endogenous transfer prices, tariffs, and a host country duopoly

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ENDOGENOUSTRANSFER PRICES,TARIFFS, AND A HOSTCOUNTRY DUOPOLYVibhas MadanPublished online: 29 Oct 2010.

To cite this article: Vibhas Madan (2000) ENDOGENOUS TRANSFERPRICES, TARIFFS, AND A HOST COUNTRY DUOPOLY, The InternationalTrade Journal, 14:2, 169-199, DOI: 10.1080/088539000271836

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ENDOGENOUS TRANSFER PRICES,

TARIFFS, AND A HOST

COUNTRY DUOPOLY

Vibhas Madan

This a rtic le ex am ines the im pac t o f tran s f e r-price e f f ec ts o n theintera c tio n be tw een a m u ltin a tio n a l f irm and a do m e s tic du o po lis t

in the pre s en ce o f re s a le -pric e re s tra in ts . The tran s f er-pric e e f f e c ts havea dire c t im pac t o n the s treng th o f the s tra teg ic re la tio n s hip betwe enthe m u ltina tio na l f irm and the do m es tic f irm . The tran s f er-pricee f f ec t m ay g ive ris e to a n ‘‘ an ti-pro tec tive ’’ ta rif f increa s e , whe rein aninc rea s e in the ta rif f ra te inc rea s e s o ptim a l ho s t-co untry s a les o f them ultin a tio n a l f irm and reduc es the o ptim a l s a le s leve l o f the do m es -

tic f irm . Thes e re s u lts a re va lid w ith Co u rno t qu antity -c o m petitio n a sw ell a s a Sta ck leberg duo po ly w ith eithe r f irm a s the leade r.

) ) ) ) )

I. INTRODUCTION

The increasing importance of intra-firm transac tions in inte rna -

tional trade has he ightened the significance of transfer price s as a( )source of conflic t be tw een multinational firms MNFs and govern -

ments . Governments have long recognized that MNFs manipulate

transfe r pric e s in orde r to shift profits, and have tried to e stablish

Vibhas Madan is Assoc iate Professor of Economic s and InternationalBusine ss at the LeBow College of Busine ss, Drex e l University.

ISSN: 0885 -3908. THE INTERNA TIONA L TRADE JOURNA L, Vo lu m e XIV, No . 2, Su m m e r 2000 169

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THE INTERNATIONAL TRADE JOURNAL170

guideline s for fair transfe r price s.1 Follow ing the seminal pape rs on( )transfe r pricing and horizontally integrated MNFs by Horst 1971 and

( )transfe r pric ing and ve rtically integrated MNFs by Copithorne 1971 ,

othe r studie s have analyzed various dimensions of the transfe r pric ing

problem. Some of the is sues addressed inc lude the impact of transfe r

price manipulation on the MNFs intra-firm trade and production-

location decisions, we lfare implications for the exporting and import -

ing countrie s, impact of minimum-profit re straints on the transfer

prices , transfe r pricing in the pre sence of a partially owned subsidiary

and the assoc iated implications for trade and gove rnment revenue s, a

comparison of exogenous ve rsus endogenous transfe r pric e s, transfer

price manipulation in the presence of local content restr ic tions, and(transfe r price regulation and asymmetric information. Among othe rs

w x w xse e Booth and Jensen 1977 ; Eden 1978, 1983 ; Gre sik and Ne lson

w x w x w x1994 ; Kant 1988a, 1988b, 1990 ; Katrak 1980, 1981 ; Itagaki

w x w x w x1979, 1981 ; Madan 1992a, 1992b ; Prusa 1990 ; and Samuelson

w x)1982 .

A common fe ature in all of the se studie s is that the analysis is

couched within the monopoly mode l of a MNF. This has enabled these

studie s to abstract from complications w hich arise from the MNF’s

re sponse s to other firms in the marke t. Although this approach fac ili -

tate s a be tter understanding of the direc t e ffec ts of transfe r price

manipulation, it ve ils the indire c t e ffe cts of transfer price manipulation

such as

( )a the re sponse of local firms to profit-shifting motivated ac tions

of the MNF and

1An ex ample of such a guideline is Se c tion 482-C of the Internal Revenue Servic e( )IRS code. This regulation state s c rite ria for establishing pric es on transac tions be tween

( )re lated partie s. For an analysis of the impac ts of this regulation see Benvignati 1985 .

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Madan : Endo g eno u s Trans f er Price s , Tarif f s . . . 171

( )b the impac t of transfer-price e ffe cts on the MNF’s response s to

the price and quantity dec isions made by domestic firms.

Consequently, the full implications of a host country’s tax and

tariff polic ie s in te rms of the ir impact on production, trade , and price s

cannot be fathomed without dec iphe ring the se indire c t e ffe cts of

transfe r price manipulation in the pre sence of imperfe c t competition.

There have been a few recent studie s which have conside red the

implications of transfe r pric ing in the presence of strategic inte rac tion.

( )Schjelde rup and Sorgard 1997 looked at the case of a decentralized

MNF fac ing a domestic duopolist in the importing country. There are

no re stric tions on the transfe r price s and it is show n that the transfe r

price w ill deviate from the cost of exporting due to a pure strategic

e ffe c t. Although the strategic e ffec t is positive under Be rtrand compe -

( )tition it has a negative effe c t under Cournot competition. Holm 1997( ) ( )combined the work of Kant 1988a w ith Brander and Spence r 1985 ,

and showed that if deviations of the transfe r price from marginal costs

are penalized with a positive probability then subsidie s and tax es have

an asymmetric impac t on the outcomes of Cournot games in ve rtically( )integrated oligopolie s. Jie -A-Joen and Sleuwaegen 1997 have shown

that the transfer pric ing ability of a MNF has a negative impac t on the

competitive position of a domestic duopolist in the host country. One

of the possible ex tensions they mention is the case of endogenous

transfe r pric e limits.

In this article w e add to the sparse lite rature on transfe r pric ing

and strategic inte rac tion. We look at a case of a centralized MNF

w hich face s transfe r price restric tions and the value of its transfer

price limits are endogenous to its price and quantity dec isions. In

particular, w e look at a duopoly mode l w here the MNF and a domestic

firm compete in quantities and the MNF is subjec t to arm’s length

transfe r price re stric tions. The optimal transfe r price rule for max imiz -

( )ing global after-tax profits first se t forth by Horst 1971 state s that the( )MNF should se t the transfe r price as high low as possible depending

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( )on whethe r the host-country tariff is lower higher than the re lative

tax -diffe rential be tween the tw o countrie s.2 Howeve r, MNFs cannot

charge arbitrarily high or low transfe r price s because gove rnments try

and regulate transfe r pricing by MNFs and invariably provide guide -

line s for e stablishing fair transfe r prices .

Because this study doe s not deal w ith problems re lating to e stab -

lishing and enforcing fair transfe r prices, the author works w ithin a

framework w here e stablishing a fair transfer price is re latively straight-

forward. An appropriate scenario is one in which the re is intra-firm

trade in finished goods and the MNF is subjec t to resale -pric e re -

straints w here the transfe r price has to conform to the price charged

on the sale s of the final good to the consumers in the host country.

This is an ex ample of an arm’s length restr ic tion where the transfe r

price is be ing constrained by the price at which the product is sold to

an unre lated party.3 Because the price of the final good is influenced

2 If the host country tariff is smaller than the re lative tax -differential be tween thehost country and the parent country, then the multinational would gain by setting anarbitrarily high transfer price on intra-firm imports. Conve rsely, if the host country tariffis large r than the relative tax -diffe rential be tween the host country and the parentcountry, then the multinational would gain by setting an arbitrarily low transfer price onintra-firm imports. Clearly such arbitrary pric e se tting is not tole rated by the taxauthorities and the multinationals invariably face administrative ly imposed upper andlower limits on the ir transfe r price s.

3 The issue of what constitute s a fair transfe r pric e is at the cente r of numerousconflic ts between MNFs and governments. Although the transfer pric e regulations ofmost countrie s differ in the ir de tails, most of them appeal to the concept of an‘‘arms-length pric e’’ as a fair transfe r price . For the United States, transfer pric eregulations are outlined in Sec tion 482 of the Inte rnal Revenue Se rvice Code . The codeallow s for four basic methods which are consistent w ith arm’s length pricing. The seapproache s are

) ( )a Comparable Uncontrolled Pric e CUP ,) ( )b Resale Pric e RP ,) ( )c Cost-Plus CP , and)d ‘‘other methods.’’

The fourth method provide s fle x ibility in the absence of the first thre e possibilitie s.

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by the MNF’s sale s dec isions, the ac tual value s of transfer price limits

are endo geno u s ly dete rmined. In a duopolistic se tting, w ith re sale -

price re stric tions, the re is an additional endogene ity to the transfe r

price decision because the domestic firm’s sale s dec isions have an

impac t on the MNF’s transfe r price due to the ir impac t on the price of

the final good sold by the MNF. It should be re ite rated that the

endogeneity re fe rs to the value of the transfe r price at the limits. Kant( )1988a showed that w ith unce rtain regulation you can ac tually ge t

endogenous transfe r price s w here they are endogenous in the sense

that they lie w ithin the limits and not at the limits. In the current

analysis we do not look at the case of unce rtain regulation and

consequently the transfe r pric e is always at the upper or lower limit.

Be fore proceeding with the analysis in this article it would be

appropriate to mention the work on transfer pricing outside the

economic s literature . The accounting lite rature and the finance lite ra -

ture focus almost ex c lusive ly on the role of transfe r price s as mecha -

(nisms for re source allocation within a multi-divisional not ne ce ssarily)multinational ente rprise . Even though there is a conside rable amount

of work on transfe r pric ing by researchers in the area of ac counting,

the transfe r pric ing lite rature in the area of finance is quite limited.

The w ork on transfe r pricing in the area of finance is mainly aimed

toward practitione rs and is found in profe ssional journals . On the

othe r hand, there is a w e ll-deve loped academically focused lite rature

in the area of accounting.

( )Benke and Bishop 1986 used a numerical ex ample to provide a

gene ral rule for transfe r pric ing which resulted in optimal financ ial( )outcomes on inte rnal sales. Luft and Libby 1997 focused on the

impac t of marke t price s on negotiated transfe r price s w ithin a com -

pany. They showed that a negotiated transfer price is much more

difficult to de te rmine if the marke t price -re lated transfe r pric e s yie ld( )unequal divisional profits. Ronen and Balachandran 1988 ex amined

transfe r pric ing w ithin the contex t of a princ ipal-agent game . They

identified transfe r pricing schemes as optimal se cond-be st solutions

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because they se rve the role of incentive functions in an uncertain( )environment w ithin the firm. Chalos and Haka 1990 explored the

e fficiency of negotiated transfer pric ing in te rms of attaining max imum

gross profits for the company as a w hole . They used an experimental

approach within the contex t of a bilate ral bargaining mode l and

pointed out the importance of divisional and global incentive s as a( )backdrop to the negotiation proce ss. Banker and Datar 1991 looked

at the transfer pric ing problem in the face of asymmetric information

and dive rgent pre ference s be tween divisions. They showed that trans -

fe r prices may arise endogenously as an optimal compensation scheme

w ithin firms. This is diffe rent from the early literature on transfe r

pric ing where transfer prices are exogenously assumed as ne ce ssary( )for optimal inter-divisional transfers Hirshle ife r, 1956 .

( )In some recent work aimed direc tly at prac titione rs Kapoor 1998

proposed an inte re sting dual transfer pric ing method where the se lling

division is c redited with the marke t price and the buying division pays

the variable cost of the product. The re sulting difference is then

debited to a central financ ial cente r. In a similar vein Cooper and( )Slagmulder 1998 proposed that the use of ac tivity-based costing is

the be st way to deve lop accurate and transparent transfe r pric ing to

enhance intra-organizational cost management. The author re empha -

size s that all of these studie s focus on the resource allocation dimen -

sion of transfe r pricing and not on the profit-shifting dimension of

transfe r pric ing which comes into play w hen the company is a MNF.

In Sec tion II the basic mode l is pre sented and the impac t of the

transfe r-price e ffe ct on the equilibrium value s of the MNF’s endoge -

nous variables is analyzed. The analysis reve als that w ith re sale -pric e

re strictions the transfe r-price e ffe ct influence s the equilibrium value of

a MNF’s sale s and production-location dec is ions. The direc tion of the

e ffe c t depends on w hethe r the MNF desire s a low or a high transfer

pric e . Sec tion III analyze s the case of Cournot-quantity competition

be tween the MNF and a domestic duopolist. The transfe r-price e ffe c t

give s rise to the possibility of an upward sloping reaction function for

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the MNF even with a simple linear demand struc ture . The compara -

tive -static analysis reveals that in the pre sence of a dominant transfe r-

price effe c t an increase in the tariff w ill c ause the MNF to expand its

total sale s in the host country. This give s rise to an ‘‘anti-prote ctive ’’

tariff increase: an increa s e in the ta rif f re s u lts in a dec line in thedo m e s tic duo po lis t ’s o ptim a l s a les . The Stackleberg leade r r follow er

mode l in the pre sence of transfer price s is analyzed in Section IV. It is

show n that the anti-protec tive tariff is a possibility w ith either the

MNF or the domestic firm as the Stackleberg leade r in a quantity-

se tting game . Sec tion V puts forth the public policy implications of the

analytical results and the analysis is conc luded in Sec tion VI.

II. THE MODEL

Conside r a host country market w ith a domestic firm, Y , and a

fore ign MNF, X . Assume that the parent division of the MNF produce s

and exports the final product for re sale to its subsidiary division in the(host country. The final good is also produced by the subsidiary. The

fore ign country is denoted by F and the host country is denoted by)H. The scenario be ing analyzed is repre sented in Figure I. To focus on

the e ffe c ts of transfe r price manipulation in the pre sence of host-

country re straints the author assumes that the parent divis ion in

country F produces solely for the purpose of exporting to the sub -

sidiary operating in H.

A simple framework is assumed where the MNF and the domestic

duopolist are se lling perfec t substitutes and the price of the final

product is

( )P s P x q y and P 9 - 0 ,

w here x is the leve l of the MNF’s total sale s and y represents the sales

of the domestic firm. The amount of production in the host-country( )subsidiary is x y m , w here m is the amount of intra-firm imports.

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Figure IA Horizontally Integrated Multinational and a Domestic Duopolist.

Assuming increasing marginal costs in both divisions we have the

follow ing cost curve s:

h ( ) h 9 h f ( ) f 9 fC x y m , C s c ) 0 and C m , C s c ) 0

w here Ch is the production cost of the subsidiary and is inc reas ing in

x and decreasing in m , C f is the production cost of the parent division

and is inc reasing in m .4 The MNF face s an ad-valorem tariff t on its

4 The inc reasing marginal cost assumptions ensure that we have an interior solutionto the max imization problem wherein there is produc tion in both divisions. Theobje c tive func tion for the multinational is a global profit func tion and this particulardec ision struc ture pre c ludes the subsidiary from independently optimizing host-countrysales. An alternative and often used specific ation is the constant marginal cost assump -

tion. Given any sort of a fixed cost this give s rise to economie s of scale due to which theMNF would typically concentrate all of its produc tion in e ither the parent firm or thesubsidiary and would not have positive production in both of its divisions. However,w ith the ex istence of profit shifting motive s it is possible that even w ith constantmarginal costs the MNF may choose to produce in both divisions. For an example of a

( )situation where this may occur see Madan 2000 .

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intra-firm imports into the host country and also encounte rs corporate

tax rate s of g f and g h in the fore ign country and the host country,

re spec tively.

The MNF’s global post-tax profits P are given by:1

( ) ( h ) w h ( ) x1 P s 1 y g Px y C y u 1 q t m1

( f ) w f xq 1 y g u m y C

w here u is the transfe r price on intra-firm trade in finished goods.

The total post-tax profits of the domestic duopolist are :

( ) ( h ) w x2 P s 1 y g Py y C2 y

w here , C is the total production cost of the domestic firm and isy

inc reasing in y .

To highlight the impact of transfe r price s on the MNF’s global( ) ( f )profits w e divide Equation 1 by the constant 1 y g . This gives us:

( ) w h x f ( )1* P s G R y C y C q 1 y GT u m1*

( h ) ( f )w here T s 1 q t , G s 1 y g r 1 y g and R is the total revenue( )of the MNF. The value of 1 y GT is exogenously de termined and

( ) ( )w hen it is positive negative the firm desires a high low transfe r

pric e .5 It is assumed that the MNF’s transfe r price s are subjec t to

5 U ( )From 1* we can see that P r u s 1 y GT m . Therefore the marginal prof-1

itability of transfe r price s for a positive level of intra-firm trade, m ) 0, depends on the( )sign of 1 y GT . In certain situations the firm may also use transfe r price s to reduce

risk. This would be done by shifting profits away from a high-risk location to a low -risklocation by over-invoic ing or under-invoicing intra-firm exports r imports. It is possiblethat the MNF will de sire a high transfer price to minimize global tax payments, but it

( )may desire a low transfer pric e at the same time to minimize risk. That would not havean impac t on the qualitative results related to profit shifting. However, the finaloutcomes w ill depend on the relative strength of the e ffec ts assoc iated with riskreduction and tax minimization. Essentially the re is no a priori reason to assume thatincorporating the risk reduc tion e lement w ill enhance or dampen the effec ts associatedw ith tax minimization.

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re sale -price re straints. With this re stric tion the transfe r price , after

accounting for the tariff payment, is constrained by the follow ing

re lationship 6 :

( ) ( )3 P s u 1 q t or u s P r T

This is an ex ample of an arm’s length re stric tion on the transfe r price

w here the inte rnal price is constrained by the price charged on sales

to an unre lated party. Arm’s length re str ic tions are among the most

common type s of transfe r price restraints imposed by gove rnments. In

some transfe r pricing situations informational conside rations make

regulation of transfe r price s quite difficult e specially if the re are no

arm’s length price s to se rve as guideposts. This would be the case , for

ex ample, when intra-firm trade involve s inte rmediate goods w hich are

not meant for re sale . Howeve r, in this case , w ith intra-firm trade in

finished goods meant for resale , informational issues do not pose a

problem when it comes to transfer price regulation. Furthermore , to

avoid additional complications, we do not explore the possibility

w here the MNF may find it optimal to violate the regulation. A fruitful

analysis of that issue would involve the spec ific ation of a penalty

scheme and the the assoc iated expec ted cost r benefit analysis of

violating the re stric tion.

6 If processing costs are allowed for, the transfer pric e would be re stric ted to( )u s P 1 q k r T, where k is a markup which reflec ts the costs incurred after importing

and be fore selling the finished product. Even though the se costs are important in te rmsof the actual profit leve ls they do not influence the relationship between u and P in aqualitative fashion.

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( )Incorporating the transfe r-price re straint in Equation 1* , the

firs t-orde r conditions for the MNF are 7:

( ) ( h ) ( )4 P r x s G r y c q 1 y GT P 9 m r T s 01*

( ) h f ( )5 P r m s Gc y c q 1 y GT P r T s 01*

w here r is the marginal revenue from host-country sale s. From the( )firs t-orde r conditions we can see that if 1 y GT s 0, i.e ., if the

transfe r-price effec t does not ex ist, then in equilibrium w e have r s c h

and Gc h s c f.8 In othe r words the MNF w ould simply equate the

marginal cost and marginal revenue, and the tax -adjusted marginal( )costs of production in the tw o countrie s. When 1 y GT / 0, a

w edge is driven be tw een marginal revenue and marginal cost and its( )direction depends on the sign of 1 y GT :

( ) ( )a If 1 y GT ) 0 then the MNF desire s a high transfe r price ,

and the optimal sale s level dec line s because the transfe r price

is dire c tly related to the host-country price of the final good.

Furthermore , the ‘‘low ’’ tariff, in this case , calls for an increase

in the value of the imports. For a given transfe r price , de ter -

mined by the value of x , the value of trade is inc reased if the

7 In this framework the author has chosen the sale s and the intra-firm trade levels asthe ex plic it choice variables. Consequently, the leve l of host-country produc tion issolved residually in the model. The author could have chosen the produc tion andimport leve ls as the ex plicit choice variables and solved for the sale s level as a residualvariable. The re sults are invariant, as they should be , w ith respec t to our choice of theexplic it choice variables, however, diffe rent fe ature s of the system are highlighteddepending on the approach we adopt. Because we are concerned w ith the transfe rprice s and hence the value of trade , the appropriate variable s are the level of sales( )which influence the transfe r pric e and the leve l of intra-firm trade .

8 It is assumed that the re is an inte rior solution to the MNF’s profit-maximizingproblem where the MNF produces in both countrie s. Clearly, it is possible that unde rcertain parametric conditions the MNF will choose to produce only in one place .

Constant marginal costs of production would be one such situation.

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proportion of host-country sale s attributed to intra-firm im -

ports is inc reased. Thus, in this case the MNF ‘‘under-se lls’’

and ‘‘over-imports.’’( ) ( )b For the othe r case w ith 1 y GT - 0, the re sults are ex ac tly

the opposite and the MNF tends to ‘‘ove rse ll’’ and ‘‘unde r-

import.’’

The benchmark levels implied by the te rms under-se lling and

over-se lling re fer to the situation w here the transfer-price e ffe ct has no

impac t on the MNF’s real dec isions, i.e .,

( )1 y GT s 0 .

The domestic firm’s first-order condition is

( )6 P r y s r y c s 0,2 y y

w here r is the marginal revenue and c is the marginal cost ofy y

production of the domestic duopolist. It is further assumed that the

marginal cost is inc reasing in y , i.e ., c X ) 0.y

III. ENDOGENOUS TRANSFER PRICES

AND A COURNOT DUOPOLY

This sec tion analyze s the impac ts of the transfe r-pric ing effe c ts on

the re lationship be tween the MNF and the domestic firm w ithin the

contex t of Cournot-quantity competition.9 The change in the optimal

leve l of intra-firm imports and total sale s of the MNF in response to a

change in the leve l of the domestic duopolist’s sale s is obtained by

9 In this framework the author does not look at cost-side inte ractions be tween theMNF and the domestic firm because this would obfuscate the demand side issuesdirec tly re lated to transfe r price s and re sale -pric e restraints.

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( ) ( )totally diffe rentiating Equations 4 and 5 with re spec t to x , m , and

y and using Cramer’s rule . To simplify the algebraic manipulations the

author assumes linear demand curves for the re st of the analysis. The

linear demand assumption also se ts the stage for an inte re sting( )counte r-ex ample to the Bulow et al. 1985 re sults on strategic com -

plementarity.

The slope s of the reac tion functions are :

( ) ( < <)7 dx r dy s 1 r H

2f 9 h 9( ) (( ) )= GP 9 c q c r T q 1 y GT P 9 r T( )

( ) ( < <)( h 9 ( ) )8 dm r dy s GP 9 r H c r T y 1 y GT P 9 r T

< < w( 2 2 )( 2 2 ) ( 2 )2 xw here H s P r x P r m y P r x m and1* 1* 1*

is assumed to be positive in orde r to ensure an inte rior solution to the

MNF’s max imization problem.

( )The slope of the sale s-reac tion function given by Equation 7 may

be positive or negative depending on the strength of the transfe r-pric e

e ffe c t. It is inte re sting to see that the impact of the transfer-pric e( )e ffe c t, w hich is captured by the second te rm in Equation 7 , is

positive in both the low - and the high-transfe r price scenarios. The( )intuition behind this is as follows: With 1 y GT ) 0, the MNF is

under-se lling in orde r to maintain a high P. When the re is an increase

in y the value of P is reduced and this reduce s the marginal benefits

from under-se lling. So in re sponse to a higher y the MNF has an( )incentive to inc rease x . Similarly, w hen 1 y GT - 0, the MNF is

over-se lling in orde r to maintain a low P. When y increase s, P falls

furthe r, thus increasing the marginal bene fits from over-se lling. Conse -

quently, w ith an increase in y the MNF has an incentive to inc rease x .

( )As the first te rm in Equation 7 indicates , as long as we have

inc reasing marginal costs of production the production e ffe c ts w ill

c ause a dec line in x when y inc rease s. If the transfer-price e ffe c t is

dominant then an increase in the domestic duopolist’s sale s w ould

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imply that the MNF would increase its optimal sales leve ls and w e

w ould have an upward sloping reaction function.10

An inte re sting implication here is that the transfe r-price e ffe c t

give s rise to the possibility of strategic complementarity even in the

pre sence of a linear demand structure . Previous work on strategic( )complementarity r substitutability by Bulow et al. 1985 showed that

w ith Cournot quantity competition, strategic complementarity arises(only if demand struc ture s are non-linear in particular a highly convex

)demand curve . But in the pre sence of re sale -pric e re straints on the

MNF’s transfe r price s, we have the c lear possibility of strategic com -

plementarity, i.e ., dx r dy ) 0, even without the pre sence of non-line ar

demand struc ture s.11

( )The second term in Equation 8 shows that the transfer-pric e

e ffe c t has a direc t impac t on the sign and magnitude of dm r dy . The( )first te rm in Equation 8 shows that as long as the re are inc reasing

marginal costs of production in the subsidiary, an increase in y will

reduce the optimal leve l of m . The transfe r-pric e e ffe ct w ill re inforce( ) ( )this if 1 y GT ) 0, and run counte r to it if 1 y GT - 0 . The

intuition behind the transfe r-price e ffe ct is as follow s: First, w ith( )1 y Gt - 0 the MNF has an incentive to under-import in orde r to

reduce the value of trade . An increase in sale s by the domestic firm

reduce s the pric e of the final good and due to the commensurate

dec line in the transfe r price it reduces the marginal gains of shifting

10 It c an be seen dire ctly that the necessary and sufficient condition for dx r dy ) 0is consistent w ith the nece ssary and suffic ient condition for an interior solution defined

< <by H ) 0:

) ( )2 ( )2 ( w x f h )a dx r dy ) 0 iff P 9 r T q GP 9 ) GP 9 2 P 9 r T y c 9 y c 9 r T and) < < ( )2 ( )2 ( w x f h ) 2 h fb H ) 0 iff P 9 r T q GP 9 - 2GP 9 P 9 r T y c 9 y c 9 r T q G c 9 c 9 .

11 What we really have he re is a kind of strategic asymmetry be cause we havedx r dy ) 0 and dy r dx - 0. In the traditional argument strategic complementarityimplies dx r dy ) 0 and dy r dx ) 0, and strategic substitutability implie s dx r dy - 0and dy r dx - 0.

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profits via the reduction in the volume of trade . The weakening of the

profit-shifting motive dampens under-importing incentive and has an( )upw ard impac t on the level of intra-firm trade . Second, w ith 1 y GT

) 0 the MNF has an incentive to ove r-import in orde r to inc rease the

value of trade . An increase in sale s by the domestic firm reduce s the

price of the final good and due to the commensurate dec line in

the transfe r price it reduces the marginal gains of shifting profits via an

increase in the volume of trade . The w eakening of the profit-shifting

motive dampens the over-importing incentive and has a downw ard

impac t on the leve l of intra-firm trade .

Summing up the re sults of this se c tion we have:

Proposition 1.

( )a With a low transfe r price, an increase in the domestic

duopolist’s sale s w ill have an uncertain impact on intra-firm

trade and host-country production by the MNF.

( )b With a high desired transfe r price an increase in the level of

the domestic duopolist’s sale s w ill alw ays cause the multina -

tional firm to reduce intra-firm trade .

Proposition 2.

If the transfe r-price e ffe c t dominate s the production effec t then

w e w ill have an upward sloping reac tion function, i.e ., dx r dy ) 0,

irre spective of whethe r the multinational firm desire s a low or a high

transfe r pric e .

The Com parative -Static Effe cts of Change s in the Tariff Rate

Totally differentiating the first-orde r conditions, repre sented by( ) ( ) ( )equations 4 , 5 , and 8 , and applying Cramer’s rule enable s us to do

comparative static s analysis w ith re spec t to marginal change s in the

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Table IComparative -Statics w ith Respec t to the Tariff Rate

( ) ( ) ( )x y m x y m x q y x y m q y

Tariff ? ? y q ? q

( )tariff. See Appendix I for de tailed expre ssions . The re sults are pre -

sented in Table I.

In the usual approach with only the production effe c t involved, a

higher tariff inc rease s the cost of the MNF’s ove rall operations and this

causes a dec line in the optimal scale of the operations , i.e ., the re is a

dec line in the leve l of sales. How eve r, the underse lling and ove rse lling

phenomena assoc iated w ith transfe r price s in the pre sence of re sale -

( )price re strictions change the story significantly. First, w ith 1 y GT -0 the firm is over-se lling the product due to the distortion created by

the ‘‘largene ss’’ of the tariff.12 A marginal increase in the tariff ac centu -

ates this largene ss, causing an increase in the leve l of sale s. Second,( )w ith 1 y GT ) 0 the MNF is under-se lling due to the distortion

created by the ‘‘smallne ss’’ of the tariff.13 A marginal inc rease in the

tariff reduces this smallne ss, causing an increase in the leve l of host-

country sale s. Co n s equ ently , an in crea s e in the ta rif f a lway s c a lls f o r

an inc rea s e in the leve l o f ho s t-co untry s a le s o n the ba s is o f thetran s f er-pric e m o tive . This o ccurs in the ca s e o f a high des ired

tran s f er price du e to the w eakenin g o f the tran s f er-pric in g m o tive ;

and in the c a s e o f a lo w des ired tran s f e r price due to the s treng then -

ing o f the tran s f e r-pric ing m o tive . In e ithe r case the transfer-pric e

e ffe c t runs counte r to the production e ffe ct. Thus, the change in total

12 ( h f ) ( h )The tariff is large r than the re lative tax diffe rential, i.e ., t ) g y g r 1 y g ,and this causes the multinational to desire a low transfe r price .

13 ( h f ) ( h )The tariff is smaller than the re lative tax differential i.e ., t - g y g r 1 y g ,and this causes the multinational to desire a high transfer pric e .

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sale s in re sponse to a marginal change in the tariff is ambiguous, and in

the event of a strong transfer-price e ffe c t w e have the possibility

w here a highe r tariff inc rease s the host-country sale s of the MNF.14

As long as w e have linear demand curve s dy r dx is negative and( ) ( )sign dy r dT s ysign dx r dT . The ambiguity of the sign of dx r dT,

due to the transfe r-pric e e ffe c ts, makes the sign of dy r dT ambiguous

and give s rise to the possibility of an ‘‘anti-prote c tive’’ tariff where a

higher tariff re sults in a reduc tion in the total sale s of the domestic

firm . This occurs if

( )a the transfe r-price e ffec ts are large and cause an increase in the

MNF’s sale s in the host country when the re is an increase in

the tariff, and, if at the same time ,( )b the domestic firm view s the MNF’s sales as strategic substi -

tutes, i.e ., dx r dy - 0.

Linear demand rules out the possibility of strategic complementarity(from the point of view of the domestic firm dy r dx - 0 is always true

)w ith linear demand , but doe s not rule out the possibility of the

anti-protec tive tariff.15

Regarding the level of intra-firm trade , the production e ffe c t

indicate s that the higher tariffs make the importing option more costly

and calls for a reduc tion in intra-firm trade . The transfer-price e ffe c t

w( ) xre inforce s this effe c t. First, w ith 1 y GT ) 0 the MNF is induced

14 For a similar re sult in the pre sence of a low desired transfer price and arm’s( )length restrictions see Samuelson 1982 .

15 With non-linear demand the othe r case of an anti-prote ctive tariff would occur if

( ) ( )a a highe r tariff reduces x the traditional result and( )b y and x are strategic complements.

If the strategic complementarity is due to the transfer pric e effec ts then once again theanti-protec tive tariff is a direc t re sult of the transfer-price e ffec t of the multinational.

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to ove r-import due to the smallne ss of the tariff. Thus, an increase in

the tariff dampens the ove r-importing phenomenon. This causes a

w( ) xreduc tion in the leve l of intra-firm trade . Second, w ith 1 y GT - 0

the largene ss of the tariff causes the MNF to under-import and a highe r

tariff w ill strengthen this motive , causing a furthe r reduc tion in the

leve l of intra-firm trade . Thus, in both case s the transfer-price e ffe c t

re inforce s the production e ffe c t and a rise in the tariff unambiguously

re sults in a reduc tion in the leve l of intra-firm trade .

(Despite the ambiguity about the change in x , the sign of d x y)m r dT is always positive . The traditional ‘‘tariff-jumping’’ result states

that an increase in the tariff w ill inc rease the leve l of host-country

production by the MNF. As the transfer price e ffe c ts have an upw ard

impac t on host-country sale s and a downw ard impac t on the level of

intra-firm trade , they undoubtedly strengthen the tariff-jumping re sult.( )The unce rtain sign of d x q y r dT indicate s that the total sales

in the host country may increase or dec rease w ith a rise in the tariff.

Furthe rmore, total sale s move in the same direction as the sale s of the

MNF in re sponse to a change in the tariff. This is due to the fact that

the tariff has a direc t impac t on the MNF’s sales and only an indire c t

impac t on the sales of the domestic firm.

( )It can also be show n that d x y m q y r dT is unambiguously

positive . This is so despite the uncertainty regarding the direc tion of

change in production by the local firm. Thus, to tal production in the

host country w ill always rise w hen the re is an increase in the tariff.

The core result of this se ction is summed up in the follow ing

proposition:

Proposition 3.

In the presence of re sale price re straints, a strong transfer-pric e

e ffe c t give s rise to the possibility of an anti-prote ctive tariff, where in

an increase in the tariff rate imposed on the multinational firm’s

imports leads to an increase in host-country sale s by the multinational

and a consequent dec line in the sale s of the domestic duopolist.

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IV. ENDOGENOUS TRANSFER PRICES

AND A STACKLEBERG DUOPOLY

The Dom e stic Duopolist as a Stackle be rg Le ade r

In this se ction the author looks at the case where the domestic

duopolist is the Stacklebe rg leade r and the MNF is the follower. The

max imand and the first-order conditions of the MNF, because it is the

follower, are the same as in the case of Cournot-quantity competition( )and we have dm r dT - 0, d x y m r dT ) 0, and the sign of dx r dT

depends on the re lative strengths of the transfe r-pric e e ffe c t and the(production e ffec t. The detailed expre ssions for the comparative -static

)re sults are provided in Appendix I. The first-order condition of the

domestic duopolist is

( ) ( )11 P r y s P q P 9 1 q dx r dy y y c s 02 y

Totally differentiating the domestic duopolist’s first-orde r condition

w ith re spec t to y and t we have :

( ) w ( ) 2 x12 dy r dT s y P 9 dx r dT q d x r dTdy r(

w ( ) ( 2 2 ) x XP 9 2 1 q dx r dy q y d x r dy y c( ))y

Because the denominator of this expre ssion is negative due to the

second-order condition for profit max imization for y , the sign of

w( )dy r dT depends direc tly on the sign of the te rm dx r dT q2 xd x r dTdy . We have seen that dx r dT can be negative or positive

depending on the strength of the transfer-price effec t. If dx r dT is( )positive negative then an increase in the tariff w ill shift the reac tion

( ) ( ) 2curve upward downward in x , y space . The te rm d x r dTdy( )capture s the change in the slope of the reaction curve x y w hen

the re is a change in the tariff. The implication is that as long as

d 2 x r dTdy is non-zero the reac tion function do es n o t shift in a

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paralle l fashion in re sponse to a change in the tariff.16 The detailed2 ( )expre ssion for d x r dTdy se e Appendix II shows that if the marginal

cost curve s are non-linear the value of this te rm in all like lihood is

non-ze ro. Consequently, by assuming linear marginal costs we ensure

that the reac tion curve s shift in a paralle l fashion and the re sponse of

y to a change in t can be w ritten as17 :

X( ) ( ) ( )12 9 dy r dT s y P 9 dx r dT r P 9 2 1 q dx r dy y cv 4y

v 4 v 4and sign dy r dT s ysign dx r dT

Figure II depic ts the situation in which the transfe r-price e ffe c t is

‘‘strongly’’ dominant and give s rise to dx r dt ) 0 and dx r dy ) 0.18

Point A is the tangency point be tween the MNF’s re ac tion curve and

the domestic firm’s iso-profit curve , and depic ts the Stacklebe rg solu -

tion for some given tariff t . A highe r tariff w ill inc rease the leve l of0

the MNF’s sale s for a given leve l of y , and this is re flec ted by the( ) ( )upw ard shift in the sale s-reac tion curve from x y to x y . The new0 1

Stacklebe rg solution for a highe r tariff leve l t is given by point B.1

Thus, a highe r tariff inc reases the equilibrium leve l of the MNF’s sales

from x to x and decrease s the equilibrium level of the domestic0 1

firm’s sale s from y to y . The diagram indicate s that as long as the0 1

re action curve s shift out in a paralle l fashion and they are linear, an

inc rease in t re sults in a dec line in y and an increase in x .

16 Non-paralle l shifts in the reaction curves imply that the reaction curve s mayinterse c t. This is consistent with the fac t that the sign of dx r dt is unce rtain.

17As long as we have linear demand and no cost inte r-dependencies the reaction( ) 2 2curve x y will be linear and this implie s that d x r dy s 0. The analysis could be

ex tended to include the case in which d 2 x r dTdy / 0. This would add an additionaldimension of ambiguity as regards the sign of dy r dT.

18 ‘‘Strong’’ and ‘‘weak’’ dominance is defined in the fo llowing way:

( )a When the both dx r dt and dx r dy are positive then the transfe r-price e ffec t isstrongly dominant, and

( )b if only one of the two terms is positive then the transfe r-price effec t is weaklydominant.

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Figure IIThe Change in the Le ve l of y and x in Response to an Increase in theTariff in the Pre sence of a ‘‘Strongly’’ Dominant Transfe r-Price Effe c t.

We w ould get the same re sult, w here the MNF’s equilibrium sales

rise and the domestic firm’s equilibrium sale s fall w ith a higher tariff, if

the transfe r-price e ffe ct is ‘‘w eakly’’ dominant where dx r dy - 0 and

dx r dt ) 0.19 This is shown in Figure III and can also be seen dire c tly( ) 20from Equation 12 9 .

19 There is also the other possible case of ‘‘weakly’’ dominant transfe r-price e ffe ctswhere dx r dy ) 0 and dx r dt - 0. To illustrate this case we would just have to reve rsethe reaction curves x and x in Figure II and we would ge t the standard re sult where0 1

a highe r tariff cause s an inc rease in the equilibrium sales of the domestic firm and adec rease in the equilibrium sale s of the MNF.

20 (Moreover, if we had non-paralle l shifts in the reaction function a consequence)of non-linear marginal costs we could ge t dy r dt - 0 even w ith non-dominant transfe r

price s. This would be the case where dx r dy - 0, dx r dt - 0, and d 2 x r dydt ) 0 and islarge.

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Figure IIIThe Change in the Le ve l of y and x in Response to an Increase in theTariff in the Presence of a ‘‘Weakly’’ Dominant Transfe r-Price Effe cts.

Multinational as the Stackle be rg Le ade r

If the MNF is the Stackleberg leade r the first-orde r conditions of

the domestic firm are similar to those in the Cournot case . Because

the transfer-price distortions do not ente r the pic ture dire c tly w hen

w e look at the domestic firm’s decisions we have the standard re sult

w ith linear demand where dy r dx - 0.

The MNF incorporate s the domestic firm’s re ac tion functions into

its max imization problem and its first-order conditions are:

( ) w ( ) h x13 P r x s G P q P 9 x 1 q dy r dx y c1*

( ) ( )q 1 y GT m P 9 1 q dy r dx r T s 0

( ) h f ( )14 P r m s Gc y c q 1 y GT P r T s 01*

In this scenario the comparative -static re sults do not reve al anything( )new and we have dm r dT - 0, d x y m r dT ) 0, and the sign of

dx r dT is unce rtain. There w ill be quantitative diffe rence s in the

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(magnitude of the se e ffe c ts as compared to the othe r scenarios se e)Appendix I . Neve rthele ss, the po s s ibility o f an an ti-pro te c tive ta rif f

w x w( )( )xs till ex is ts and sign dy r dt s sign dy r dx dx r dt .

The author could have e stablished the relationship be tween the

‘‘anti-prote c tive’’ tariff and the w eakly dominant and strongly dominant

transfe r-price e ffec ts w ithin the Cournot case and arrived at the same

conc lusions as in the Stackleberg case . The significance of this is that

the effec ts of endogenous transfe r price s on duopolistic inte rac tion

are invariant across a few diffe rent type s of marke t structure s and this

make s the case stronge r for acknowledging the importance of the se

e ffe c ts . Summing up the main implication of this se c tion we have the

follow ing:

Proposition 4.

In addition to the case of a Cournot-quantity duopoly, the anti-

prote c tive tariff remains a possibility in the case of a Stacklebe rg

duopoly irrespec tive of struc ture of the leade r-follower re lationship.

V. PUBLIC POLICY IMPLICATIONS OF AN

ANTI-PROTECTIVE TARIFF

Gove rnments in host countrie s are typically concerned about the

impac t of MNFs on consumer we lfare , local employment leve ls, and

the competitive position of domestic firms . The analysis of the previ -

ous sec tions enables us to draw some implications regarding some of

the se issues in the pre sence of anti-prote c tive tariffs. One must ke ep in

mind that these are conjec ture s which re late to the specific case of

horizontal-integration and re sale -price re straints. In a recent study Kim( )1993 surveyed 168 U.S. multinational firms and found that 27 per -

cent of the se firms used the resale -price method. This was second only

to the cost-plus method, w hich was used by 47 percent of the firms( )se e footnote 3 . This show s us that despite the fac t that the implica -

tions of the analysis apply to a spec ific scenario, the ir empirical

re levance is quite significant.

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Consumer w elfare changes are related to changes in total sales

and price s, and with an anti-protec tive tariff change , highe r tariffs

actually result in an increase in total sale s in the host country as the

dec line in sales of the domestic firm are dominated by the increase in

sale s of the MNF. This implie s that highe r tariffs may ac tually make

domestic consumers be tte r off. Part of the reason is that the tariff is

imposed on intra-firm imports and consequently a higher tariff doe s

not translate dire c tly into higher consumer price s.

The anti-prote c tive tariff also give s rise to an unorthodox implica -

tion regarding the competitive position of domestic firms. With strong

transfe r-price e ffec ts the domestic firms are w orse off if the host

country raises tariffs . This implie s that lobbying for higher tariffs may

not always be the optimal thing for the domestic firm if it is competing

w ith a fore ign MNF that is manipulating transfe r pric e s.

The issue of local employment e ffe cts in the presence of anti-

prote c tive tariffs depends on two things:

( )a the change in total production in the host country in re sponse

to the tariff change , and( )b the ex tent to which the MNF uses local inputs in the produc -

tion of the final goods in its subsidiary.

The previous sec tion showed that the transfe r-price e ffe c ts re inforce

the tariff-jumping effec t and this dominate s the reduced production by( )the domestic firm. In othe r words, d x y m q y r dT is positive . This

w ill in gene ral imply a positive impac t on employment as long as the

patte rns of input use and the te chnologie s of the MNF and the

domestic firm are fairly s imilar. How eve r, it is not unreasonable to

visualize situations in which a unit change in MNF output has a smaller

impac t on domestic employment as compared to a unit change in the

output of the local firm. If this was the case then it is not guaranteed

that increased domestic production is leading to increased employ-

ment and the reason is the change in the mix of locally produced

output.

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Once again, although the se effe c ts w ill be quantitatively diffe rent

for the Cournot and Stacklebe rg cases, the qualitative implications are

symmetrical across the diffe rent marke t struc tures.

VI. SUMMARY AND CONCLUSIONS

The primary contribution of this artic le is to deciphe r the e ffe cts

of transfe r price manipulation on the strategic inte raction be tween a

fore ign MNF and a domestic duopolist in the pre sence of re sale price

re straints . The study also trace s the implications of production-

location and intra-firm import re sponse s to a change in the host-coun -

try tariff rate .

In the case of Cournot quantity-competition the transfer-pric e

e ffe c t has a dire c t impact on the strategic re lationship betw een the

MNF and the domestic firm. In particular, there is the possibility of

strategic complementarity in quantities , even with linear demand

curves purely due to the ex istence of profit-shifting motive s. The

analysis shows that an exogenous increase in the domestic duopolist’s

sale s leve l has a negative impact on the marginal profitability of

intra-firm imports if the MNF desires a high transfe r price , and a

positive impac t on the marginal profitability of intra-firm imports if the

MNF desire s a low transfe r price .

The comparative -static analysis reve als that the transfer-pric e e f-

fe ct strengthens the tariff-jumping e ffe ct assoc iated w ith highe r tariffs.

With re sale -price re stric tions on transfe r price s, a higher tariff may

cause an increase in the MNF’s sale s in the host country. Finally, w e

have the paradox ic al possibility of an anti-protec tive tariff inc rease ,

w here an increase in the tariff cause s a decline in the total sales of the

domestic firm. The anti-prote ctive tariff is a possibility in the Cournot

quantity-duopoly and the Stacklebe rg quantity-duopoly w ith e ithe r the

MNF or the domestic duopolist as the leade r.

The results of this study also indicate that the public policy

implications in the face of an anti-protec tive tariff may be quite

diffe rent from those we encounter when higher tariffs are assoc iated

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w ith traditional prote ctionist e ffe c ts. This artic le furthe rs our under -

standing of the large ly unexplored issue of the impac t of transfe r-pric e

manipulation on oligopolistic inte raction in international trade . There

are a number of possibilities for further research within this frame -

w ork such as a comparison of the quantity-se tting game w ith a

pric e -se tting game with resale price re straints, and a rigorous analysis

of we lfare implications in the pre sence of a host-country duopoly and

transfe r-price manipulation by a fore ign multinational firm.

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APPENDIX I

COMPARATIVE-STATICS FOR THE COURNOT

QUANTITY -COMPETITION CASE

X 2( ) < <dx r dT s y 2 P 9 y c r D Ty

v h 9 ( ) f 9 ( ) 4= Gc P 9 m q P q P 9 m c q 1 y GT P 9 P r T

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w < < 2 xdy r dT s P 9 r D T

v x 9 ( ) f 9 ( ) 4= Gc P 9 m q P q P 9 m c q 1 y GT P 9 P r T

< <w here D is the de te rminant of the Hessian of the system of first-order( ) ( ) ( )conditions 4 , 5 and 8 , and is assumed to be negative in orde r to

assure an inte rior solution to the Cournot quantity game .

w < < 2 xdm r dT s 1 r D T

( X ) w h 9 ( ) x= 2 P 9 y c yGc P 9 m q P q GP 9 Px y

2X( ) ( ) ( )q P 9 y c y P 9 m r T q GP 9 P q P 9 m 5y

( ) w < < 2 xd x y m r dT s y 1 r D T

w X x w f 9 x= 2 P 9 y c P 9 m c q P 9 P r Tx y

2Xw x ( ) ( )y P 9 y c P 9 m r T y GP 9 P 9 m q P 5y

( ) w < < 2 xd x y m q y r dT s P 9 r D T

( X ) w f 9 ( ) x= c y P 9 c m q P r Tx y

( ) h 9 XqG P 9 m q P c q c y P 9( )y

( )(q P 9 m r T P 9 y c y

COMPARATIVE-STATICS WITH THE DOMESTIC FIRM

AS THE STACKLEBERG LEADER

v 2 < <4dx r dT s y1 r T H

( ) ( )= P 9 m q P Gch 9 q P 9 m c q 1 y GT P 9 P r Tv 4f 9

v 2 < <4dm r dT s y1 r T H

2( ) ( ) ( )= P 9 m q P Gch 9 q P 9 m r T y P 9 m q 2 P GP 9v 4

( )d x y m r dT

v 2 < <4s y1 r T H

v ( ) ( ) 4= P 9 m c f 9 q P 9 m q P GP 9 y P 9 m y P P 9 r T

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is positive due to the second-order condition for profit-max imization

for the MNF.

w ( ( ) ) xdy r dT s y P 9 q P 0 1 q dx r dy y dx r dT r2 2 2( ) ( )2 P 9 1 q dx r dy q y 1 q dx r dy P 0 q yP 9 d x r dy

and with linear demand w e have

v w x w ( ) ( 2 2 )4dy r dT s y dx r dT r 2 1 q dx r dy q y d x r dy

COMPARATIVE-STATICS WITH THE MULTINATIONAL FIRM

AS THE STACKLEBERG LEADER

v < < 2 4dx r dT s y1 r H T

v h 9 ( ( ) ) f 9 ( )= Gc P q P 9 m 1 q dy r dx q c m P 9 1 q dy r dx

( )( )4qPP 9 1 y GT 1 q dy r dx

v < < 2 4dm r dT s y1 r H T

h 9 ( ( ) )= Gc P q P 9 m 1 q dy r dxv2

( )( ( ))q 1 r T P 9 1 q dy r dx m

( ) w ( ) xyP 9 1 q dy r dx G 2 P q P 9 1 q dy r dx m 4

( )d x y m r dT

v < < 2 4s y1 r H T

f 9 ( ) ( )( )= c m P 9 1 q dy r dx q PP 9 1 y GT 1 q dy r dxv2

( )( ( ))y 1 r T P 9 1 q dy r dx m

( ) w ( ) xqP 9 1 q dy r dx G 2 P q P 9 1 q dy r dx m 4

( )( )dy r dT s dy r dx dx r dT


is positive due to the second-orde r condition for profit-max imization.

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APPENDIX II

( )The position of the multinational’s reac tion curve x y changes

w ith a change in the tariff and d 2 x r dTdy reflec ts the change in the

slope of the reaction curve for any given value of y if there is a change

in the tariff. From the main tex t we know that the expre ssion for

dx r dy is

w h 9 f 9 x w ( ) xGP 9 Gc q c q 1 y GT P 9 r Th 9w w ( ) x x= Gc q 1 y GT P 9 r T

dx r dy sh 9 f 9 h 9 f 9( ) ( )y2GP 9 Gc q c q c c y Gc 1 y GT P 9 r Th 9

2w ( ) xy 1 y GT P 9 r T

With linear demand curve s the expre ssion for d 2 x r dTdy is

( h 9 f 9 ) h 9 f 9 h 9 ( )y2 GP 9 Gc q c q c c y Gc 1 y GT P 9 r T(2

w ( ) xy 1 y GT P 9 r T )h 0 f 0 h 0( w x w ( ) x )= GP 9 Gc q c q 1 y GT P 9 r T Gch 9 f 9( w x w ( ) xq GP 9 Gc q c q 1 y GT P 9 r T

h 9w w ( ) x x )= Gc q 1 y GT P 9 r Th 0 f 0 h 0 f 0( ( )= y2GP 9 Gc q c q c c

h 0 ( )yGc 1 y GT P 9 r T2d x r dTdy s

h 9 f 9 h 9 f 9w ( )y2GP 9 Gc q c q c c22h 9 ( ) w ( ) xy Gc 1 y GT P 9 r T y 1 y GT P 9 r T

From the numerator of this expre ssion it is c lear that if marginal costsare linear, i.e ., c 0 s 0 and c f 0 s 0, then it is guaranteed thatd 2 x r dTdy s 0 and the reac tion curves are paralle l.

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endogenous transfer prices, tariffs, and a host country duopoly

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