist areas can be
  explained by difference in information costs
  between tourist and non-tourists.

• Tourists are outsiders and do not know the place.
  They face a higher information cost in purchases
  than local people. Tourists find it more costly
  to search sellers, check quality and compare
  prices. Thus, they are likely to be prepared to
  pay a higher price for a good than local people
  in the tourist areas.

• You might argue that their price elasticities of
  demand are low because it is costly for tourists
  to find substitutes available in the non-tourist
  areas. This is a case of third degree price
  discrimination.
• Or you may argue that the higher price paid
  is the result of difference in information costs.
  For a tourist, the full price or cost he pays
  is higher than the local residents owing to his
  higher information costs.

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Price Differentials VS Price Discrimination

• Price differentials of the same good may not
  imply price discrimination, they may reflect the
  difference in costs or the associated services
  and attributes that come with a commodity.

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Price Differentials VS Price Discrimination

• Sometimes, a good sold at the same price may
  mean price discrimination!
• When China began her four modernization
  programmes, foreigners travelling in China had to
  use the Foreign Exchange Certificate which
  officially is equivalent to Renminbi. The FEC is
  convertible into foreign currencies at officially
  controlled exchange rates the RMB is not
  similarly convertible. As a result, although the
  FEC and the RMB have the same nominal value,
  dollar for dollar the FEC is worth significantly
  more than the RMB in the black or free
  market.

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Price Differentials VS Price Discrimination
a. If both the foreigners and local Chinese are
asked to pay the same nominal price for a good,
then the seller is practising price
discrimination, The foreigners pay a higher price
than the local Chinese for the same good.

• Ironically, if the foreigners are paying in FEC
  for a good, then the local Chinese who are paying
  in RMB have to add a premium. Actually, they pay
  the same price for the same good and there is no
  price discrimination. The price differential may
  simply reflect the higher value of FEC in the
  black exchange rate market.
• For instance, if the black market price of
  one dollar FEC is RMB 1.5, then a lemonade sold
  for five dollars FEC will be worth RMB 7.5. That
  is , a premium of RMB 2.5 is added if one pays
  in RMB.

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Price Differentials VS Price Discrimination

• It is found that the same type of products are
  sold at different labels as economy, standard and
  deluxe and at different prices.
• It is argued that the seller practises third
  degree price discrimination based on different
  income classes rich people buy the deluxe model
  and the poor people buy the economy model. The
  argument is wrong because (i) the products are
  not the same and (ii) the market is not
  separated as a poor consumer may buy the deluxe
  model while a rich consumer may buy the economy
  model.
• Do not confuse the argument with the type of
  price discrimination practised by the medical
  doctors. Patients from different income groups
  are charged differently for the same treatment.
  Third degree price discrimination may exist
  unless the seller can separate its customers into
  different income groups and sell the deluxe model
  to the rich only. And those who buy the economy
  models at a lower price must not be able to
  resell the goods to the rich.

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The END