Journalof IntcmationaIEcor~omics24 (1988) 147-157.North-Holland

ENDOGENOUS TRANSFER PRICING AND THE EFFECTS OF UNCERTAIN REGI.JLATION chander KANT* Cbtblic

University4pAmerica, W~hingtor~,DC ZUM4, USA

Received February1986,revisedversionreceivedJune 1987

A scenario is counder wbicb a multinationalfirm (MNF) fm a threat of a penalty, the probabilityof which is based on the MNFs @an&r price. Given this scenario,the MNFs ~~~priacouldkintheinterior,ardsinsultaaeclue~tenctionol~trandb priaandreelvorirrMes~Inataseds~~oTthetraJukxpricemekert&ZvlNFmove its transl& price towards the arm’s Ien@ price and &a&s fiscal abuses. But it worsens the intemationaIaMocationof rcsoWcecventhou~the~advan~ofthecxportingctnmtry illCWR&Sti&thCimpwtol@obaltmtfiueb~~us.

1. MroducW

The subject of the transfer price charged by a muhinational firm (MNP) on trade among its constituents has recently drawn some attention. Perhaps the most influential work on this subject is by Horst (1971) who demonstrated that depending on tax and tariff schedules, a MNFs optimum trand- price would either be the highest or the lowest possible. These limits on tr;msfer price were determined by government rules and regulations. Subsequent analytical work OQ the MNF has usually adopted Horst’s scenario in which the level of the profit-n&mixing transfer price is the exogenously determined limit [e.g Batra and Hadar (1979), Itagaki (1979,1981)]. Two recent contributions [see Samuelson (3982) and Eden (1983)] have argued that the limits on the transfer price are themselves functions of the MNFs sales and/o&intra-firm trade. Thus, the level of limiting transfer price charged by the %JFis aikctcd by the firm’s &cision variabtes, and is cndogenous. However, these authors also, like the other authors cited above, conclude that the MNFs opthum tracker p&x is the limiting transfer prk. Eden (1978,198~) compares the comparative static effects of tax, tariff and ex*I wisb to thank Josef Wadar,Arvind B-y% Takao Itgaki, Larry Samuelson, two anonymous r&rees and a cealitpr to this Journal for very detailed and helpful c~mmcnts 00 earIic d&s oftbe paper.However,I an responsiblefor all remainingerrors.

148

C. Kant,

Trani$iv pricW

change rates when the profit-maximking liu&ing tran&?rprice is greater or less than the marginalcost of productionin the source country- often taken as the shadow or the arm’s length transfer price. Itagaki’s (1982) and Diewert’s(1985) comparisonis with respezt to the limiting (Itagaki) or the optimaiiy regulated (Diewert) transfer price in the initial situation and a relaxationin regulation.To this author’sknowledge, none of the analytical writings on this subject has shown that MNF’s profit-maxim&g transfer price could be in the interior,or has examinedthe effects of changes in such a transferprice. This paper constructs a scenario under which the MNF may charge a transfa price in the interior.An increasedsurveillanceof the transferprice by a governmentmakes the MNF move its transferprice towards the arm’s length price and checks fiscal abuses. But it worsens the international allocation of resources even though the cost advantage of the exporting country increases.1thasbeensuggestedthattransferpricingisaneScient response by MNFs to exogenously imposed imperfections like market segmentation, di%erentialtaxes and tari& [see Rugman (1981), Aliber (198511.This paper shows that a reduceduse of the transferprice mechanism increases consumer surplw in the source country an& as stated above, checks fiscal abuses. However, it decreases consumer surplus in the host country so that no general conclusions on the efllixtsof transferpricing on global welfareare possible, The plan of this paper is as follows. Section 2 outlines the scenario, constructs the model, and presenta optimixing condition The &cts of changes in government’sattitude when the MNF underinvoicesits exports are presentedin section 3. Section 4 summaks comparativestatic etkts that are d&rent in the overinvoicing case. section 5 gives concluding remarks.

Considera MNF producingand selling a final good in two countries. It produces under increasingcosts and cost/rcvenu~ considerations are such that it exports part of its output from the parent firm in country 1 (source country)to its affiliatein country 2 (host country).There is some penalty of known size that can be imposed on the MNF with some probability.The probabiiityof imposition of the penalty depends on the extent of diifiicc between the transferprice charged and the ‘arm’siength price’,so that the MNF faces endogenousuncertainty. Let xi, &,si, xi, &&), C&J, q, q, ti, and c; representgross profits, profit tax rate, sales, production,total revenue and total cost functions, marginal revenue, marginal cost, and slopes of marginal revenue and marginal cost functions in country i (i= 1,2), and let 1;=( 1-t,). The MNF faces imper-

C.Kant, Tran@r pi&g

149

fectly cumpetitivemarkets and can pricediscriminatein the two ccnmtries. its global net profitfunction,x, is: where

~l=wlbG(st

-w+m

m are the MNFs imports from wuntry 1 into country 2, p is the transfer price and s the ‘ad valorem’tariffon importsin country 2.’ Let z* =( 1+ t). The derivativeof R with respsct to transferprice is: ~3(T~-~?*)llt=TZ(T*-~)m,

(2)

where T+=(tz-t#(l-t2)>0(by assumption) and (T*-r)s0.2

(3)

Following Horst (1971), P can be termedas the relative tax differentialin the two countries.The two situations 8tt: (i) the tax rate diierential is not enough to dominate the tari& i.e. (T*-z)isnegative;and (ii) the tax rate differentialoverrides the tariff, i.e. (T*- z)ispositive. If there were no prospect of the penalty, in the former (latter) situation the MNF would underinv&e (overinvoice) its exports as much as possible. The analysis below is presented for the underinvoicingcase. That for the overinvoicing case can be similarlypresented. This model dif&rsfrom the models cited above in assumingthat the MNF does not face any legal requirementon the transf&r price. However,a penalty can be imposedon the MNE But that is not certain. Trm&?r

pricing

penalty

It is assumed that although the government does not have a legal requirementon the transferprice, it has a guideline that the transferprice *TheMNF urukrinvti if t2 is lower than or equal to t,. If it is higher,dependingon tax and tariffrate4 it may eitherunderinvoiceor ovcrinvoicc.In this paper t2 >t, is assumed.This allows us to analym both the underinvoicingand the overiuvoicingcases, and makes the efkctire tax rate on foreignprofitsequal to ts whetheror not these profits ate repatriatedto country 1, and whetherO-o.z+t thereis d&ma1 of home tax on non-repatriatedprofits.See Eden (1985,foobtote 1).The analysis and conclusionsof the case with the other configurationof tax ntc& i.e.t&r,, is SimiIacto the luMkilkvoidngam pmellted here. 2when (P-r)=Q the transfkrprice has no effectOQnet profits,and is arbitrary.Hence,I amune (Ts-T)#O

C. Kant, Tmn&r

150

pri&g

should be equal to the arm’s length price. This situation is similar to that between wage and price guideposts and wage and price controls. Thus, althoughtransferprice guidelinesexist, there is no control on transferprice. Then, the probability Q of the imposition of a transfer price penalty depends on the divergence hetwccn the transfer price charged, p, and the arm’slength price, #. For the underinvoicingcast being discussed,as long as p is greaterthan or equal to fl, the probabilityof penalty is zero. For p less than $, a is positive. Let pc be the transferprice which triggers a trantier price penalty with certainty.Then, as p gets closet to pE, the probabiity of and I assume that it promulgationof a transfer price penalty U increasesat an increasingrate. For p less than p. the scenario faced by the MNF is that not only is the penalty imposed with certainty but also the MNF%profits, and tariffsand profit taxes, are recalculatedby disallowing p less than pa. Given this scenario,and to protect its iu~ge, the MNF does not chargea p less than pe.3 In symbols:

forPh%

a(p-&9=4

Fig 1 illustratesthe probabiity function. Let &O representthe penalty. Then as one possible source of the penalty we may consideran infiniteperiod model in which a transferprice regulation requiring,say, the MNF to charge a transferprice equal to the arm’s length price is not imposed for some period of time, but in which there are always later periods to provide the threat of regulationand thus discouragetransfer pricingin the present.The penalty then would be the effect on the present value of the entire futureof the firm due to whatever regulationis imposed. The expectedloss due to the penalty is:

Ca(p-#b++o{1 -dP-m

=ca(p-lwo*

(9

STaeformulation of the probability of pe&ty function is & and it may apply to either country. Simiily, it is assumed that either due to international collvcatioIl or otherwise, both the countries adopt the same defmition of arm’s length price. Intuitively, and with a view to check profit tax avoidance we ma!: expect the exporting country to impose the tran&r pricing pena!ty in the underinvoicing case, and the importing country to do so in the overinvoicing case. I shall assume so in the following. Vhe properties of the a-function for the overinvoicing case are:

4~+)=4 forBcpqk, 0<4p-B)< 1, d(p-#)>O, ti@-B)>O,

for 4&B, and far yzp,,

4p-B)= 1.

C.Kant,Trun#erpri&g

0

(PdO

b

Fig, 1. The probability function.

The objective function of the MNF is, therefore:

The first-orderconditions for an interior maximum are? (7)

92= Tara=4

(8) (9)

~~=~~(T+-~)m-~~~-B)=o,

(10)

where 4 = a#/&,

#,=a#iTrn

and #,,=a#@

(i= 1,2).

The above equations differ from those in other MNF models in showing that :the slope of the MNFs objective function with respect to p does not have the same sign for ah permissible values of pF and the MNF may not find it optimal to charge the comer or the limiting transfer price. The sign of 4, depends on the relative magnitudes of the variables aud parameters tin the right-hand side of (10). Let us define Tz(T* - r)mand - (a'@- fl) as the marginal gain and the margkl loss, respectively, from underinvoicing. For a “Interior maximum here means s,>q O0. Assuming the probability tknction tu k diIf’tiable at #, for p&3, a@-fl)=O, $,=q(T*-t)mcO and the objective function does not attain its maximum. For pp,), and is given by eq. (10) so that dkussion in the text of that equation is applicab!e~

p

increasingly lower than fl the marginalgain is constant but the marginal

loss increasesdue to increasein the probabilityof imposition of the -penalty. Only if the former dominates the latter for all pc sp S# will the optimium transfer price be pc. But, due to the increasingmarginalloss, the more lilceiy outcome is that the MNF shall charge a transferprice in the interior, i.e. betweenfi and pc. Hirshle%er (1957) proved that the arm’slength price, #, equals cl. Thus, in a situation of ~lntirinvoicin~ the optimum transferpti~ can be lower than cl. The equilibriumconditions also show a complete integrationof real and financialvariablesof the MNF. As noted above, Samuelson(1982) and Eden (1983) show that the kvels of MNFs i&a&xi trade and sales in the two countries alkt the actual level of limiting transferprice. At the same time, Horst (1971), Samuelson(1982), and Eden (1978,198s) prove that comparative static elkcts on real variables depend on whether the MNF underinvoices or averinvoices its exports, and Itagaki (1982) and Diewert (19g5) demonstratethat relaxationof the limit (Itagaki) or the optimum regulatiofi (Diewert) on transfer price aff’ real variables. Still, it appears that no author on this subject has shown the two-way and simultaneousinteraction of transferprice and the real variables.Allowingfor an interiortram&rprice and for simultaneouself&s of real variables and interior trader price on each other are uniquefeaturesof the model presentedhere. 3a changesingovernmen

t’s

am

wLBie&g

The attitude towards the MNF may change,for example due to a change in the governmentin either country. Or, an existing government%attitude may changedue to its own study and policy review.The probabilityfirnction can now be stated as:

where g is the shift parameter.It is assumedthat the government’sestimate of arm’slength price is unchangedat $. Bit for fl> p>pc, in the situation of a more strict attitude, the probability of penalty increases. Thm the probabilityof penalty lknction pivots upwards around fi and the absolute value of its slope also increases.6In symbols: %y iumlyds of ;: cimp io g~vc~nmeuh attitude towards the MNF may tz PA~REW RI that in Ikwcrt (193f;l,= follows: Diewert d&es an optimally regulatedtraasfkre W, as the transferpice wbicb, in a situation of unequal profit tax rates and tari&, yields the same level of intra-firmtrade as that when the MNF faced no taxes or tariS. §+khg with a situation where tbe MNF was requiredto charge w* (in a situation of unequal profittaxesand tari%), be examines tbe efkcts of hxting the MNF charge a tram&r f&e beh -@ (in a situation d underinvoicing)or above w* (in a situation of overinvoiciag)on the volume of intrahn trade.My scenario does not require MNF to chargeeither tbe optimally regulated,w*, or

C.Kant, Tran#erpricing

153

Fig. 2 illustratesshift in the probabilityfbction. The comparative static ekts of a change in govemment’s attitude are prescntti in table 1 for both the underinvoicingand the overinvoicingcases! It has alreadybeen stated that in the underinvoicingcase the penaltyis likely

(PC?(PC)’

0

;

Fig Z Sift in !he probabilityfimction. Tabk 1 E&t!8 of an increasein the threatof regulation.

sales

underinvoicing

overinvoicing

+

+

PtOdUCtiOll

Profits

+

ProdWT sluphls(4) Country

2

I-%oda~?t!l Profits Impa

+

c TransferkW ? Importbill ? Balafla of paymlzzts -_*A Trofits ckrs to currentprofitsonly.

4

9

+

arm’s iength price, 8, in the beginning. Starting with an interior solution, m&&ing tran&r price lying between jl and pr, I examine the &xts

i.e. with the profitof an inmase (or dccmasc)in the threat of q~~Gtion of transf’ priu~ peaaltjCMI IMNFs decisionvariablesand other variablesof interest. ‘For the ovknvoicing case, we have &/8g>Q an = i?aJiTg>O. %4athemtical proofs arc availablefrom the author on request.

to be imposed by country I. In reqonse to a more strict attitu home country, the MNF moves its jransfer price towards the price. Although changes in transfer l&e are accompa changes in real varigblti, all the variables change in such a way th profits and tax collections in home country improve. Thus, the source country succeeds in its e&t to check tax avoidance by the MNF. (Gross profits in the host country decrease.) Sales and consumer surplus increase in the source count and there is a downward pressure on the price level in that country. reverse happens in country 2. But all these benefits in country 1 are accompanied by a decrease in output in country I while that in country 2 increases. The source country thus faces a dilemma. In order to meet its fiscal objectives, it should adopt a more strict attitude towards the MNF. However, to counter the alleged home employmentdecreasing elfof multinational investment, it should adopt a more lenient attitude on the transfer price. These results can be explained as followa Increased threat of penalty makes the MNF move up its transfer price. The increase in transfer price makes it more advantageous to produce in country 2 than to import from country 1 leading to the stated eIfects on outputs and exports. Exports decrea~ even though (due to output chanmj the cost advantage of the exporting country increases. Thus, a policy which corrects Iiscal abuses leads to a perverse international allocation of resources. These effects can be illustrated with the help of a relatively simple diagram if it is assumed that the rate of profit taxation is the same in the two countries. The MNF would still underinvoice so as to save on tariff revenues. The first-order conditions, and the comparative static elIec$s have to be restated now by replacing, say, Tt by Ti eveqwhere. For example, eq. (9) now implies (c2 -ci)=pr, and T,(T+-r) in eq. (10) becomes -nnT,. The signs of the comparative static effpsts shall remain unchanged. Fig. 3 then shows initial equilibrium as well as the eI&ts of an increased threat of pen&y. Following Horst (1973), fig 3(b) shows the marginal cost of exporting c,, and marginal revenue from importing, r,, schedules. The former (latter) is the horizontal distance between r&) and cI(c2) curves. Fig. 3(d), on the other hand, pricing. The mrT1 curve is horizontal use it is the m change in transfer price, and is a constant function of p. tive slope since it measures the marginal pro y and an increase in p (in a situation of underinvoicing) decreases it.

consumer surplus.

a)

urce Country

b)

_-_

Fig- 3. Etkcts of an incmase in the hat

ml mo

Intra-Firm Trade

_

c! of irqmition of penalty.

-

x’2s,o

Host Country

d)

Transfer Price

135

C. Kant,

Trclryrerpriciq

These results also shed some light on the debate as to whether the use of the transfer price mechanism by a MNF improves global werare. Rugman (1981) and Aliber (1985) argue that it does, since transfer pricing counteracts exogenous imperfections like tax differentials --_-and_ tariffs. On the other hand, Bond (i%O),Qiewert (1985) and Eden (1983) (Eden, for the overinvoicing case only) argue that global weRare is reduced since &an&r pricing worsens the global allocation of resources. In my model, an increased threat of penalty makes the MNF reduce the use of the transfer price mechanism. But such reduced use neither unambiguously decreases global welfare nor increases it. Thw no general conclusions on the e&W of transfer pricing or& global welfare are possible.

In this section some of the comparative static effects under overinvoicing

which are different from those in a situation of underinvoicing are highlighted. These are on the trgnsfer price and gross profits in the two countries. An increased threat of penalty now makes the MNF lower its transfer price. Both volume of trade and the transfer price are lowered, i.e. in contrast to the underinvoicing case, exports now do not counterbalance the movements in transfer price. This allows us to determine the effects on the import bill and balance of payments of country 2. The former decreases and the latter improves even though pro&s payable by country 2 to ~untry 1 increase (rather than decrease as in the underinvoicing case).

Transfer pricing by MNFs is viewed with suspicion by governments and most authors who have written on this subject. Yet the effects of a greater or smaller use of the transfa price mechanism have not been adequately analyxed. This is mainly due to the fact that virtually all existing MNF models find an MNFs optimum transfer price to be the comer or the limiting tranxfer price. This paper shows the possibility of an interior profitmaximizing transfer price and allows for the simultaneous and two-way interaction of transfer price and rtil variables. It emphasixes tax differentials and tariffs, and ignores factors like local shareholding and restrictions on profit repatriation in the host country as causes for transfer pricing These other factors are likely to be especially important when host countries are developing countries. They tend to make the MNF overinvoice its exports by causing its perceived or effective tax rate in the host country to be significantly higher than the official rate. Thus, when the host country is a developing country, the MNF is likely to overinvoice its exports, and the comparative static ef%ct~for that case shall be applicable.

References Alibcr, R.2, 1985, Tram&r pricing:A taxonomy of impacts on coonomic welfare,in: A.M. Rugman and L. Eden, eds- Multinationalsand transfm pricing (St. Martin’s,New York) 82-97. $mm Fix4 vceu &at& B&a, RN. md Ji I#&, 19795‘n”..w.n i ----_i; of *& m&&t&& &umge rate&oxford EconomicPapers31.258-269. Boa E.W- 1980,Optimal transferprifhg when tax ratesdi%r, SouthernEconomicJournal47, 191-200. Gkwcrt, W.E.,1985,Transk pricingand axmomic &cicncy, in: A.M. Rqglg sod L. Eden, cds., bRhationals and transferpriciug(St.Martin’s,New York)47-81. Eden, L., 1918, Vcrkally integrated multiaationak A micro-economiccnaly&s, p&aadian hrUl of Ecenomics l&534-546. Eden,L, 1983,Tram&r pricingpoliciesunder tariffbarks, Cawdian Journalof Economics14, myb85 The mkroeconomicsof tram&r prick@,in: A.M. Bugman and L. Eden, ads., Mul&atio& and transk pricing(St.Martin’s,New York) 1H. Hirs&ifcr, J, 1957,Economb of t&edivisionalhd Gnu,Journalof Business30,96-W. Hot%,T., 1971,The theoryof the multinatiom!lbc Optimalbehaviorunder&&rent &ff and tax rates,Journalof PoliticalEconomy 79,lw-1072. Homt,T., 1973,Tbc simpk aaalytic~of multinationallinn behavior,in: M.B.Connallyand AX. Swoboda,eds.,Internationaltradeand money (GeorgeAllenand Unwin, London)72-84. Itagaki,T, 1979,Theory of the multhational firm: An analysisof cffbctsof governmentpolicies, Ia*Wa&.ion&l &onomic Review2Q 437-448. Itag& T* 1981, The tbcory of the multiaational firm under exchange rate unaztainty, Chadian Journalof Economics14,276-297. Itagaki,T., 1982, Systems of tation of multinational hrms under cxclumgerisk.,Southern EconomicJournal48,708-723. Rugbtan,A.M., 1981, Inskk the multinational Tbc economics of internal markets (Groom Helm,London d Columbia UniversityPress,New York). Samudso~ L, 198%The multinationalfirm with arm’s kngtb tram&r price limits, Journalof Illtcn6atiollalEconomics13.365-374.