Who Wins a Trade War? Mark Melatos, Pascalis Raimondos-Møller and Matthew Gibson. August 31, 2007

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1 Who Wns a Trade War? Mark Melatos, Pascals Ramondos-Møller and Matthew Gbson August 31, 2007 Abstract. A trade war provdes an economc ratonale for the exstence of barrers to trade. The man result n ths lterature s that bg countres wn trade wars. Ths paper extends ths result by consderng a wder range of factors that determne the outcomes of trade wars. In a purely non-cooperatve two-country Heckscher-Ohln model of trade, the country sze result s confrmed. However, a country whose preferences exhbt a suffcently large degree of substtutablty relatve to those of ts rval may wn a trade war regardless of ts sze. In partcular we demonstrate that a small country can wn a trade war aganst a larger rval f ts preferences exhbt suffcent substtutablty. Separately, we also demonstrate that the more smlar the relatve factor endowments of two countres, the smaller the welfare gans or losses from a trade war wll be to each. PRELIMINARY VERSION - PLEASE DO NOT QUOTE Acknowledgement: Melatos gratefully acknowledges the fnancal support of an Australan Research Councl research grant. Melatos and Gbson: Dscplne of Economcs, Faculty of Economcs and Busness, Unversty of Sydney Australa. Ramondos-Møller: Department of Economcs, Copenhagen Busness School, Denmark. Keywords: Trade Wars, Optmal Tarffs JEL Classfcaton Codes: F13 Address of Contact Author: Mark Melatos: Economcs, Faculty of Economcs and Busness, Unversty of Sydney, Sydney, N.S.W. 2006, Australa. Tel: 61 (2) , Fax: , Emal: m.melatos@econ.usyd.edu.au 1

2 Who Wns a Trade War? 2 1. Introducton It s well known that, relatve to free trade, countres can gan from mposng optmal nonzero tarffs even n the face of retalaton by ther tradng partners. A trade war occurs when all countres choose levels of protecton that maxmse ther own welfare gven the trade barrers of other natons. A country wns a trade war f t experences hgher welfare n a world of optmal protecton than t would under global free trade. The concept of a trade war therefore provdes a purely economc ratonale for the observed presence of barrers to free trade. If a country wns a trade war, then t wll most lkely oppose moves to ntroduce free trade, and s unlkely to agree to the abolton of trade barrers wthout a compensatory transfer payment. The lterature addressng these ssues s somewhat sparse. Ths s, at least n part, due to the complexty of modellng and analysng trade wars. Johnson ( ) demonstrates that a country can gan relatve to free trade from settng a non-zero tarff, even n the face of retalaton by ts tradng partner. 1 In partcular, he fnds that a country wth a suffcently hgh elastcty of mport demand relatve to ther tradng partner wll wn a trade war. Of course, the elastcty of mport demand s tself dependent on more fundamental country characterstcs. The am of ths paper s to determne how the fundamental characterstcs of countres affect the outcome of a trade war. The characterstcs analysed here nclude country sze and the nternatonal dstrbuton of endowments of factors of producton, as well as the structure of consumer preferences. We smulate a 2-country, 2-good, 2-factor general equlbrum model of world trade. The results of our smulatons suggest that: 1. a country that s suffcently large relatve to ts tradng partner wll wn a trade war; 2. n a Heckscher-Ohln model of trade, the magntude of a country s welfare gan or 1 The lterature followng Johnson ( ) and consdered n ths paper has generally assumed tarff settng to be a smultaneous move game n contnuous strateges, however other researchers have relaxed ths structure. Syropoulos (1994) and Ramondos-Moller and Woodland (2000) model tarff settng as a dynamc game n whch the tmng of sequental tarff choce s chosen endogenously. Kuga (1973) consders dscrete tarff strateges and presents an example wth a mxed strategy tarff equlbrum. Nether of these approaches has dealt wth trade war outcomes n a way that dffers from the Johnson approach.

3 Who Wns a Trade War? 3 loss from a trade war wll shrnk the more smlar are ts relatve factor endowments to those of ts tradng partner; 3. a country wth a suffcently large degree of substtutablty n ts preferences wll wn a trade war; and 4. contrary to the exstng lterature, a small country can n some crcumstances wn a trade war aganst a larger rval. There are few general results lnkng the welfare mpact of a trade war to the characterstcs of the countres nvolved. What few results exst concentrate on the role of relatve country sze n determnng the outcome of a trade war. The elastcty of mport demand has been wdely nterpreted as a measure of the degree of relatve monopoly/monopsony power that a country holds n world commodty markets. The sze of a country relatve to ts tradng partners has strong ntutve appeal as a fundamental determnant of a naton s market power on world markets. However, a satsfactory defnton of relatve sze has proved somewhat elusve. Analytcal results have been derved by Kennan and Rezman (1988) for the specal case of a pure exchange tradng world n whch consumers have Cobb-Douglas preferences. From the resultng lnear expendture system they derve the condton for each country to wn a tarff war as a functon of each country s share of the world endowment of each good. Kennan and Rezman (1988) conclude that a bg country can expect to gan by startng a tarff war. Ther defnton of country sze s the relatve sze of the elements of a country s endowment vector. Whether ths defnton makes sense s contngent on whether dfferentgoodsarevaluedon thesamebass.ingeneralthswll notbetrue.a possble soluton to ths problem would be to value each country s endowment at world or domestc prces, allowng a common bass of comparson between non-dentcal endowment vectors. Syropoulos (2002), n presentng the lterature s most general treatment yet of the role of country sze, ponts out the specfcty of the Kennan and Rezman (1988) case. He adopts a defnton of country sze as a scalar multple of a fxed factor endowment vector. That s, he specfes a per capta endowment vector for each country, then treats

4 Who Wns a Trade War? 4 a change n sze as a change n populaton, holdng the elements of ths endowment vector constant. Therefore, populaton sze s a scalar multple of the endowment vector and so the relatve populatons of countres can be used as the bass for comparson of sze. Usng ths defnton of country sze, Syropoulos (2002) shows the effects of dfferng relatve country szes on trade war outcomes n a two country, two good model where countres have dentcal and homothetc preferences and constant returns to scale technology. The beneft of hs approach s that t does not rely on functonal forms for technology or preferences, so long as the structure descrbed above holds. Syropoulos (2002) shows that country sze unambguously determnes whether or not a country gans from a trade war n the lmt. Usng lmt arguments, he show that an nfntely large country wll () have dentcal per capta welfare n autarky, free trade or a trade war, () experence an ncrease n per capta welfare wth an nfntesmal ncrease n the relatve sze of the other (nfntely small) country n a trade war; and () experence no change n per capta welfare wth an nfntesmal ncrease n the relatve sze of the other (nfntely small) country under free trade. He also shows thast there exsts a threshold relatve sze above whch the relatvely large country wll unambguously wn a trade war. As Syropoulos (2002) hmself acknowledges, the defnton of country sze employed assumes that per capta endowments reman fxed. Thus any role that endowment dstrbutons play n determnng trade war outcomes are gnored, as varyng country sze s equvalent to the equ-proportonal varaton of all factor endowments. Ths contrasts wth the flexblty of the Kennan and Rezman (1988) approach, whch allowed them to use a defnton of country sze based on combnatons of goods endowment shares. Both approaches lead to the same result n the lmt. Hamlton and Whalley (1983) seek to calculate optmal tarff rates for comparson wth observed tarff levels. They numercally smulate a model whch uses a smlar defnton of country sze to Syropoulos (2002). Ther smulatons show that a suffcently large country relatve to ts tradng partner wll wn a tarff war. Unfortunately they make no menton of ths n ther dscusson, snce ther emphass s on calculatng optmal tarff rates and comparng them to observed tarff rates. However, usng ther results t s possble to

5 Who Wns a Trade War? 5 calculate the threshold level of relatve country sze as approxmately 1.8 tmes as large as the country s tradng partner. Other country characterstcs have also been brefly consdered n the lterature. Hamlton and Whalley (1983) smulate the welfare effects of varatons n consumpton substtuton elastctes, producton elastctes and the dstrbuton of goods endowments as well as sze. characterstcs other than sze. However, snce ther man am s to claculate optmal tarff rates, they do not nterpret these results from the pont of vew of trade war outcomes. Besdes these results, Gros (1987) mentons the mpact of varyng the elastcty of substtuton n consumpton on the threshold relatve country sze n the context of a monopolstcally compettve model of ntra-ndustry trade. However ths s not the focus of hs work, as he only computes the threshold sze for four dfferent elastctes. Nevertheless, these smulatons suggest that the threshold sze decreases as the elastcty of substtuton ncreases. That s, when all countres have a hgher elastcty, a country may be more lkely to gan from a tarff war. Importantly, Gros mantans the assumpton of dentcal preferences between countres, so hs results reveal lttle about how dfferences n preferences between countres affect trade war outcomes. 2. The general model We buld up a standard perfectly compettve trade model of N countres that trade M goods. Trade s restrcted by tarffs. A postve tarff term s a tax on mports or a subsdy on exports, dependng on whether t corresponds to a negatve or postve net export term. On the other hand, a negatve tarff s ether an mport subsdy or an export tax Consumpton. Let superscrpts ndex countres, subscrpts commodtes. Country has a sngle representatve consumer wth a utlty functon: U = U x, =1, 2 (1) where x s an M 1 vector of goods consumed n country. The representatve consumer n country owns all frms and factors of producton n country, and therefore receves the Gross Domestc Product (GDP) of country as ncome. The representatve consumer s maxmsaton problem can be wrtten as:

6 Who Wns a Trade War? 6 max U x s.t p T x p T y + R =0, (2) x where y s a M 1 vector of outputs (wth elements y j), p a M 1 vector of domestc prces (elements p j),and R the tarff revenue n country. T denotes a transposed matrx. Tarff revenue s redstrbuted lump-sum to consumers. The domestc prce of good j n country s gven by p j = p w j 1+t j,wherep w j s the world prce of good j and t j s the tarff leved by country on good j. The soluton to ths maxmsaton problem s country s vector of Marshallan demands: x = x p w,t,y,r, (3) where t s the M 1 vector of tarffs ncountry, ofwhchthej -th element s t j,andp w t the M 1 vector of world prces wth elements p w j. However, tarff revenue can be rewrtten as: R = MX t j p w j j=1 x j yj. (4) Therefore equaton (3) can be expressed as: x = x p w,t,y. (5) 2.2. Producton. The j -th element of the M 1 vector of country outputs s gven by: yj = fj v j, (6) where fj s ndustry j s producton functon n country, andvj s a H 1 vector of factor nputs for ndustry j of country. Frms choose vj n order to mnmse ther M 1 vector of cost functons. Thus the producers problem becomes:

7 Who Wns a Trade War? 7 mn C vj j = w T vj s.t. fj v j = y j, (7) where w s a H 1 vector of factor prces n country. ThsyeldstheH 1 vector of condtonal factor demands n ndustry j : v j=v j w,yj. (8) The proft maxmsng problem for each ndustry j n country s: max π yj j = p T j yj w T vj, (9) where π j s ndustry j s proft ncountry, andv j s the H 1 vector of factors demanded by ndustry j n country. Snce producton s perfectly compettve, we can rewrte (9) as the followng zero proft condton: π j = p T j y j w T v j =0, (10) The soluton to these condtons s the supply of good j n country : yj = yj p w j,t,w, (11) rememberng that domestc prce s a functon of the world prce and domestc tarff rate. The factor market n country clears f: MX j=1 v j w,yj = Q, (12) where Q s the H 1 vector of factor endowments n country. Equaton (12) states that the sum of demands for each factor by each ndustry must equal the endowment of that factor for all factors of producton n country. Solvng these equatons for output yelds an alternatve specfcaton for output n country : yj = yj w,q. (13)

8 Who Wns a Trade War? Equlbrum. Gven the optmsng behavour of agents as set out, the followng condtons wll determne a compettve general equlbrum: NX x j =1 p w,t,y = NX yj =1 w,q, j = {1,..., M 1} (14) π j = p w j 1+t j y j w v j =0, [1,N], j [1,M] (15) where y s the M 1 vector of ndustry supples, the j -th element of whch s yj.these condtons state that all but one commodty market clears (14), and all ndustres n all countres make zero proft (15). Snce the representatve consumers budget constrants hold wth strct equalty, Walras Law states that the value of aggregate excess demand n the world s dentcally equal to zero. Therefore, f M 1 commodty markets clear, then the M -th market must clear also. As a result, there are only M 1 ndependent prces n the model, so good M s chosen as the numerare good wth prce normalsed to unty. All other commodty and factor prces are determned relatve to ths prce. Solvng the equaton system (14) and (15) yelds solutons for all world prces, p w, and each country s factor prce vector, w, n terms of tarffs andofworldprcesandthe parameters of the model,.e. p w = p w t 1,..., t N and w = w t 1,...,t N. Inthecaseofatradewar(TW)nwhchallcountres stand alone, each country choses ts tarff rates so as to maxmse ts polcymaker s objectve functon. The polcymaker s assumed to be benevolent, so that her objectve functon s natonal welfare, measured as the utlty level of the representatve consumer. Therefore the polcymaker s problem n country becomes: max V p w,t,w,q, (16) t where V = V (p w,t,w,q ) s the representatve consumer s ndrect utlty functon, obtaned by substtutng the commodty demand vector (5) nto the consumer s drect utlty functon (1), evaluated at ŷ =ŷ (w,q ). Note that by the goods market clearng condton (14), p w wll depend on the tarff ratesneachcountry. Therefore the polcymaker s problem can be wrtten:

9 Who Wns a Trade War? 9 max V p w t,t t,w,q, (17) t where t s a M (N 1) matrx of tarffs set on every good by countres other than. Snce the tarff rates of other countres mplctly enter the polcymaker s objectve functon through ther mpact on world prces, the tarff choces of the polcymaker wll depend on the tarff choces of other polcymakers. Hence tarff rates are strategc varables, and optmal tarff choce requres that polcymakers play a game n tarff strateges. There are M N players, one for each country and good, so that each country s polcymaker acts as M players. The strategy set for each player s t j R 1. The frst order condtons for the polcymaker n country are: dv dt j =0, j [1,M]. (18) These mplctly defne a best response functon for t j: t j = t j t j,t, (19) where t j are the tarff rates set by the polcymaker n country on goods other than j. Therefore the Nash equlbrum n tarff strateges s gven by the smultaneous soluton of (18). At ths pont each polcymaker s choosng ther best response tarff rate on each good, holdng all other tarff chocesbythemselvesandotherpolcymakersfxed. Therefore the equlbrum under a trade war must satsfy condton (18), the optmal tarff condtons, [1,N], along wth condtons (14), the goods market clearng condtons and (15), the zero proft condtons. A trade-war equlbrum s defned as a set of factor and commodty prce vectors, and optmal tarff vectors that satsfy these condtons Global Free Trade. Thecaseofglobalfreetrademposesthefollowngrestrcton on the tarff matrx:

10 Who Wns a Trade War? 10 t 1 1 t N t =. t j. =. 0.. (20) t 1 M tn M 0 0 That s, all elements of the M N tarff matrx are set equal to zero. In ths case p = p w [1,N], snce any devaton from ths prce vector would present opportuntes for proftable arbtrage n commodtes. No tarffs are determned strategcally, so polcymakers do not play a tarff settng game. Hence the condtons for equlbrum under FT can be wrtten by substtutng a vector of zeroes for each t nto condtons (14) and (15). Ths yelds the equlbrum condtons, choosng good M as the numerare: NX x j =1 p w,y = NX yj =1 w,q, j = {1,..., M 1} (21) π j = p w j yj w vj =0, [1,N], j [1,M] (22) A compettve free trade equlbrum s a vector of world prces and the matrx of factor prces p w,w that satsfy these condtons. 3. Smulatng a H-O model The model ntroduced n the prevous secton s naturally too general to answer the queston of what types of countres wn trade wars wth other countres. Syropoulos (2002) has shown that general results on country sze are possble f the model s smplfed to two countres and two goods. The method he uses, however, s not sutable for nvestgatng endowment changes n two dmensons or dfferences n preferences, and can offer no nsght nto the magntude of relatve sze dfferences requred for a country to wn a trade war. As a result, ths secton smulates a stylsed model of world trade, n order to more fnely nvestgate the effects on trade war outcomes of a wder range of country characterstcs. Take the model ntroduced n the prevous secton and set M=N=H=2(the2

11 Who Wns a Trade War? 11 x 2 x 2 case). Denote countres one and two by superscrpt and goods one and two by subscrpt as prevously. Wthout loss of generalty, choose good 2 as the numerare. The two factors of producton are captal (K) andlabour(l), and ther prces rent (r) and wages (w) respectvely. Unlke prevous models of retalatory trade wars (see for example Kennan and Rezman (1988)) no specfc pattern of trade s assumed ether country may mport or export ether good. Trade s balanced at world prces by vrtue of the representatve consumer s budget constrant: p w 1 1+t 1 x t 2 x 2 p w 1 1+t 1 y 1 1+t 2 y 2 R =0 (23) Substtutng n the value of the tarff revenue, R rearrangng yelds: = p w 1 t 1 (x 1 y 1)+t 2 (x 2 y 2) and p w 1 x 1 y1 + x 2 y2 =0. (24) Ths s the balanced trade condton for country Consumer Preferences. The representatve consumer n each country s assumed to have a Constant Elastcty of Substtuton (CES) utlty functon of the form: σ C 2X U = φ jx j=1 j σ C 1 σ C σ C σ C 1 (25) s the elastcty of substtuton n consumpton of the representatve consumer n country, andφ j s a parameter that determnes the contrbuton of each good to the consumer s utlty. The economc nterpretaton of σ C s dscussed n detal n secton 2.6. The assumpton of ths functonal form s restrctve, partcularly as t mposes the restrcton that the elastcty of substtuton s constant across all levels of consumpton. It does, however, ncorporate several functonal forms often assumed n analyss. σ C 0 the CES utlty functon approaches the Leontef utlty functon, as σ C t approaches the lnear utlty functon, and as σ C 1 t approaches the Cobb-Douglas functonal form. Therefore the CES functonal form s more general than any of these As

12 Who Wns a Trade War? 12 forms, and s n partcular more general than the Cobb-Douglas utlty functon assumed by much of the optmal tarff lterature, both wth and wthout trade agreements, followng Kennan and Rezman (1988, 1990). Solvng the consumer s maxmsaton problem wth ths functonal form, and wth good 2 desgnated the numerare, yelds demand functons of the form: ˆx 1 = ˆx 2 = φ 1 (1 + t 2) σ C (p w y 1 + y 2) p w φ 1 (1 + t 2) σ C + φ 2p w (1 + t 1) σ C φ 2p w (1 + t 1) σ C (p w y 1 + y 2) p w φ 1 (1 + t 2) σ C + φ 2p w (1 + t 1) σ C (26) These demand functons depend on the endogenous parameters of tarff rates, world prces, and the level of output Technology. The ncorporaton of producton nto ths trade war model adds a layer of complexty and realsm to the analyss of Johnson ( ) and Kennan and Rezman (1988), who both assume a pure exchange settng. Syropoulos (2002) does ncorporate producton nto hs analyss of trade wars, however he does not provde any smulated examples that llustrate the threshold szes for trade war outcomes that he derves. The model of trade wars used n ths secton can therefore be used to answer prevously neglected questons related to the process of producton n trade war outcomes. FrmsneachndustryneachcountryareassumedtoproducewthaCESproducton functon: yj = γ KjKj σ Pj 1 σ Pj + γ LjL j σ Pj 1 σ Pj σ Pj σ Pj 1 (27) Ths functon has the same features as the CES utlty functon, wth σ Pj beng the elastcty of substtuton between captal and labour n the producton process. γ Lj and γ Kj are the weghts on labour and captal respectvely n producton. The functon s homogeneous of degree one, and therefore producton exhbts constant returns to scale.

13 Who Wns a Trade War? 13 Solvng the cost mnmsaton problem for each frm yelds the condtonal factor demand functons: foruntfactorrequrements: K j = k jy j L j = l jy j (28) k j = l j = Ã! σ rγ Pj 1 γ Kj + γ Lj Lj wγ Kj à rγ Lj wγ Kj σ Pj σ Pj 1! σ Pj Ã! σ rγ Pj 1 γ Kj + γ Lj Lj wγ Kj σ Pj σ Pj 1 (29) Equaton (28) s a corollary of constant returns to scale, as demand for factors wll be a lnear functon of output for any gven factor prces. As a result of ths lnearty, t s possble to solve the factor market clearng condtons n equaton (12) explctly for output n each ndustry n each country: y1 = k 2L l2k, y k2l 1 l2k 1 2 = l 1K k1l k2l 1 l2k 1 (30) 3.3. Tarff Choce. For smplcty and wthout loss of generalty, each country wll set ts tarff on exports equal to zero. However, whch goods are exported wll depend on the endogenously determned pattern of trade. Ingeneraltwllnotbepossbleto explctly solve for each country s tarff reacton functon wthout mposng qute restrctve functonal forms on the preferences of the representatve consumers. 2 Each country s tarff reacton functon can be obtaned, however, by totally dfferentatng ts ndrect utlty functon, contaned n equaton (17) wth respect to t j: 2 Ths s done by Kennan and Rezman (1988, 1990), amongst others n order to derve analytcal welfare results.

14 Who Wns a Trade War? 14 dv dt j = V p w 1 dpw 1 dt j + V w dw dt j + V r dr + V dt t j j =0 (31) where good j s country s mported good. It s necessary, however to derve the total dervatves dpw 1, dw and dr, n order to wrte down the mplctly defned tarff reacton dt j dt j dt j functon for country. Thsspossblebytotallydfferentatng and smultaneously solvng the world excess demand functon for good 1 (the non-numerare good) and the zero proft condtons n country. Ths allows (31) to be wrtten n terms of partal dervatves whch can be explctly solved for usng the equlbrum condtons stated below. So the equlbrum condtons that descrbe a Nash equlbrum n tarff strateges for the 2 x 2 x 2 case are gven by equatons (14) and (15) wth M=N=H=2, and (31), for, j = 1, 2 and Q =(K,L ). Equaton (14) can be rewrtten as: z 1 = 2X x 1 p w,t 1,y =1 2X y1 w,q =0 (32) =1 Ths s the world excess demand functon for good 1. In the smulatons that follow the free trade equlbrum s gven by the smultaneous soluton of equatons (32), the goods market clearng condton, and (22), the four zero proft condtons for M=N=H=2. The Nash equlbrum n tarffs s gven by the smultaneous soluton of those fve equatons plus the two optmal tarff condtons (31). These systems of equatons were solved numercally n GAUSS, usng the nlsys procedure to solve the non-lnear system by a Newton-Raphson algorthm. A welfare comparson between the Nash equlbrum and the equlbrum under global free trade determnes the outcome of a trade war, as set out n defnton 1: Defnton 1 Country wns (loses) a non-cooperatve trade war (TW) ff: V TW > ( )V FT, where V FT s country s ndrect utlty under global free trade (FT) and V TW s country s ndrect utlty n a non-cooperatve trade war.

15 Who Wns a Trade War? 15 Defnton1statesthattownatradewar,acountrymuststrctlymprovetswelfare above ts free trade level. If ths does not occur, the country s sad to lose the trade war. 4. The country-sze effect Parameter values are set such that consumer preferences and producton technology are dentcal n each country. However, technology dffers between the two ndustres, such that ndustry one uses labour relatvely ntensvely, and ndustry two uses captal relatvely ntensvely n the absence of factor ntensty reversals. The parameter values used are set out n Table 1 below. Parameter (equal n both countres) Symbol Value Weght on Consumpton of Good 1 φ Weght on Consumpton of Good 2 φ Elastcty of Substtuton n Consumpton σ C 1.5 Weght on Captal n Producton of Good 1 γ K1 0.1 Weght on Captal n Producton of Good 2 γ K2 0.9 Weght on Labour n Producton of Good 1 γ L1 0.9 Weght on Labour n Producton of Good 2 γ L2 0.1 Elastcty of Substtuton n Producton of Good 1 σ P Elastcty of Substtuton n Producton of Good 2 σ P Tabel 1: Parameter values used n the smulaton The world endowment of captal and the world endowment of labour are both normalsed to unty. Ths can be done wthout loss of generalty due to constant returns to scale n producton. Wthn the range set by the world endowments of each factor of producton, each country s endowment of each factor s vared from 0.1 to 0.9 by ncrements of 0.1, and both the free trade and trade war equlbra are smulated for each par of captal and labour endowments.

16 Who Wns a Trade War? 16 Some dffculty was encountered n smulatng the TW equlbrum, snce the system exhbted multple equlbra. Consderable care was taken n selectng equlbra for each (K,L ) par that were related n such a way that the endogenous varables of the system are of comparable magntude and sensbly related to the varables determned at neghbourng values of (K,L ). Ths laborous process greatly lmted the number of smulatons that t was feasble to run, but s a necessary and not unexpected consequence of the complexty of ths model. In partcular, the ncorporaton of producton nto ths model ncreases the number of relatve prces from one to fve, and greatly complcates the optmal tarff condtons of each country when compared to the pure exchange case. Fgure 1: Trade war outcomes n a Heckscher-Ohln model. The results of the smulatons are presentedn Fgure 1,usng Defnton 1 to determne the outcomes. Ths fgure measures country 1 s endowment of captal along the horzontal axs, and ts endowment of labour along the vertcal. At each pont country 2 s endowment

17 Who Wns a Trade War? 17 of each factor can be calculated by subtractng country 1 s endowment from unty. Thus, movng towards the north-east corner of the dagram, the absolute magntude of country 1 s endowment vector approaches the world endowment vector, and lkewse for country 2 movng towards the south-west. Fgure 1 confrms the exstng result n the lterature, that a country whch s of suffcent sze relatve to ts opponent can wn a trade war. Ths s true by the commonly used defnton of country sze n the lterature (Kennan and Rezman, 1988, 1990), of therelatveszeofacountry sendowments. 34 It s also true by more sensble defntons of country sze. A country whose Gross Domestc Product (GDP) s greater at domestc prces than ts rval wll not be the sole loser from a trade war, although both countres may lose. An equvalent to GDP as a measure of country sze n ths model s the value of a country s factor endowment at domestc TW factor prces, snce domestc ndustres make zero proft. Valung a country s factor endowment at free trade prces yelds dentcal results. The value of a country s factor endowment s an appealng defnton of country sze, snce t provdes a bass of comparson between the relatve contrbuton of two dstnct factors of producton to country sze. Fnally, defnng country sze as GDP valued at world prces does not alter the results. 5 It s not possble to drectly compare the results of these smulatons to the analyss of Syropoulos (2002), who uses a defnton of country sze whch requres the relatve abundance of each factor endowed to a country be fxed. Ths s because t s not possble to hold the per capta endowment of captal (K /L ) constant for both countres whlst varyng L, except along the path where K /L =(K 1 + K 2 ) / (L 1 + L 2 ) for both countres, as the world endowment of each factor s fxedatagvenlevel,nthscase1unt of each factor. In order to precsely examne Syropoulos result t would be necessary to allow the sze of the world endowment of each factor to vary. 3 Snce Kennan and Rezman study models of pure exchange, ther defnton of country sze s couched n terms of goods rather than factor endowments. Interpretng the output of each good n a country as the endowment of that good (gnorng the change n producton between FT and NE), ther result s confrmed n these smulatons. 4 Why ths s not an adequate defnton of country sze: explan... 5 These country sze results are also confrmed by smulatons usng a model wth nter-country dfferences n technology.

18 Who Wns a Trade War? 18 Examnng the role of country sze along the path where K /L =(K 1 + K 2 ) / (L 1 + L 2 ) s not feasble, snce n the Heckscher-Ohln framework assumed there wll be no trade along ths path, whch may be termed the zero-trade lne. The reason for ths s that along ths path the countres wll be have an dentcal relatve abundance of each factor, and therefore produce goods n the same proporton. Snce ther preferences are dentcal, ths removes any ncentve to trade. Ths can be seen n Fgure 1, as along the zero-trade lne (runnng from north-east to south-west) nether country wns the trade war. Snce the countres do not trade along ths lne, welfare levels n each country under both FT and TW are equal to the autarky level of welfare. The next secton wll more fully dscuss the zero-trade lne and ts nfluence on trade war outcomes. Notwthstandng the dffculty n replcatng the country sze result of Syropoulos (2002), the sprt of hs result can be seen. As a country s share of the world endowment of each factor approaches unty, only that country wns the trade war. There are no examples n whch the wnner of a trade war reverses as the relatve share of a country n the world factor endowment approaches a total share. Although ths s only an ndcatve replcaton, t does seem to confrm Syropoulos country sze results. The customary nterpretaton of the country sze result s that larger countres can use ther monopoly/monopsony power to alter the terms of trade n ther favour by settng postve tarffs. The degree of ths market power s nterpreted as ncreasng wth country sze. In wder nternatonal trade theory a small country s one that cannot nfluence world prces (and thus ts terms of trade), whle a large country can. The market power nterpretaton of the country sze result shows the reasonng behnd the large/small country defntons. Of course, n ths model all countres are large, but the results of ths secton show that the market power defnton of large and the GDP/factor endowment defnton of large are related. The results of ths secton are summarsed and generalsed n Conjecture 1. Conjecture 1 In the context of the Heckscher-Ohln model of trade, a country wth a suffcently hgh value of ts endowed factors wll wn a trade war, except where t has the same relatve

19 Who Wns a Trade War? 19 factor endowments as ts rval. In ths latter case, both wll lose. 5. The trade-channel effect It s obvous from an nspecton of Fgure 1 that there s another effect than smply country sze nfluencng trade war outcomes. Whereas the lne runnng from north-west to south-east marks the path along whch the countres are of approxmately equal sze, 6 the lne runnng from north-east to south-west s the path along whch the countres have dentcal captal/labour ratos, as noted prevously. Nether country wns a trade war along ths latter path, a phenomenon desgnated the trade-channel effect for reasons that were dscussed n the prevous secton. Fgure 2 shows the relatonshp between the pattern of trade and captal/labour ratos under free trade for 10,000 combnatons of the latter smulated usng the model of ths secton. 7 Country 1 s captal/labour rato s reported on the vertcal axs, country 2 s on the horzontal. The whte lne along the dagonal s the locus of ponts at whch the two countres have dentcal captal/labour ratos, that s K /L =(K 1 + K 2 ) / (L 1 + L 2 ). Along the path where K /L =(K 1 + K 2 ) / (L 1 + L 2 ), there s no ncentve to trade for ether country, snce autarky prces are equal n the two countres that have dentcal technology and tastes, and that are endowed wth factors of producton n the same proporton. For ths reason, call ths path the zero-trade lne. Aboveandtotheleft of the zero-trade lne country 1 s relatvely well endowed wth captal and hence by the Heckscher-Ohln-Samuelson theorem exports good 2 (the captal ntensve good) and mports good 1. Ths feature s llustrated n Fgure 2 by the yellow shadng. Below and to the rght of the zero-trade lne (the green shaded area), country 2 s relatvely well endowed wth captal, and wll export good 2 and mport good 1. Returnng to Fgure 1, the north-east to south-west lne s the zero-trade lne, to the north-west of whch country 2 s relatvely abundant n captal and wll tend to export good 2, and to the south-east of whch, country 1 wll tend to export good 2. 8 Along the zero-trade lne there s nether gan nor loss to ether country from a trade war, snce t wll 6 Along ths lne the GDP/value of endowment of each country at free trade s equal. 7 Each country s captal/labour rato was vared by ncrements of 0.1 n a range of 0.1 to The tarff equlbra selected dd not alter the pattern of trade between FT and TW.

20 Who Wns a Trade War? 20 result n autarky, just as a free trade stuaton would. Ths was confrmed n smulaton, n whch an equlbrum was found for each pont along the zero-trade lne at whch Nash equlbrum tarffs were zero. Other equlbra were found at whch non-zero tarffs were leved, however snce these equlbra nvolved at least one country beng worse off than at autarky, they were dsregarded as not feasble snce a country could unlaterally choose autarky and mprove ts welfare. Fgure 2: around here The mpact of ths zero-trade lne can most clearly be seen n cross-sectons of the welfare gans (losses) that each country experences movng from FT to a TW. Fgure 3 shows two of these cross-sectons as the endowment of captal s held constant n each country but the endowment of labour s vared from 0.1 to 0.9 n country 1, and from 0.9 to 0.1 n country 2. In both dagrams the vertcal axs measures the welfare gan calculated by subtractng the utlty of the representatve consumer at FT from her utlty n a TW. In (a) the endowment of captal n country 1 s equal to 0.9, n (b) t s equal to Welfare Gans from a Trade War L 1 Country 1 Country (a) (b) Fgure 3: Welfare gans movng from FT to NE, varyng L 1 from 0.1 to 0.9, holdng K 1 constant at (a) 0.9; (b) 0.5.

21 Who Wns a Trade War? 21 In Fgure 3(a) the zero-trade lne cuts the graph at L 1 =0.9, nfgure3(b)tcutsthe graph at L 1 =0.5. In both graphs the sze of country 1(2) s ncreasng (decreasng) from left to rght, snce ts endowment of labour s ncreasng (decreasng) and ts endowment of captal s non-decreasng (non-ncreasng). In both graphs the gans or losses of each country from NE shrnk to zero at the zero-trade pont. In Fgure 3(b) t s easy to observe the prevous result on country sze, as country 1 moves from a welfare loss to a smaller welfare loss to ncreasng welfare gans as ts endowment of labour ncreases. In Fgure 3(a) country 1 s weakly larger throughout, snce each element of ts factor endowment vector s at least as great as the correspondng element of country 2 s factor endowment vector. The country sze effect of the prevous secton seems to domnate up to L 1 =0.5, however once L 1 ncreases beyond 0.5 country 1 s gans and country 2 s losses both decrease n magntude towards zero at the zero-trade pont. The ntuton behnd the decreasng welfare gans/losses as countres move towards the zero-trade lne can be understood n terms of the tradtonal decomposton of the welfare effects of tarffs, shown below. E U du = tdm mdp w (33) Here E s the expendture functon, U utlty, t the vector of specfc tarff rates, m the vector of net mports and p w the vector of world prces. Although ths decomposton does not consder the welfare effects of strategc nteracton, and s couched n terms of specfc rather than ad valorem tarffs, t s stll useful for nterpretng the results of ths secton. The frst term, tdm sthevolumeoftradeeffect and measures the welfare loss created by ncreasng tarffs due to shrnkng trade volumes. The second term mdp w s the terms of trade effect, whch measures the potental welfare gan a country wth monopoly/monopsony power can extract by mprovng ts terms of trade through ncreasng tarffs. The analyss of ths secton s prmarly concerned wth ths second term.

22 Who Wns a Trade War? 22 Fgure 4: Factorendowmentsandthevolumeoftrade The prevous secton confrmed that larger countres can wn trade wars, and offered the ntuton that ths s possble due to ther sze gvng them monopoly/monopsony power to mprove ther terms of trade. The second effect nvolvng the zero-trade lne s not concerned wth market power as such, but the channel through whch market power can be exerted. Ths s why the effect s named the trade channel effect. Note that the terms of trade effect depends on the sze of the mport vector m, as well as the extent to whch a country can affect the terms of trade. Approachng the zero trade lne, m approaches a vector of zeroes. Therefore, even f a country has enough market power to sgnfcantly mprove ts terms of trade, because the channel through whch t can explot ths power (that s, the trade channel) s shrnkng, the gans t can extract approach zero. Ths can be clearly seen Fgure 3(a), n whch the welfare gans of a sgnfcantly larger country(byanydefnton) shrnk to zero as t approaches the zero trade lne. 9 Fgure 4 shows the relatonshps between the endowment of each factor and trade volumes n a trade war equlbrum. The vertcal axs shows the volume of trade, measured 9 Kennan and Rezman (1988) note a smlar effect n a footnote, that n the context of a pure exchange model gans shrnk to zero approachng a lne of no trade. They do not dscuss or nterpret ths result however.

23 Who Wns a Trade War? 23 by the value of mports (exports) of one good by one country. Due to the fact that trade s balanced, ths s equal to the value of exports (mports) of the other good by that country. By symmetry, both countres trade volumes are equal by ths measure. Thepontsatwhcheachlevelcurvereacheszeroleonthezero-tradelne,andts clear that the volume of trade monotoncally ncreases as the dstance from the zero trade lne ncreases. Ths suggests that the trade channel effect operates unformly throughout the range of factor endowments, and not just n the neghbourhood of the zero-trade lne. The results of smulatons presented above bear out ths predcton, and suggest the followng conjecture, whch summarses the results of ths secton. In ths conjecture sze s defnedntermsofthefreetradevalueofacountry sendowment(freetradegdp). Conjecture 2 In the context of the Heckscher-Ohln model of trade, the magntude of a country s welfare gan or loss from a trade war relatve to free trade wll decrease (ncrease) as t approaches (moves away from) the zero-trade lne, holdng the relatve szes of the country and ts rval constant. 6. Net mpact of the country-sze and trade-channel effects The prevous two sectons have dentfed and dscussed the economc ntuton behnd the country sze and the trade channel effects. The country sze effect s that a larger country wll tend to wn a trade war because t has greater market power. The trade channel effect n the Heckscher-Ohln model s that countres whch have smlar factor endowment patterns wll tend experence smaller welfare gans and losses n a trade war. Ths s because the channel through whch market power can be exerted s smaller. Fgure 3(a) clearly demonstrates that the effects can oppose one another, snce country 1 s relatve sze advantage ncreases from left to rght, but ts welfare gans are not monotoncally ncreasng. On the other hand, Fgure 3(b) gves an example where the effects renforce one another so that each country experences monotoncally ncreasng welfare gans as t moves from the zero-trade pont n the drecton of ncreasng sze. It s therefore of nterest and mportance to nvestgate the net mpact of these effects on trade war outcomes as they oppose or renforce one another.

24 Who Wns a Trade War? 24 Fgure 5 shows the nteracton between the country sze and trade channel effects for several values of K 1. In addton to the welfare gans and losses n each country, t shows on the vertcal axs the value of traded goods at world prces, and the absolute dfference between the equlbrum tarff rates set by each country. 10 The latter s a proxy for the relatve dfferences n market power between the two countres, and s defned as t 1 j t 2 k, where j s country 1 s and k country 2 s export good respectvely. When one country has greater market power t sets a hgher tarff than ts opponent n order to nfluence the terms of trade n ts advantage, and the dfference n market power ncreases. Fgure 5 (a) shows the level curves for these varables when country 1 s endowed wth 0.9 unts of captal, (b) when country 1 s endowed wth 0.7 unts of captal, and (c) when country 1 s endowed wth 0.5 unts of captal. Fgure 5(a) and (c) llustrates the effects nteractng n the stuatons shown n Fgure 3. In Fgure 5 (a), the trade volume decreases from left to rght towards the zero-trade pont L 1 =0.9, whereasthedfferental n tarffs ncreases 11 as country 1 gets steadly larger and grows n market power. The nteracton between these two opposng effects results n the observed rse and fall n the welfare gans (losses) of country 1(2). In Fgure 5(c), both trade volume and tarff dfferental decrease ntally towards the zero-trade pont L 1 =0.5, and then ncrease from that pont. Ths llustrates how the market power and zero-trade lne effects renforce one another n ths case. Note that to the left of the zero trade pont t s country 2 that has the hgher tarff, totherght country 1 has the hgher tarff. The absolute value of the dfference n tarffs stakenn order to show graphcally how the sze of ths effect alters, just as the value of trade s postve rrespectve of the trade pattern. Ths allows comparson between the relatve mpact of the effects, whch s the pont of nterest n analysng ther nteracton. The absolute sze of the effects tells us ther relatve mpact, snce a larger tarff dfference suggests a larger gan or loss to each country, just as a larger trade volume wll ncrease the gan or loss to each country due to the ncreased channel of nfluence. 10 The former s scaled down by a factor of ffty, the latter by a factor of twenty-fve so that the curves ft on the graphs at a comparable scale to the changes n welfare. 11 Dsregardng the autarky (zero-trade) pont, at whch tarff levels are meanngless (and at whch an equlbrum where zero tarffs are set exsts). Snce tarffs are mposed only on mports t s also ambguous as to whch tarffs would be chosen at ths pont, snce nether good s mported by ether country.

25 Who Wns a Trade War? 25 Fgure 5: around here Fgure 5(b) shows an ntermedate cross-secton at whch the country sze and trade channel effects oppose and renforce one another at dfferent ranges of L 1.ForL 1 0.3, that s up to the pont at whch the countres have equal GDP n free trade, the effects renforce one another, causng the welfare gans and losses of each country to reduce. For 0.4 L 1 < 0.7 the effects oppose one another and the welfare gans/losses of each country frst ncrease, then dmnsh to zero at the zero-trade pont L 1 =0.7. For L 1 > 0.7, the effects renforce one another once more, and each country s welfare gan or loss ncreases n magntude. The nteracton of the country sze and trade channel effects over the entre rangeoffactorendowmentsssummarsednfgure6. GDP equal at FT Increasng Welfare Gans to Country 1 Zero-Trade Lne L 1 Increasng Welfare Gans to Country 2 Increasng Welfare Gans to Country 1 Increasng Welfare Gans to Country 2 K 1 Fgure 6: WelfareOutcomesnaHeckscher-OhlnModel

26 Who Wns a Trade War? Consumer preferences and trade war outcomes The precedng sectons consder the nfluence of the factor endowments of countres on trade war outcomes. Ths secton addresses the queston of whether any other fundamental characterstcs of countres wll systematcally affect trade war outcomes. In partcular, t s of nterest to know whether a country wth a less valuable factor endowment or lower GDP can wn a trade war aganst a larger rval f they dffer n other characterstcs. In order to address ths queston, smulatons were carred out n whch the elastcty of substtuton n consumpton (σ C) was vared n each country. The parameter values assumed before hold also here, wth the excepton that the vector of factor endowments s fxedneachcountry,andσ C s vared. Each country s endowed wth 1 unt of labour, but whereas country 1 s endowed wth 1 unt of captal, country 2 s endowed wth 0.8 unts of captal. These parameter values determned a sngle pattern of trade for the range of elastctes smulated, and meant that country 1 was the larger country by vrtue of havng the more valuable endowment at both FT and TW prces throughout the range. The choce of the range of σ C to smulate s somewhat problematc, as there are no estmates of ths elastcty drectly avalable n the lterature. There are, however, estmates of other consumpton related elastctes of substtuton, such as the Armngton elastcty. Ths elastcty s the elastcty of substtuton between mported and locally produced goods. The analogy between ths elastcty and σ C s not perfect, snce σ C s an elastcty of substtuton between goods and the Armngton elastcty between ports of orgn. However, snce for the parameter ranges smulated one good s mported and the other exported for each country, σ C and the Armngton elastcty wll not be entrely unrelated. For these reasons a range n whch to vary σ C s selected on the bass of estmated Armngton elastctes reported n Gallaway, McDanel and Rvera (2003). These estmates are based on dsaggregated U.S. data at the ndustry level, and as such are not useful n suggestng the range of nter-country dfferences n σ C. σ C s vared over the range [0.7, 2.9]. Ths range s chosen to cover the mddle 90% of postvely sgnfcant Armngton elastctes reported by Gallaway et al.. σ C s vared by ncrements of 0.2 along ths range n smulaton.

27 Who Wns a Trade War? 27 The results of the smulatons are presented n Fgure 7. The vertcal axs measures country 1 s elastcty of substtuton n consumpton, and the horzontal axs country 2 s. Defnton 1 s used to determne trade war outcomes. Fgure 7 shows that when ether country has a hgh enough σ C relatve to ts rval, t wll wn the trade war. In partcular, for these countres of smlar sze, the asymmetry n elastctes of substtuton s suffcent for the smaller country 2 to wn the trade war for 29 of the 144 cases smulated. Remember that country 2 s smaller throughout the whole matrx of (σ 1 C,σ 2 C) combnatons. Fgure 7: Trade war outcomes and the elastcty of substtuton n consumpton. Fgure 8 shows a cross-secton of the affect on relatve market power of varyng σ C. As before, the absolute dfference n tarff rates between the two countres s used on the vertcal axs to measure the relatve market power of each. Fgure 8 shows that country 1 s relatve market power advantage dmnshes as σ 2 C ncreases. Ths ndcates that the country wth a relatvely larger σ C can wn a trade war by explotng ts greater market power n tarff settng to mprove ts terms of trade.

28 Who Wns a Trade War? Absolute Dfference n Tarffs between 1 & Fgure 8: Dfference n tarffs, σ 2 C =2.9 To understand the ntuton note that consumers wth a hgher σ C are more flexble n ther pattern of consumpton than those wth a lower σ C. Therefore, f the representatve consumer of one country n a trade war has a hgher σ C, then they are more able to respond to terms of trade changes by substtutng consumpton of the good whose relatve prce has ncreased for the good whose relatve prce has decreased. Ths gves a country n whch σ C s relatvely hgher a strategc advantage n a trade war, as ts more flexble pattern of consumpton means that t s able to respond more effectvely than ts rval to terms of trade changes. An nterestng pont to note s that the market power ganed from havng a hgh σ C s able to outwegh the market power of beng a larger country for the parameter values chosen n smulaton. The queston of whether a bg country wns a tarff war has been answered, all thngs beng equal, affrmatvely. However the results of ths secton suggest

29 Who Wns a Trade War? 29 that ths affrmatve answer needs to be qualfed. A bg country can wn a tarff war, but so can a smaller country, provded ts σ C s suffcently hgh relatve to ts rval. The results of ths secton and the ntuton underlyng them lend support to Conjectures 3 and 4 that follow. Conjecture 3 A country wth a suffcently hgh elastcty of substtuton n ts preferences, relatve to ts rval, wll wn a trade war. Conjecture 4 Acountrywthasuffcently hgh elastcty of substtuton n ts preferences, relatve to ts rval, can wn a trade war even f t s smaller than ts rval. Conjecture 3 summarses the result that countres wth a hgher degree of substtutablty n ther preferences tend to wn trade wars. Conjecture 4 strengthens Conjecture 3 to state the result that a smaller country can wn a trade war. 8. Concluson Ths paper has ntroduced a stylsed 2 x 2 x 2 general equlbrum model of world trade to nvestgate the queston of what sorts of countres wn trade wars. Numercal smulaton results suggest that a large country, n terms of the value of ts endowment, wll wn a trade war, all thngs beng equal. Ths confrms the exstng results n the lterature that suggest by varous other measures of country sze that a bg country wns a tarff war. In the context of a Heckscher-Ohln model t was shown that dfferences n the relatve abundance of factors between countres wll affect the magntude of trade war gans or losses. A greater dfference n relatve factor abundance results n greater gans or losses to each country. Ths effect, the trade-channel effect, suggests that f countres wth dentcal technology and preferences are sgnfcantly dfferent n ther endowment of one factor relatve to another, then the country wth greater market power wll have greater opportunty to extract welfare gans from a trade war, at the expense of ts rval. In a stuaton such as ths, the country wth greater market power s lkely to be a