1. Industrial Organisation Off and On the Internet
Some Lessons From the Past
Greg Taylor
Oxford Internet Institute
University of Oxford

2. Economics
The study of constrained choice.

3. Economics
The study of constrained choice.
Build mathematical models of decision makers’ behaviours.

4. Economics
The study of constrained choice.
Build mathematical models of decision makers’ behaviours.
Typically gives us very sharp conclusions.

5. Economics
The study of constrained choice.
Build mathematical models of decision makers’ behaviours.
Typically gives us very sharp conclusions.
Suggests effects of policy changes—comparative statics.

6. Economics
The study of constrained choice.
Build mathematical models of decision makers’ behaviours.
Typically gives us very sharp conclusions.
Suggests effects of policy changes—comparative statics.
But hard: the world is very complex, so we need assumptions.

7. Economics
The study of constrained choice.
Build mathematical models of decision makers’ behaviours.
Typically gives us very sharp conclusions.
Suggests effects of policy changes—comparative statics.
But hard: the world is very complex, so we need assumptions.
Thus another advantage of the mathematical approach:
encourages transparency of assumptions.

8. Economics
The study of constrained choice.
Build mathematical models of decision makers’ behaviours.
Typically gives us very sharp conclusions.
Suggests effects of policy changes—comparative statics.
But hard: the world is very complex, so we need assumptions.
Thus another advantage of the mathematical approach:
encourages transparency of assumptions.
Let’s take a look at a textbook example of how some simple
assumptions can be turned into a model.

9. Outline
Price discrimination: from assumptions to policy statements
Assumptions and applicability

10. Price discrimination
Price discrimination is the practice of pricing such that
different groups of consumers yield different price-cost
margins for the firm.

11. A price discrimination example
Imagine a monopolist firm that sells some products of varying
quality.

12. A price discrimination example
Imagine a monopolist firm that sells some products of varying
quality.
Assume that quality can be indexed by a number, q.
Let q be continuous.
Suppose that it costs C(q) to provide a product with quality q.
Let C (q) > 0 (increasing costs), C (q) > 0 (convex costs),
and C(0) = 0.

13. A price discrimination example
Imagine a monopolist firm that sells some products of varying
quality.
Assume that quality can be indexed by a number, q.
Let q be continuous.
Suppose that it costs C(q) to provide a product with quality q.
Let C (q) > 0 (increasing costs), C (q) > 0 (convex costs),
and C(0) = 0.
There are two types of customer: low (L), and high (H).

14. A price discrimination example
Imagine a monopolist firm that sells some products of varying
quality.
Assume that quality can be indexed by a number, q.
Let q be continuous.
Suppose that it costs C(q) to provide a product with quality q.
Let C (q) > 0 (increasing costs), C (q) > 0 (convex costs),
and C(0) = 0.
There are two types of customer: low (L), and high (H).
A type i ∈ {L, H} consumer enjoys surplus
Ui = θi q − p.
where p is the price to be paid to the firm, and θi is the
consumer’s willingness to pay for a one unit increase in quality.

15. A price discrimination example
Imagine a monopolist firm that sells some products of varying
quality.
Assume that quality can be indexed by a number, q.
Let q be continuous.
Suppose that it costs C(q) to provide a product with quality q.
Let C (q) > 0 (increasing costs), C (q) > 0 (convex costs),
and C(0) = 0.
There are two types of customer: low (L), and high (H).
A type i ∈ {L, H} consumer enjoys surplus
Ui = θi q − p.
where p is the price to be paid to the firm, and θi is the
consumer’s willingness to pay for a one unit increase in quality.
Let θL < θH .

16. First order discrimination
In a perfect world, the firm would know the type of consumer
it is facing.
It could then design a product/price combination for each
type.

17. First order discrimination
In a perfect world, the firm would know the type of consumer
it is facing.
It could then design a product/price combination for each
type.
i.e. Sell a ‘budget’ product with q = qL at price pL to L-type
consumers, and a ‘luxury’ product with q = qH at price pH .

18. First order discrimination
In a perfect world, the firm would know the type of consumer
it is facing.
It could then design a product/price combination for each
type.
i.e. Sell a ‘budget’ product with q = qL at price pL to L-type
consumers, and a ‘luxury’ product with q = qH at price pH .
The firm’s objective would then be to
max pi − C(qi )
qi ,pi

19. First order discrimination
In a perfect world, the firm would know the type of consumer
it is facing.
It could then design a product/price combination for each
type.
i.e. Sell a ‘budget’ product with q = qL at price pL to L-type
consumers, and a ‘luxury’ product with q = qH at price pH .
The firm’s objective would then be to
max pi − C(qi )
qi ,pi
subject to the constraint
θi qi − pi ≥ 0.

20. First order discrimination
In a perfect world, the firm would know the type of consumer
it is facing.
It could then design a product/price combination for each
type.
i.e. Sell a ‘budget’ product with q = qL at price pL to L-type
consumers, and a ‘luxury’ product with q = qH at price pH .
The firm’s objective would then be to
max pi − C(qi )
qi ,pi
subject to the constraint
θi qi − pi ≥ 0.
This kind of behaviour is called first degree price
discrimination.

21. First order discrimination
max pi − C(qi ) s.t. θi qi − pi ≥ 0.
qi ,pi

22. First order discrimination
max pi − C(qi ) s.t. θi qi − pi ≥ 0.
qi ,pi
In fact, since the firm knows θi , it can just set pi = θi qi .

23. First order discrimination
max pi − C(qi ) s.t. θi qi − pi ≥ 0.
qi ,pi
In fact, since the firm knows θi , it can just set pi = θi qi .
Substituting this into the maximisation problem gives
max θi qi − C(qi ).
qi

24. First order discrimination
max pi − C(qi ) s.t. θi qi − pi ≥ 0.
qi ,pi
In fact, since the firm knows θi , it can just set pi = θi qi .
Substituting this into the maximisation problem gives
max θi qi − C(qi ).
qi
Increasing qi by one unit increases revenue by θi , and cost by
C (qi ).

25. First order discrimination
max pi − C(qi ) s.t. θi qi − pi ≥ 0.
qi ,pi
In fact, since the firm knows θi , it can just set pi = θi qi .
Substituting this into the maximisation problem gives
max θi qi − C(qi ).
qi
Increasing qi by one unit increases revenue by θi , and cost by
C (qi ).
It is therefore profitable to increase quality if and only if
θi > C (qi ).

26. First order discrimination
max pi − C(qi ) s.t. θi qi − pi ≥ 0.
qi ,pi
In fact, since the firm knows θi , it can just set pi = θi qi .
Substituting this into the maximisation problem gives
max θi qi − C(qi ).
qi
Increasing qi by one unit increases revenue by θi , and cost by
C (qi ).
It is therefore profitable to increase quality if and only if
θi > C (qi ).
∗
So quality qi is produced where θi = C (qi ), i.e. where
marginal cost of qi is equal to marginal willingness to pay for
it.

27. What can we say about these qs?
Firstly, by giving firms so much information about consumers,
we have left the latter with no surplus.

28. What can we say about these qs?
Firstly, by giving firms so much information about consumers,
we have left the latter with no surplus.
However, that θi = C (qi ) implies the chosen qualities are
efficient!

29. What can we say about these qs?
Firstly, by giving firms so much information about consumers,
we have left the latter with no surplus.
However, that θi = C (qi ) implies the chosen qualities are
efficient!
Social welfare given by consumer + firm welfare:
(θi qi − p) + (p − C(qi ))

30. What can we say about these qs?
Firstly, by giving firms so much information about consumers,
we have left the latter with no surplus.
However, that θi = C (qi ) implies the chosen qualities are
efficient!
Social welfare given by consumer + firm welfare:
(θi qi − p) + (p − C(qi )) = θi qi − C(qi ).
This is exactly what the firm is maximising!

31. What can we say about these qs?
Firstly, by giving firms so much information about consumers,
we have left the latter with no surplus.
However, that θi = C (qi ) implies the chosen qualities are
efficient!
Social welfare given by consumer + firm welfare:
(θi qi − p) + (p − C(qi )) = θi qi − C(qi ).
This is exactly what the firm is maximising!
That θi = C (qi ) also implies that qL < qH , and hence
pL < pH .

32. What can we say about these qs?
Firstly, by giving firms so much information about consumers,
we have left the latter with no surplus.
However, that θi = C (qi ) implies the chosen qualities are
efficient!
Social welfare given by consumer + firm welfare:
(θi qi − p) + (p − C(qi )) = θi qi − C(qi ).
This is exactly what the firm is maximising!
That θi = C (qi ) also implies that qL < qH , and hence
pL < pH .

33. Segmentation breakdown
Now, firms typically cannot observe θi and so must depend on
the consumer to buy the product designed for them.

34. Segmentation breakdown
Now, firms typically cannot observe θi and so must depend on
the consumer to buy the product designed for them.
Therein lies a problem: if high consumers buy the high quality
product, they get
θH qH − pH = θH qH − θH qH = 0,

35. Segmentation breakdown
Now, firms typically cannot observe θi and so must depend on
the consumer to buy the product designed for them.
Therein lies a problem: if high consumers buy the high quality
product, they get
θH qH − pH = θH qH − θH qH = 0,
whereas if they buy the low quality product, they get
θ H qL − p L

36. Segmentation breakdown
Now, firms typically cannot observe θi and so must depend on
the consumer to buy the product designed for them.
Therein lies a problem: if high consumers buy the high quality
product, they get
θH qH − pH = θH qH − θH qH = 0,
whereas if they buy the low quality product, they get
θH qL − pL > θL qL − pL

37. Segmentation breakdown
Now, firms typically cannot observe θi and so must depend on
the consumer to buy the product designed for them.
Therein lies a problem: if high consumers buy the high quality
product, they get
θH qH − pH = θH qH − θH qH = 0,
whereas if they buy the low quality product, they get
θH qL − pL > θL qL − pL = 0.

38. Segmentation breakdown
Now, firms typically cannot observe θi and so must depend on
the consumer to buy the product designed for them.
Therein lies a problem: if high consumers buy the high quality
product, they get
θH qH − pH = θH qH − θH qH = 0,
whereas if they buy the low quality product, they get
θH qL − pL > θL qL − pL = 0.
Thus, all consumers will buy the budget product—this is
called adverse selection.

39. Solution: mechanism design
Question: What can the firm do about this?

40. Solution: mechanism design
Question: What can the firm do about this?
Answer: Change it’s maximisation problem.

41. Solution: mechanism design
Question: What can the firm do about this?
Answer: Change it’s maximisation problem.
Suppose a consumer is of type L with probability α and of
type H with probability (1 − α).

42. Solution: mechanism design
Question: What can the firm do about this?
Answer: Change it’s maximisation problem.
Suppose a consumer is of type L with probability α and of
type H with probability (1 − α). The new problem is then:
max α(pL − C(qL )) + (1 − α)(pH − C(qH ))
qL ,pL ,qH ,pH

43. Solution: mechanism design
Question: What can the firm do about this?
Answer: Change it’s maximisation problem.
Suppose a consumer is of type L with probability α and of
type H with probability (1 − α). The new problem is then:
max α(pL − C(qL )) + (1 − α)(pH − C(qH ))
qL ,pL ,qH ,pH
subject to the constraint
θH qH − pH ≥ θH qL − pL (ICH)
θ L qL − p L ≥ θ H qH − p H (ICL)
θH qH − pH ≥ 0 (IRH)
θL qL − pL ≥ 0 (IRL)

44. Solution: mechanism design
Question: What can the firm do about this?
Answer: Change it’s maximisation problem.
Suppose a consumer is of type L with probability α and of
type H with probability (1 − α). The new problem is then:
max α(pL − C(qL )) + (1 − α)(pH − C(qH ))
qL ,pL ,qH ,pH
subject to the constraint
θH qH − pH ≥ θH qL − pL (ICH)
θ L qL − p L ≥ θ H qH − p H (ICL)
θH qH − pH ≥ 0 (IRH)
θL qL − pL ≥ 0 (IRL)
Solving such a problem is known as second degree price
discrimination.

45. IRL is ‘binding’
Let’s begin by establishing that IRL holds with equality i.e.
that θL qL − pL = 0.
This means that home users are left with no surplus.

46. IRL is ‘binding’
Let’s begin by establishing that IRL holds with equality i.e.
that θL qL − pL = 0.
This means that home users are left with no surplus.
ICH says
θ H qH − p H ≥ θ H qL − p L

47. IRL is ‘binding’
Let’s begin by establishing that IRL holds with equality i.e.
that θL qL − pL = 0.
This means that home users are left with no surplus.
ICH says
θ H qH − p H ≥ θ H qL − p L ≥ θ L qL − p L

48. IRL is ‘binding’
Let’s begin by establishing that IRL holds with equality i.e.
that θL qL − pL = 0.
This means that home users are left with no surplus.
ICH says
θ H qH − p H ≥ θ H qL − p L ≥ θ L qL − p L
Thus, if θL qL − pL > 0, then it must also be true that
θH qH − pH > 0 so that neither IRL nor IRH bind.

49. IRL is ‘binding’
Let’s begin by establishing that IRL holds with equality i.e.
that θL qL − pL = 0.
This means that home users are left with no surplus.
ICH says
θ H qH − p H ≥ θ H qL − p L ≥ θ L qL − p L
Thus, if θL qL − pL > 0, then it must also be true that
θH qH − pH > 0 so that neither IRL nor IRH bind.
But then the firm could increase both pL and pH without
violating any condition.

50. IRL is ‘binding’
Let’s begin by establishing that IRL holds with equality i.e.
that θL qL − pL = 0.
This means that home users are left with no surplus.
ICH says
θ H qH − p H ≥ θ H qL − p L ≥ θ L qL − p L
Thus, if θL qL − pL > 0, then it must also be true that
θH qH − pH > 0 so that neither IRL nor IRH bind.
But then the firm could increase both pL and pH without
violating any condition.
This implies that IRL must bind at the optimum.

51. ICH is ‘binding’
We next show that ICH holds with equality i.e. that
θ H qH − p H = θ H qL − p L .
This means if the deal for the luxury product got any worse
then H type consumers would switch to buying the budget
product.

52. ICH is ‘binding’
We next show that ICH holds with equality i.e. that
θ H qH − p H = θ H qL − p L .
This means if the deal for the luxury product got any worse
then H type consumers would switch to buying the budget
product.
Suppose that this weren’t true:
θH qH − pH > θH qL − pL

53. ICH is ‘binding’
We next show that ICH holds with equality i.e. that
θ H qH − p H = θ H qL − p L .
This means if the deal for the luxury product got any worse
then H type consumers would switch to buying the budget
product.
Suppose that this weren’t true:
θH qH − pH > θH qL − pL ≥ θL qL − pL

54. ICH is ‘binding’
We next show that ICH holds with equality i.e. that
θ H qH − p H = θ H qL − p L .
This means if the deal for the luxury product got any worse
then H type consumers would switch to buying the budget
product.
Suppose that this weren’t true:
θH qH − pH > θH qL − pL ≥ θL qL − pL = 0

55. ICH is ‘binding’
We next show that ICH holds with equality i.e. that
θ H qH − p H = θ H qL − p L .
This means if the deal for the luxury product got any worse
then H type consumers would switch to buying the budget
product.
Suppose that this weren’t true:
θH qH − pH > θH qL − pL ≥ θL qL − pL = 0
Thus, if ICH does not bind then neither does IRH.

56. ICH is ‘binding’
We next show that ICH holds with equality i.e. that
θ H qH − p H = θ H qL − p L .
This means if the deal for the luxury product got any worse
then H type consumers would switch to buying the budget
product.
Suppose that this weren’t true:
θH qH − pH > θH qL − pL ≥ θL qL − pL = 0
Thus, if ICH does not bind then neither does IRH.
But then the firm could increase pH without violating any
condition.

57. ICH is ‘binding’
We next show that ICH holds with equality i.e. that
θ H qH − p H = θ H qL − p L .
This means if the deal for the luxury product got any worse
then H type consumers would switch to buying the budget
product.
Suppose that this weren’t true:
θH qH − pH > θH qL − pL ≥ θL qL − pL = 0
Thus, if ICH does not bind then neither does IRH.
But then the firm could increase pH without violating any
condition.
This implies that ICH must bind at the optimum.

58. Can neglect IRH and ICL
That ICH binds implies θH qH − pH = θH qL − pL .

59. Can neglect IRH and ICL
That ICH binds implies θH qH − pH = θH qL − pL .
IRL implies θL qL − pL = 0.

60. Can neglect IRH and ICL
That ICH binds implies θH qH − pH = θH qL − pL .
IRL implies θL qL − pL = 0.
Thus we have
θH qH − pH = θH qL − pH > θL qL − pL = 0.

61. Can neglect IRH and ICL
That ICH binds implies θH qH − pH = θH qL − pL .
IRL implies θL qL − pL = 0.
Thus we have
θH qH − pH = θH qL − pH > θL qL − pL = 0.
So IRH can be neglected.

62. Can neglect IRH and ICL
That ICH binds implies θH qH − pH = θH qL − pL .
IRL implies θL qL − pL = 0.
Thus we have
θH qH − pH = θH qL − pH > θL qL − pL = 0.
So IRH can be neglected.
This means that business customers get strictly positive utility.

63. Can neglect ICL
It can also be shown that ICL does not bind.
Briefly: since ICH binds θH (qH − qL ) = pH − pL .

64. Can neglect ICL
It can also be shown that ICL does not bind.
Briefly: since ICH binds θH (qH − qL ) = pH − pL .
But ICL says (after rearranging) θL (qH − qL ) ≤ pH − pL .

65. Can neglect ICL
It can also be shown that ICL does not bind.
Briefly: since ICH binds θH (qH − qL ) = pH − pL .
But ICL says (after rearranging) θL (qH − qL ) ≤ pH − pL .
The inequality must be strict since θH > θL .

66. Can neglect ICL
It can also be shown that ICL does not bind.
Briefly: since ICH binds θH (qH − qL ) = pH − pL .
But ICL says (after rearranging) θL (qH − qL ) ≤ pH − pL .
The inequality must be strict since θH > θL .
This means that the home bundle is strictly more attractive to
home users than is the business edition.

67. qH is the set at the efficient level
∗
Now we will show that the chosen qH is qH —i.e. where
C (qH ) = θH just like in the first order discrimination case.
This implies that the quality offered to B-types is socially
optimal.

68. qH is the set at the efficient level
∗
Now we will show that the chosen qH is qH —i.e. where
C (qH ) = θH just like in the first order discrimination case.
This implies that the quality offered to B-types is socially
optimal.
Suppose that the optimal qH has C (qH ) < θH .

69. qH is the set at the efficient level
∗
Now we will show that the chosen qH is qH —i.e. where
C (qH ) = θH just like in the first order discrimination case.
This implies that the quality offered to B-types is socially
optimal.
Suppose that the optimal qH has C (qH ) < θH .
The firm could change qH to qH + ∆, and increase pH to
pH + ∆θH without violating ICH, IRH, or ICL.

70. qH is the set at the efficient level
∗
Now we will show that the chosen qH is qH —i.e. where
C (qH ) = θH just like in the first order discrimination case.
This implies that the quality offered to B-types is socially
optimal.
Suppose that the optimal qH has C (qH ) < θH .
The firm could change qH to qH + ∆, and increase pH to
pH + ∆θH without violating ICH, IRH, or ICL.
When ∆ is small, the change in the firm’s profits is
approximately (1 − α)∆(θH − C (qH )) > 0.

71. qH is the set at the efficient level
∗
Now we will show that the chosen qH is qH —i.e. where
C (qH ) = θH just like in the first order discrimination case.
This implies that the quality offered to B-types is socially
optimal.
Suppose that the optimal qH has C (qH ) < θH .
The firm could change qH to qH + ∆, and increase pH to
pH + ∆θH without violating ICH, IRH, or ICL.
When ∆ is small, the change in the firm’s profits is
approximately (1 − α)∆(θH − C (qH )) > 0.
Thus, original qH was not optimal.

72. qH is the set at the efficient level
∗
Now we will show that the chosen qH is qH —i.e. where
C (qH ) = θH just like in the first order discrimination case.
This implies that the quality offered to B-types is socially
optimal.
Suppose that the optimal qH has C (qH ) < θH .
The firm could change qH to qH + ∆, and increase pH to
pH + ∆θH without violating ICH, IRH, or ICL.
When ∆ is small, the change in the firm’s profits is
approximately (1 − α)∆(θH − C (qH )) > 0.
Thus, original qH was not optimal.
Similarly, if C (qH ) > θH : The firm can reduce qH to qH − ∆,
provided it cuts its price for H by at least ∆θH .

73. qH is the set at the efficient level
∗
Now we will show that the chosen qH is qH —i.e. where
C (qH ) = θH just like in the first order discrimination case.
This implies that the quality offered to B-types is socially
optimal.
Suppose that the optimal qH has C (qH ) < θH .
The firm could change qH to qH + ∆, and increase pH to
pH + ∆θH without violating ICH, IRH, or ICL.
When ∆ is small, the change in the firm’s profits is
approximately (1 − α)∆(θH − C (qH )) > 0.
Thus, original qH was not optimal.
Similarly, if C (qH ) > θH : The firm can reduce qH to qH − ∆,
provided it cuts its price for H by at least ∆θH .
When ∆ is small, the change in the firm’s profits is
approximately ∆(C (qH ) − θH ) > 0

74. Optimal prices
Now we can set about characterising the optimal prices.

75. Optimal prices
Now we can set about characterising the optimal prices.
Since IRL binds, we know that pL = θL qL .

76. Optimal prices
Now we can set about characterising the optimal prices.
Since IRL binds, we know that pL = θL qL .
Since ICH binds, we know that θH qH − pH = θH qL − pL , or
∗
equivalently, that pH = pL + θH (qH − qL ).

77. Optimal prices
Now we can set about characterising the optimal prices.
Since IRL binds, we know that pL = θL qL .
Since ICH binds, we know that θH qH − pH = θH qL − pL , or
∗
equivalently, that pH = pL + θH (qH − qL ).
∗
Combining these two statements: pH = θL qL + θH (qH − qL ).

78. Firm’s objective
The firm’s objective is
max α(pL − C(qL )) + (1 − α)(pH − C(qH )).
qL ,pL ,qH ,pH

79. Firm’s objective
The firm’s objective is
max α(pL − C(qL )) + (1 − α)(pH − C(qH )).
qL ,pL ,qH ,pH
Substituting in the material we just derived (Note: since
∗
qH = qH , we only need to worry about the choice of qL .):
∗ ∗
max α(θL qL −C(qL ))+(1−α) [θL qL + θH (qH − qL ) − C(qH )] .
qL

80. Firm’s objective
The firm’s objective is
max α(pL − C(qL )) + (1 − α)(pH − C(qH )).
qL ,pL ,qH ,pH
Substituting in the material we just derived (Note: since
∗
qH = qH , we only need to worry about the choice of qL .):
∗ ∗
max α(θL qL −C(qL ))+(1−α) [θL qL + θH (qH − qL ) − C(qH )] .
qL
We can easily calculate the qL that maximises this by
differentiating:
α θL − C (qL ) + (1 − α) [θL − θH ] = 0

81. Firm’s objective
The firm’s objective is
max α(pL − C(qL )) + (1 − α)(pH − C(qH )).
qL ,pL ,qH ,pH
Substituting in the material we just derived (Note: since
∗
qH = qH , we only need to worry about the choice of qL .):
∗ ∗
max α(θL qL −C(qL ))+(1−α) [θL qL + θH (qH − qL ) − C(qH )] .
qL
We can easily calculate the qL that maximises this by
differentiating:
α θL − C (qL ) + (1 − α) [θL − θH ] = 0
1−α
Rearranging: C (qL ) = θL − α [θH − θL ]

82. Firm’s objective
The firm’s objective is
max α(pL − C(qL )) + (1 − α)(pH − C(qH )).
qL ,pL ,qH ,pH
Substituting in the material we just derived (Note: since
∗
qH = qH , we only need to worry about the choice of qL .):
∗ ∗
max α(θL qL −C(qL ))+(1−α) [θL qL + θH (qH − qL ) − C(qH )] .
qL
We can easily calculate the qL that maximises this by
differentiating:
α θL − C (qL ) + (1 − α) [θL − θH ] = 0
1−α
Rearranging: C (qL ) = θL − α [θH − θL ] < θL

83. Discussion of the model
The name of the game is to separate clients into groups and
milk each group for as much as possible.

84. Discussion of the model
The name of the game is to separate clients into groups and
milk each group for as much as possible.
The monopolist can squeeze more profit from high value
customers, who will pay more for a given increase in quality.

85. Discussion of the model
The name of the game is to separate clients into groups and
milk each group for as much as possible.
The monopolist can squeeze more profit from high value
customers, who will pay more for a given increase in quality.
But they can’t squeeze too hard—otherwise high value
consumers will just buy the cheap product.

86. Discussion of the model
The name of the game is to separate clients into groups and
milk each group for as much as possible.
The monopolist can squeeze more profit from high value
customers, who will pay more for a given increase in quality.
But they can’t squeeze too hard—otherwise high value
consumers will just buy the cheap product.
Solution: deliberately degrade the usefulness of the budget
product to ensure that high-value customers refuse to buy it.

87. Discussion of the model
The name of the game is to separate clients into groups and
milk each group for as much as possible.
The monopolist can squeeze more profit from high value
customers, who will pay more for a given increase in quality.
But they can’t squeeze too hard—otherwise high value
consumers will just buy the cheap product.
Solution: deliberately degrade the usefulness of the budget
product to ensure that high-value customers refuse to buy it.
Then the firm can charge a high price for the premium
product, without worrying about customers switching to
cheaper versions.

88. Discussion of the model
The name of the game is to separate clients into groups and
milk each group for as much as possible.
The monopolist can squeeze more profit from high value
customers, who will pay more for a given increase in quality.
But they can’t squeeze too hard—otherwise high value
consumers will just buy the cheap product.
Solution: deliberately degrade the usefulness of the budget
product to ensure that high-value customers refuse to buy it.
Then the firm can charge a high price for the premium
product, without worrying about customers switching to
cheaper versions.

89. Examples
£2/kg £2/kg £10/kg £18/kg

90. Examples
It is not because of the few thousand francs which would have to
be spent to put a roof over the third-class carriage or to upholster
the third-class seats that some company or other has open
carriages with wooden benches. . . What the company is trying to
do is prevent the passengers who can pay the second-class fare
from travelling third class; it hits the poor, not because it wants to
hurt them, but to frighten the rich. . . (Ekelund [1970])

91. Note that the distortion of qL away from its optimal level is a
market failure.

92. Note that the distortion of qL away from its optimal level is a
market failure.
However, it does not follow that the optimal policy is to
prevent firms from second degree discrimination. . .

93. Second-degree discrimination & social welfare
What will the firm do if it cannot price discriminate?

94. Second-degree discrimination & social welfare
What will the firm do if it cannot price discriminate?
∗ ∗ ∗ ∗
Will provide either qH at price θH qH , or qL at price θL qL .

95. Second-degree discrimination & social welfare
What will the firm do if it cannot price discriminate?
∗ ∗ ∗ ∗
Will provide either qH at price θH qH , or qL at price θL qL .
In the efficient allocation, social welfare is
∗ ∗ ∗ ∗
α [θL qL − C(qL )] + (1 − α) [θH qH − C(qH )] .
(we can ignore the ps which simply move surplus around).

96. Second-degree discrimination & social welfare
What will the firm do if it cannot price discriminate?
∗ ∗ ∗ ∗
Will provide either qH at price θH qH , or qL at price θL qL .
In the efficient allocation, social welfare is
∗ ∗ ∗ ∗
α [θL qL − C(qL )] + (1 − α) [θH qH − C(qH )] .
(we can ignore the ps which simply move surplus around).
In the second order price discrimination case, social welfare is
∗ ∗
α [θL qL − C(qL )] + (1 − α) [θH qH − C(qH )] .

97. Second-degree discrimination & social welfare
What will the firm do if it cannot price discriminate?
∗ ∗ ∗ ∗
Will provide either qH at price θH qH , or qL at price θL qL .
In the efficient allocation, social welfare is
∗ ∗ ∗ ∗
α [θL qL − C(qL )] + (1 − α) [θH qH − C(qH )] .
(we can ignore the ps which simply move surplus around).
In the second order price discrimination case, social welfare is
∗ ∗
α [θL qL − C(qL )] + (1 − α) [θH qH − C(qH )] .
∗
If the firm offers only qH , social welfare is
∗ ∗
(1 − α) [θH qH − C(qH )] .
Thus social welfare falls.

98. Second-degree discrimination & social welfare
What will the firm do if it cannot price discriminate?
∗ ∗ ∗ ∗
Will provide either qH at price θH qH , or qL at price θL qL .
In the efficient allocation, social welfare is
∗ ∗ ∗ ∗
α [θL qL − C(qL )] + (1 − α) [θH qH − C(qH )] .
(we can ignore the ps which simply move surplus around).
In the second order price discrimination case, social welfare is
∗ ∗
α [θL qL − C(qL )] + (1 − α) [θH qH − C(qH )] .
∗
If the firm offers only qH , social welfare is
∗ ∗
(1 − α) [θH qH − C(qH )] .
Thus social welfare falls.
∗
If the firm offers only qL , social welfare is
∗ ∗ ∗ ∗
α [θL qL − C(qL )] + (1 − α) [θH qL − C(qL )] ,
so that welfare may fall or increase relative to second-order
PD.

99. More current examples
In fact, when one thinks about it, there are similar-looking
cases in many information markets:

100. More current examples

101. More current examples

102. More current examples

103. More current examples

104. More current examples

105. Outline
Price discrimination: from assumptions to policy statements
Assumptions and applicability

106. Assumptions, assumptions. . .
But these examples are a little different to the ones considered
before:
Cost to MS of “surprising” a customer by giving them the
professional, rather than home edition of Windows is basically
zero.

107. Assumptions, assumptions. . .
But these examples are a little different to the ones considered
before:
Cost to MS of “surprising” a customer by giving them the
professional, rather than home edition of Windows is basically
zero.
Corresponds to C (q) = 0, C (q) = 0—which is contrary to
our assumptions.

108. Assumptions, assumptions. . .
But these examples are a little different to the ones considered
before:
Cost to MS of “surprising” a customer by giving them the
professional, rather than home edition of Windows is basically
zero.
Corresponds to C (q) = 0, C (q) = 0—which is contrary to
our assumptions.
When we try to put this into the model things break down.
Let’s see why. . .

109. Graphical treatment (assuming α = 1/2)
Price
Quantity
Quality

110. Graphical treatment (assuming α = 1/2)
Price
θH
Quantity
Quality

111. Graphical treatment (assuming α = 1/2)
Price
Willingness to pay
θH
Quantity
qH Quality

112. Graphical treatment (assuming α = 1/2)
Price
C’(q)
Quantity
Quality

113. Graphical treatment (assuming α = 1/2)
Price
C’(q)
Cost of production
Quantity
qH
Quality

114. Graphical treatment (assuming α = 1/2)
Price
C’(q)
θH
θL
Quantity
Quality

115. First degree discrimination
Price
C’(q)
θH
θL
Quantity
qL
* qH
*
Quality

116. Graphical treatment
Price
CS of high types from buying C’(q)
low quality good
θH
pL
θ L=
qL
Quantity
qL qH Quality

117. Graphical treatment
Price
CS of high types from buying C’(q)
low quality good
θH
pL
θ L=
qL
Quantity
qL qH Quality

118. Graphical treatment
Price
C’(q)
θH
pH
qH
pL
θ L=
qL
Quantity
qL qH Quality

119. Graphical treatment
Price
CS of high types from buying C’(q)
high quality good
θH
pH
qH
pL
θ L=
qL
Quantity
qL qH Quality

120. Graphical treatment
Price
C’(q)
θH
pL
θ L=
qL
Quantity
qL qL+Δ qH Quality

121. Graphical treatment
Price
Loss (must reduce pH to maintain ICH) C’(q)
θH
pL
θ L=
qL
Quantity
qL qL+Δ qH Quality

122. Graphical treatment
Price
Loss (must reduce pH to maintain ICH) C’(q)
θH
pL
θ L=
qL
Gain (can charge more
to low type consumers)
Loss (higher q is more
expensive to produce)
Quantity
qL qL+Δ qH Quality

123. Graphical treatment
Price
C’(q)
θH
pL
θ L=
qL
Quantity
qL qL
* qH
*
Quality

124. Constant marginal cost
Price
θH
pL
θ L=
qL
C’(q)
Quantity
Quality

125. What goes wrong?
Price
θH
pL
θ L=
qL
C’(q)
Quantity
qL qL+Δ Quality

126. What goes wrong? (i)
Price
θH
pL
θ L=
qL
C’(q)
Quantity
qL qL+Δ qL qL+Δ Quality

127. What goes wrong? (ii)
Price
θH
pL
θ L=
qL
C’(q)
Quantity
qL qL+Δ qL qL+Δ Quality

128. Declining marginal willingness to pay.
Price
θH
C’(q)
θL
Quantity
Quality

129. Declining marginal willingness to pay.
Price
Declining ΔWTP
θH
Quantity
Δq Δq Quality

130. First degree descrimination.
Price
θH
C’(q)
θL
Quantity
qL qH Quality

131. Profit effect of a quality increase.
Price Loss (Need to lower pH to maintain ICH)
θH
Gain (Can charge more to low value consumers)
C’(q)
θL
Quantity
qL qL
* qH
*
Quality

132. Other assumptions
In a similar manner, one can relax other assumptions e.g.:
Oligopoly suppliers.
Many consumer types.
Non-continuous q.

133. Summary
Social science is about understanding society.

134. Summary
Social science is about understanding society.
That, at least in part, means trying to understand the
fundamental forces that drive social phenomena.

135. Summary
Social science is about understanding society.
That, at least in part, means trying to understand the
fundamental forces that drive social phenomena.
Often, behaviour is fundamentally unchanged by new
technology. Looking into the past can offer hints on how to
understand and interpret the present.

136. Summary
Social science is about understanding society.
That, at least in part, means trying to understand the
fundamental forces that drive social phenomena.
Often, behaviour is fundamentally unchanged by new
technology. Looking into the past can offer hints on how to
understand and interpret the present.
Moreover, the result of linking related phenomena is often an
insight that exceeds the sum of its parts.

137. Summary
Social science is about understanding society.
That, at least in part, means trying to understand the
fundamental forces that drive social phenomena.
Often, behaviour is fundamentally unchanged by new
technology. Looking into the past can offer hints on how to
understand and interpret the present.
Moreover, the result of linking related phenomena is often an
insight that exceeds the sum of its parts.
Sometimes the process works backwards: new contexts can
generate insights into old puzzles—e.g. two-sided markets.

138. Summary
Social science is about understanding society.
That, at least in part, means trying to understand the
fundamental forces that drive social phenomena.
Often, behaviour is fundamentally unchanged by new
technology. Looking into the past can offer hints on how to
understand and interpret the present.
Moreover, the result of linking related phenomena is often an
insight that exceeds the sum of its parts.
Sometimes the process works backwards: new contexts can
generate insights into old puzzles—e.g. two-sided markets.
A key ingredient in making these links is an understanding of
the assumptions upon which alternative conceptualisations are
predicated.

139. Summary
Social science is about understanding society.
That, at least in part, means trying to understand the
fundamental forces that drive social phenomena.
Often, behaviour is fundamentally unchanged by new
technology. Looking into the past can offer hints on how to
understand and interpret the present.
Moreover, the result of linking related phenomena is often an
insight that exceeds the sum of its parts.
Sometimes the process works backwards: new contexts can
generate insights into old puzzles—e.g. two-sided markets.
A key ingredient in making these links is an understanding of
the assumptions upon which alternative conceptualisations are
predicated.