Transcript Chapter 4 Rights Management

Chapter 8 Price Dispersion and
Search Theory
• Price Dispersion
• Search Theory
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National Chiao Tung University
Price Dispersion
• Fact: (Price Dispersion) Prices of identical
products often vary from one store to another
• Explanation:
– Acquiring information on prices is costly to consumers,
and consumers always weigh the cost of searching
against the expected price reduction associated with
the search process
– Consumer with a high value of time will rationally
refrain from searching for the information on lower
prices and buy the product from the first available
store
– Consumers with a low search cost will find it beneficial
to engage in a search in order to locate the store
selling the lowest price
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National Chiao Tung University
A Model of Price Dispersion
• Consider an economy with a continuum of
consumers, index by s on the interval [L,H]
according to their cost for going shopping
(H>3L>0)
• Consumers indexed by a high s are high timevalued consumers, whose cost of searching for
the lowest price is high
• There are three stores selling a single product at
zero cost.
– One store, denoted by D is called discount store,
selling the product for a unit price of pD
– Two stores, denoted ND, are expensive (not discount)
stores, are managed by a single ownership that set a
uniform price, pND for the two nondiscount stores
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National Chiao Tung University
A Model of Price Dispersion (cont’)
L
s
H
Average product price
pD  2 pND
p
3
The loss function of consumer type s
 p   s if search and purchases at a discount store
Ls   D
if purchases at a store randomly
 p
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A Model of Price Dispersion (cont’)
L
ŝ
H
There exists a consumer denote by ŝ who is indifferent
to the choice between searching and shopping at
random
p  2 pND
pD   s  D
3
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sˆ 
2( pND  pD )
3
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A Model of Price Dispersion (cont’)
The discount store’s decision
The demand function
EbD  s  L 
H  sˆ H
4( pND  pD )
 L
3
3
9
The profit function
4( pND  pD ) 
H
E D  pD EbD  pD   L 

9
3

Pricing strategy
pD  BRD ( pND ) 
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3 ( H  3L) pND

8
2
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A Model of Price Dispersion (cont’)
The expensive store’s decision
The demand function
EbND 
2( H  sˆ) 2H 4( pD  pND )


3
3
9
The profit function
 2H 4( pD  pND ) 
E ND  pND EbND  pND 


3
9


Pricing strategy
pND  BRND ( pD ) 
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3 H pD

4
2
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A Model of Price Dispersion (cont’)
PD
BRND
 (2H  3L)
BRD
2
3 ( H  3L)
8
3 H
4
PND
 (5H  3L)
4
Price dispersion equilibrium
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National Chiao Tung University
A Model of Price Dispersion (cont’)
Equilibrium price
e
pD

 (2H  3L)
2
e
pND

 (5H  3L)
4
sˆe 
H  3L
6
e
e
e
e
pD
pND
 ( pND
 pD
)
sˆe
 0;
 0;
 0;
0




Equilibrium demand
EbD 
2(2H  3L) 5H  3L EbND


9
18
2
The expected number of shopper in discount store is
greater than the expected number of shoppers at a
expensive store
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National Chiao Tung University
A Model of Search Theory
• Consider a city with n types of stores
selling identical product, The price
charged by each store of type i is pi=i
• Suppose the consumer visits a store and
receives a price offer of p
• Define v(p) as the consumer’s expected
price reduction from visiting one additional
store, while having a price offer p in hand
p 1 p  2
v( p) 


n
n
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1 p2  p
 
n
2n
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A Model of Search Theory (cont’)
The loss function of the customer
p
if buys

L( p )  
 s  p  v( p ) if search one more time
The reservation price p is defined as
v( p )  s
p2  p
v( p ) 
s
2n
1  1  8ns
p
2
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p
 0;
s
p
 0; p  1
n
s 0
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A Model of Search Theory (cont’)
L(p)
s  p  v( p)
p
buy
p
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continue search
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A Model of Search Theory (cont’)
Denote σ the probability that a customer will not buy when he
or she randomly finds visits a store
n p
1  1  8ns

1
n
2n
Denoteμ the expected number of store visits


 t
t 1
t 1
1
2n
(1   ) 

1   1  1  8ns
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National Chiao Tung University