Bargaining Power and Subcontracting Trade Policy Ku-Chu Tsao Shih-Jye Wu Yan-Shu Lin.

Bargaining Power and

Subcontracting Trade PolicyKu-Chu Tsao

Shih-Jye Wu Yan-Shu Lin

Introduction

Introduction

About subcontracting literature• 陳芳岳與洪進朝 (1997)• Shy and Stenbacka (2003) • Chen and Liang (2008)• Chen et al. (2004) • Ornelas and Turner (2008)• Maiti and Mukherjee (2013)Vertical related market & subcontracting• Arya et al. (2008)• 王光正與邱俊榮 (2004)• Liang et al. (2006)• Kawabata (2010)、 (2012)• 吳世傑與陳宏易 (2014)

陳芳岳與洪進朝 (1997)一文討論在一個國際廠商之間存在「委託代工」 (OEM) 契約的雙占模型中探討受委託國之最適貿易政策。 OEM 市場為買者訂價的假設下，其代工與否不僅取決於貿易政策變數與貿易國家之比較利益，並且必須考慮廠商間之策略性

互動。此文得到：對其 OEM 產品之出口應予課稅，但對出口至第三國之產品則應予補貼。

Chen and Liang (2008) 則探討在事前協議代工下兩個跨國廠商競爭之間的關係。這表示出口國可以選擇在最終產品和代工產品中透過差別的或是相同的貿易政策來達到最適貿易政策。他們得到，同時對最終產品課出口稅與對代工產品出口補貼的這種差別貿易政策不一定是最適的貿易政策。若出口廠商是純代工廠商，則課徵出口稅會是最適貿易政策。

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

third-country

firm D

Dm

firm F

Fm

Dq Fq

sqsubcontracting

t

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.

• Assumptions:1.The linear demand function:

2.Two final good firms are substitute.

3.Marginal cost of intermediate good in firm F is higher than firm D.

4.One unit of the intermediate good is required to produce one unit of the final good.

.0,0),,( i

pp

i

p

FDiiii qqppq

The Model

0j

i

pq

FS qq

0 tmm DF

• According to Spiegel(1993) model, the surplus generating from subcontracting is given by

• The transfer payment is chosen to split between the firms according to their bargaining powers. Thus, following Spiegel,

),()(

),()(),(),(),(),(FDFDF

FDFDFDDDFDFFFDDDFD

ppqtmm

ppqtmppqmppqmppqmppS

The Model

),(),())(1(

0),(

),(),()(),()1()p,(p

' cos

' cos

FD

FDFFFDFD

opreationproductionsFfirmfromderivedsavingt

FDFF

opreationproductionsDfirmtoaddedtlincrementa

FDDDFDFDFDDD

ppqmppqtm

ppqm

ppqmppqtmppqm

The Model

• Let α (resp. (1-α)) denote firm D’s (resp. firm F’s) bargaining power on subcontracting and

• Profit functions of firm D and firm F:

(1)

(2)

0,1

),,()]([),()(

),()(),(),(),(,FDFDFFDDDD

FDFDFDDDFDFDDDFDD

ppqtmmppqmp

ppqtmppqmppppqppp

),,()]([1 ),()(

),(),(,FDFDFFDFFF

FDFDFFFDF

ppqtmmppqmp

ppppqppp

The Model

• first-order conditions

(3)

(4)

,0)]([)(),(:

effect surplus tingsubcontraceffect ecompetitiv

F

p

DFD

P

DDFDDD

p

DDDD qtmmqmpppqR

,0)]()[1()(),(:

effect surplus tingsubcontraceffect ecompetitiv

F

p

DFF

p

FFFDFF

p

FFFF qtmmqmpppqR

The Model

• In order to ensure that the firm D and firm F all will be improved after subcontracting.

• The profit function without subcontracting

• where if

• first-order conditions

,ii jiiiiijii ppqmpmpp ,,,

,,,,0)(,: jiFDiqmpppqR i

P

iijiii

p

iii

.

The Model

• The shifting on reaction function between with and without subcontracting is dependent on α.

• When α is higher, is farther from , but is closer

from

figure 1.

)0( DR)1( DR )1( FR

)1( FR

Fp

Dp

)1( DR)0( DR

)1( FR

)1( FR

0

E

E

1E

2E

The Model

• figure 1.

Fp

Dp0

)0( DR

)1( FRE

)1( DR

)1( FR

E

1E

2E

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 subc

ontracting.

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 (5-1)

(5-2)

• A higher α increases the prices of two firms’ final good.• For domestic firm: a higher α→ increase the subcontract

ing 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.

F( ) ( )(2 )0,

D F F F D F D F F

D F D F D F D FDp p p p p p p p p

m m t q q qdp

d H H

,0)2)((

H

qqqqtmm

Hd

dpF

p

F

p

D

p

F

p

DFF

pp

D

p

F

p

D

ppF

DDDFDFDFDD

The Model

• A higher α increases the equilibrium prices of two firms’ final good.

Fp

Dp

DR

FR

0

)( E

DR

FR)( E

The Model

(6-1) (6-2)

• domestic firm: A higher t →decrease subcontracting surplus effect→ 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→ is upward shifting.

* ,0

)2(2

H

qqq

Hdt

dpFp

Dp

Fp

Ftp

Dpp

Fpp

Dtp

D FFDFFDFFD

** ,0)2(2

H

qqqq

Hdt

dpFp

Fp

Fp

Dp

Fpp

Dtp

Ftp

Dpp

F DDFDDFDFDD

DR

FR

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.

figure 2

0tRF

0tRD

)0( tE

Fp

Dp

0tRD

0tRF

0

)0( tE

• 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 . However, when , the domestic equilibrium prices is negatively but foreign equilibrium prices is positively.

The Model

***1 ***

The Model

• From Envelope Theorem ( Exogenous t )

(7)

• 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.

0)()]([)(

;

effect surplus tingsubcontrac )(

)()(

effect ecompetitiv )(

FFF

p

DFFD

P

DD

DFD

p

D

qpqtmmpqmp

pd

td

FF

F

Optimal Trade Policy

• The domestic welfare function:

(8)

• FOC:

(10)

,,,, tptptqttptptW FDFFDDD

effectrevenuetax

F

effectsurplustingsubcontrac

FFt

F

p

DF

effectecompetitiv

Ft

D

p

DD

t

D

qqpqmmpqmpdt

dWFF

)( )( )?(

0


• (11)

where

• →subcontracting surplus effect < competitive effect + tax revenue effect→optimal trade policy: tax.

• →subcontracting surplus effect > competitive effect + tax revenue effect→optimal trade policy: subsidy.

~ ,00

ifdt

dW

t

D

Ft

F

p

DFFFt

D

p

DDF pqmmqpqmpq FF ~

~

~


• Proposition 2.

When domestic bargaining power is large(small), the domestic optimal trade policy is subsidy(tax).


• Optimal trade policy is:

(12)

• Since is quadratic function in t, there is a maximum, and the second-order condition is satisfied.

,

)-(1

][max

Ft

F

p

Dt

F

p

FFFt

F

p

DFFt

D

p

DD

W

pqpq

qqpqmmpqmpt

FD

FF

DW


• From Envelope Theorem ( Endogenous t )

• 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.

,)()]([)(

)()]([)(

),(

effecttax (?)export

effect surplus tingsubcontrac (?)

)()(

effect ecompetitiv )()(

)(

FFt

F

p

DFFt

D

P

DD

FFF

p

DFFD

P

DD

Dt

Ft

D

p

DFD

p

D

qpqtmmpqmpt

qpqtmmpqmp

pt

pd

td

FF

FF

FF


• 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.


• 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.


• We can prove all of the above discussion from this utility function:

(14)

where .

1.

2. if .

3.

is ambiguous, where

,22

1,

22 FDFDFDFD qqqqqqamqqumU Fma

2213 tmmtpp DFDD

.02281121),;( 2223 ttttdtd D

0max Wt

dtd D ),),(( .3 ,2 ,1 amm FD

2222 2 tmmtpp DFFF

Extensions---OUTSIDE OPTION

• Outside option• Foreign firm has an outside option to subcontract the intermed

iate good to another country---K(pure subcontractor).• We assume , 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) (16) (17)

,),()( FDDDDDO ppqmp ),,(][1),()( FDFFFDFFFFO ppqvmppqmp

),()( FDFFKO ppqcm

ctmD


• (18)

• (19)

• The firm F's optimal profit when firm F subcontract to firm K:

(20)

22

122 2 cmmap

FDDO

22

1222 2 cmmap

FDFO

,1122

12222

222

cmma FD

FO

• 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)

→ (21)

• If , firm F subcontract to firm D(K).

• A higher α increases .

• From →

• A higher α decreases and . (proposition 2)


FOF ,

1221

212112ˆ2

222

vmm

tFD

tt ˆ)(t̂

tt W ˆmax 1,,, vrmm FD

Wt max1~t


• If α=α1,

1

1

DOW

t

W

Wt max1~t

1

DW

1

F

t̂ 1

FOF ,

1

FO

t

i. If →

• The welfare cure is ABEGH.• The optimal trade policy is

.


1 1max ~ˆ ttt W

Wtt max*

t̂ 1

A

b

1

DOW

t

W

Wtt max* 1~t

H

E

GB

1

DW

1

DW

1

DW

a

1

F

t̂ 1

FOF ,

1

FO

1

FO

1

F

t

ii. If →

• The welfare cure is IJLMN.• The optimal trade policy is

.


1 1max ~ˆ ttt W

tt ˆ*

c

1

F

t̂ 1

FOF ,

1

FO

1

FO1

FO

t

NM

tt ˆ* Wt max

I J

L

1

1

DOW

t

W

1

DOW

1

DW1

DW

d


• Proposition 4.

When the foreign firm has the outside option

i. If domestic bargaining power is large, ,the optimal trade policy still be .

ii. If , the optimal trade policy is .

1 Wtt max*

1 tt ˆ*


• 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 →a higher collusion effect→The outside option does not threaten the domestic optimal trade policy.

• If →a lower collusion effect→The outside option does threaten the domestic optimal trade policy.

1

1

• Relationship between α and optimal trade policy.

• (a)without outside option

• (b)with outside option


11

*t

0

a

~

ttt W ˆmax*

tt ˆ*

0

Wtt max*

b *t


• 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.

(22)

strategic effect• which is the incentive for firm F subcontract to firm D, becaus

e firm F can gain the profit through collusion.cost difference effect• which is positive by above assumption. The large cost differen

ce effect denote that the firm K’s marginal cost is relatively low, so which is the incentive for firm F subcontract to firm K.

,0

22 ,

effect difference)cost (effect )strategic(

2

2

ctmtmm

if DDF

FOF


• 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~

Bargaining Power and Subcontracting Trade Policy Ku-Chu Tsao Shih-Jye Wu Yan-Shu Lin.

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