Part 6B. Pricing & Advertising
4.
Multimarket Price
Discrimination
市場區隔差別取價


Multimarket Price Discrimination with 2 Groups
Welfare Effects of Multimarket Price
Discrimination
2015.5.28
1
Multimarket Price Discrimination
with 2 Groups

Multimarket Price Discrimination
 Firms divide potential customers into two or
more groups (based on some easily observable
characteristic) and set a different price for each
group.
l can separate
t
Market Separation
Separation: a monopoly
its buyers into a few identifiable markets. e.g.,
senior
i or student
t d t discounts
di
t
2

The Discriminating
g Monopoly’s
p y Decision
Problem
The firm chooses quantities sold to each group, Q1
and Q2, such that
max   TR1 (Q1 )  TR2 (Q2 )  C (Q1  Q2 )
{Q1 ,Q2 }
F.O.C.:
d dTR1 (Q1 ) dC (Q) dQ


0
dQ
Q1
dQ
Q1
dQ
Q dQ
Q1
d dTR2 (Q2 ) dC (Q) dQ


0
dQ2
dQ2
dQ dQ2
 MR1  MC  MR2
3
The F.O.C.s imply
p y that marginal
g
revenue from each
group should be the same and equal to marginal
cost:
MR1  MC  MR2
Because MR is a function of elasticity, we can write:

1
MR1  p1 1  1
 e
D, p



1
  MC  p2 1  2

 eD , p

 MR2

1  1/ e1D , p
p2


p1 1  1/ e1D , p
The higher price will be charged in the less
elastic market segment.
4

Figure:
g
Market Separation
p
If two markets are separate, maximum profits
occur by
b setting
i different
diff
prices
i
in
i the
h two markets.
k
Price
The market with the less
elastic demand will be
charged the higher price.
p1
p2
MC
MC
D
D
MR
Quantity in Market 1
MR
Q1*
0
Q2*
Quantity in Market 2
5

Figure:
g
Multimarket Price Discrimination
The higher price will
be charged in the less
elastic market
segment.
Perloff (2014, 3e, GE), Fig. 12.3, p. 441.
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Welfare Effects of
Multimarket Price Discrimination

Multimarket Prices
Welfare under multimarket price discrimination is
lower than it is under either competition or perfect
price discrimination
discrimination.
Under competition, more output is produced and
t
CS iis greater.
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
Uniform Price
The welfare effects relative to uniform price
monopoly are indeterminate.
Both types of monopolies set price above MC, so
output is lower than in competition
competition.
Welfare is likely to be lower with
di i i ti bbecause off consumption
discrimination
ti
inefficiency and time wasted shopping.
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
Example:
p
Suppose that the inverse demand curves in two
separated markets are given by
P1 = 24 – Q1
P2 = 12 – 0.5Q2
Suppose that MC = 6
Profit maximization requires that
MR1 = 24 – 2Q1 = 6 = MR2 = 12 – Q2
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Optimal
p
choices and pprices are
Q1* = 9
P1* = 15
Q2* = 6
P2* = 9
Note: The competitive
p
output
p would be 18 in
market 1 and 12 in market 2.
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Profits for the monopoly
p y are
 = (P1 – 6)Q1 + (P2 – 6)Q2 = 81 + 18 = 99
We can calculate the DWL in the two markets
DW1 = 0.5(P
( 1 – MC)(18
)( – Q1)
= 0.5(15 – 6)(18-9) = 40.5
DW2 = 0.5(P
0 5(P2 – MC)(12 – Q2)
= 0.5(9 – 6)(12 – 6) = 9
DW = DW1 + DW2 = 40.5 + 9 = 49.5
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If this monopoly
p y were constrained to charge
g a
single price, there are two possible solutions:
Case 1: p* = 11,
11 Q1* = 9,
9 Q2* = 6,
6
 = (p1 – 6)(Q1 + Q2) = 5  15 = 75
Case 2: p* = 15, Q1* = 9 (sell only in the first
market),
market)
 = (p1 – 6)Q1 = 9  9 = 81 > 75
DW = DW1 + DW2 = 40.5 + 0.5(12 – 6)(12 – 0)
= 40.5
40 5 + 36 = 76.5
76 5 > 49.5
49 5
 DWL: Total potential CS in market 2 is lost.
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