Bargaining Power
and
Subcontracting Trade Policy
Ku-Chu Tsao
Shih-Jye Wu
Yan-Shu Lin
Introduction
Introduction
About subcontracting literature
• 陳芳岳與洪進朝(1997)
陳芳岳與洪進朝(1997)
• Shy and Stenbacka
(2003)
一文討論在一個國際廠商之間存在「委
Chen and Liang (2008)
• Chen and Liang
(2008)
託代工」(OEM)
契約的雙占模型中探
則探討在事前協議代工下兩個跨
討受委託國之最適貿易政策。OEM 市
• Chen et al. (2004)
國廠商競爭之間的關係。這表示
場為買者訂價的假設下，其代工與否不
• Ornelas and Turner出口國可以選擇在最終產品和代
(2008)
僅取決於貿易政策變數與貿易國家之比
工產品中透過差別的或是相同的
• Maiti and Mukherjee
(2013)
較利益，並且必須考慮廠商間之策略性
貿易政策來達到最適貿易政策。
Vertical related market
& subcontractingOEM 產品之出
互動。此文得到：對其
他們得到，同時對最終產品課出
• Arya et al. (2008)
口應予課稅，但對出口至第三國之產品
口稅與對代工產品出口補貼的這
則應予補貼。
• 王光正與邱俊榮 (2004)
種差別貿易政策不一定是最適的
• Liang et al. (2006) 貿易政策。若出口廠商是純代工
廠商，則課徵出口稅會是最適貿
• Kawabata (2010)、(2012)
易政策。
• 吳世傑與陳宏易 (2014)
Introduction
Using bargaining power to share the surplus
• Spiegel (1993)
• Liang et al. (2006)
• Ghosh and Saha (2008)
• Yang and Maskus (2009)
• Ishikawa et al. (2010)
The Model
• Two vertically related activities in two countries, domestic and
foreign country.
• Each country has one firm producing a homogeneous
intermediate good and also a differentiated final good.
• Two firms export all of their final good to a third-country final
good market, where they compete in a Bertrand duopoly.
The Model
firm D
t
firm F
subcontracting
m
D
q
s
qD
mF
qF
third-country
The Model
Three stage game
• Stage 1: Domestic government determines the
optimal trade policy, t.
• Stage 2: Bertrand duopoly, P
• Stage 3: firms' subcontracting strategy.
• Backward induction, sub-game perfect
equilibrium.
The Model
• Assumptions:
1. The linear demand function:
q i ( p D , p F ), q ip i  0, q ip i p i  0.
2. Two final good firms are substitute.
qip j  0
3. Marginal cost of intermediate good in firm F is
higher than firm D.
mF  mD  t  0
4. One unit of the intermediate good is required to
produce one unit of the final good.
qS  qF
The Model
• According to Spiegel(1993) model, the surplus generating from
subcontracting is given by

S ( p D , p F )  m D q D ( p D , p F )  m F q F ( p D , p F )  m D q D ( p D , p F )  (m D  t )q F ( p D , p F )



 m F  (m D  t ) q F ( p D , p F )
• The transfer payment is chosen to split between the firms according
to their bargaining powers. Thus, following Spiegel,
 (p D , p F )  (1   )
m D q D ( p D , p F )  (m D  t )q F ( p D , p F )  m D q D ( p D , p F )

incremental cos t added to firm D ' s productionopreation

mq
( p , p )  0


F
F
D
F
cos t saving derived from firm F ' s productionopreation
 (1   )( m D  t )q F ( p D , p F )   m F q F ( p D , p F )
The Model
• Let α (resp. (1-α)) denote firm D’s (resp. firm F’s)
bargaining power on subcontracting and    0,1
•
Profit functions of firm D and firm F:
 D  p D , p F   p D q D ( p D , p F )   ( p D , p F )  m D q D ( p D , p F )  (m D  t )q F ( p D , p F )
 ( p D  m D )q D ( p D , p F )   [m F  (m D  t )]q F ( p D , p F ),
(1)
 F pD , pF   pF qF ( pD , pF )  ( pD , pF )
 ( p F  m F )q F ( p D , p F )  1   [m F  (m D  t )]q F ( p D , p F ),
(2)
The Model
• first-order conditions
R D :  pDD  q D ( p D , p F )  ( p D  m D )qPDD   [m F  (m D  t )]q pFD  0,


 
competitive effect
subcontracting surplus effect
R F :  pFF  q F ( p D , p F )  ( p F  m F )q pFF  (1   )[ m F  (m D  t )]q pFF  0,


 
competitive effect
(3)
subcontracting surplus effect
(4)
The Model
• In order to ensure that the firm D and firm
F all will be improved after subcontracting.
• The profit function without subcontracting
 i  p i , p j , mi    p i  mi q i  p i , p j 
• where  i   i , if    .
•
first-order conditions


R i :  pi i  q i p i , p j  ( p i  mi )qPi i  0, i  D, F , i  j ,
The Model
• The shifting on reaction function between with and
without subcontracting is dependent on α.
• When α is higher,
R D (    1) is farther from R D (  0), but R F (  1) is closer
from R F (    1)
pF
R D (  0)
R D (    1)
R F (  1)
E
E1
R F (    1)
E
figure 1.
E2
0
pD
The Model
• figure 1.
pF
R D (  0)
R D (    1)
R F (  1)
E
E1
R F (    1)
E
E2
pD
0
The Model
• Proposition 1
Consider    , the prices of final good will increase or
decrease after subcontract, which depends on firm’s
bargaining power. If the domestic firm’s bargaining
power is sufficiently great (small), both prices of final
good will increase (decrease). However, if firm’s
bargaining power is middle value, the price of domestic
final good is increased but the foreign’s is decreased.
The Model
Domestic firm
 who has incentive to increase price → increase amount of
subcontracting.
Foreign firm.
 firm F has incentive to decrease the price → cost reducing.
 Since the price competition is strategic complement, the
different equilibrium price in subcontract before and after is
depending on the bargaining power.
The Model
If α is sufficiently great,
• the foreign equilibrium price will increase rather than
decrease, because the effect of strategic complement
dominate the incentive to decrease price by firm F.
If α is sufficiently small,
• the domestic equilibrium price will decrease rather than
increase, because the effect of strategic complement
dominate the incentive to increase price by firm D.
If bargaining power is middle value,
• the strategic complement is not important,
• the domestic and foreign equilibrium prices will
respectively increase and decrease.
The Model
• comparative statics
D
F
F
D
F
D
F
D
F
dp D (  p D ) p F p F   p F p D p F (m  m  t )(2q p D  q p F )q p F


 0,
d
H
H
D
F
D
F
F
D
F
D
F
F
dp F   p D p D  p F   p D  p F p D (m  m  t )( 2q p F q p D  q p D q p D )


 0,
d
H
H
(5-1)
(5-2)
• A higher α increases the prices of two firms’ final good.
• For domestic firm: a higher α→ increase the
subcontracting surplus effect→more profit by
subcontracting→ increase the amount of subcontracting.
• For foreign firm: a higher α→ decrease the intensity of
subcontracting surplus effect→ strengthen the foreign
firm’s incentive to increase the price.
The Model
• A higher α increases the equilibrium prices of two firms’
final good.
pF
R D    
R D    
R F    
E(   )
R F    
E(   )
0
pD
The Model




D
F
D
F
2q FpD  (2   )q D
q FpF
dp D   p Dt  p F p F   p D p F  p F t
pF


 0,    *
dt
H
H



D
F
D
F
D F
F
F 
dp F   p D p D  p F t   p Dt  p F p D 2(2   )q p D q p F  q p D q p D


 0,    * *
dt
H
H


(6-1)
(6-2)
• domestic firm: A higher t →decrease
subcontracting surplus effect→ R D shifts to left hand
side.
• foreign firm: A higher t →not only decreases the
surplus of subcontracting but also increase the
marginal cost of final good→ R F is upward shifting.
The Model
• Since the range of shifting of the reaction functions would be
affect by α .
→the effect of optimal price on the domestic export tax will
depend on α.
pF
R D t  0
R D t  0
R F t  0
E (t  0)
R F t  0
E (t  0)
figure 2
0
pD
The Model
• Corollary 1.
A higher bargaining power of domestic firm increases the
prices of two countries’ final good. The effect of price on the
export tax depends on domestic bargaining power. The
equilibrium prices are negatively(positively) with the export
tax if 1     **      *  . However, when  *     ** , the
domestic equilibrium prices is negatively but foreign
equilibrium prices is positively.
The Model
• From Envelope Theorem ( Exogenous t )
d D t ;  
  pDF pF   D
d
()
()



 
 ( p D  m D )qPDF pF  [m F  (m D  t )](q pFF pF  q F )  0
 
(  ) competitive effect
(7)
(  ) subcontracting surpluseffect
• where direct effect dominate indirect effect→subcontracting
surplus effect is positive.
• A higher α increases the profit of domestic firm when export
tax, t, is exogenous.
Optimal Trade Policy
• The domestic welfare function:




W D t    D p D t , p F t , t  tq F p D t , p F t  ,
(8)
• FOC:
dW D
dt

t 0




F
 p D  m D q pDF ptF   m F  m D q pFF ptF  q F 
q
 
 (  )tax revenue effect
( ? ) competitive effect
(  ) subcontracting surpluseffect
(10)
Optimal Trade Policy
• dW
dt

D
 0, if
t 0


  ~
(11)

where ~  q F   p D  m D q pD
F
ptF
 q  m
F
F

 m D q pFF ptF

•   ~
→subcontracting surplus effect < competitive effect + tax
revenue effect
→optimal trade policy: tax.
•   ~
→subcontracting surplus effect > competitive effect + tax
revenue effect
→optimal trade policy: subsidy.
Optimal Trade Policy
• Proposition 2.
When domestic bargaining power is large(small), the domestic
optimal trade policy is subsidy(tax).
Optimal Trade Policy
• Optimal trade policy is:
t
max W

p
D



 m D q pDF ptF   [ m F  m D q pFF ptF  q F ]  q F
q pFD ptD  (1 -  )q pFF ptF
,
(12)
• Since W D is quadratic function in t, there is a maximum, and
the second-order condition is satisfied.
Optimal Trade Policy
• From Envelope Theorem ( Endogenous t )
t D F
d D t ( ),  
 p F pt   tD
  pDF pF   D 

d




 ( p D  m D )qPDF pF  [m F  (m D  t )](q pFF pF  q F )



)

(






( )
()

 
 



t  D
F 
F
F
D
F
F
D
D
),
q


(

p
q
)]
t

m
(

m
[


p
q
)
m

p
(

F
F

t
t
p
P







 




effect
e
competitiv
)

(
(?) subcontracting surpluseffect
() 



(?)export tax effect
• If export tax effect is positive, a higher α increases domestic
profit.
• If export tax effect is negative and must be large enough, a
higher α decreases domestic profit.
Optimal Trade Policy
• Proposition 3.
When export tax is exogenous, a higher α increases the
domestic profit. However, when export tax is endogenous, a
higher α decreases the domestic profit if export tax effect is
negative and must be large enough.
Optimal Trade Policy
• When export tax is exogenous:
a higher α
→increase the profit from subcontracted.
→the domestic profit increases.
• When export tax is endogenous:
a higher α
→decrease export tax
→decrease foreign firm marginal cost
→domestic firm face more competition from foreign firm
→the domestic profit may decrease.
Optimal Trade Policy
• We can prove all of the above discussion from this utility
function:




U  m  u qD , qF  m  a qD  qF 
where
a  mF.




  
1 D 2
q  qF
2

2

 2q D q F ,
(14)
1. p D  p D t    3  1 m F  m D  t 2   2   
p F  p F t   2  2   2 m F  m D  t  2   2   
2. t maxW  0 if      .
2
2
D
3
2



 0.










d

(
t
;

,

)
d


1

t
12




1

t

8
t




t
2


2


3.
d D (t ( ),  ,  ) d is ambiguous, where m D  1, m F  2, a  3.

Extensions---OUTSIDE OPTION
• Outside option
• Foreign firm has an outside option to subcontract the
intermediate good to another country---K(pure subcontractor).
• We assume m D  t   c , c represent the firm K’s marginal
cost when firm F subcontract to it. This assumption is a
incentive for firm F subcontract to firm K.
• If firm F subcontract to firm K, the profit functions is:
(15)
 DO  ( p D  m D )q D ( p D , p F ),
 FO  ( p F  m F )q F ( p D , p F )  1   [m F  v]q F ( p D , p F ), (16)
(17)
 KO   (m F  c)q F ( p D , p F )
Extensions---OUTSIDE OPTION
•
•
p
DO
p FO




a 2     2  2m D  m F  c 1   

2   2   
a 2     2  m D  2m F  2c1   

2   2   
(18)
(19)
• The firm F's optimal profit when firm F subcontract to firm K:
 FO
 a2      m  2   m

2
D
2
F
 ,
 c1   
  22   22 1   1   
2
(20)
Extensions---OUTSIDE OPTION
• When the profit WITHOUT outside option (under firm F
subcontract to firm D ) equal to the profit WITH outside
option (under firm F subcontract to firm K)
 F   FO → tˆ  m 21      1  2  m   v1   2    , (21)
D
2
F
2
 2 1  2   21   
•
•
•
•
If t  ()tˆ , firm F subcontract to firm D(K).
A higher α increases tˆ .
From t maxW  tˆ →  m D , m F , r , v   1
A higher α decreases t maxW and ~t1. (proposition 2)
2
Extensions---OUTSIDE OPTION
 F ,  FO
• If α=α1,
 F  
1
 FO  
1
tˆ
t
1
W
W DO
WD
 1
~
t1
t
t max W
1
 1
Extensions---OUTSIDE OPTION
a 
i. If   1 →
 F ,  FO
~
tˆ  t max W  t1
 F  
1
 F  
1
 FO  
• The welfare cure is ABEGH.
• The optimal trade policy
is t *  t maxW .
1
 FO  
1
tˆ
b 
W
E
W
B
A
t
1
G
H
WD
W DO
D
 1
WD
 1
~
t1
t *  t maxW
tˆ
t
1
 1
 1
Extensions---OUTSIDE OPTION
F
ii. If 1    
→ t max W  tˆ  ~t1
 F ,  FO
 1
c 
 FO
 1
 FO
• The welfare cure is IJLMN.
• The optimal trade policy
is t *  tˆ .
 1
 FO
t
tˆ
d 
 1
1
W
L
J
I
M
W DO
N
W DO
WD
 1
WD
 1
t
t  tˆ
*
t
maxW
1
 1
 1
Extensions---OUTSIDE OPTION
• Proposition 4.
When the foreign firm has the outside option
i. If domestic bargaining power is large,   1 ,the optimal trade
policy still be t *  t maxW .
ii. If 1     , the optimal trade policy is t *  tˆ .
Extensions---OUTSIDE OPTION
• Since firm D and firm F compete in final good market, there is
the collusion effect between them.
• since a higher α →increases final goods price→a higher
collusion effect.
• If   1 →a higher collusion effect→The outside option
does not threaten the domestic optimal trade policy.
• If   1 →a lower collusion effect→The outside option does
threaten the domestic optimal trade policy.
Extensions---OUTSIDE OPTION
a 
t*
• Relationship between α and
optimal trade policy.
• (a)without outside option
• (b)with outside option

0
b 

 1 ~

1
t*
t *  t maxW  tˆ

0
t *  t maxW
t *  tˆ
Extensions---OUTSIDE OPTION
• Finally, we obtain that foreign firm may still subcontract to
domestic firm even if domestic firm have a higher total cost of
intermediate good than the outside option.
 
F
FO
 2 m F  m D  t 
D


, if

m
 t   c   0,
2




2   2   
(

)cost
difference
effect



(22)
(  )strategiceffect
strategic effect
• which is the incentive for firm F subcontract to firm D,
because firm F can gain the profit through collusion.
cost difference effect
• which is positive by above assumption. The large cost
difference effect denote that the firm K’s marginal cost is
relatively low, so which is the incentive for firm F subcontract
to firm K.
Extensions---OUTSIDE OPTION
• Proposition 5.
When the foreign firm has the outside option, he may still
subcontract to the domestic firm even if the domestic firm
have a higher total marginal cost of intermediate good than the
outside option.
Conclusion
1. The price of foreign final good is decreased (increased) after subcontracting
when the domestic firm’s bargaining power (α) is sufficiently small (large).
However, the price of domestic final good is always increased after
subcontracting.
2. When domestic bargaining power is large(small), the domestic optimal
trade policy is subsidy(tax).
3. When export tax is exogenous, a higher α increases the domestic profit.
However, when export tax is endogenous, a higher α decreases the
domestic profit if export tax effect is negative and must be large enough.
4. When the foreign firm has the outside option, if domestic bargaining
power is large, the optimal trade policy does not be threatened. But not the
small bargaining power.
5. When the foreign firm has the outside option, he may still subcontract to
the domestic firm even if the domestic firm have a higher total marginal
cost of intermediate good than the outside option
~MANY THANKS~