Parallel Imports, Product Innovation
and Market Structures
Hong Hwang, Cheng-Hau Peng and Pei-Cyuan Shih
To presented at the Department of Economics, NCCU
2014/11/03
What Is Parallel Import?
• Parallel import (PI) occurs when a genuine product is sold back by
licensed foreign distributers without the permission of the domestic
intellectual property owner who, we call it the manufacturer, also
serves the domestic market.
• Examples:
•
•
•
•
DVD
Textbook
Automobile
Medicine
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Motivation
• Evidences have shown that there is a burgeoning trend in parallel
imports around the world.
• Ganslandt and Maskus (2004) show that EU loses approximate $3 billion
sales per year owing to the occurrence of PI.
• The value of PI in the US rose from 7–10 billion USD in the mid-1980s to
20 billion USD in the 1990s (Cespedes et al., 1988; Computer Reseller
News, 2001)
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Related Literature
• Trade cost : Maskus and Chen (2004), Chen and Maskus(2005),
Mueller-Langer (2012)
• Labor union: Mukherjee and Zhao (2012)
• Process R&D:
• Li and Maskus (2006)
• Product R&D:
• Li and Robles (2007)
• Matteucci and Reverberi (2014)
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Aims
• Consider the effect of PI on the manufacturer’s product innovation by
assuming the manufacturer sells its product to the foreign distributor
via two-part tariff pricing.
• Explore the effect of local rivals in the domestic market, which is
commonly observed in the real world but has been overlooked in this
line of research.
• Examine the case in which the manufacturer has multiple distributors
in the foreign market.
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Preview of the Findings
• PI necessarily decreases the manufacturer’s product R&D if the
domestic market is monopolized by the manufacturer.
• PI definitely stimulates product innovation of the manufacturer if it
faces local rivals.
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Preview of the Findings
• If the manufacturer can authorize its product to multiple foreign
distributors, its product innovation can be either positively or
negatively affected by PI, depending on consumers’ preferences for
innovation in the domestic and the foreign markets.
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Outlines
• Section 2 introduces the basic model and examines the optimal
product innovation with no parallel imports.
• Section 3 investigates the effect of parallel imports on the
manufacturer’s product innovation.
• Section 4 explores the product innovation of the manufacturer when
it faces domestic rivals or authorizes its product to multiple
distributors.
• Section 5 concludes the paper.
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The Model
• Assume there are two countries, H and F, hosting one firm each.
Variables with a star are those associated with the foreign firm.
• In the home country, there is a manufacturer with marginal cost c
selling its product, x in the home market and authorizing a foreign
distributor to sell its product, y * in country F.
• The distributor can sell back to the home country through parallel
import, x , and the transport cost is nil.
• The manufacturer and the distributor compete in quantity in the
home country if PI is permitted.
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The Model
• The inverse demand functions for countries H and F are

and p  p

y

,

with p x  p x *  0 , p  0 ,
*
y
p  p  x  x ,
*

p  0 , p  0 and
*
the second derivatives of the demands are assumed to be zero.
• The manufacturer engages in product innovation  with the cost
function V ( ), V  0, and V
 0.
• The manufacturer adopts two-part tariff pricing (the per-unit wholesale
price, w, plus a fixed fee, T ) when selling the product to the distributor.
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Game Structure
• The game in question consists of three stages.
Stage1: The manufacturer determines its optimal product R&D.
Stage 2: The manufacturer determines its optimal two-part tariff
pricing contract.
Stage 3: The two firms determine their optimal sales in the two
markets with or with no PI.
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The No-PI Regime
• The profit functions of the manufacturer and the distributor can be
expressed respectively as follows:
 ( x ; w , T ,  )   p  x ,    c  x  ( w  c ) y  T  V ( ),





 ( y ; w, T , )  ( p  w ) y  T .
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(1)
(2)
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No-PI regime—The Third-stage Game
• The FOCs
 x  p  c  p x x  0,


(3)

 y  p  w  p y * y  0.
*
(4)

• The second-order conditions are satisfied given the linear demands
and constant marginal cost.
• The comparative static effects are derivable as follows:


*

*
x    p  2 p x  0, y    p  2 p y *  0, and y w  1 2 p y *  0 .
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No-PI Regime—The Second-stage Game
• The profit function of the manufacturer for the second-stage game
is as follows:
M ax  ( x , y ( w ), w , T ;  )  ( p  c ) x  ( w  c ) y ( w )  T  V ( ),
(5)
where T  ( p  ( y  ( w ))  w ) y  ( w )


w
• The FOC:
d
dw

 y
y


w


w

 T
T w

 (w  c) yw  0
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(6)
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Proposition 1
If the manufacturer adopts two-part tariff pricing and parallel
trade is prohibited, product innovation has no effect on the
wholesale price.
Intuition: Under two-part tariff pricing, the manufacturer always sets
its wholesale price w = c. Product innovation affects only the demand,
yielding no effect on the equilibrium price.
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No-PI Regime—The First-stage Game
• The profit function of the manufacturer in the first-stage game can be
expressed as follows:

(7)
M ax   ( p ( x ( ),  )  c ) x ( )  T ( y ( ),  )  V ( ).

• The FOC:
d
d

  dT
T d





 p  y  p  x  V  0
(8)
• From (8), we can derive the optimal product innovation level  N
under the no PI regime.
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The PI Regime
• Now let us consider that country H adopts international exhaustion (i.e.,
the PI regime).
• Under the PI regime, the foreign distributor can engage in PI if it is
profitable.
• All the assumptions and model settings are the same as those in the
previous section, except that the foreign distributor competes with the
manufacturer in Cournot fashion in country H.
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PI Regime— The Third-stage Game
The profit functions of the two firms under the PI regime can be
written respectively as follows:





 ( x , x , y ; w , T ,  )   p  x  x ,    c  x  ( w  c )  x  y   T  V ( ),


 ( x , x , y ; w , T ,  )   p  Q ,    w  x   p






y

,   w  y  T


(9)
(10)
The FOC:
 x  p  c  p x x  0,

(11)
(12)
(13)

 x  p  w  p x * x  0.




 y  p  w  p y * y  0.
*

The SOCs and the stability condition are satisfied.
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PI Regime-- The Second-stage Game
The profit function of the manufacturer for the second-stage game can
be expressed as follows:


M ax  ( x ( w ), x ( w ), y ( w ), w , T ;  )
w


 ( p ( Q ( w ))  c ) x ( w )  ( w  c )  x ( w )  y ( w )   T  V ( )
(14)
The FOC:
d
dw

 x
x


w

 y
y


w


w

  dT
 T dw




 p x x w x  ( w  c )  y w  x w   p x x w x  0
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(15)
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PI Regime– The Second-stage Game
• We can derive from the FOC:
w (  )   2 p x (2 x  x ) 5  c
*
and also the comparative static effect as follows:
w    w  ww  0 ,
where  w   p 9 p x  0 .
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Proposition 2
If the manufacturer adopts two-part tariff pricing and parallel
import is permitted, the wholesale price is necessarily higher
than its marginal cost and is positively related to the product
innovation level.
Intuition: The manufacturer raises the wholesale price to lower the
competition in its home market.
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PI regime– The First-stage Game
• The profit function of the manufacture firm is as follows:


M ax  ( x ( w ( ),  ), x ( w ( ),  ), y ( w ( ),  ), w ( ), T ( w ( ),  ),  ; t )

*


  p ( x  x )  c  x   w ( )  c   x  y   T ( )  V ( )
(16)
• By differentiating the above equation with respect to  , we can
derive the first-order condition for profit maximization as follows:
d
d

 w
w 

 y
y




 x
x




 T x
T x 

 T
T 



 (w  c)

  ( w  c ) 2( x  x  ) 


 p 

 y   V  0
  p 
*
3
 2 p y *

 3 px

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(17)
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Product Innovation with and without PI
• Assume that the inverse demand functions of the home and the
foreign markets take respectively the following linear forms as



 
p  a ( )  b ( x  x ) and p  a ( )  b y . By evaluating the above
equation at the product innovation level derived under the no-PI
regime, we obtain:
d
d

 
N
 p

2(4 b  9 b )
 a ( )  c   0.
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Proposition 3
If the manufacturer adopts two-part tariff pricing, parallel
import definitely reduces the product innovation of the
manufacturer.
• Intuition: (1) duopoly in the home market
(2) w is too high
• Matteucci and Reverberi (2014)
• Li and Maskus (2006)
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Product Innovation and Market Structures
• In the existing literature on PI, it is commonly assumed that there are
only two firms- one manufacturer and one distributor- in the models.
• In this section, we shall relax this assumption to investigate if the
domestic or the foreign market becomes oligopolistic, how it affects
the manufacturer’s product innovation with and with no PI.
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The Existence of Domestic Rivals
• All the model settings are the same as those in the previous sections
except that now there are n homogeneous rivals in the domestic
market whose product innovation is predetermined and whose
outputs are sold to the home market only.
• The inverse demand functions under the PI regime are
n
p  a ( )  x   x  x
i
i 1





and p  p  y ,    a ( )  y, and x   0 if there is no PI.
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
The First-stage Game with No PI
• The second- and the third- stage games are akin to the previous
section, we need to work out the first-stage game.
• With no PI, the profit function of the manufacturer for the first-stage
game is as follows:

M ax  ( x ( ), x ( ), y ( ), w , T ( w ,  ),  )
i




 ( p ( Q ( ),  )  c ) x ( )  ( p ( y ( ),  )  c ) y ( )  V ( ).
• FOC:
d
d

(18)

 np x x x  p y  p x  V  0
i
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The Second-stage Game with PI
• The third-stage game is the same as before, we need to work out the
first and the second-stage games.
• Proceeding as before, we can derive the optimal wholesale price as
follows:


w  2  2 x ( c )  ( n  1) x ( w )  (3 n  7 )  c .
• It can be shown that the optimal wholesale price is equal to (lower
than) c if n  (  )1.
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Proposition 4
If the manufacturer faces domestic rivals, parallel import reduces
the wholesale price to a level lower that the marginal cost. If there
is only one rival in the domestic market, PI has no effect on the
wholesale price (i.e., w = c).
Intuition: If n = 1, the effective output of the manufacturer is the same as
that of the Stackelberg leader. It is optimal to set w =c. If n >1, the
Stackelberg leader’s output is higher. It means that the manufacturer
needs to set w to a lower level (i.e., lower than c).
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The First-stage Game with PI
In the first stage, the manufacturer faces the following maximization
problem:


M ax  ( x ( w ( ),  ), x ( w ( ),  ), y ( w ( ),  ), x ( w ( ),  ), w ( ), T ( w ( ),  ),  )
i

  p ( Q ( w ( ),  )  c  x ( w ( ),  )


  w ( )  c   y ( w ( ),  )  x ( w ( ),  )   T ( w ( ),  )  V ( )
The FOC:
 ( w  c ) 2( x  x  ) 
  (w  c)

 p 


p

y
 V  0
 


d
( n  3) 
2


 ( n  3)
d
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Product Innovation with and with No PI
• By evaluating the above equation at the product quality level
derived under the no PI regime, we can derive:
d
d

 
N
2 p
 ( n  2) x   ( n  1) x N 

( n  1)( n  2) 
2 p   a ( )  c  ( 2 n  2 n  1)
2

( n  2 ) ( n  10 n  13)
2
2
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0
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Proposition 5
If there are rivals in the domestic market, parallel import
stimulates the product innovation of the manufacturer.
Intuition: If there are rivals in the domestic market, PI increases the
market share of the manufacturer, raising its marginal benefit from
innovation and thus the investment.
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Multiple Distributors
• For simplicity, we assume that all the distributors are symmetric and
can engage in PI if it is permitted by the home country.
• The inverse demand functions for country H and country F under the
n
n
n
i 1
i 1
i 1
i
PI regime are p  a ( )  x   x  i and p   a  ( )   y  i , and  x  0
if there is no PI.
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The Second-stage Game with No PI
• The third stage game is similar to that in Section 3. Proceeding as
before, we can derive the optimal wholesale price as follows:
w
N

  ( n  1) p y  c
*
y*
with w n  0 .
N
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The First-stage Game with No PI
• The profit function of the manufacture firm is as follows:

M ax  ( x ( ), y ( ), w ( ), T ( w ,  ),  )




 ( p ( x ( ),  )  c ) x ( )  ( p ( y ( ),  )  c ) y ( )  V ( ).
• The FOC:




a
(

)

c
p
d

    a ( )  c  p
 
 p y  p x  V 
 V  0
d
2
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Proposition 6
With no PI, the optimal wholesale price increases with the number of
authorized distributors in the foreign market. However, the equilibrium
outputs of the two markets, the optimal product R&D and the profits of
the manufacturer are not affected by the number of the authorized
distributors.
Intuition: With no PI, the home market is unaffected by n. Since the
distributors are symmetric, the manufacturer can always set the output at
the first-best level, via two-part tariff pricing.
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The Second-stage Game with PI
The third stage game is similar to that in Section 3. Proceeding as
before, we can derive the optimal wholesale price under the PI regime
as follows:

w
2( n  1) x  (2  n )( n  1) x  ( n  2)(1  n ) y
(3 n  4)
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
c
37
The First-stage Game with PI
The objective function of the manufacturer for the first-stage game is
as follows:


M ax  ( x ( w ( ),  ), y ( w ( ),  ), x ( w ( ),  ), w ( ), T ( w ( ),  ),  )



  p  c  x ( w ( ),  )  n  w ( )  c   y ( w ( ),  )  x ( w ( ),  ) 
 nT ( w ( ),  )  V ( ).
The FOC:


 ( w  c ) n 2( n  1) x
2 nx 
2y 
  (w  c)
 p 



  np 
  V  0.
d
( n  2)
( n  2) 
 ( n  2)
 ( n  1) ( n  1) 
d
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Product innovation with and with No PI
By evaluating the above first-order condition at the product quality
level derived under the no-PI regime, we can obtain:
d
d
 
N
 a ( ) n  a  ( )(1  n )  c   ( n  1) p  np  




 0
2
2(2 n  6 n  5)

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
if ( n  1) p

 np .

39
Proposition 7
If the manufacturer authorizes its product to multiple distributors in the
foreign country, parallel imports may increase or decrease its product
innovation, depending on the consumers’ quality valuations in the two
countries.
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Intuition: PI has two effects on innovation:
• A negative effect: With PI, the domestic market becomes oligopolistic which
discourages product innovation.
• A positive effect: The manufacturer has an incentive to do more product R&D
as it can raise the wholesale price, mitigating the amount of PI.
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Conclusions
• Product innovation of the manufacturer is definitely stifled by parallel
import if the domestic market is monopolized by the manufacturer.
• Contrarily, if there are rivals in the domestic market, permitting
parallel import necessarily enhances the production innovation.
• If the manufacturer authorizes its product to multiple distributors in
the foreign country, parallel import may increase or decrease the
product innovation depending on the consumers’ preferences for
product innovation in the two countries.
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Thank you
Comments and suggestions are welcome
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