The document discusses third-degree price discrimination, where a firm can segment consumers based on observable characteristics and charge different prices to different groups. Under third-degree price discrimination, optimal profits are achieved by separating markets and setting different prices (pa ≠ pb) in each. However, whether using single or multiple prices, monopoly pricing depends on demand characteristics like price elasticity. The firm finds the profit-maximizing quantities (qa* and qb*) and corresponding prices (pa* and pb*) by setting marginal revenue equal to marginal cost in each market. The market with less elastic demand will face a higher price and larger markup over cost.

1. Lecture Notes on Monopoly Third-Degree
Price Discrimination
Sener Salci
April 24, 2018

2. At the end of this lecture
You will develop knowledge and understanding on:
• the ideas behind price discrimination
• implications of third- degree price discrimination on firms
2

3. Price Discrimination
Price discrimination is when the firm charges different prices to
different people for the same product.
Formally, “price discrimination is present whenever two or more
similar goods are sold at prices that are in different ratios to
marginal costs.” Stigler (1987).
3

4. Set of [optimal] Prices (𝒑 𝒂
∗
, 𝒑 𝒃
∗
, 𝒑 𝒄
∗
, … , 𝒑 𝒏
∗
)
Price discrimination is not hypothetical, and it is very common in our world.
4

5. • movie tickets (different ticket pricing for children, adults movie lovers)
• airline tickets (different flight pricing for economy class, business class travelers)
• restaurant meals (different menu prices for adults and seniors / 14th February, 31st
Dec!)
• cleaning products (different brands offered for high and low income consumers – so
products need not to be identical, and also quality of these products differ!
• and many other forms such as loyalty cards, coupons etc.
In real life, consumers are rarely homogenous with respect to their preferences and, hence,
demands.Therefore, firms can segment heterogeneous consumers based on their observable
characterstics.
5
Set of [optimal] Prices (𝒑 𝒂
∗
, 𝒑 𝒃
∗
, 𝒑 𝒄
∗
, … , 𝒑 𝒏
∗
), cont.

6. Motivation for price-discriminating behavior
• Price discrimination is a business strategy that allows a
monopoly firm to make greater profits than it would make by
charging both groups the same price.
• It might also give the business the opportunity to get rid of bulk
amount of stocks, and expand its market.
6

7. Conditions for price discrimination work effectively
1. Price-maker: The firm must be able to set the price. To do this, a firm must operate in
imperperfect competition, so must have some degree of monopoly (or oligopoly)
power.
2. Separate markets with different elasticities of demand: The firm must identify two
or more sub-markets and have to keep these market separate. In other words, a firm
must have ability to sort customers.
3. No arbitrage: Ability of firm to prevent/or minimize re-sales (no arbitrage profits across
markets).
4. Low admin costs. It must be be relatively cheap to separate markets and implement
price discrimination.
7

8. Is it an arbitrary decision or random-walk process?
Strictly speaking, the answer is NO. In addition to what we have just discussed:
• Profit maximizing firm will have to extract market's consumer surplus by considering two
principles.
Fact 1: −𝝅 < 0 < +𝝅 and firm’s objective is to generate extra revenue,
better cash-flow, max 𝝅.
Fact 2: Customers want to be treated fairly, therefore, firm should allow
customers to swallow the price and price discrepancies. To be precise,
monopolist must set the price(s) using demand function!! And. yes, again:
price elasticity of demand).
8

9. Assumptions
1. No capacity constraints
Implication: A firm will be able to supply [optimum] output without facing any capacity constraint. The capacity is
so much so plentiful that it does not constrain-off the level of production and sales of the firm.
2. The marginal cost is a constant (i.e., MC = c)
Implication: Allow the firm to set profit-maximizing linear prices independently in n different markets, so markets
can be treated independently. In other words, if there is a shift in demand in one market, then the quantity sold
in all markets cannot change.
And, the marginal revenue across the N markets (e.g., n=1 for children, n=2 students, n=3 other adults, …, N )
is the same at the optimum. Intuitively, if firm/supplier found herself with one more unit of the good, it would not
matter in which market (to which group of consumers/demanders) she sold it.
3. Good/service produced/consumed is assumed to be pure private good.
Implication: A firm can exclude consumers who do not want to or even cannot pay for the product (concepts:
rivalry and excludability in consumption)
Note: These issues are indeed critical because they are the assumptions underlying the analysis throughout
this lecture. However, for now, we will stick to them to understand the important concepts in price-
discrimination. Later, we will come back to these issues and tackle the importance of them.
9

10. Third degree price discrimination
(also known as multimarket price discrimination)
• Consumers differ by some observable characteristic(s).
• The market is separated (e.g., EU market, Asian market).
• Different uniform prices are charged to different groups.
It is linked directly to consumers' ability and willingness to pay for a
good or service. In such cases, the prices charged may bear little or no
relation to the cost of production.
10

11. Finding optimal levels of quantities and prices…
11
Profit Equation
1 𝜋 = 𝑇𝑅 𝑎 𝑞 𝑎 + 𝑇𝑅 𝑏 − 𝑇𝐶
Objective: The seller’s problem is
2 max
𝑞 𝑎,𝑞 𝑏
𝜋 𝜋 𝑞 𝑎, 𝑞 𝑏 = 𝑝 𝑞 𝑎 ∙ 𝑞 𝑎 + 𝑝 𝑞 𝑏 ∙ 𝑞 𝑏 − 𝑐 𝑞 𝑎 + 𝑞 𝑏
First-order conditions (FOC):
3
𝜕𝜋
𝜕𝑞 𝑎
=
𝑑𝑝 𝑎
𝑑𝑞 𝑎
𝑞 𝑎 + 𝑝 𝑎 𝑞 𝑎
𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑟𝑒𝑣𝑒𝑛𝑢𝑒
𝑓𝑟𝑜𝑚 𝑚𝑎𝑟𝑘𝑒𝑡 𝑎
−
ณ
𝜕𝑐
𝜕𝑞
= 𝟎
𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙
𝑐𝑜𝑠𝑡
5
𝜕𝜋
𝜕𝑞 𝑏
=
𝑑𝑝 𝑏
𝑑𝑞 𝑏
𝑞 𝑏 + 𝑝 𝑏 𝑞 𝑏
𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑟𝑒𝑣𝑒𝑛𝑢𝑒
𝑓𝑟𝑜𝑚 𝑚𝑎𝑟𝑘𝑒𝑡 𝑏
−
ณ
𝜕𝑐
𝜕𝑞
= 𝟎
𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙
𝑐𝑜𝑠𝑡
4 Find 𝑞 𝑎
∗
𝑤ℎ𝑒𝑛 𝑴𝑹 𝒂 = 𝑴𝑪
6 Find 𝑞 𝑏
∗
𝑤ℎ𝑒𝑛 𝑴𝑹 𝒃 = 𝑴𝑪
MR denotes marginal revenue
and MC denotes marginal cost.

12. Optimal quantities (q*a and q*b)
AC=MC
MRa
price (£/unit)
Quantity (units)q*a
12
price (£/unit)
Quantity (units)
MRb
Da
Db
q*b
market a market b

13. 13
The “rule of thumb” for optimal pricing (p*a and p*b)
The quantities that satisfy both FOCs are 𝑞 𝑎
∗ and 𝑞 𝑏
∗
. Therefore, plugging these
quantities into inverse demand curves will give us the respective optimal prices:
7 𝒑 𝒂
∗
= 𝑝 𝑞 𝑎
∗
8 𝒑 𝒃
∗
= 𝑝 𝑞 𝑏
∗

14. MRa
price (£/unit)
Quantity (000s of units)q*a
14
price (£/unit)
Quantity (000s units)
MRb
Da
Db
p*a
p*b
q*b
Optimal prices (p*a and p*b)
AC=MC
market a market b

15. 15
Elasticity and the Lerner Markup Rule
We can re-write equation [3] and [5]
9
𝑑𝑝 𝑎
𝑑𝑞 𝑎
𝑞 𝑎 + 𝑝 𝑎 𝑞 𝑎
𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑟𝑒𝑣𝑒𝑛𝑢𝑒
𝑓𝑟𝑜𝑚 𝑚𝑎𝑟𝑘𝑒𝑡 𝑎
=
𝑑𝑝 𝑏
𝑑𝑞 𝑏
𝑞 𝑏 + 𝑝 𝑏 𝑞 𝑏
𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑟𝑒𝑣𝑒𝑛𝑢𝑒
𝑓𝑟𝑜𝑚 𝑚𝑎𝑟𝑘𝑒𝑡 𝑏
=
ด
𝜕𝑐
𝜕𝑞
𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙
𝑐𝑜𝑠𝑡
10 𝑀𝑅 𝑎 𝑞 𝑎
∗
= 𝑀𝑅 𝑏 𝑞 𝑏
∗
= 𝑀𝐶 𝑞 𝑎
∗
+ 𝑞 𝑏
∗
We can re-write these as follows:
11 𝑀𝑅 𝑎 = 𝑝 𝑎 1 +
𝑑𝑝 𝑎
𝑑𝑞 𝑎
𝑞 𝑎
𝑝 𝑎
= 𝒑 𝒂 𝟏 +
𝟏
𝜼 𝒂
12 𝑀𝑅 𝑏 = 𝑝 𝑏 1 +
𝑑𝑝 𝑏
𝑑𝑞 𝑏
𝑞 𝑏
𝑝 𝑏
= 𝒑 𝒃 𝟏 +
𝟏
𝜼 𝒃
Rearranging the terms in equation [10, 11 and 12]
𝟏𝟑 𝒑 𝒂 𝟏 +
𝟏
𝜼 𝒂
= 𝒑 𝒃 𝟏 +
𝟏
𝜼 𝒃
= 𝑀𝐶 𝑞 𝑎
∗
+ 𝑞 𝑏
∗
In words (economics)
The monopoly shifts outputs among the various
markets in which it sells until marginal revenue in all
markets are equal to each other and equal to the
common marginal cost.

16. 16
Elasticity and the Lerner Markup Rule
In words (economics)
1. Ratio of marginal cost to the price charged
by monopolist equals to 1 plus inverse of the
elasticity of demand facing the monopolist.
2. Elasticity of demand determines markup.
There will be a greater mark-up in market
with a lower elasticity of demand. Monopoly
price in market will get closer to the marginal
cost with higher price elasticity of demand.
3. As long as the demand curve is downward
sloping, increases in marginal cost will cause
monopolist to reduce output and thereby
raise prices. (Show this on figure presented
in previous slide)
From the relationship described in equation [13], we can
derive the following four relationship (just a math):
Statement 1
𝑴𝑪
𝒑 𝒂
= 𝟏 +
𝟏
𝜼 𝒂
𝑴𝑪
𝒑 𝒃
= 𝟏 +
𝟏
𝜼 𝒃
Statement 2
𝒑 𝒂
∗
= 𝑝 𝑞 𝑎
∗
=
𝑀𝐶
1 +
1
𝜂 𝑎
𝒑 𝒃
∗
= 𝑝 𝑞 𝑏
∗
=
𝑀𝐶
1 +
1
𝜂 𝑏

17. 17
Elasticity and the Lerner Markup Rule
Statement 3*
𝑝 𝑎
∗
𝑝 𝑏
∗ =
1 +
1
𝜼 𝒃
1 +
1
𝜼 𝒂
𝒑 𝒂−𝑴𝑪
𝒑 𝒂
= −
𝟏
𝜼 𝒂
𝒑 𝒃−𝑴𝑪
𝒑 𝒃
= −
𝟏
𝜼 𝒃
*Assuming constant marginal costs)
Definition: A monopolist will have a Lerner Index
greater than zero, and the index will be determined by
the amount of market power that the firm has. A
larger Lerner Index indicates more market power.
In words (economics)
4. Ramsey pricing rule: Roughly speaking,
consumers with less-elastic demands should be
charged higher price. For example, if 𝜂 𝑎 <
𝜂 𝑏 𝑡ℎ𝑒𝑛 𝑝 𝑎 > 𝑝 𝑏
5. In general, price-discriminating monopolist (same
for single-price policy monopolist) follows inverse
elasticity rule with respect to each group.
6. The less elastic is demand (i.e., as it decreases
towards 1), the greater the percentage of the price
that is a markup over cost. Also, we can see that
the portion of the price that is a markup over cost
cannot be greater than the price itself. Hence, the
firm must operate on the elastic portion of demand
in each market.
Statement 4

18. MRa
price (£/unit)
Quantity (000s of units)q*a
18
price (£/unit)
Quantity (000s of units)
MRb
Da
Db
p*a
p*b
q*b
𝒑 𝒂
∗
> 𝒑 𝒃
∗
AC=MC
Larger
mark-up
smaller
mark-up
In graph…
market a market b

19. Summary
Firms can segment consumers based on some observable characteristics, and profits can be
maximized by separating markets: 𝑚𝑎𝑥 𝜋: 𝜋 𝑞1, 𝑞2 = 𝜋 𝑎 𝑞 𝑎 + 𝜋 𝑏 𝑞 𝑏
In this case, different consumers charged different prices 𝒆. 𝒈. , 𝒑 𝒂 ≠ 𝒑 𝒃 . However, whether
single-price or multiple-price monopolist, monopoly pricing depends on the characteristics of
demand.
Consumers’ ability and willingness-to-pay always holds (i.e., price elasticity of
demand plays a key role in setting a price or set of prices when monopolist practice
price discrimination).
Find you have to find stars e. g. , 𝐩 𝐚
∗
𝐟𝐨𝐫 𝐪 𝐚
∗
and 𝐩 𝐛
∗
𝐟𝐨𝐫 𝐪 𝐛
∗
so that you make 𝛑 𝐚
∗
from market a and 𝛑 𝐛
∗
from market b.
19

20. PART II: NUMERICAL EXAMPLE
20

21. Suppose a monopolist faced the demand curve in market A and market B:
𝑞 𝑎 = 24 − 2𝑝 𝑎 𝑎𝑛𝑑 𝑞 𝑏 = 24 − 𝑝 𝑏
And, assume that firm’s total cost of production is given by:
c(𝑞 𝑎 + 𝑞 𝑏) = 6(𝑞 𝑎 + 𝑞 𝑏)
Situation 1: Monopolist cannot independently determine the price in each market.
Situation 2: Monopolist is free to discriminate between both markets.
Task: In each situation described above, find the optimum level(s) of production, corresponding
level(s) of price, amounts of profit.
21

22. 22
Mapping Situations

23. 23
Mapping Situation 1 (uniform pricing, without price
discrimination)
𝑞 𝑎 = 24 − 2𝑝 𝑎 𝑓𝑜𝑟 𝑝 𝑎 ≤ 12£/𝑢𝑛𝑖𝑡
𝑞 𝑏 = 24 − 𝑝 𝑏 𝑓𝑜𝑟 𝑝 𝑏 ≤ 24 £/𝑢𝑛𝑖𝑡
Price Range: 12£/𝑢𝑛𝑖𝑡 ≤ 𝑃 𝑀 ≤ 24 £/𝑢𝑛𝑖𝑡
Therefore, when markets are combined, single-
price monopolist must charge less than 50 £/𝑢𝑛𝑖𝑡.
𝑄 𝑚(𝑞 𝑎+𝑞 𝑏) = 48 − 3𝑃𝑚 𝑓𝑜𝑟 𝑷 𝒎 < 𝟏𝟐 £/𝒖𝒏𝒊𝒕
At these prices only market B is active
Now both markets are active 

24. 𝑸 𝒎(𝒒 𝒂 + 𝒒 𝒃) = 𝟒𝟖 − 𝟑𝑷 𝒎
The inverse demand function is: 𝑷 𝒎=
𝟏
𝟑
𝟒𝟖 − 𝑸 𝒎 = 𝟏𝟔 −
𝟏
𝟑
𝑸 𝒎
𝝅 𝒎 = 𝑷 𝒎 ∙ 𝑸 𝒎 − 𝑻𝑪
𝐦𝐚𝐱
𝑸 𝒎
𝝅 =
𝟏
𝟑
𝟒𝟖 − 𝑸 𝒎 ∙ 𝑸 𝒎 − 𝟔𝑸 𝒎
𝝏𝝅
𝝏𝑸 𝒎
= 𝟏𝟔 −
𝟐
𝟑
𝑸 𝒎 − 𝟔 = 𝟎
𝑸 𝒎
∗ = 𝟏𝟓 𝒖𝒏𝒊𝒕𝒔
Plugging 𝑸 𝒎
∗
into our inverse demand function: 𝑷 𝒎
∗
= 𝟏𝟔 −
𝟏
𝟑
𝑸 𝒎
∗
= 𝟏𝟏 £/𝒖𝒏𝒊𝒕 24
Situation 1 (without price discrimination), cont.

25. 25
Situation 1 (without price discrimination), cont.

26. 26
Situation 1 (without price discrimination), cont.
Prove/check if your prices adhere to the optimal mark-up rule based on demand elasticity (check with slides 16
and 17).
At the optimal levels of quantities and prices:
𝜂 𝑚 = −3
11
15
= −2.2 where -3 is the slope of the inverse demand curve; dq/dp (see slide 25).
𝑝 𝑚
∗ =
6
1 +
1
−2.2
𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝒑 𝒂
∗ = 𝟏𝟏 £/ 𝒖𝒏𝒊𝒕
𝑝 𝑚−𝑀𝐶
𝑝 𝑚
=
11−6
11
=
5
11
= −
1
−2.2
= 𝟎. 𝟒𝟓𝟒𝟓 > > 𝟎
Correct 
High market power.

27. 27
Looking at demand curves, we are
also able to tell that consumers
located in market B will pay higher
than what consumers in market A will
pay for the same product/service.
Mapping Situation 2 (with price-discrimination)

28. Situation 2 (with Price Discrimination), cont.
28
𝜋 = 𝑇𝑅 𝑎 + 𝑇𝑅 𝑏 − 𝑇𝐶
max
𝑞 𝑎,𝑞 𝑏
𝜋 = 12 −
1
2
𝑞 𝑎 ∙ 𝑞 𝑎 + 24 − 𝑞 𝑏 ∙ 𝑞 𝑏 −6𝑞
𝜕𝜋
𝜕𝑞 𝑎
= 12 − 𝑞 𝑎 − 6 = 0
𝜕𝜋
𝜕𝑞 𝑏
= 24 − 2𝑞 𝑏 − 6 = 0
𝒒 𝒂
∗ = 𝟔 𝒖𝒏𝒊𝒕𝒔 𝒒 𝒃
∗
= 𝟗 𝒖𝒏𝒊𝒕𝒔
Substituting these optimal quantities into inverse demand curve:
𝑝 𝑎
∗
= 12 −
1
2
𝑞 𝑎
∗
𝑝 𝑏
∗
= 24 − 𝑞 𝑏
∗
𝒑 𝒂
∗
= 𝟗 £/𝒖𝒏𝒊𝒕 𝒑 𝒃
∗
= 𝟏𝟓 £/𝒖𝒏𝒊𝒕

29. 29
Situation 2 (with Price Discrimination), cont.

30. 30
Prove/check if your prices adhere to the optimal mark-up rule based on demand elasticity (check with slides 16
and 17).
At the optimal levels of quantities and prices:
𝜂 𝑎 = −2
9
6
= −3 𝑎𝑛𝑑 𝜂 𝑏 = −1
15
9
= −1.6667 where -2 and -1 are the slopes of inverse demand curves;
dq/dp (see slide 28).
𝑝 𝑎
∗
=
6
1 +
1
−3
𝑎𝑛𝑑 𝑝 𝑏
∗
=
6
1 +
1
−1.667
𝒑 𝒂
∗
= 𝟗 £/ 𝒖𝒏𝒊𝒕 𝒑 𝒃
∗
= 𝟏𝟓 £/ 𝒖𝒏𝒊𝒕
𝒑 𝒂
∗
𝒑 𝒃
∗ =
9
15
= 𝟎. 𝟔 =
1+
1
−1.667
1+
1
−3
= 𝟎. 𝟔 Correct 
Situation 2 (with Price Discrimination), cont.
Correct 

31. 31
Prove/check if your prices adhere to the optimal mark-up rule based on demand elasticity (check with slides
16 and 17).
At the optimal levels of quantities and prices:
𝜂 𝑎 = −2
9
6
= −3 𝑎𝑛𝑑 𝜂 𝑏 = −1
15
9
= −1.6667
𝑝 𝑎 − 𝑀𝐶
𝑝 𝑎
=
9 − 6
9
=
3
9
= −
1
−3
= 𝟎. 𝟑𝟑 𝒂𝒏𝒅 > 𝟎
𝑝 𝑏 − 𝑀𝐶
𝑝 𝑏
=
15 − 6
15
=
9
15
= −
1
−1.667
= 𝟎. 𝟔 𝒂𝒏𝒅 > 𝟎
.
Situation 2 (with Price Discrimination), cont.
More market power within market B.
Price --- so the mark-up in market B
is larger –as expected

32. Short reading on price discrimination in
action
I got it cheaper than you
Scott Woolley
Forbes, November 2, 1998
32

33. Movie
Movie: The Jerk (1979)*
In this an American comedy movie, you will come across the
following economic concepts: patents and monopoly power.
*Source: Sexton, R. 2006. Using Short Movie and Television Clips in the Economics Principles Class.
Journal of Economic Education, 37(4), 406-417
33

34. Other Important Issues
1. implications of monopoly power on consumers (consumer
surplus) and social welfare (deadweight loss)
2. natural monopolies (large fixed cost infrastructure facilities
such as electricity, railway transport, golf clubs) and
applications of two-part pricing
3. natural monopoly and regulations (regulations matter a lot
especially when dealing with public goods)
34

35. Role and Importance of Institutions (e.g., UK Competition
Commission)
Implication/Relevance: Is your firm under threat by regulators?
It depends on whether prospective/planned antitrust
enforcement (regulation) a cost effective way to improve social
welfare.
Note that the welfare-maximizing quantity is where P=MC. But it
is dual problem as such if P = MC the monopolist would operate
at a loss. 35