consignments into lots of different sizes, and would therefore have a large volume of entrepot trade.

Transcription

1 1. Introducton Despte more than a quarter century of ntense research nto the phenomenon of ntra-ndustry trade (the mport and export of goods belongng to the same ndustry, hereafter abbrevated as IIT), several mportant puzzles reman: the exstence of IIT even at hghly dsaggregated levels of classfcaton, the growng sgnfcance of IIT n developng countres, and the contradctory results of econometrc studes that seek to relate IIT to economes of scale or trade polcy. After a bref recaptulaton of the evdence, and why exstng theory does not adequately explan t, I present a model that provdes a new explanaton, whch of course could be one of several. Most emprcal studes of IIT defne an `ndustry' at the 3-dgt level of the Standard Internatonal Trade Classfcaton. However, several authors have found sgnfcant IIT even at the 4 and 5 dgt levels. One response has been to queston the prncple of classfcaton, and dsmss the fndng as a statstcal artefact (Vona, 1990). Another s to nsst that the goods beng traded are ndeed dfferentated, and to dentfy them as vertcally (horzontally) dfferentated dependng on whether the unt values of the mported and exported products dverge by more (less) than a certan threshold percentage (Greenaway, Hne and Mlner, 1995). Few authors have ventured to suggest that there could be two-way trade n absolutely dentcal products. However, although the poneerng work by Grubel and Lloyd (1975) was subttled The Theory and Measurement of Internatonal Trade n Dfferentated Products, t dd also pay serous attenton to IIT n "functonally homogeneous" products -- that s, products perceved as dentcal by consumers when avalable at the same tme and place. The explanatons Grubel and Lloyd provded for such trade nvolved dfferentaton along some other dmenson, or a hdden element of comparatve advantage. For example, transport costs mght make t more economcal for one regon n a country to export a commodty across a nearby nternatonal border, even as another regon s mportng the same commodty (dfferentaton by locaton). A country mght also export and mport the same agrcultural commodty n dfferent seasons, or electrcty at dfferent tmes of day (dfferentaton by tme). Government polces such as subsdes or contractual mports mght also result n IIT n dentcal products. Alternatvely, a labour-abundant country located on major trade routes mght have an advantage n reconsttutng and repackagng 1

2 consgnments nto lots of dfferent szes, and would therefore have a large volume of entrepot trade. In the decade after the publcaton of Grubel and Lloyd's book, attenton shfted to theoretcal models of IIT based on mperfect competton. Among the many offsprng produced by the frutful marrage of trade theory and ndustral organzaton were models of IIT n dentcal products under nternatonal olgopoly (Brander and Krugman, 1983; Dxt, 1984). Dutfully noted n surveys and textbooks, t was regarded as a theoretcal curosty, wth attenton beng lavshed on ts slghtly older sblngs, the models of IIT n dfferentated products under monopolstc competton. Even Krugman, despte beng one of the co-authors of the orgnal model, and publcsng t n hs surveys n both the older and newer volumes of the Handbook of Internatonal Economcs, readly admtted that "two-way nternatonal trade n lterally dentcal products s surely rare" (Krugman 1995, p.1271). Ths perod of bengn neglect may now be endng, and several extensons have been offered n recent years: Dastdar (1998) ncorporated ncreasng returns and trade polcy nto the Brander-Krugman model; Murray and Turdalev (1999) have generalsed t to several frms n several countres; Naylor (1999) has ncorporated unonzed labour markets nto an nternatonal olgopoly model; Horn and Levnsohn (2001) have used t to examne nternatonal competton polcy; whle at long last Bernhofen (1999) has successfully subjected a model n ths tradton to emprcal testng. However, ths show of nterest should also draw attenton to some of the unsatsfactory aspects of these olgopoly models of IIT. For one, they retan a somewhat ad hoc assumpton of segmented markets, leavng unexploted arbtrage opportuntes between countres. 1 They also share wth the monopolstc competton models a vson of frms exercsng market power n export markets. The same apples to mperfect competton models of IIT n vertcally dfferentated products n the tradton of Shaked and Sutton (1984), whch are agan based on olgopoly at home and abroad. On the other hand, models of vertcal IIT n the Heckscher-Ohln tradton, where superor varetes 1 Ben-Zv and Helpman (1992) show that n an nternatonal olgopoly where cross-country prce dfferentals are bounded by transport costs, so that no unexploted arbtrage opportuntes exst n equlbrum, IIT n dentcal products does not occur. 2

3 requre more captal-ntensve technques of producton (Falvey 1981; Flam and Helpman, 1987), assume perfect competton everywhere. Olgopolstc ndustres that are prce-takers n compettve world markets do not ft ether descrpton, and the 2 x 2 taxonomy n Greenaway, Hne and Mlner (1995), formed by classfyng models accordng to small/large numbers competton and horzontal/vertcal product dfferentaton overlooks ths mxed case. What seems to be mssng n the theoretcal lterature s an explanaton for the sgnfcant and rsng level of IIT observed n countres whose frms would not be expected to have market power n foregn markets, nor to be exportng horzontally dfferentated products, 2 even though they may have olgopolstc home markets and mport and export vertcally dfferentated products. 3 The fnal puzzle s the relatonshp of IIT to some explanatory varables commonly used n the lterature. Most authors expect that lower polcy-nduced trade barrers should promote IIT, just as lower transport costs, smaller shppng dstances, and common borders are emprcally well establshed as conducve to IIT. However, trade polcy ndcators often emerge wth regresson coeffcents that are nsgnfcant, wrongly sgned, or nconsstent as between dfferent studes and dfferent ndcators. Varous measures of scale economes also perform poorly n most studes, whch s agan bad news for the monopolstc competton models. 4 The model to be developed below generates IIT n absolutely dentcal products, wth no economes of scale, hdden dfferentaton or comparatve advantage, whle retanng the prce-takng small country assumpton of tradtonal trade theory. One verson can also be appled to vertcal dfferentaton, agan under the small country assumpton. The key element n ths model s the role of mport quotas and smlar 2 Hummels and Levnsohn (1995) carred out a test of a gravty equaton consstent wth the monopolstc competton model and found that t performed well on a sample of developng countres whch dd not have these characterstcs. 3 The results of several emprcal papers surveyed by Lee (1992) show that developng countres show much greater concentraton n the same ndustres as compared to ndustral countres. Early nvestgatons of the extent and nature of IIT n developng countres nclude Culem and Lundberg (1986) ; see the surveys cted n the followng footnote for more recent evdence. 4 See Tharakan and Calfat (1996) and Perdks and Kerr (1998, ch.6) for summares of these fndngs, and earler attempts to explan them. 3

4 quanttatve restrctons (QRs) n permttng olgopolstc home frms to prcedscrmnate between the protected domestc market and the compettve foregn market. Although many QRs are beng phased out and replaced by prce-based measures n the course of the mplementaton of the Uruguay Round agreements, most of the emprcal work on IIT pertans to a perod when they were stll n force. To the extent that the explanaton provded n ths paper s applcable to ths evdence, we should expect a reducton n IIT from the abolton of QRs. On the other hand, the new Bush admnstraton's drectve to the Unted States Trade Representatve to nvestgate measures to safeguard the US steel ndustry from mport competton may result n the reappearance of QRs. The model s a varaton on Bhagwat (1992), who showed that under certan crcumstances a tarff allows a domestc monopolst wth ncreasng margnal costs and facng a compettve world market to export, even though exports are not feasble under free trade. Ths yelds "mport protecton as export promoton" wthout any of the usual nfant ndustry consderatons such as economes of scale and learnng by dong that play a central role n the wdely cted eponymous paper by Krugman (1984). I extend Bhagwat's dea to protecton through QRs, wth provson for transport costs and olgopolstc market structures. It turns out that QRs can promote exports n stuatons where tarffs cannot, and unlke tarffs, they nduce ntra-ndustry trade wthout the usual assumptons of scale economes, mperfectly-compettve export markets, or product dfferentaton. In fact, we get `cross-haulng' of dentcal products n a settng where frms subject to dmnshng returns to scale are prce-takers on a compettve world market. Agan n contrast to tarff protecton, the model also yelds a non-monotonc relatonshp between the degree of mport restrcton and socal welfare. In relaton to earler work, whle there are several models of the effects of QRs n nternatonally olgopolstc markets, the combnaton of domestc mperfect competton and a compettve world market has receved less attenton. Buffe and Spller (1986) and Eldor and Levn (1990) for example, explored the comparatve statcs of varyng QR levels under ths market structure, but ruled out the possblty of exports and therefore IIT. On the other hand, Agarwal and Barua (1994) allow for exports, but mantan a prohbton on mports, agan precludng IIT. They also analyzed a 4

5 partcularly favorable confguraton of world prces vs a vs domestc demand and costs, and assumed away transport costs. Ths s only the frst of three possble cases explored below n a more general model. Secton 2 brefly restates Bhagwat's result, wth some addtonal observatons. Secton 3 examnes the postve effects of a QR n promotng exports and IIT, frst dagrammatcally n a smple model wth a domestc monopoly and lnear demand, and then algebracally for a domestc olgopoly wth general demand. Secton 4 draws on results obtaned by earler authors to extend the model to cases where the QR s set as a proporton of the domestc market, and where t s auctoned to domestc resdents. Welfare analyss s presented n secton 5, whch also qualfes and extends the results of some of the earler lterature even for a scenaro wthout IIT. Secton 6 concludes. 2. Export-promotng tarffs The settng n Fgure 1 s a domestc monopolst facng domestc demand curve ED, the assocated margnal revenue curve, and compettve foregn supply S F at the exogenous world prce P 1. Under free trade, the monopolst can charge at most P 1, and thus the effectve margnal revenue curve concdes wth S F upto ts ntersecton wth the demand curve. The monopolst produces P 1 C, wth CA beng mported, whch s the outcome that would obtan f domestc producton was perfectly compettve. A tarff at rate t per unt rases the cost of mports to P 1 +t = P 3. If the monopolst can also export at the world prce P 1, effectve margnal revenue s now P 3 FBS F, and the monopolst maxmzes profts by supplyng P 1 B to the domestc market at a prce of P 3, and exportng BC at the world prce P 1. Protecton does seem to promote exports, and from beng an mporter, the home country becomes an exporter of the same good, wthout any "nfant ndustry" phenomena such as economes of scale or learnng by dong. 5 As Bhagwat (1992) ponts out, ths argument hnges on the world prce beng hgh relatve to domestc costs. Call ths Case I. 6 Now consder the same scenaro, but 5 The tarff has been drawn so as to maxmze the volume of exports. It can easly be seen that any hgher tarff wll leave ths equlbrum unaffected, whle a lower tarff wll result n a smaller volume of exports. Exports vansh entrely f P 3 cuts the demand curve below pont G. 6 Another possblty, whch wll not be mentoned agan, s that the world prce for both exports and 5

6 wth a lower world prce P 2 below the level at whch MC and MR ntersect. In ths stuaton--call t Case II--t s clear that any tarff merely reduces mport competton and never results n exports. Ths leads to an mportant qualfcaton to Bhagwat's argument. He assumed that both mports and exports take place at the same world prce, but n the presence of transport costs (or vertcal product dfferentaton, where the domestc varety can only be exported at a dscount 7 ) the (FOB) export prce wll be below the (CIF) mport prce, shrnkng the range BC over whch exports are forthcomng. 8 In partcular, the export prce may be below the ntersecton of MR and MC, even f the mport prce s above t. Such a stuaton s depcted n Fg. 1, f P 2 s the export prce and P 1 the mport prce. Call ths Case III. Agan, exports are unproftable regardless of the tarff. Even f t promotes exports, a tarff reduces welfare, as conventonally measured by the sum of consumer and producer surpluses, even after ncludng export profts. It s easy to see that welfare declnes monotoncally n the tarff. Gong back to Case I, although exports are maxmzed at tarff rate t, welfare s n fact mnmzed; the area correspondng to the deadweght loss s trangle FBA. Note also that wth ths tarff n place, the monopolst charges a prce from domestc consumers that s hgher than what t would have charged under autarky, snce the possblty of exportng nduces t to restrct domestc sales even more than t would have otherwse. 3. Export-promotng quanttatve restrctons 3.1: A smple model From the lterature on non-equvalence of tarffs and quotas under mperfect competton begnnng wth Bhagwat (1965), we know that for the same degree of mport restrcton, mports les above the ntersecton of the domestc demand curve wth the monopolst's MC curve, but below the monopolst's autarky prce (not drawn). The monopolst then exports under free trade -- but exports even more wth tarff protecton. 7 In ths nterpretaton, the domestc and mported "varetes" are perfect substtutes n domestc producton and consumpton -- ndeed they are the same product -- but the domestc varety can only be exported at a lower prce due to foregn consumers' perceptons or unfamlarty wth ts qualty. 8 Even n Cases I and II, we need to assume some postve but arbtrarly small transport costs or qualty premum to rule out the possblty of exports under free trade, for otherwse the monopolst would be ndfferent between supplyng the domestc and foregn markets at a common world prce. 6

7 a quota gves the monopolst greater monopoly power. Ths carres over to the case where exports are possble. I shall use the terms QR and quota nterchangeably; t s only n ther normatve mplcatons (dscussed n secton 5) that quotas dffer from so-called Voluntary Export Restrants, or VERs. To fx deas, and to heghten the contrast wth the tarff case of the prevous secton, I begn wth a dagrammatc exposton usng the same rudmentary model. Refer agan to Fgure 1, allowng for the present that, subject to the qualfcaton n n.8, both exports and mports are possble at P 1 (Case I). Wth free trade, we have already seen that there are no exports. Tarff rates that rase P 1 +t to cross the demand curve n the range GH are prohbtve, but stll do not nduce exports. Now consder the equvalent quota, that s, a ban on mports. Ths allows the monopolst to operate anywhere along the domestc demand curve, or export along S F. Margnal revenue s therefore EBS F, and the monopolst sells P 1 B n the domestc market at prce P 3, and exports BC at the world prce. Ths s exactly what was delvered by the export-maxmzng tarff depcted n Fgure 1. What about quotas that permt some mports? Assume for the present that mport lcenses are compettvely held, so mports equal the entre quota. The effects of enlargng the quota can be seen by translatng the segment EA of the demand curve to the left by the amount of the quota. (At prces below P 1 the monopolst can undercut mports and supply the entre home market along AD.) Fgure 2 llustrates ths for a quota of JA, whch shfts the demand curve confrontng the monopolst n the home market so that t s now E'JAD. 9 The correspondng margnal revenue curve follows MR' upto the pont vertcally below the knk n the demand curve at J, and then jumps up to concde wth the horzontal segment of ths demand curve, JA. (Ths jump s not shown, to avod clutterng the dagram, but ts relevance wll become apparent.) However, the export opton provdes another MR schedule P 1 S F, so that the effectve MR schedule becomes E'B'S F. The monopolst now maxmzes profts by sellng P 1 B' to the domestc market 9 Although changes n QRs are nvarably represented by parallel shfts of the resdual demand curve n the trade polcy lterature, strctly speakng ths assumes ether "effcent ratonng" of mports, or costless arbtrage between domestc consumers. For clarty, the quota shown exceeds the free-trade level of mports CA, but ths s not necessary for the result. Also, remember that we are stll consderng Case I, so gnore P 2 for the moment. 7

8 at a prce P q1 and exportng B'C, whle the quota lmts mports to JA. We now observe two-way trade n dentcal products. Extendng ths logc, a very large mport quota set close to P 1 A maxmzes exports at almost P 1 C, gvng essentally the same outcome as wth free trade, wth net mports of CA. Notce from Fgure 2 that the monopolst wll always produce P 1 C, wth the changes n the quota level only dvdng ths amount between the home and export markets by shftng B' horzontally. In Case II, wth the world prce at P 2, we saw that a tarff can never nduce exports. Unlke n Case I, nether can a ban on mports, as can be seen from Fgure 1: MR n the protected home market exceeds that from exports over the entre range P 2 K. However, a large enough quota can result n exports. The one llustrated n Fgure 2 makes t optmal for the monopolst to supply P 2 L to the home market at prce P q2, and to export LK. The same outcome obtans n Case III, where mports are avalable at P 1 but exports can only be sold at P 2 because of sgnfcant transport costs, a qualty dfferental perceved by foregn consumers, or a tarff t = P 1 -P 2 leved n addton to the QR so as to dvert quota rents to the government. (I shall henceforth use the term transport costs to descrbe the gap P 1 -P 2, referrng to the other nterpretatons wherever approprate.) If the gap s very large, exports and IIT may not emerge at all for modest quotas. It mght seem that a large enough quota can always push the MR' curve to the left of pont K, so that exports wll eventually emerge. However, enlargement of the quota depresses monopoly profts n the protected home market, whle the monopolst always has the opton of slghtly undercuttng the mport prce and replcatng the free trade outcome, supplyng P 1 C only to the home market at P 1 and earnng profts OP 1 C. Such a devaton s not attractve n Case I, where both exports and mports are possble at ths prce, for the monopolst can always earn an extra proft correspondng to an area lke P q1 NB'P 1 over and above OP 1 C whle contnung to export. But f transport costs are sgnfcant, so that exports are possble only at the lower prce P 2 (Case III), then the proft from servng both home and export markets (the area of the rregular polygon P q2 MLKO) wll eventually be reduced by quota enlargement to fall below the free trade level of profts, OP 1 C. The monopolst wll then revert to the free trade outcome, 10 and 10 Another way of lookng at ths s to vsualze the quota-shfted margnal revenue curve facng the monopolst jumpng up to J and then followng S F. Ths ntersects the margnal cost curve agan at C, 8

9 IIT wll dsappear. Thus, f transport costs are sgnfcant, IIT wll not emerge f QRs are ether too small or too large, conformng to the consderable emprcal evdence (as well as the predctons of the Brander-Krugman model) that IIT s facltated by low transport costs. A smlar caveat apples to changes n the world prce, or changes n the local currency prce of mports and exports brought about by exchange-rate changes. Ths s not llustrated n order to avod clutterng the dagram, but t can be vsualsed that for any gven quota consstent wth IIT, a hgher world prce (represented by both P 1 and P 2 beng hgher, gven MC) ncreases the level of exports, but also reduces sales and profts n the domestc market. Once agan there s a crtcal level at whch the monopolst does better by undercuttng the mport prce and supplyng only the home market. What ths smple model has establshed s that for a range of confguratons of world prces and domestc cost and demand, quotas permt dumpng and also IIT n dentcal (or vertcally dfferentated) commodtes for a small country. Exports and ntra-ndustry trade emerge n Cases II and III only after the home market s substantally opened to mports: t s ths whch depresses domestc proftablty so much that the monopolst prefers to export. Further mport lberalzaton ncreases exports even more, although for a monopolst facng lnear domestc demand, exports clearly rse by only half the ncrease n mports, and that too only untl the dscontnuous reverson to the free trade outcome descrbed n the precedng paragraphs. Note from the dagrams that the prce at whch the monopolst can export plays a role analogous to constant margnal costs n determnng the monopolst's proftmaxmzng level of domestc sales. Call ths prce P x, whch s dentcal to P 1 n Case I and P 2 n Cases II and III. Then P x represents the constant opportunty cost of servng the domestc market, an analogy that wll be used frequently below. Beyond a pont, creatng multple equlbra from amongst whch the monopolst chooses the one yeldng the hghest proft. 9

10 margnal revenue from domestc sales falls below P x, and t s optmal to supply further output to the world market as long as P x > MC. In the presence of sgnfcant transport costs, the mport prce, whch corresponds to P 1 n Case III, has no role to play n the model, other than demarcatng the crtcal level at whch frms revert to the free trade outcome. Formal welfare analyss s undertaken below, but t s clear that ths polcy always reduces welfare relatve to free trade, and that t amounts to squeezng out an exportable surplus from domestc consumers by sheldng frms from compettvely-suppled mports and thus renforcng ther monopoly power. In fact, n Case I, wth mports barred and export possbltes encouragng frms to restrct ther domestc sales even more than otherwse, the domestc prce s hgher than t would have been under autarky. Demonstratng the paradoxcal nature of optmal polces n a second-best world, f for some reason t s not possble to abolsh the ban on mports, t s welfare-mprovng to mpose a parallel ban on exports. 3.2: A General Model To formalze ths analyss, and extend t to domestc olgopoly and general demand, let the home market be characterzed by nverse demand P = p(q + q ), p' < 0, where Q s the home ndustry's domestc sales and q the quota lmt on mports. There are n domestc frms wth strctly convex cost functons, C = C ( q + x ), where q and x represent the domestc sales and exports respectvely of frm, C ( 0) = 0, C (.) > 0, and C (.) > 0. Also, C ( 0) < Px, otherwse there s no queston of exports. The frms compete as a Cournot olgopoly n the domestc market, subject to mport competton. Each frm thus takes as gven the total output for the domestc market of all other frms q -, and the quota level q set by the government. Consder Case I to begn wth, where (allowng for the neglgble dfference explaned n n.8 above) exports and mport are possble at the same prce P x. Frm maxmzes 10

11 Π p( q + q + q ) q + P x x - C ( q + x ) - (1) The frst order condtons are Π q q p + P C = 0. (2) Π = P x x - C = 0 (3) The model thus far s smlar to that employed by Agarwal and Barua (1994), who however gnored the possblty of Cases II and III. They also mantaned a prohbtve tarff on mports, precludng the possblty of ntra-ndustry trade. In what follows, I assume all frms are dentcal to begn wth, and return brefly to the asymmetrc case below. (2) and (3) mply that n equlbrum q p + P = P x (4) That s, each frm's perceved margnal revenue s equated to the exogenous prce of exports, whch (as explaned n the prevous secton) s effectvely the constant margnal opportunty cost of supplyng the home market. Total dfferentaton of (3) gves - C dq - C dx = 0, or dx = - dq (5) (3) determnes a frm's total output, whle (4) determnes ts domestc sales, wth exports varyng as the resdual, as shown by (5). The second order condtons for a maxmum are 2 p Π 2 / q =(2p + q - C )<0 (6) 11

12 x = - C <0 2 2 / Π (7) 2 Π 2 q 2 Π 2 x =(2p + q p - 2 C )(- C )>(- C ) = [ Π ] q x 2 2 (8) Convexty of the cost functon satsfes (7), whch also enables (8) to be wrtten as (2p + q p )<0 (9) whch n turn, along wth (7), satsfes (6), establshng the concavty of the frm's proft functon n ts own output n an equlbrum wth exports. Wth prohbtve QRs n cases II and III, equatons (3) and (4) -- and hence (5), (7), (8) and (9) -- are redundant, snce satsfacton of (2) leaves the frm wth ts perceved margnal revenue above P x and therefore wth no ncentve to export. Totally dfferentate (2) and rearrange to get (2p + p q - C ) dq + ( q + p ) dq + ( q p + p p - )d q - C dx = 0 (10) The last term on the LHS s zero n Cases II and III, before any exports emerge, and wth symmetrc frms, rearrangng, dq =(n - 1) dq. Makng these substtutons n (10) and - dq = dq C - p + q p [(n + 1)p + nq p ] (11) Usng symmetry agan, Q = nq and dq/d q= n(d q /d q ). Usng an amalgam of Seade (1985) and Buffe and Spller (1986), defne E - (Q + q )p /p, the elastcty of the slope of the market demand curve; s Q / (Q + q ), the share of the domestc ndustry n total avalablty; and k 1 - (C /p ). 12

13 E s zero, postve or negatve as the market demand curve s lnear, convex or concave. Then (11) can be wrtten dq = d q n se - n + k - se (12) The necessary and suffcent condtons for stablty of the olgopoly equlbrum, adaptng Seade (1985), are k > 0, whch s satsfed by our assumpton of convex costs, and n+k-se > 0. Consequently, the effect of quota relaxaton on domestc output can go ether way, dependng on the sgn of se-n. Many analysts preclude a "perverse" expansonary effect by assumng the so-called Ruffn condton, or the Hahn stablty condton, both of whch mply E < 1. However, the weaker Seade condtons keep open the possblty of a perverse effect, although they do mpose the restrcton that (12) must be less than unty n absolute amount. I hghlght ths as a Lemma for future reference: LEMMA: (dq / d q < 1 Consequently, lberalzaton must ncrease domestc avalablty ( Q depresses domestc output: + q ) even when t d (Q + d q q ) = n + k k - >0 se (13) Quota relaxaton must therefore reduce the domestc prce. Dfferentatng (1), and usng the frst order condtons to apply the envelope theorem, dπ = p Q <0 d q (14) These basc comparatve statc results can be summed up as: 13

14 PROPOSITION 1: Quota relaxaton reduces (ncreases) domestc output as se s less (greater) than n, but always reduces domestc prce and profts. Seade's stablty condtons lmt the possblty of the perverse case to n < se < n+k (15) I show n the Appendx that quota enhancement eventually makes se drop out of the crtcal regon defned by (15). Assume therefore that a large enough relaxaton of the quota depresses domestc sales suffcently to produce exports even n Cases II and III, provded transport costs are not so large as to nduce the frms to revert to supplyng only the domestc market before that pont s reached. Let q o be ths crtcal mnmum level of the quota at whch exports emerge, and q r the level at whch the reverson to the domestc market occurs. 11 Thus (2), (3) and (4) descrbe a possble equlbrum wth exports n all three cases, subject to q > q 0, wth r o q o equal to zero n Case I and strctly postve (and nversely related to P x ) n Cases II and III. Ths can be summed up as PROPOSITION 2: If transport costs are not too hgh, some non-zero level of quanttatve restrcton on mports results n exports of the same product by an mperfectlycompettve ndustry whch could not export under free trade or under tarff protecton, and thus leads to ntra-ndustry trade n dentcal products. Once exports have emerged after the QR has been enlarged beyond the crtcal 11 In the symmetrc olgopoly case, each frm's reservaton payoff s the profts t can earn by undercuttng mports and supplyng only the home market upto the pont where P m = C'. When quota relaxaton depresses per-frm profts below ths level, all frms smultaneously fnd a devaton to ths outcome attractve, precludng a potental Nash equlbrum wth exports. The case of asymmetrc costs s dscussed below. 14

15 level q o, we can retrace the prevous analyss from (10), ths tme applyng (5), to fnd that the effect of quota relaxaton on total ndustry exports X s dx = - dq n dq = d q n n - se - se + m (16) 1 (Ths could have been obtaned drectly from (10) by notng that n the exportng equlbrum, the world prce acts as a constant margnal cost, so that k = 1.) In Fgure 1, wth lnear demand and a sngle domestc frm, n = 1 and E = 0, so m = 1/2: exports rse by half the amount the quota s relaxed, as argued nformally n the prevous subsecton. In the general case, the mpact on the "trade balance", or net exports for ths partcular product s necessarly negatve: wrtng dm = dq, (16) mples d(x - M) = dq n n - se - se + 1-1= n se + 1 < 0 (17) In other words, "export promoton" va quota relaxaton s self-defeatng: exports ncrease by less than the addtonal mports permtted. (In the "perverse" case dscussed above, exports actually fall.) And recall that exports emerge only after the quota s relaxed beyond q o. Ths gves us PROPOSITION 3: Relaxaton of the QR always reduces net exports of that commodty. COROLLARY: Prohbton of mports s the optmal (net) export-promotng polcy. In Cases II and III, of course, ths optmal polcy "maxmzes" net exports at zero. Even for Case I t s, as was ponted out nformally above and wll be shown formally n secton 5, a very costly way of promotng exports. For the rest of ths secton, followng from the earler dscusson, I assume that any equlbrum nvolvng IIT must be characterzed by market demand low enough and/or quota large enough, to rule out the perverse output response descrbed above. Ths means that n > se, so 0 < m < 1 n (16). Wth QR relaxaton servng to ncrease both mports and exports, t s obvous that t rases the volume of IIT, but t may be useful to 15

16 derve a quantfable relatonshp. Consder adaptng the standard Grubel-Lloyd (1975) ndex to an ndvdual commodty: G 1 - X X - M + M (18) From (16), G = 1 - m( q m( q - q ) - q o (19) - q ) + q o For q > q o = 0 (Case I), G = m m + 1 (20) For the monopoly/lnear demand example, m = 1/2, so G = 2/3 for Case I at all levels of the quota untl frms revert to the domestc market. For cases II and III, G = 0 upto q o and rses asymptotcally to 2/3 as the quota s ncreased beyond that level. Of course, snce m depends on se and hence on the quota level tself, t can be be treated as a constant only for lnear demand, or for very small changes n the quota. However, the mportant pont s that a range of values of the IIT ndex s consstent wth ths model. In prncple, all the foregong results are unaffected f we allow for domestc frms to have asymmetrc costs, as long as the least effcent frm s exportng some output n an ntal equlbrum. Then, as Agarwal and Barua (1994) showed wth a prohbtve tarff on mports, the frms operate symmetrcally n the domestc market, wth only ther exports nversely related to ther cost levels. The nterpretaton gven above of the world prce P x as the relevant MC curve helps to see ths mmedately: although each frm may have a dfferent cost functon, they all have ths common opportunty cost, whose ntersecton wth the common quota-shfted perceved MR curve determnes ther equlbrum n the home market. The gap between ths and each frm's ndvdual MC 16

17 curve (correspondng to LK n Fgure 2) represents ts exports, whch s nversely related to ts cost level. Our comparatve statc results concernng changes n the QR also go through n an IIT equlbrum wth heterogeneous frms. However, the reservaton proft levels obtaned by undercuttng the mport prce and supplyng only the domestc market wll obvously be hgher for the lower cost frms, whose devaton wll undermne the prcedscrmnatng equlbrum at lower levels q r of the QR. As each such frm devates to supply an amount lke P 1 C to the home market, the resdual demand curve facng the remanng frms moves left by the same amount, tppng the balance for those wth slghtly hgher costs and nducng them to devate as well. The IIT equlbrum may unravel and be relevant only to very restrctve QRs, or not at all. 4. Extensons 4.1: Proportonal quotas QRs on mports are often mposed n terms of a maxmum share of the domestc market, rather than an absolute amount. A recent result derved by Dencolo and Garella (1999) can be ncorporated nto our model. Ther Proposton 1 showed that wth proportonate quotas and constant margnal costs (whch s effectvely the case n our IIT equlbrum), domestc consumpton s unaffected by changes n the market share of reserved for mports. Consequently, domestc output falls (and so exports rse) one-for-one wth ncreases n the level of mports. In our notaton, m = 1, and therefore G = 1 n Case I In cases II and III, G remans zero untl the crtcal level at whch exports are nduced, and then rses asymptotcally towards unty, droppng to zero agan when domestc frms revert to compettve behavor as descrbed above. 4.2: "Sleepng" Quotas Suppose the mport lcenses that provde access to the quota-restrcted mports are auctoned to domestc resdents. Cunha and Santos (1996) have derved condtons under whch a monopolst facng compettve mports fnds t proftable to buy up the quota 17

18 lcences and not utlze them. Ther analyss, though rewardng, s somewhat cumbersome. Our model has the same market structure, and a dagrammatc exposton makes the analyss of pre-empton and `sleepng' quotas much more tractable, and also provdes a new result. Referrng agan to Case I of Fgure 2, the monopolst's purchase of any part of the quota at aucton would have two effects on ts proft-maxmzaton problem. Frst, the porton of ts margnal cost curve above P 1 would be translated to the rght by the amount of the quota t obtans. Ths s because the quota s effectvely a second plant for producng the same product at a cost of P 1, and the margnal cost curve s now the horzontal summaton of MC and P 1 up to the amount of the quota the monopolst holds. In Fgure 2, the monopolst s assumed to buy the entre quota JA, and thus (recallng that P 1 also represents the margnal opportunty cost of domestc producton n the presence of the export opton) ts effectve margnal cost curve follows P 1 Q (where CQ = JA by constructon) and then MC' n Case I. Effectve MC s P 2 Q' and then MC' n Case II, and P 2 KCQ and then MC' n Case III. The second effect of purchasng the quota s to gve the monopolst the ablty to shft the resdual demand curve back to the rght by the amount of the quota t chooses not to utlze. The correspondng margnal revenue curve also shfts, and so does the equlbrum pont B' n Fgure 2. The augmented margnal cost curve MC' s also translated leftwards by the amount of the quota that s not used. But B' cannot le to the rght of B, whch s the equlbrum pont when mports are completely shut out, and s therefore necessarly to the left of C n Cases I and III (see Fg. 1). The augmented MC' curve extends rghtwards from C n these two cases, and s thus rrelevant to the monopolst's problem. Ths also llustrates Cunha and Santos' proposton that the monopolst does not use any part of the quota that t acqures. I deal wth Case II below. It remans only to check whether the monopolst fnds t worthwhle to outbd a compettve frnge of mporters to pre-empt all or part of the quota. I confne myself to the case where the quota s perfectly dvsble and s auctoned off pecemeal. Wth the translaton of the MC curve beng rrelevant n Cases I and III, the value of a margnal unt of the quota to the monopolst s dentcal to the effect on ts profts of tghtenng the quota by that amount. A margnal tghtenng of the quota ncreases ts profts by the 18

19 negatve of (14). Usng (2), (3) and (14), dπ - = P - Px >0 d q (21) n any equlbrum n whch the monopolst s exportng, and dπ - = P - C >0 d q (22) when t s not, wth margnal cost renterpreted to nclude the possblty of the monopolst also becomng a trader n the mported product when t buys part of the quota. Recall from n.8 that the export prce must be at least slghtly lower than the mport prce P m. The frnge mporters wll bd at most P-P m per unt to secure quota rents. Hence the monopolst wll outbd them n any equlbrum n whch t s exportng, as long as any lcenses reman unsold. Ths results n pre-empton of the entre quota n Cases I (wth some exports remanng) and III (wth exports extngushed). In both cases, the monopolst's effectve margnal cost remans below P m for every unt untl the quota s sold out. In Case II, the monopolst buys and does not utlze LK of the quota and stops exportng. For the remander of the quota C' > P m, and the frnge traders outbd the monopolst (compare Cunha and Santos' Proposton 7). In all three Cases, recallng the earler comparatve statc results on quota relaxaton, we get PROPOSITION 4: Auctonng an mport quota results n a reducton of exports and IIT (possbly to zero), but an mprovement n the trade balance and an ncrease n the domestc prce and monopoly proft. Just as an ncrease n the quota ncreased exports, but by less than the ncrease n mports, the pre-empton of the quota reduces mports by more than t reduces exports. In effect, the monopolst swtches ts capacty away from exports to domestc sales to replace the mports t has succeeded n keepng off the market by pre-emptng the quota. These results have an nterestng mplcaton for poltcal economy. Many governments, especally n developng countres, are more nterested n fscal revenue, protectng 19

20 powerful domestc ndustral nterests, and n controllng the balance of payments through admnstratve measures, than n maxmzng the usual anodyne noton of socal welfare. Such a government could further ts objectves whle appearng to yeld to pressures to be more "market frendly", by relaxng quotas and auctonng them. The enlarged quotas would be fully or partly bought up and "put to sleep" by the monopolst, the government would pocket the revenue, the reducton n monopoly proft would be lmted, 12 and deteroraton of the `trade balance' (n ths sngle commodty) prevented or amelorated, despte the apparent lberalzaton of mport restrctons. 5. Welfare analyss Despte the reservatons expressed n the precedng paragraph, I do not ntend to sdestep the conventonal noton of socal welfare as the sum of domestc consumer and producer surplus, plus any quota rents. Wth the usual quas-lnear specfcaton of consumers' utlty, ths s : W = Q+q 0 P(v)dv - PQ + n[pq - C(q)] + [(P - P m )q ] (23) So that dw dq = dq P - [(nq + q ) dq dp dq dp dq dq + P ] + n[q + P C ] + d q dq dq dq d q [(P - Pm ) + dp q ] d q (24) whch smplfes to 12 It would be reduced by (slghtly more than) P-P m, whch s what the monopolst must pay for one unt of the quota lcense n order to outbd the traders, nstead of the reducton of P-P x that a margnal relaxaton of the quota would have otherwse entaled 20

21 dw dq dq =(P - C ) + (P - Pm ) (25) d q Ths s of course postve f quota relaxaton has the perverse expansonary effect on domestc output. Assumng the condtons that rule out perverse case, Eldor and Levn (1990) derved a smlar expresson, and showed that t was stll postve for P m < C'. The sgn of (25) remans ambguous otherwse. Our analyss permts us to probe deeper. The "perverse" case s not pathologcal; for a domestc monopoly (whch s what Eldor and Levn assumed) t always holds for a small ncrease n a prohbtve quota f demand s so-elastc. In that case, s = n = 1 < E < k +1 n (15). Even absent the perverse case, our exportng equlbrum, whch s ruled out by ther assumpton that P m < C', n fact provdes another way of resolvng the ambguty. In such an equlbrum, as noted several tmes above, the home market prce and quantty are determned as f domestc frms faced the same constant and dentcal margnal cost P x, even f ther ndvdual margnal producton costs are dspersed and ncreasng n q. The same apples to comparatve statcs nvolvng the welfare expresson. For, as can be seen from Fgure 2, profts correspondng to area OP 1 C (n Case I) reman unchanged and only profts correspondng to P 1 q 1 NB' change as the quota s vared -- exactly as f margnal costs were constant at P 1. Changes n consumer surplus and quota rents depend on the domestc prce, whch agan s determned by ths "as f" MC. Ths allows us to replace C' wth P x n (25). Ths stll does not resolve the ambguty, but n Case I where essentally P m = P x, we get dw dq dq =(P - P x )( + 1) (26) d q whch s strctly postve, by the Lemma n secton 3.2. Clearly, ths wll contnue to hold f the gap between P m and P x s not too large. Thus, extendng the Eldor-Levn result, PROPOSITION 5: Wth quota rents accrung to domestc resdents, relaxaton of a quota mproves welfare f t ether (a) has an expansonary effect on domestc output, or (b) the mport prce s lower than domestc margnal costs, or (c) the domestc ndustry exports at a prce that s not much lower than the mport prce. 21

22 If there are exports and transport costs are too hgh, quota lberalzaton may result n a welfare loss. Ths s attrbutable to the wasteful cross-haulng of the same good, as demonstrated n a dfferent context by Brander and Krugman (1993). 13 If the quota s pre-empted by the monopolst at aucton, relaxaton has no effect on welfare; t merely transfers some rents to the government wthout beneftng consumers. In the case of Voluntary Export Restrants (VERs), however, quotas are allocated to foregn supplers and the rents go abroad. (By the same token, they cannot be auctoned at home, and there s thus no queston of a domestc frm pre-emptng them.) Eldor and Levn (1990) showed that a VER that margnally relaxes an mport prohbton necessarly reduces welfare. It can be easly shown that ths result depends once agan on ther rulng out perverse output responses to the QR. Droppng the last expresson on the rght sde of (23) now gves dw dq dq dq =(P - C ) - p q( + 1 ) (27) dq dq Evaluated at q = 0, the sgn of ths s dentcal to that of dq/d q. The Seade condton allows the sgn of ths dervatve to be postve n certan crcumstances, and the Eldor- Levn result can be thus be qualfed and generalzed as PROPOSITION 6: A voluntary export restrant that margnally relaxes an mport prohbton ncreases (decreases) welfare f E s greater (less) than n. In Case I, where an mport prohbton results n exports, P x as usual replaces C' n (23): the one-for-one dverson of output from the shrnkng domestc market nto 13 In the present formulaton, transport costs erode the margn for quota rents -- whch s also why they do not fgure explctly n the analyss of VERs that follows. 22

23 exports softens the mpact of mport penetraton on domestc profts and welfare. Ths margnal relaxaton of a prohbtve QR s rather unnterestng, and for nonzero VERs the second term n (27) counteracts any negatve effect from the frst term. Eldor and Levn showed that the effect of further relaxaton can be descrbed as a U- shaped relatonshp between the welfare level and the permtted level of mports. Farrell and Shapro (1990) obtaned a very smlar result for a domestc olgopoly, by treatng a tghtenng of an mport quota as analogous to an output-reducng merger by foregn frms, whle Syropoulos (1996) drectly modeled VERs selectvely mposed on a subset of foregn frms to yeld a smlar result. In the specal case of lnear demand and constant costs, they showed that welfare reaches a mnmum where mports provde for half of domestc consumpton, and then rses agan as the VER s relaxed further. 14 However, t s possble to derve some addtonal results wth lnear demand, n Case I of the present model. In order to show that the ensung result carres over to extend the earler authors' non-iit models wth constant costs, and to explot readers' famlarty wth expressons for a domestc olgopoly equlbrum, I shall use c to represent the margnal cost level, whch can be replaced by P x n the approprate context. Wth lnear domestc demand P = a - b( nq + q ), the th frm's proft functon becomes Π = [a - b( q + q + q ) - c] - q (28) The usual technques gve us the symmetrc equlbrum quantty q( q )= a - bq - c b(n + 1) (29) 14 Dxt (1984) and Rchardson (1998) obtan smlar welfare results for the entry of olgopolstc foregn frms nto the domestc market under free trade. The results are smlar to the relaxaton of a VER because foregn profts do not enter domestc welfare, just lke the quota rents for a VER, and because of the assumpton of Cournot competton. The latter means that domestc frms treat the quantty suppled by each foregn frm as gven, so that comparatve statcs wth respect to an exogenous change n the number of foregn frms s the same as that wth respect to an exogenous change n a VER. Ths holds whether the VER apples to all or only some foregn frms, provded the restraned and unrestraned frms have the same costs, as n Syropolous (1996). 23

24 Welfare s the sum of consumers' and producers' surplus: W = a(nq + q ) - b[(nq + q ) 2 ]/2 - P(nq + q ) + n(p - c)q (30) Substtutng (29) nto (30) and smplfyng, q (2n + 1) - 2nbq(a - c) b W = 2 2b(n + 1 ) n(n + 2)(a - c ) 2 (31) Dfferentatng (31) wth respect to q and equatng to zero gves a smple expresson for the VER level at whch welfare s at a mnmum: n(a - c) q Wmn = b(2n + 1) (32) Substtutng ths back nto (29) gves q( q Wmn a - c )= b(2n + 1) (33) It can be easly shown that the quanttes gven by (32) and (33) correspond to an mport share of half the domestc market, as shown by the authors mentoned above. However, gong a step further, the reduced-form expressons enable us to calculate the mnmum welfare level tself. Substtutng (32) nto (31), W( q Wmn 2 n(a - c ) )= b(2n + 1) (34) Ths s the trough of the U-shaped curve mentoned above. Evaluatng (31) at q = 0 gves the welfare level under autarky: 24

25 2 n(n + 2)(a - c ) ( 0) = (35) 2b(n + 1 ) W 2 Dvdng (34) by (35), 2 W Wmn ( q W (0) ) 2(n + 1 ) = (2n + 1)(n + 2) (36) It can readly be seen that ths expresson s equal to 8/9 for n = 1, and rses asymptotcally to unty as n ncreases. Further, equatng the expressons n (31) and (35) gves the crtcal VER at whch welfare recovers to the autarky level (that s, where the rght branch of the U rses to the level where the left branch began): = q c 2n(a - c) b(2n + 1) (37) Substtutng ths nto (29) gves the output level of the representatve domestc frm at ths crtcal level of the VER: a - c q( q )= c b(2n + 1)(n + 1) (38) Fnally, the market share of mports at ths crtcal level can be obtaned as q c qc + nq( q c 2(n + 1) = ) 2n + 3 (39) Eldor and Levn (1990) showed for a domestc monopoly (n =1) wth constant costs that relaxaton of the VER returns welfare to ts autarky level when mports capture 80% of the home market. (39) generalzes ths to domestc olgopoly wth possbly dspersed and ncreasng costs, showng that the larger the number of domestc frms, the 25

26 greater the mport penetraton requred to restore the autarky level of welfare. 15 Wth even a handful of domestc frms, the requred level of mport penetraton could be well over 90%. The new results derved here can be summed up as PROPOSITION 7: Wth lnear domestc demand, f all domestc frms ether (a) export under autarky or (b) have constant and equal margnal costs, then relaxng a VER reduces welfare by upto 1/9 of the autarky level, and restores the autarky level only when the restrcted mports capture at least 80% of the domestc market. Paradoxcally, the crtcal level of the VER gven by (37) at whch welfare s restored to the autarky level s qute lkely to exceed the free trade level of mports! Further relaxaton beyond ths level gven does rase welfare towards ts free trade level; ths may even occur as a dscontnuous jump at more restrctve VERs, f the defecton repeatedly mentoned above causes an IIT equlbrum to break down. For these two reasons, the U-shaped curve relatng welfare to the level of mport penetraton should be more accurately descrbed as a J-curve. Admttedly, QRs that restrct mports to "only" 80% or more of the market are unheard of, and a government that has already allowed ths level of mport penetraton would surely prefer free trade. However, snce tghtenng the usual knd of restrctve VER can mprove profts, welfare and the trade balance (even wth IIT), concevably t can appeal to some governments, who mght prefer to clmb the left-hand branch of the J rather than slde nto ts trough wth partal lberalzaton. 6. Conclusons Ths paper has presented a model of ntra-ndustry trade n dentcal or vertcally dfferentated products n a settng that has not been explored before for ths purpose: 15 A smlar result on entry by foregn olgopolsts under free trade s derved n Bhattacharjea (2000). See also the prevous footnote. 26

27 olgopoly at home and competton n the rest of the world. Admttedly, ths s only one of several possble market structures, but there seems to be growng recognton amongst theorsts that dfferent models are needed to analyze dfferent products enterng nto nternatonal trade. The model also lacks the grandeur of general equlbrum models of IIT, and does not even pretend to model the mcrofoundatons for vertcal product dfferentaton. It also cannot predct the extent and pattern of IIT between specfc pars of countres wth dfferent characterstcs. Gven these lmtatons, n terms of ts postve predctons, the model shows that QRs can nduce IIT n a narrowly defned commodty, consstent wth vrtually any level of the Grubel-Lloyd ndex. The QR must be loose enough to allow for some mports, but not so loose as to cause the reverson to the free trade outcome dscussed above. The threshold levels of the QR that demarcate the range where IIT occurs depend on the confguraton of domestc demand, frm costs, world prces, and transport costs (or qualty dfferentals). It s hardly surprsng, then, that the relatonshp between QRs and IIT has not been pcked up by cross-secton econometrc studes. On the prescrptve sde, the model shows that although a QR can promote exports, t causes a welfare loss, except locally n the case of an already restrctve VER. For the specal case of lnear demand, I demonstrated results that went some way beyond those n the exstng lterature to show the extent of welfare loss resultng from the relaxaton of such a VER., wth or wthout IIT. 27