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wk7.pdf-Monopoly & Price Discrimination Ram Shivak...
wk7.pdf-Monopoly & Price Discrimination Ram Shivakumar
wk7.pdf-Monopoly & Price Discrimina...
wk7.pdf-Monopoly & Price Discrimination Ram Shivakumar
Page 28
28
Why distort Q*(1)?
Pric
e
Q*(2)
Q*(1)
A
Quantity
B
C
Profit-maximizing non-linear pricing
1
2
Quantity
Q**(1)
Q*(2)
Total Outlay
OBHQ**(1)
OAEQ*(2)- BAIH
Seller’s Profit
N(1) * CBHG
N(2) * (CAE-BAIH)
n(1) = # in group 1
n(2) = # in group 2
E
D
F
O
I
H
G
Q**(1)
Page 29
29
Why distort Q(1) from Q*(1) to Q**(1)?
ΔΠ
= n(1) [CBHG
–
CBD] + n(2) [ (CAE- BAIH)
–
CAE
–
BAFD)]
= - n(1) GHD + n(2) HIFD
As long as n(2) > 0, there will always be a sufficiently small distortion,
Q*(1)
–
Q**(1) such that
ΔΠ
> 0 because for Q**(1) close to Q*(1) GHD is
approximately equal to 0 while HIFD is greater than 0
“Low
-
demand” consumers derive no consumer surplus while “high
-
demand” consumers derive positive consumer surplus
The binding personal arbitrage constraint is to prevent “high
-
demand”
consumers from buying the “low
-
demand” consumers’ bundle
Page 30
30
Group pricing (or 3
rd
degree PD)
Why engage in pricing by group?
How to segment by group?
Segment by geography (zip code, country, state)
Segment by time of use (peak-time versus off-peak)
Segment by age (senior citizen versus non-senior citizen)
Segment by income (high versus low)
Page 31
31
The economics of 3
rd
degree PD
Price
10
Price
MC
15
Q
Q
25
Q*(a)
Market a
Market b
Q*(b)
P(a) > P(b) but we cannot say that Q(a) < Q(b)
Page 32
32
An example
Tourists: Q
t
= 1700
–
P
t
; Locals: Q
l
= 2400
–
10P
l
; MC = 100
Set up the optimization problem for the firm
What is the first-order condition?
What price should the monopolist charge each “group” of consumers?
What is the profit from each segment?
What if the monopolist could only charge a single price?
Page 33
Examples
A month’s supply of Zoloft (2008)
Mexico: $40.97
USA: 64.47
Autos in Canada are 0% to 10% lower than
in the US
Page 34
34
Bundling: an example
You run an Italian restaurant:
Sell eggplant parmesan and tiramisu (amongst other things)
Want to know which type of pricing method maximizes your profits:
Individual pricing: A la carte
Pure bundling: Buffet only
Mixed bundling: Buffet and A la carte
Suppose that the a-la-carte menu lists each item at $8:
And suppose that the price of the buffet is $12
Page 35
35
A la carte
versus
pure bundling
(buffet only)
Value of tiramisu
Value of tiramisu
Value of eggplant parmesan
Value of eggplant parmesan
A la carte
Bundling
8
8
10
6
6
10
8
8
10
6
6
10
12
12
Buys nothing
Buys only tiramisu
Buys only eggplant
parmesan
Buys both
z
x
y
z
y
x
Buys nothing
Buys bundle
How much surplus do x, y and z get in each case?
Page 36
36
Mixed bundling
: A la carte and buffet
Value of tiramisu
Value of eggplant
parmesan
8
8
10
6
6
10
12
12
z
y
x
Buys nothing
Buys bundle
Buys only eggplant
parmesan
Buys only
tiramisu
How much surplus do x, y and z get?
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