Trade and Insecure Resources

Transcription

1 Trade and Insecure Resources Mchelle R. Garfnkel Unversty of Calforna, Irvne Stergos Skaperdas Unversty of Calforna, Irvne Constantnos Syropoulos Drexel Unversty Current Verson: September 10, 2013 bstract: We construct a model of conflct and trade to study the consequences of nterstate dsputes over contested resources (land, ol, water or other resources) for armng, welfare and trade flows. Dfferent trade regmes mply dfferent costs of such dsputes n terms of armng. Dependng on world prces, free trade can ntensfy armng to such an extent that the addtonal securty costs t brngs swamp the tradtonal gans from trade and thus render autarky more desrable for one or all rval states. Free trade, though, s always an equlbrum, and sometmes s a domnant one wth features of a prsoner s dlemma outcome. Furthermore, contestaton of resources can reverse a country s apparent comparatve advantage relatve to ts comparatve advantage n the absence of conflct. nd, where such conflct s present, comparsons of autarkc prces to world prces could be naccurate predctors of trade patterns. JEL Classfcaton: D30, D70, D72, D74, F2, F10. Keywords: trade openness, property rghts, nterstate dsputes, conflct, securty polces. The authors wsh to thank Daron cemoglu, Erc Bond, Merwan Engneer, Ethan Kapsten, Govann Magg, Mchael McBrde, Robert Powell, Prya Ranjan, and partcpants of the CEPR workshop on Conflcts, Globalzaton and Development, the Yale-Prnceton workshop on War and Trade, the Canadan Economcs ssocaton Meetng and other venues for helpful comments and suggestons on earler drafts of ths paper.

2 country of our sze, wth ts focus on exports and thus relance on foregn trade, must be aware that mltary deployments are necessary n an emergency to protect our nterests, for example, when t comes to trade routes, for example, [sc] when t comes to preventng regonal nstabltes that could negatvely nfluence our trade, jobs and ncomes. Horst Köhler, former Presdent of Germany (quoted n NY Tmes, May 31, 2010) 1 Introducton It s unusual for promnent publc offcals lke the former Presdent of Germany to make such seemngly poltcally ncorrect statements. Mltary deployments for the protecton of a country s own nterest and trade routes nstead of, say, the protecton of human rghts and the promoton of democracy perhaps sound too crass and cyncal for today s nternatonal norms. lthough Dr. Köhler was forced to resgn from the Presdency of Germany for utterng the words quoted above, he dd not ultmately dsavow hs essental belef n them. Gven that the nternatonal system s essentally anarchc wthout the thrd-party enforcement that usually exsts wthn ndvdual states, economsts would not fnd t controversal to assert that the defense expendtures of countres are related to ther perceved nterests, such as mantanng access to resources that mght be n dspute. fter all, as amply demonstrated n Fndlay s and O Rourke s (2007) overvew of Eurasa s economc hstory, mltary competton for resources and the expanson of world trade were nextrcably lnked over the whole of the past mllennum. Whle nterstate wars have become less common n the post-world War II perod than they had been n the thrty years pror to that, there have been both enough of them and, more serously, enough dsputes to keep almost all countres armed. Examples of hot dsputes n the postwar perod nclude the Suez Canal crss n the 1950s, Iraq s nvason of Kuwat that resulted n the frst Gulf war n the early 1990s, and the Kashmr dspute between Inda and Pakstan. Numerous other dsputes from that over the Spratly and Paracel slands n the South Chna Sea, to dsputes over water (e.g., flowng through rvers lke the Nle and the Brahmaputra), and to others nvolvng ol, mnerals, or smply land mght have not resulted n hot ncdents; however, they keep the mltares of almost all countres busy. 1 The drect and ndrect costs of such dsputes are large. For example, the latest estmates of the costs of the Iraq and fghanstan wars to the Unted States are around 4 to 6 trllon dollars (Stgltz and Blmes, 2012). 2 1 See, Klare (2001), for an overvew and many examples. 2 Mltary expendtures alone were about 2.6 percent of world GDP durng 2004, varyng from less than 1 percent for a few countres to more than 10 percent for Saud raba (SIPRI, 2005). To get some sense of the overall costs of conflct (ncludng cvl war), Blomberg and Hess (2012) estmate a lower bound for the yearly cost of conflct of 9 percent of steady state consumpton for the 1950 to 2004 perod. For hgh-ncome

3 The quanttatve mportance of securty costs naturally rases some questons as to how nterstate dsputes over resources matter for trade openness and vce versa. More specfcally, how do dfferent trade regmes (e.g., autarky and free trade) affect the extent to whch productve resources are dverted nto armng? Recognzng that securty polces themselves are trade-regme dependent, what s the relatonshp between trade openness and welfare? Is free trade an equlbrum polcy? nd, f t s, what are ts mplcatons for the drecton and volume of trade flows? In general, there are two channels through whch trade openness n the presence of nsecurty could matter for the allocaton of productve resources. Frst, a swtch from autarky to free trade alters product prces and thus factor prces, and thereby nfluences the relatve costs of hrng productve resources for armng purposes. Second, product prces and thus the terms of trade could themselves depend on securty polces; ths feedback channel would also be relevant for the determnaton of securty polces and more generally the allocaton of productve resources. In ths paper, we am to address the questons dentfed above, emphaszng the frst of these two channels that hghlghts the role of endogenous factor prces. Specfcally, our analyss bulds on a modfed verson of the Heckscher-Ohln-Samuelson model of trade, focusng on the case of two small countres (.e., countres havng no nfluence on the world prce) that possbly trade wth the rest of the world, whch we treat as exogenous. 3 The model s augmented to allow for nsecurty more precsely, conflct between the two small countres over a resource and ts accompanyng costs. The neoclasscal model (whch we also call the Nrvana model, to use Demsetz s (1969) apt term) s a lmtng case of our model when securty s costless and perfect. In the model, one factor of producton ( labor ) s perfectly secure, whle the other ( land ) s, n part, nsecure. The dstrbuton of nsecure land between the two countres depends on the relatve amount of armng by each. rmng tself s produced wth the two factors of producton and the cost of ts producton represents securty costs. key feature of ths framework s that t captures the trade-regme dependence of the net margnal beneft of armng and thus of the ncentve to arm. Wth armng endogenous, the factor endowments left over for use n cvlan producton of the two fnal goods are also endogenous countres lke the Unted States and France the cost was roughly 4.5 percent of consumpton, whereas for Iraq and Iran, largely as a result of the war between then, t was nearly 77 percent and 16 percent of ther respectve yearly consumptons. 3 To be sure, as noted below, we vew the large-country case where the second channel comes nto play as mportant. Such an analyss, however, s beyond the scope of the present paper. Nevertheless, n ongong research, we are explorng the consequences of nsecure resources n a Rcardan model wth a non-traded goods sector, to capture both factor-prce effects and product-prce effects. The results n that settng, however, are qualtatvely smlar to what we fnd n the present paper that focuses solely on the consequences of factor-prce effects. 2

4 and depend on the trade regme prevalng n the two countres. Thus, both securty costs and the factor endowments used n cvlan producton are endogenous to the prevalng trade regme. The two trade regmes we consder and compare are autarky and free trade. Our comparson of welfare under these two regmes shows that the relatve factor ntenstes of the two cvlan goods play an mportant role. For example, when the countres are dentcal and they both mport the land-ntensve good under free trade, free trade s superor to autarky for both countres. In ths case, because the good produced ntensvely wth the contested resource can be obtaned more cheaply n world markets than t could be produced domestcally under autarky, free trade reduces the ncentve to arm and thus the securty costs relatve to the autarkc outcome. Therefore, free trade s better due to both the tradtonal gans from trade and the lower costs of securty. However, when both countres export the land-ntensve good, they mght very well prefer autarky. In partcular, the hgher export prce compared wth the prce of the good under autarky makes competton over land more ntense, thereby ncreasng the costs of securty. Of course, a hgher export prce also brngs gans from trade. But, for export prces not too hgh, these gans are outweghed by the ncreased securty costs, to render autarky preferable to free trade. More generally, the two tradng regmes consdered mply very dfferent securty costs. Under autarky, these costs depend on the domestc factor and goods prces n both countres, whereas under free trade they tend to be equalzed across countres because of factor prce equalzaton. utarky wll be preferable for one or both countres when free trade nvolves hgher added securty costs relatve to the gans from trade. These results mght be taken to mply that adversaral countres would choose to mpose barrers to trade for those world prces that make autarky preferable to free trade for both countres. However, an extended analyss of the model to consder the non-cooperatve choce of trade regmes by two dentcal countres shows that free trade s always a subgame perfect equlbrum for such world prces; and, for a subset of those prces, t s the unque, domnant-strategy equlbrum, thus leadng to a prsoner s dlemma outcome. By the same token, n the presence of resource nsecurty and the absence of nsttutons to deal wth t, cooperaton n the form of freer trade polces can lead to perverse outcomes and alone cannot address the fundamental problem at hand. That s to say, realzng the gans from free trade requres that we address the problem of resource nsecurty. We also show how resource nsecurty nduces dstortons n resources left for producton of traded goods and thus n comparatve advantage. It does so n at least two possble ways: () by causng trade patterns to dffer from the ones that would have emerged under Nrvana; and, () by alterng the nformaton content of the dfference between free-trade and autarkc prces, and thus possbly leadng to erroneous predctons of the drecton of trade flows. If, for example, the technology for armng s suffcently ntensve n the 3

5 use of the perfectly secure resource (labor), then nsecurty mples relatvely less of that resource s left for the producton of traded goods. Consequently, the world prce of the consumpton good employng the secure resource ntensvely that mples no trade tends to exceed the analogous prce that would have prevaled under Nrvana. The net effect s that there exsts a range of world prces for whch a country s an mporter of that consumpton good when there s nsecurty, whereas t would have been an exporter of the same good under Nrvana. Smlarly, because the ntroducton of free trade n consumpton goods alters product and factor prces, armng ncentves along wth the mx of resources absorbed n armng, and thus the resources left for the producton of consumpton goods, a country s true comparatve advantage (gven nsecurty) can dffer from that whch s mpled by a smple comparson of autarkc prces to world prces. Both of these dstortons mply that the presence of nsecurty plays an mportant role n the determnaton of a country s actual trade patterns that tradtonal approaches fal to capture. Our substantve characterzaton results do not depend on specfc functonal forms of producton or utlty functons. The resultng generalzed treatment sets the stage for applcatons and extensons of the basc model to settngs n whch nsecure property rghts fgure promnently n world affars. In partcular, such applcatons and extensons can provde new nsght nto the relatonshp between trade and securty polces of adversares and alles, whch s of great relevance to the felds of nternatonal relatons and nternatonal poltcal economy. Ths paper s contrbuton s related to lteratures n both poltcal scence and economcs. Poltcal scentsts have long been nterested n the lnkages between nternatonal trade and conflct. 4 Economsts, by contrast, have only begun to explore these lnkages. Examples nclude nderson and Marcouller (2005) and nderton et al. (1999), who analyze Rcardan models n whch traded goods are nsecure ether because of the presence of prates and bandts or because the contendng sdes nfluence the terms of trade through armng. Both approaches emphasze the mportant, though basc, pont that nternatonal trade can be hampered by the anarchc nature of nternatonal relatons. Skaperdas and Syropoulos (2001, 2002) address some of the mplcatons of nsecure property n the context of smple exchange models. cemoglu et al. (2012) explore the mplcatons for ntertemporal prcng and the exhauston of a contested resource n a dynamc settng. Martn et al. (2008) also 4 See Barber and Schneder (1999), who survey much of the theoretcal and emprcal lteratures on the subject. Many of the analyses, n contrast to ours, emphasze the aggregate ncome effects of trade, wth the gans of trade reflected n hgher ncomes that tend to amplfy ncentves to arm. Rowe (1999, 2005) s, to our knowledge, the sole poltcal scentst who emphaszes the role of factor endowments. lthough he does so n a qualtatve fashon (focusng on mltary costs, whle effectvely abstractng from the potental benefts of securty polces), hs analyss of how globalzaton n the late 1800s and early 1900s set the stage for World War I ponts to the mportance of the mechansm hghlghted n our study namely, the lnk between product and factor prces that determnes the costs of securty. 4

6 consder the lnkages between conflct and nternatonal trade, but they take a very dfferent approach, one that abstracts from armng decsons and the endogenous determnaton of securty costs, emphaszng nstead the role of expanded multlateral trade opportuntes n possbly creatng an envronment that s more conducve to blateral conflct. Whle extant trade theory has ruled out securty problems by assumpton, there are some exceptons that focus on the related problem of open-access resources. Chchlnsky (1994) argues that trade can reduce welfare n the South by accentuatng the over-explotaton of an open-access resource n whch t has a comparatve advantage, 5 and Brander and Taylor (1997a) formally prove ths dea. Hotte et al. (2000) also study the effects of trade n an open-access resource and extend the analyss to consder the evoluton of prvate enforcement n dynamc envronments. Margols and Shogren (2002) consder a North- South trade model wth enclosures. The key dfference between these models and ours s that enforcement costs are due to the actve contestaton of resources. In the next secton, we present the formal model and a prelmnary analyss that proves useful n subsequent sectons. In Secton 3, we nvestgate optmal securty polces under autarky and free trade. Then, n Secton 4, we explore the mplcatons of nternatonal conflct for trade patterns and trade volumes. comparson between autarky and free trade n terms of ther mplcatons for securty costs and welfare follows n Secton 5. Secton 6 examnes the strategc consderatons that come nto play n the non-cooperatve choce of trade regmes by each country. Lastly, n Secton 7, we offer several concludng comments. ll techncal arguments and proofs have been relegated to the ppendx. 2 Framework and Prelmnary nalyss Consder a global economy that conssts of two countres, ndexed by = 1, 2, and the rest of the world (ROW), whch for smplcty s treated as a sngle entty and taken as exogenous. Each country can produce two consumpton goods (say butter and ol ), ndexed by j = 1, 2, usng labor and land under constant returns to scale. In the sprt of the Heckscher-Ohln-Samuelson (HOS) trade model and as a benchmark, we assume the countres have access to the same producton technology; consumers have dentcal and homothetc preferences defned over the two consumpton goods; and, all markets are perfectly compettve. Each country possesses L unts of secure labor and K unts of secure land. However, departng from the HOS trade model, we assume there exsts an addtonal K 0 unts of land. (Of course, what we call land (K) could also be nterpreted as a natural resource (e.g., ol, water) or physcal captal.) lthough ths addtonal land s dvsble, ts dvson between the two countres s subject to dspute. Polcymakers use armng to gan control of the dsputed resource, wth the ultmate goal of maxmzng 5 Her analyss also ponts to the mportance of open-access resources for the pattern of trade. 5

7 natonal welfare. 2.1 Introducng conflct Let country s guns be denoted by G, a varable most accurately vewed as a producble composte good that reflects country s mltary capablty. Country s share of K 0, then, s determned by the followng contest success functon (or technology of conflct): φ (G, G j ) = { f(g ) f(g 1 )+f(g 2 ) f 1 2 f =1,2 G > 0; =1,2 G = 0, for = 1, 2 (j ), where f( ) 0, f(0) = 0, f ( ) > 0, lm G 0 f (G ) =, and f ( ) 0. 6 ccordng to (1), the fracton of the dsputed resource a country secures n the contest depends on ts own guns as well as those of ts adversary. Specfcally, t s ncreasng n the country s own guns (φ φ / G > 0) and decreasng n the guns G of ts adversary (φ φ / G j < 0, j ). The nfluence of guns on a country s share, G j φ (G, G j ), could be taken lterally or vewed as the reduced form of a barganng process, n whch relatve armng fgures promnently n the dvson of the contested resource. 7 In any case, each country has an ncentve to produce guns, whereby t can obtan a larger share of the contested land and thus more ncome. But, there s an opportunty cost of dong so namely, the loss n ncome due to the dverson of resources away from the producton of consumpton goods. Ths trade-off, whch s trade-regme dependent, plays an mportant role n the determnaton of the countres securty polces. 8 The settng here s an anarchc one, so that wrtng enforceable (bndng) contracts on the prolferaton of arms and the dvson of K 0 s not possble. Instead, we vew guns as the enforcement varable that determnes each country s share of the contested resource, 6 In the ppendx we derve some useful propertes of ths specfcaton. The condton that lm G 0 f (G ) = and the assumed concavty of f( ) help establsh exstence and unqueness of equlbrum n the nteror of the strategy space (see the proof to Theorem.1 n the ppendx). Skaperdas (1996) axomatzes (1), requrng only that f( ) s a non-negatve, ncreasng functon. One functonal form for f( ) that has been wdely used n the rent-seekng lterature, as well as n the lteratures on tournaments and conflct, s f(g) = G γ where γ (0, 1] (Tullock, 1980). See Hrshlefer (1989) for a comparson of the propertes of ths form wth those of f(g) = e γg. s noted below, employng alternatve specfcatons for φ (G, G j ) that allow for ether non-addtvty or asymmetry would not change the results to follow. For a more general analyss of the comparatve statc results of conflct, see cemoglu and Jensen (2011). 7 See nbarc et al. (2002) for an analyss of ths ssue and how, n partcular, dfferent barganng soluton concepts lead to dvson rules that vary n ther senstvty to guns. 8 Whle countres often buld ther own mltares, they can, n practce, also buy or sell certan weapons n the world market, as well as hre mercenares or foregn securty experts. The analyss could easly be extended to allow for the nternatonal trade of guns. In partcular, vewng guns as a composte good produced accordng to a lnearly homogenous functon wth weapons and solders as ts arguments, the lnk between product (and arms) prces and factor prces would reman, so that our man nsghts would go through. However, to hghlght how pure trade n goods affects armng ncentves, we abstract from such possbltes n ths analyss. (1) 6

8 whch n turn can be combned wth the country s remanng secure endowments of labor and land to produce consumpton goods. ccordngly, the sequence of events s as follows: () Gven the ntal dstrbuton of secure factor endowments (L and K ), the two countres ( = 1, 2) smultaneously choose ther producton of guns G. () Once these choces are made, the contested land s dvded accordng to (1): each country receves φ K 0 unts of the contested resource. () Wth the quanttes of land and labor left for the producton of consumpton goods havng thus been determned, prvate producton and consumpton decsons take place. Under autarky, prces adjust to clear domestc markets. Under free trade, the prces of consumpton goods are fxed n the world market. conflctual equlbrum s the Nash equlbrum n guns, condtonal on the prevalng trade regme. To complete the basc model, we now specfy the supply and demand sdes of each economy. 2.2 Producton Startng wth the supply sde, let ψ ψ(w, r ) and c j c j(w, r ) represent respectvely the unt cost functons of guns and goods j = 1, 2 n country, where w and r denote compettvely determned factor prces respectvely, the wage pad to labor and the rental rate pad to landowners. These unt cost functons have the usual propertes, ncludng concavty and lnear homogenety n factor prces. By Shephard s lemma, the unt land and labor requrements n arms producton are gven respectvely by ψ r ψ / r > 0 and ψ w ψ / w > 0. Smlarly, a Kj c j / r > 0 and a Lj c j / w > 0 represent the unt land and labor requrements n producng good j. Therefore, the land-labor rato n guns s k G ψ r/ψ w, and the correspondng rato n ndustry j s k j a Kj /a Lj. Industry 2 s land ntensve f k2 > k 1 (or labor ntensve f k 2 < k 1 ) at all relevant factor prces. (We follow much of the lterature based on the HOS trade model n rulng out factor ntensty reversals.) lthough we wll show how the rankng of factor ntenstes across ndustres j = 1, 2 matters, for specfcty we emphasze throughout much of the dscusson the case where good 2 s produced ntensvely wth the nsecure resource (.e., land). Takng good 1 as the numerare, let p denote the relatve prce of good 2 n country. Perfect competton requres zero profts, or assumng dversfcaton n producton, c 1 (w, r ) = a L1w + a K1r = 1 (2) c 2 (w, r ) = a L2w + a K2r = p, (3) 7

9 for = 1, 2. These equatons, together wth the assumpton of dentcal technologes across countres and the propertes of unt cost functons, mply that the wage-rental rato, ω w /r, can be wrtten as a functon of the relatve prce (.e., ω = ω(p )). By the Stolper- Samuelson (1941) theorem, a rse n p ncreases the return to that factor whch s used ntensvely n the producton of good 2, and at the same tme decreases the return to the other factor: ωp( ω/ p ) 0 as k2 k 1 (see Lemma.1(a) n the ppendx). Let (KX, L X ) denote the vector of resdual quanttes of resources left for the producton of consumpton goods n country at the end of stage (), once labor and land resources have already been employed n the producton of guns G, respectvely ψ wg and ψ rg, and the dstrbuton of the contested resource has been realzed, φ K 0. Furthermore, let X j denote country s output of good j. Then, factor-market clearng and dversfcaton n producton requre n each country, a K1X 1 + a K2X 2 = K X ( K + φ K 0 ψ rg ) (4) a L1X 1 + a L2X 2 = L X ( L ψ wg ). (5) Now, let k X denote country s resdual land-labor rato: k X K X L X = K + φ K 0 ψ rg L ψ wg, for = 1, 2. (6) Then, t s straghtforward to verfy, from (4) and (5) along wth the lnear homogenety of unt cost functons and the fact that ω = ω(p ), that the relatve supply of good 2 (ol), RS X2 /X 1, can be wrtten as RS = RS(p, kx ). In the ppendx (Lemma.1(b)) we show that the relatve supply of good 2 s ncreasng n ts relatve prce, due to ncreasng opportunty costs: RS / p > 0. In addton, Lemma.1(c) establshes, consstent wth the Rybczynsk (1955) theorem, that an exogenous ncrease n the resdual land-labor rato causes an ncrease n the relatve supply of the good that uses land ntensvely: RS / k X 0 as k 2 k 1. Of course, as can be seen from (6) keepng n mnd that ω = ω(p ), the resdual land-labor rato tself s endogenously determned, and can be wrtten as a functon of the relatve prce of good 2, the guns produced by the two countres, and resource endowments. To avod clutterng of notaton, we wrte ths functon as k X = k X (p, G, G j ). Lemma.2 n the ppendx descrbes the dependence of kx on ts arguments. t ths pont, t s only mportant to recognze the mplcaton that the relatve supply of good 2 can also be wrtten as a functon of the prce and guns: RS = RS(p, G, G j ). In the next secton, we characterze the exact nature of ths relatonshp, as needed n the dentfcaton of market-clearng prces and n the analyss of conflct under autarky. 8

10 2.3 Payoffs Turnng to the demand sde, let R denote net natonal ncome and µ µ(p ) denote the margnal utlty of ncome. Country s ndrect utlty (aggregate welfare) functon can then be wrtten as 9 V V (p, G, G j ) = µ(p )R (p, K X, L X), for = 1, 2 (j ). (7) Equaton (7) mplctly assumes that polcymakers fnance the cost of armng wth nondstortonary ncome taxes. Ths assumpton, together wth that of perfect competton, mples that country s net natonal ncome (R ) s the country s maxmzed value of domestc producton of consumpton goods and, at the same tme, the mnmzed value of rental payments pad to resdual labor and land owners. Then, equatons (2) (5) mply R = X1 + p X2 = r KX + w L X for = 1, 2, whch explans the arguments of R and V n (7). R should be dentfed wth the famlar gross domestc product (GDP) or revenue functon (Dxt and Norman, 1980), excludng arms expendtures. s one can verfy, R s ncreasng and convex n p, and the supply of good 2 satsfes X2 = R p ( R / p ), where X2 / p = Rpp Usng Roy s dentty, country s demand functon for good 2 can be wrtten as D2 = αd R /p, where the assocated expendture share s gven by αd α D(p ) = p µ p/µ (> 0). Therefore, the excess demand for (or net mports of) good 2 s gven by M D2 X 2, where X2 = R p. Then, holdng fxed the secure resource endowments (K and L ) as well as the dsputed resource (K 0 ), total dfferentaton of (7) yelds dv = µ(p ) [ M dp + (r K 0 φ G ψ )dg + r K 0 φ G j dg j] for = 1, 2 (j ). (8) The frst term nsde the square brackets, weghted by the margnal utlty of ncome µ(p ), s a terms of trade effect. For net mporters of good 2 (M > 0), an ncrease n p ncreases the domestc cost of good 2, and s thus welfare-reducng. By contrast, a prce ncrease s welfare-mprovng for net exporters of good 2 (M < 0). The second term n the brackets (weghted by µ(p )) captures the welfare effect of a change n country s guns, G. Ceters parbus, an ncrease n G ncreases country s share of the contested land and thus ts natonal ncome (the frst term nsde the parentheses). t the same tme, however, the ncrease n G draws addtonal resources away from the producton of consumpton goods and thus reduces natonal ncome (the second term). 9 In ths expresson, we suppress the obvous dependence of V on resource endowments to avod clutterng. 10 One can also show that R s ncreasng and concave n the resdual factor nputs (K X, L X) and that factor prces satsfy w = R L ( R / L X) and r = R K ( R / K X). 9

11 The thrd term n the brackets (agan weghted by µ(p )) captures the welfare effect of a change n arms by country s opponent, G j. n ncrease n G j reduces country s share of the contested resource and thus ts ncome, and thereby adversely affects that country. Note that, for fxed product prces, an equ-proportonate expanson of both countres guns, where G 1 = G 2 ntally, mples no change n the dvson of the contested land, whle ncreasng the resource cost of guns, and thus necessarly leaves both countres worse off. 2.4 Incentves for armng We now demonstrate how the above deas nform the dervaton of the optmzng securty polces (armng) under alternatve trade regmes. key feature of the optmzaton problem for each country s armng choce G (gven G j ) s that, wth dversfcaton n producton, the correspondng frst-order condton (FOC), gven by V G (p, G, G j ) = µ(p )r [ K 0 φ G ψ /r ] = 0 for = 1, 2 (j ), (9) s the same n form regardless of the trade regme n place. 11 Under autarky, domestc product market clearng requres p to adjust so that M = 0. Ths requrement mples that the frst term nsde the brackets n (8) vanshes, thereby yeldng (9) as the relevant FOC. Under free trade n consumpton goods, product prces are nvarant to securty polces for small countres; thus, the frst term also vanshes under ths trade regme. Equaton (9) shows that country s net margnal payoff from armng conssts of two key components: () the margnal beneft of producng guns, whch s gven by MB K 0 φ G when measured n land unts; and () the margnal cost of producng guns, whch s gven by MC ψ /r (agan measured n land unts). Lemma.3 establshes some mportant propertes of both of these components and thus of the net margnal payoff from armng, partcularly ther dependence on armng by both countres and on the relatve prce. For now, observe from the specfcaton of the conflct technology (1) and n partcular the assumed concavty of f(g ), that MB s decreasng n s guns (G ) gven the guns chosen by ts rval (G j ), as llustrated n Fg Furthermore, MB rses or falls wth G j (.e., MB n Fg. 1 shfts up or down) dependng on whether country or j ntally produces more guns. But, snce changes n the relatve prce p (gven G and G j ) have no nfluence on MB, the margnal beneft s ndependent of the trade regme n place. By contrast, MC does depend on p through factor prces. In partcular, the lnear 11 Our dscusson here and to follow s based on the assumpton that, under both trade regmes, the dstrbuton of factor endowments between the adversares s such that ther producton of arms s not constraned by ther secure land holdngs. We assume further that, under free trade, technology, the dstrbuton of factor endowments, the quantty of the contested resource and the world prce are such that producton of consumpton goods s dversfed. 12 In addton, from equaton (.1), the condton that lm G 0 f (G ) = mples lm G 0 MB =. 10

12 homogenety of the unt cost functon of guns (ψ = ψ(w, r )) mples that the margnal cost of armng can be wrtten as a functon of the wage-rental rato, ω w /r : MC = ψ /r = ψ(ω, 1). Snce the unt labor requrement n the producton of guns (ψw) s postve, MC s ncreasng n ω. ccordngly, an ncrease n the prce of the good that uses land ntensvely, whch by the Stolper-Samuelson theorem causes ω to fall, results n a decrease n the margnal cost of armng. Thus, MC s decreasng n p f good 2 s land ntensve, and otherwse s ncreasng n p. But, ether way, the mere nfluence of product prces on MC mples that the relatonshp between a country s margnal cost and ts armng s trade-regme dependent. Under free trade when producton s dversfed, the world prce alone determnes the wage-rental rato, ω. Snce ω s nvarant to changes n G, so s the margnal cost of armng, as llustrated by MCF (the dotted lne) n Fg. 1. Under autarky, a country s product and factor prces are endogenously determned along wth ts choce of guns. In the next secton, we show that a country s margnal cost of armng under ths regme s generally ncreasng n ts own guns, as depcted by MC n Fg Trade Regmes and Insecurty Buldng on the results above, we now explore the mplcatons of autarky and free trade for armng. The central objectve here s to characterze how the trade regme n place nfluences armng ncentves. We dfferentate between trade regmes wth subscrpts for autarky and F for free trade. 3.1 utarky The frst-order condtons n (9) show that, regardless of the trade regme n place, the two countres optmzng choces for guns (G for = 1, 2) depend on the factor prces and thus the product prces prevalng n the respectve country, p. Thus, to close the model we need an addtonal condton, one for each country, that determnes the autarkc prce, p (for = 1, 2). These condtons requre domestc markets to clear: M = 0 or equvalently, RD ( p ) = RS ( p, kx ( p, G, G j)) for = 1, 2, j, (10) where RD(p ) denotes the relatve demand for good 2. Whle the demand for good 2, as noted above, s gven by D2 = α D R /p, the demand for good 1 s D1 = (1 α D )R ; therefore, the relatve demand for good 2 s RD(p ) D2 /D 1 = 1 α D (p ). One can show p 1 α D (p ) that RD(p ) s unquely determned by and decreasng n the relatve prce of good 2, p. In addton, as noted above, the relatve supply of good 2 (RS ) s ncreasng n p. Usng (10), Lemma.4 presented n the ppendx shows how the equlbrum prce s nfluenced by changes n the resdual land-labor rato (kx ) nduced by exogenous changes 11

13 n guns and resource endowments. Most mportantly for our purposes here, part (a) of the lemma mples that a country s margnal cost of armng under autarky, MC = ψ(ω(p ), 1), s ncreasng n the country s own guns regardless of the rankng of factor ntenstes n the consumpton goods ndustres. The logc here s as follows. In the neghborhood of the optmum mplctly defned by (9), an ncrease n G (gven G j ) rases country s resdual land-labor rato (see Lemma.2(b)). By the Rybczynsk theorem, ths ncrease translates nto an ncrease n the relatve supply of the good produced ntensvely wth land, causng the relatve prce of that good to fall.e., p / k X 0 as k 2 k 1. Whether good 2 or good 1 s produced ntensvely wth land, the Stolper-Samuelson theorem mples, n turn, that the resultng prce adjustment wll force the wage-rental rato ω to rse and thus nduce MC to rse wth G, as Fg. 1 shows. Notng that an ncrease n the opponent s armng G j (gven G ) decreases country s resdual land-labor rato, one can apply analogous reasonng to part (b) of the lemma to establsh that a country s margnal cost of armng s negatvely related to the opponent s armng. Obvously, the ntersecton of MC wth MB, such as at pont n Fg. 1, gves country s best-response functon under autarky, B (Gj ). The shape of ths functon depends on how both the margnal cost and margnal beneft functons are nfluenced by the rval s armng, G j. Of course, as we have just seen, MC s negatvely related to Gj and MB s ncreasng n G j when G > G j and decreasng n G j when G < G j. Thus, as llustrated wth sold-lne curves n Fg. 2, B (Gj ) depends postvely on G j (reflectng strategc complementarty) up to and beyond ts pont of ntersecton wth the 45 lne; however, at some pont beyond that ntersecton, the functon can become negatvely related to G j (reflectng strategc substtutablty). One can show, under farly general crcumstances, that an nteror Nash equlbrum n pure strateges (securty polces) exsts n the autarkc trade regme and that t s unque. 13 The conflctual (Nash) equlbrum under autarky s depcted by the ntersecton of the two countres best-response functons. 14 One such equlbrum a symmetrc one s pont n Fg. 2, where B 1 and B2 ntersect along the 45 lne. Pont (where B 1 ntersect) shows an asymmetrc equlbrum. and B2 13 s shown n the proof, whch s presented n the ppendx, unqueness of equlbrum s ensured f ether the technology for arms s not very land ntensve or f the nputs to arms are not very close complements. These condtons, whch are suffcent but not necessary, serve to lmt the responsveness of each contender s securty polcy to the opponent s guns choce. We should add that the proof s based on the assumpton that not all secure land supples are absorbed nto the producton of guns. lthough ths assumpton s made for convenence and could be relaxed, we mantan t for clarty. One suffcent condton that precludes the volaton of ths assumpton s that the degree of land nsecurty (.e., the fracton of contested land) s not too hgh. nother possble condton s that guns are produced wth labor only. (Note that, provded that both factors are essental to the producton of consumpton goods, labor wll never be fully absorbed n the producton of guns n the autarkc regme.) 14 Note that, because each country always has an ncentve to produce a small (but postve) quantty of arms when ts rval produces none, (0, 0) s not a Nash equlbrum. 12

14 Whether the autarkc equlbrum s symmetrc or asymmetrc depends on the technologes for producng consumpton goods, the technology of conflct (1), the degree of resource nsecurty (nsttutons), and the sze of the secure endowments of land and labor, as each nfluences autarkc prces and thus the margnal cost of armng. To proceed, consder frst the benchmark case, where countres 1 and 2 have dentcal secure endowments. We dfferentate the resultng symmetrc equlbrum values from others, by placng a tlde ( ) over the assocated varables. Snce the countres are dentcal, they face dentcal armng ncentves; therefore, G = G for = 1, 2, wth each country thus recevng one half of the contested resource, K 0. Not surprsngly, then, equlbrum product prces and thus factor prces as well as the resdual land-labor ratos are also the same across countres: p = p, ω = ω and k X = k X for each. For the results to follow, t s useful to dstngush between two dstnct sets of secure endowments of land and labor that dffer n ther predctons for the relatve amounts of arms the two countres produce under autarky: S 0 denotes the set of secure endowment dstrbutons mplyng a symmetrc soluton such that G 1 = G 2 = G, and S denotes the set of secure endowment dstrbutons mplyng an asymmetrc outcome such that G > G j (j ). Clearly, S 0 ncludes the benchmark case where the two countres have dentcal secure endowments. The next lemma establshes that S 0 ncludes other dstrbutons as well, and t characterzes equlbrum prces and the resdual land-labor ratos for dstrbutons n both S 0 and S. Lemma 1 (rmng and utarkc Prces) Under autarky, there exsts a non-empty set of asymmetrc factor dstrbutons under whch contendng states face dentcal market-clearng prces, produce dentcal quanttes of arms, and are equally powerful. ll other asymmetrc dstrbutons generate dfferent prces and unequal armng and power. Specfcally, for each country = 1, 2 (j ), (a) G = G and p = p for secure factor dstrbutons n S0, where k X = k X ; (b) G > Gj and p pj as k 2 k 1 for secure factor dstrbutons n S, where kx < kj X. To see what other dstrbutons, asde from the symmetrc one, yeld the symmetrc outcome, suppose that, startng from the benchmark case, both land and labor resources are transferred from country 2 to country 1, such that dk X kx dg =dp =0 = dk dl = 0, whch KX L X requres dk = K dl X = k L X for each. By constructon, such a redstrbuton of resources, for X constant guns and prces, leaves the value of country s resdual land-labor ratos unchanged at kx = k X, = 1, 2. Thus, the countres relatve supply and relatve demand functons do not shft; and, there s no pressure for autarkc prces to change. But, gven prces do, n fact, reman fxed at p, armng ncentves reman unchanged n both countres. Thus, S 0 conssts of all secure resource dstrbutons mplyng the same resdual land-labor rato 13

15 as that for two dentcal countres, kx 1 outcome. 15 = k2 X = k X. They all mply the same symmetrc To see how S 0 dffers from S, the set of secure resource endowments mplyng an asymmetrc outcome such that G > G j, consder an ntal secure resource dstrbuton n S 0. For such a dstrbuton, the conflctual equlbrum s ntally on the 45 lne of Fg. 2, at pont, where B 1 and B2 ntersect. Now arbtrarly transfer labor only to country 1 from country 2, mplyng that country 1 s resdual land-labor rato falls, whle that of country 2 rses. Thus, the prce of the good produced ntensvely wth land rses n country 1 and falls n country 2. To fx deas, suppose good 2 s produced ntensvely wth land (.e., k2 > k 1 ). Then, the transfer of labor to country 1 ncreases p1, whch n turn decreases ts wage-rental rato and thus ts margnal cost of armng; at the same, country 2 s loss of labor reduces p 2, and thus ncreases ts margnal cost of armng. In ths case, snce the margnal beneft of armng s ndependent of the prce, country 1 wll behave more aggressvely, whle country 2 wll behave less aggressvely, as shown n Fg. 2 by the clockwse rotaton of B 1 to B 1 and that of B2 to B2. The unqueness of equlbrum ensures that the ntersecton of the new best response functons, B 1 and B2, les below the 45 lne, such as pont n the fgure, where clearly country 1 arms more heavly than ts adversary. s confrmed n the proof (presented n the ppendx), ths effect on the countres armng ncentves holds regardless of the rankng of factor ntenstes of the two consumpton goods. But, ths rankng does matter for the rankng of ther autarkc prces. Specfcally, as suggested by the dscusson above, the autarkc prce of the good produced ntensvely wth land s hgher n the more aggressve country that s, G 1 > G 2 mples p 1 > p2 when k 2 > k 1 and p 1 < p2 when k 2 < k 1.16 Ths dfference n autarkc prces across countres = 1, 2 allows us to dstngush further S 1 from S 0. Recall that, for dstrbutons of secure endowments n S 0, kx 1 = k2 X = k X. By contrast, snce the equlbrum prce of the good that s produced ntensvely wth land s decreasng n the resdual land-labor rato, we have kx 1 < k2 X for dstrbutons n S 1 regardless of the rankng of factor ntenstes across ndustres Notce that the logc of ths experment remans ntact for numerous conflct technologes, ncludng those that permt non-addtvty but mantan symmetry and some that permt asymmetry such as that axomatzed by Clark and Rs (1998): φ 1 (G 1, G 2 ) = ϕf(g 1 )/[ϕf(g 1 ) + (1 ϕ)f(g 2 )] and φ 2 (G 1, G 2 ) = 1 φ 1 (G 1, G 2 ), where ϕ (0, 1). In the presence of a more general sort of asymmetry, guns need not be equalzed even when secure endowments are dentcal, but ther values wll not change from the benchmark case wth transfers of secure land and labor that mply kx = k X. 16 See Lemma.5 n the ppendx for a formal proof of these equlbrum relatonshps. 17 See Lemma.4. For dstrbutons n S 1 adjacent to S 0, we have kx 1 < k X < kx 2, as mpled by the proof to Lemma.6 n the ppendx. 14

16 3.2 Free trade Turnng to trade, we suppose the contendng countres are small n world markets and that there are no trade costs. Lettng π denote the nternatonal prce of the non-numerare good, free trade n consumpton goods requres p = π, for = 1, 2. Snce π s gven by world markets and s thus ndependent of natonal securty polces, a country s payoff functon can be dentfed wth ts ndrect utlty functon, V, as shown n (7) where p = π. Dependng on fundamentals, the degree of land nsecurty, and the nternatonal prce level, t s possble, as n the case of autarky, for arms producton to be constraned by the countres secure land holdngs. 18 However, t s also possble now for one or both countres to specalze completely n the producton of one consumpton good. But, to hghlght the factor-prce effects of openng borders up to free trade and the strkng mplcatons ths can have for armng ncentves, we abstract from these two possble complcatons. One can show that when () free trade n consumpton goods leads to nternatonal factor prce equalzaton, and () the producton of arms does not exhaust ether country s secure land endowment, an nteror Nash equlbrum n securty polces wll exst, and wll be unque and symmetrc. Here we focus on the logc underlyng the symmetrc feature of the free-trade equlbrum. 19 Suppose for now that the two countres have dentcal secure resource endowments, and that the world prce equals the equlbrum prce that would obtan n each country f there were no trade: π = p. Provded condtons () and () stated above are satsfed, the ntersecton of MB and MCF (as llustrated n Fg. 1 at pont ) determnes country s best-response under free trade, BF (Gj ; p ). Snce product and thus factor prces are ndependent of ether country s securty polcy n ths trade regme, the shapes of best-response functons are determned solely by the propertes of the conflct technology (1), φ that s, B F / Gj = V G G j /V G G = φ G G j /φ G G 0 when G G j. Thus, as llustrated n Fg. 2, the best-response functons under free trade are upward-slopng (reflectng strategc complementarty) up to ther pont of ntersecton wth the 45 lne, and downward slopng (reflectng strategc substtutablty) thereafter. When the two contendng countres hold dentcal endowments of secure resources, they face dentcal margnal beneft and margnal cost functons for guns, thereby yeldng the symmetrc equlbrum, pont n Fgure 2 where G F = Gj F = G F and snce π = p, G F = G.20 What about when secure endowments are unevenly dstrbuted across the two countres? 18 s n the case of autarky, countres wll not use ther entre labor endowments n the producton of guns, provded that both factors are essental n the producton of consumpton goods. 19 The proofs of exstence and unqueness of equlbrum are smlar to those presented for the case of autarky (see the ppendx). To be sure, exstence and unqueness of equlbrum arse under less restrctve condtons than () and (). However, relaxng these two condtons only complcates the analyss wthout alterng the key nsghts of our comparson of conflct under autarky and free trade. 20 s before, the pont (0, 0) s not an equlbrum (see footnote 14). 15

17 Provded that the dstrbuton s such that free trade n consumpton goods mples nternatonal factor prce equalzaton 21 and such that the producton of guns does not exhaust ether country s secure land resources, 22 the contendng states wll contnue to face dentcal margnal beneft and margnal cost functons for guns, thus agan yeldng the symmetrc Nash equlbrum: G F = G for = 1, 2 when π = p. We label ths set of dstrbutons the arms equalzaton set (ES). Under free trade gven π = p, redstrbutons of secure endowments across the two contendng countres wthn the ES have no effect on ther armng. 23 We note that, whle the sets S 0, S 1, and S 2 are defned under autarky and thus are ndependent of the world prce, the ES subsets of S 0, S 1, and S 2 for whch free trade leads to arms equalzaton are not: as π moves away from p, these subsets shrnk. We now turn to explore the mplcatons of changes n nternatonal prces for armng. To proceed, note that, gven the allocaton of secure resources, there exsts a range of prces (π, π ) for each country that ensures dversfcaton n the producton of consumpton goods for that country. Then, for world prces π (π, π), where π = max{π 1, π 2 } and π = mn{π 1, π 2 }, producton s dversfed n both countres. By contrast, for world prces π / (π, π), where π mn{π 1, π 2 } π and π max{π 1, π 2 } π, both countres specalze n producton. 24 Usng these defntons, we have the followng: Lemma 2 (rmng and Internatonal Prces) ssume that secure land endowments are not exhausted n the producton of guns. Then, (a) equlbrum guns are ncreasng n the world prce of the land-ntensve good for world prces π (π, π) (.e., dg F /dπ 0 π (π, π) f k 2 k 1, for = 1, 2); and, (b) equlbrum guns are nvarant to prce changes for all world prces π / (π, π) (.e., /dπ = 0, π / (π, π)). dg F 21 The condtons for nternatonal factor prce equalzaton nclude, as n the standard HOS trade model, constant returns to scale n producton, the absence of factor ntensty reversals, dentcal technologes across countres, dversfcaton n producton, absence of market falures or dstortons, no trade barrers, and the exstence of at least as many productve factors n the tradable goods sectors as there are traded goods (Samuelson, 1949). For dstrbutons of secure resources where these condtons are not satsfed, at least one country wll specalze n the producton of one consumpton good. Such specalzaton precludes the possblty of nternatonal factor prce equalzaton and renders a country s margnal cost of producng guns ndependent of the world prce, but ncreasng n ts arms. 22 Even where one country s secure land constrant bnds n the producton of guns, free trade n consumpton goods can nonetheless lead to factor prce equalzaton. Once the dsputed land s dvded, both countres dversfy n ther producton of the two goods. However, due to the bndng resource constrant, the margnal beneft of producng more arms s not equalzed across countres. ccordngly, free trade does not lead to arms equalzaton n ths case, and more generally factor prce equalzaton alone need not mply arms equalzaton. 23 These fndngs would reman unchanged assumng alternatve specfcatons for the conflct technology as descrbed earler n footnote Of course, for dentcal adversares, π = π and π = π. But, for adversares havng dfferent secure factor endowments, there also exst prce ranges for whch one country s gun choces depend on prces whle the other country s do not namely, (π, π) and (π, π). However, these complcatons are not relevant for our arguments. 16

18 The proof of ths lemma s farly straghtforward. Suppose once agan that good 2 s land ntensve (k2 > k 1 ). If the condtons specfed n part (a) are satsfed, factor prces and arms are equalzed across countres. Now, let the world prce of good 2 (π) rse. Whle ths prce change has no effect on ether country s margnal beneft of armng (MB ), by the Stolper-Samuelson theorem the wage-rental rato n each contendng country wll fall; and, as prevously dscussed, ths adjustment n factor prces wll cause each country s margnal cost of armng (MCF ) to fall, thereby nducng both to arm more heavly. (nalogous reasonng establshes that, when good 1 s land ntensve (k1 > k 2 ), an ncrease n π (π, π) wll nduce less armng.) Turnng to part (b), note that, from equatons (2) (5), prce changes outsde the relevant range for country, π / (π, π ), force all factor prces to rse proportonately n that country and thus have no effect on the margnal cost of armng. Part (b), then, follows from the condton mposed mplyng both countres specalze n producton. But, for our purposes, the mportant pont s that changes n world prces can nduce changes n the two contendng countres armng choces. lthough the qualtatve nature of the lnk between the relatve world prce of good 2 and the countres armng choces n the free-trade equlbrum depends on technology (and n partcular the relatve factor ntenstes of the producton of goods 1 and 2), for smplcty and clarty we henceforth mantan the assumpton that good 2 s land ntensve.e., k2 > k 1. Unless otherwse noted, the results that follow reman ntact regardless of the rankng of factor ntenstes. 4 Trade Patterns and Trade Volumes Naturally, the drecton of a country s trade flows depends on the world prce. To explore ths ssue, defne π as the level of the world prce that elmnates country s trade: MF (π) 0 f π π.25 In what follows, we contrbute two deas to the lterature. Frst, we llustrate that nternatonal contestaton of resources alters a country s trade-elmnatng prce relatve to the case of no conflct and can thus affect ts observed comparatve advantage. Second, we show that such conflct can drve a wedge between a country s autarkc prce and trade-elmnatng prce under free trade such that a smple comparson of nternatonal and autarkc prces need not provde an accurate predcton of trade patterns n 25 s n the neoclasscal verson of ths settng wth no nsecurty, the negatve nfluence of the world prce π on each country s excess demand MF (π) follows from what s effectvely a condton for stablty of general equlbrum under free trade. However, when there s nsecurty, one has to account for the ndrect nfluence of a change n π on the country s resdual land-labor rato kx, through ts effect on armng by both countres. s such, the presence of nsecurty makes the condton for stablty slghtly more complcated. Interestngly, ths condton s dentcal to a suffcent condton for unqueness of the Nash equlbrum under autarky (see equaton (.17) and the surroundng dscusson n the ppendx). Intutvely, ths makes sense, snce prces under autarky change to clear domestc markets and polcymakers take that effect nto account when choosng ther guns. 17