Signaling unobservable quality choice through price
and advertising: The case with competing firms
Speaker: Wu Fulan
3rd August,2009
Outline
 Motivation
 The model
 Results
 Conclusions
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Wu Fulan/NUS
Motivation
 Literature on price and/or advertising as signals of firms’
unobservable quality
 Exogenous quality literature
 Endogenous quality literature
 Examples of exogenous quality literature
 Kihlstom and Riordan (1984), Milgrom and Roberts (1986), and
Bagwell and Roirdan (1991)
 Examples of Endogenous quality literature
 Klein and Leffler (1981), Sharpiro (1983), Wolinsky (1983), Riordan
(1986), Bester (1998) and more recently Rasmussen (2008)
 In and Wright (2009)
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The monopoly model setup
 There are four stages
 In stage 1, each firm chooses its quality from
 In stage 2, each firm chooses a price
expenditure
and an advertising
 In stage 3, a representative consumer observes these choices but
not the quality level and decides whether to buy from the firm or
not
 In stage 4, if the consumer buys, it observes the firm’s true
quality, and with probability
decides whether to repurchase
or not
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The monopoly model setup (continued)

is strictly concave, increasing
 The firm and consumer discount the last period payoffs by
 Consumers wishing to buy in a period, buy a single unit, receiving
utility
from the good of type t
 The unit cost of production is
for the good of type t
 Assume
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Reordering invariance refinement by In and Wright
(2009)
 Multiple perfect Bayesian equilibria for the game we consider
 Equilibrium refinement “reordering invariance” in In and Wright
(2009)
 Reordered variant of the original game
 This game shares the same reduced normal form as the original
game.
 A unique pure strategy subgame perfect Bayesian equilibrium
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Analysis of the monopoly model
 Assume
 The minimum level of advertising is
 Assume 1    A   v

H
 cH   A  1    AL    vL  cL   AL
 A high quality equilibrium in which
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 vH  cL   A  1    A    vH  cH   A
P  vH
A  A  AH
1    A   v

H
 cH   A
Wu Fulan/NUS
The duopoly model setup
 There are two firms that are maximally differentiated in the
standard Hotelling fashion.
 The timing here is the same as before, except now consumers
choose one firm in stage 3 based on their location on the unit
interval, and in stage 4 decide whether to repurchase
 Stage 3 is divided into two sub stages: stage 3a and stage 3b
 Suppose a measure 1 of consumers are uniformly distributed on
the interval
 Let a consumer located at
on
get an additional firmspecific utility of
from firm 1 and
from firm 2, where
v measures competition intensity
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The duopoly model setup (continued)
 The bigger
, the more intense is competition
 This additional utility is obtained by shopping at firm i at stage 3a
regardless of whether the consumer buys anything at firm i in
stage 3b.
 However, consumer can only shop at one firm and must buy from
where they choose to shop
 This specification ensures that the market will be covered, with all
consumers buying from one and only one firm , but also at the
same time avoiding the possibility that a firm can charge above
vv and still make some sales.
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The duopoly model setup (continued)
 Thus if both firms charge a price at or below
, all consumers
will want to shop at one of the firms to get the added utility from
shopping, and will just be willing to buy the good from the firm
they choose if they think it is high quality.
 This implies if firm which is thought to be high quality price
above
, consumers very close to that shop may still shop there,
but they will not buy anything, and they know that when they
make their choice of where to shop.
 Thus, although the consumer makes two decisions, given the
assumption that consumers can only buy from where they shop,
they actually can make two decisions together, which is where to
buy from.
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Necessary conditions for a high quality equilibrium
 An equilibrium in which both firms chooses high quality
 If both firms charges price above
, all consumers will want to
shop at the firms, but they will not buy anything
 If
, then
 Quality ensuring condition
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Necessary conditions for a high quality equilibrium
(continued)
 Further,
 A consumer at
is indifferent between firm 1 and firm 2 if
 Firm 1’s demand function
 Firm1’s profit function is
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Necessary conditions for a high quality equilibrium
(continued)
 Maximize firm 1’ profit




 c c 
c  c 
c  c 
1 
 1    A1    vH   cH  H L    1    A2    vH   cH  H L   ) 1    A1    H L   A1


   A  


2 2
  A1   
  A2    
1 






1  ( 
subject to

then set


0
0
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
2
 '  A1  vH  cH   1
 vH  cH 




1 
1
1   
  cH  cL  1 
 cH  cL     vH  cH  1 
 
  1
2 


   A1     A1   
   A1    

1
Wu Fulan/NUS
A high quality equilibrium
 A high quality equilibrium in which the two firms choose high quality,
P1  P2
A1  A2
vH  P1  cH 
cH  cL
 vL
 A1
1

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 

2
 cH  cL 
 '  A1 
  A 

c c
 ' A  vH  cH  H L
2

 A1


0
Ai  A  AH
 

1
  

1
2

  c  c  cH  cL
H
L
2 
 A1
 

 




 vH  cH 




1 
1
1   
  cH  cL  1 
 cH  cL     vH  cH  1 
 
  1
2 


   A1     A1   
   A1    

1
Wu Fulan/NUS
A numerical example
 Consider a example with

1 
(cH  cL ) 1 
    vH  cH   1
 vH  vL 
 This assumption implies that
 If we further assume that
AL  AH  0
  0.9 vH  1
and
  A  A 1  A
A  (cH  cL )   vH  cH   (cH  cL )   0
vL  0.2
cH  0.1
cL  0
 The monopoly solution has A=0.14, P=1, and profit=0.86
 Now we extend the example to consider competition. Assume
 2
 The solution has A1=A2=0.21, P1=P2=0.74
 Each firm’s profit is 0.16
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Wu Fulan/NUS
Check the proposed equilibrium for high quality
 Check a firm can not do better by deviating and choosing a lower
price and advertising level, such that it will want to set low quality
 If firm 1 did this, then its demand function is








 A1  

cH  c L
1 
 0.21105   


s1  
1   
   vL  P1   1   
  vH  c H 
0.21105
2 2  
1

A
1

0.21105









1 


 



 1  0.21105    



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Check the proposed equilibrium for high quality
(continued)
 Substitute
into the demand function









cH  cL
1 
 0.21105   


s1  
 vL  P1   1   
  vH  c H 
0.21105
2 2
1

0.21105










 



 1  0.21105    














cH  cL
1 
 0.21105   

     P1  cL 
1  
v  P   1  
  vH   c H 
 2 2  L 1 
0.21105
1

0.21105









    



 1  0.21105     





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gives P1=0.2, and its resulting profit is 0.04(<0.16)
Wu Fulan/NUS
Results
 Pure strategy equilibrium exists when    0, 3.15 , but there is no pure
strategy equilibrium when   3.15
 The case of monopoly corresponds to
equilibrium
   0,1
in the high quality
 When the competition effect is weak, the monopoly price and
advertising level remains an equilibrium outcome.
 As the competition effect gets stronger, the high quality firms
lower their prices and raise their advertising levels as shown in
figure 1.
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Results: relationship between price, advertising and
competition(
)
1.1
advertising A1
price p1
advertising A1 and price p1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.5
1.0
1.5
2.0
2.5
3.0
competition intensity 
Note: A and p1 are advertising and price level respectively in the proposed high quality equilibrium
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Conclusions
 The high quality equilibrium outcome under monopoly
 Price and advertising level
 Profit and social welfare
 Social welfare with a ban on advertising
 The high quality equilibrium outcome under duopoly
 Price and advertising level
 Social welfare owing to the price and advertising
 Social welfare with a ban on advertising
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Thank you
The End
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