Intra-Industry Trade in Intermediate Products, Pollution and Internationally Increasing Returns *

Transcription

1 Itra-Idustry rade i Iterediate Products, Pollutio ad Iteratioally Icreasig Returs * By Michael Bearroch ad Rolf Weder** his Versio: Noveber 2003 [he paper is curretly (March 2004 i revisio. If you quote it, please ask the authors for a revised versio.] Abstract: his paper exaies the relatioship betwee itra-idustry trade i iterediate products, pollutio ad icreasig returs. We develop a two-coutry odel i which productio occurs i two stages, fial ad iterediate good productio. Iterediate goods are produced uder oopolistic copetitio ad fial good productio exhibits icreasig returs with respect to the uber of varieties of iterediates. Pollutio occurs i the productio of the fial good whe pollutig iterediates are used. We aalyze the effects of iteratioal trade i iterediate products o pollutio, output ad welfare uder both a exogeous ad edogeous tax sceario. he results show that, because of icreasig returs, iteratioal trade either leads to lower total pollutio i each coutry or lower pollutio per uit of output i at least oe coutry. I additio, if pollutio taxes are exogeous trade causes coutries to iport the eviroetal quality of their tradig parters. Keywords: rade ad Eviroet, Itra-Idustry rade, rade i Iterediate Products JEL Classificatio: F2, F8 * We wish to thak Bria Copelad as well as participats of seiars at the Uiversity of Basel, Lakehead Uiversity, Uiversity of British Colubia, Caadia Ecooics Associatio Aual Meetig, Swiss Ecooics ad Statistics Associatio Aual Meetig, ad the Midwest Iteratioal Meetigs for helpful coets. Michael Bearroch ackowledges SSHRC for fiacial support. **Authors' address: Michael Bearroch, Departet of Ecooics, Uiversity of Wiipeg, 55 Portage Aveue, Wiipeg, Maitoba, R3B 2E9, Caada, eail:.bearroch@uwiipeg.ca. Rolf Weder, Departet of Ecooics (WWZ ad Europaistitute, Uiversity of Basel, Petersgrabe 5, CH-4003 Basel, Switzerlad, eail:rolf.weder@uibas.ch.

2 . Itroductio he literature o trade ad eviroet has priarily cocetrated o the iteractio betwee iter-idustry trade ad the eviroet, i.e. o trade drive by coparative advatage based o cross-coutry differeces (see Copelad ad aylor (2003. he ephasis of this literature has bee o exaiig how trade alters the aout of pollutio geerated withi coutries whe idustries or firs igrate fro oe coutry to aother coutry, the pollutio have hypothesis (Boer (999, Markuse, Morey ad Olewiler (993, ad Birdsall ad Wheeler (992, or whe a coutry specializes i productio of a dirty good due to coparative advatage based o factor abudace (Siebert (985 ad Copelad ad aylor (994. Oe of the ai cotributios of this iter-idustry literature has bee to separate the effects of trade o the eviroet ito a scale, techique ad copositio effect (Grossa ad Krueger (995, Copelad ad aylor (994, 997. he iportace of itra-idustry trade i overall trade is, however, well docueted i the literature. A large proportio of the icrease i iteratioal trade i the recet past is due to growth i itra-idustry trade. his is particularly true for developed coutries though there is soe evidece of growig itra-idustry trade betwee OECD ad less developed coutries (haraka (984. Much of this icrease i itra-idustry trade is across aufactured goods, soe of which are the ost pollutio-itesive idustries i.e. cheicals, iig, pulp ad paper, etallurgy (Fug ad Maechler (2000 ad Markuse et. al. (995 ad petrocheicals (Berhofe (999. he purpose of the curret paper is to exted the literature by cosiderig the effects of trade o the eviroet i the presece of itra-idustry trade ad icreasig returs. o this ed we costruct a two-coutry odel of itra-idustry trade i iterediates to exaie the

3 2 relatioship betwee iteratioal trade ad pollutio. Productio is assued to occur i two stages ad i a fashio siilar to that foud i Ethier (982. I the first stage, ay varieties of two iterediate products are produced with oe factor of productio i a oopolistically copetitive arket odeled siilar to Kruga (980. Both iterediate goods are traded iteratioally ad o pollutio is geerated i this first stage. I the secod stage, oe fial otraded good is produced uder perfect copetitio by cobiig the two iterediate products. As i Ethier (979, 982, there are exteral ecooies i fial good productio with respect to the uber of varieties of each iterediate product. Pollutio is created whe the dirty iterediate is used i fial good productio. he pollutio tax is thus, paid by the producers of the fial good. he paper is otivated by the observatio that i ay idustries pollutio arises i the productio of a fial good whe certai iterediate products are used. he odel is iteded to capture the otio that i certai sectors productio is ade up of a ix of ay iterediates. Soe of these iterediates are eviroetally friedly, while others are ore harful to the eviroet. 2 How producers egaged i itra-idustry trade choose to allocate resources betwee clea ad dirty iterediates, ad the effect of both a eviroetal tax ad iteratioal trade o this choice are the ai issues we cosider. As is well kow i odels of itra-idustry trade with oopolistic copetitio, iteratioal trade allows coutries to access a greater variety of products. I the curret odel, this creates the possibility that trade will yield iteratioally icreasig returs (Ethier, 979, ad a icrease i output without ecessarily raisig pollutio. I fact, pollutio ay eve fall with trade. o our kowledge there are few trade ad eviroet papers that allow for itra-idustry trade. Fug ad Maechler (2000, eploy a odel with itra-idustry trade drive by

4 3 iteratioal oligopolies that cocetrates oly o the copositio effect. I this paper the global ecooy ca beefit fro trade if pollutio is trasboudary ad the ost pollutio-itesive coutry liberalizes trade. Gürtzge ad Rauscher (2000 ad Chapter 6 i Rauscher (997, o the other had, adopt Kruga s odel of oopolistic copetitio to exaie issues relatig to trasboudary pollutio. Gurtzge ad Rauscher (200 fid that if eissios per fir are fixed ad the hoe coutry chooses a tight eviroetal policy, pollutio ca fall i both coutries. Ulike these papers, we show that tighter eviroetal policy ca lead to lower pollutio i both coutries without the eed to itroduce trasboudary pollutio, fixig either the aout of pollutio per fir or the eviroetal tax rate, or cocetratig solely o the copositio effect. Our aalysis leads to a uber of iterestig results. For exaple, we fid that trade leads to higher output of the fial good because it allows coutries to gai access to a greater variety of iterediate iputs ad take advatage of the iteratioal returs to variety. With costat returs i the pollutio fuctio, total pollutio ca fall with trade. his provides a alterative theoretical explaatio for the epirical result foud i Atweiler, Copelad ad aylor (200 that trade ay lower pollutio. Whe the pollutio fuctio exhibits icreasig returs, both output ad pollutio always rise with trade. Pollutio per uit of output ca however, rise or fall i a coutry depedig o the relative eviroetal tax rates betwee the coutries. he coutry with the lower eviroetal tax, the coparatively dirtier coutry, will experiece a relatively saller icrease i pollutio tha the coutry with the higher eviroetal tax. Pollutio per uit of output will therefore, fall i the dirtier coutry. Rather tha the dirty coutry becoig dirtier, as with trade based o coparative advatage, this coutry attracts a relatively larger proportio of clea iterediates to be used i doestic fial good productio. Regardless of how pollutio is odelled or whether the eviroetal tax rate is fixed or edogeous, itra-idustry

5 4 trade works to equalize pollutio per uit of fial good productio across coutries. he rest of the paper is structured as follows. he odel is outlied i Sectio 2. he autarky equilibriu ad the pollutio dead ad supply fraeworks are derived i Sectio 3. Sectio 4 ad 5 deterie the free-trade equilibriu with a exogeous ad edogeous pollutio tax respectively. I Sectios 3 to 5 the results are derived with icreasig-returs-to-scale i the pollutio fuctio, whereas i Sectio 6 the results are deteried with a pollutio fuctio subject to costat returs to scale. Coclusios are foud i Sectio he Model We assue there are two coutries, Hoe ad Foreig, ad oe hoogeeous cosuptio or fial good, Y, produced with two differetiated iterediates X ad X 2. here are ay varieties of the iterediate goods each produced with oe factor of productio, labour, uder oopolistic copetitio. Productio of the fial good exhibits costat returs to scale with respect to the quatity of either iterediate good used i productio, but icreasig returs with respect to the uber of varieties of each iterediate good. he use of X i fial good productio Y geerates a egative exterality, pollutio, which adversely affects cosuer utility. Productio takes place i two stages. I the first stage, two differetiated iterediate goods are produced usig oly labour as a factor of productio. I stage two, the two iterediates are cobied to geerate a fial good, Y, which is cosued. Productio of the fial good requires that soe of each iterediate be used i productio but as i Ethier (982 is otherwise costless to asseble. he use of iterediate good X i fial good productio geerates a egative exterality, pollutio Z, which adversely affects cosuer welfare. Iterediate good X 2, coversely, does ot cause ay pollutio. 3 he odel s structure is otivated by the followig observatios. I the pulp ad paper

6 5 idustry, pulp is produced through a cheical pulpig process. Virgi wood is the priary iput but eergy, water, recycled paper ad chlorie are also used. he pulp is bleached before beig ade ito paper. I this process pollutats are released. Further, i the bleachig operatios chlorie is used to bleach pulp leadig to chloriated orgaic copouds i effluets that are liked to adverse health effects. he idustry is udertakig to reduce the foratio of copouds i effluets by usig ew cheicals, iproved bleachig techiques ad addig recyclable aterial to reduce the use of virgi tiber. I the textile dyig idustry, cheical dyes are ixed with water ad fabric to produce fiished textiles. For the fabric to absorb the dye, large aouts of salt are ixed ito the dyig copoud. Effluets ot absorbed i the garets lead to high phosphorus cocetratio i wastewater discharge. Ioizig the salt ad addig additioal cheicals ca iprove the dyig process. Soe dyestuffs ted to be ore copletely absorbed i the garets tha others ad thus, produce fewer effluets ad eviroetal probles. Fially, i agriculture, seeds are cobied with fertilizers, pesticides, soil ad water for productio. he developet of ew varieties of seeds, pesticides, cheical ad o-cheical fertilizers reduces the aout of eviroetal daage. Access to a wider variety of these eviroetally friedly iputs is critical to the reductio of eviroetal daage. Likig these observatios with the curret odel, oe could thik of Y as textiles, pulp ad paper, or agricultural goods produced with differet types of iterediates, where X 2 (X is coposed of a group of eviroetally (less friedly dyestuffs, cheicals or other iputs Productio Productio of the fial good, Y i.e. stage two is characterized by perfect copetitio with the followig Cobb-Douglas productio fuctio: Y = X X α ( α 2 (0<α<. (

7 6 Each iterediate, X ad X 2, is coposed of ay varieties that eter syetrically ito the productio fuctio. We describe this by a Dixit-Stiglitz (977 "love for variety" approach, origially used to deterie utility ad adopted for productio by Ethier (982. Followig Ethier (982, it is assued that each iterediate eters the productio fuctio for the fial good with the followig CES productio fuctios: X = x j ad 2 = X x2 j where >. (2 Note that the elasticity of substitutio,, is costat. he fuctioal for of equatio (2 esures that there are costat returs to scale with respect to output for each variety of the iterediate good, x ij, but icreasig returs with respect to the uber of varieties, ad. Substitutig equatio (2 ito ( yields the productio fuctio for the fial good Y. It iplies that firs sped a costat share, α ad ( α, of their total costs o the two iterediate goods, ad that derived dead for each variety is characterized by a costat price elasticity of. Productio of iterediates i.e. stage oe is characterized by oopolistic copetitio with each variety beig subject to icreasig returs to scale due to legth of rus or size of the plat. As i Kruga (980 there is oly oe factor of productio i iterediate goods aufacturig, labour, that is perfectly obile withi a coutry. he cost fuctios, i ters of uits of labour, for all varieties of both iterediate goods are give by: l ij = a + bx ij i=,2 (3 where l ij is the labour eployed i iterediate good i for variety j, a is a paraeter represetig fixed costs, ad b is a costat argial cost paraeter. We assue that each variety is produced with the sae cost fuctio. Moopolistic copetitio the leads to the usual ark-up pricig

8 7 rule-- wb = pi (-/ --where w is the wage rate ad p i is the price of iterediate X or X 2. he profit-axiizig price is the: p ij = wb(/(-. (4 With free etry ad icreasig returs to scale, profits for each fir are drive to zero ad i equilibriu oly oe fir produces each variety. Settig the represetative fir s profit equal to zero ad substitutig for the price fro equatio (4 yields π ij = wb(/(-x ij - w(a + bx ij = 0. Sice all firs i both iterediate goods sectors face the sae cost fuctios ad elasticity of substitutio, the profit fuctio applies to all varieties ad ca be solved for output: x ij = (-(a/b. (5 he profit-axiizig level of output is the sae for all varieties of iterediates regardless of whether they are of type X or X 2. he sae is true for prices of all varieties as derived i equatio (4. his arises fro the siplifyig assuptio that products do ot becoe better substitutes with icreasig arket size, is costat. It also iplies that real wages i stage reai costat give that w = pi ( / / b. For siplicity we drop the subscripts o x ad p to save o otatio: x j = x 2j = x ad p j = p 2j = p. Fially, the icreasig returs at each stage of productio are the sae as i Ethier (982. I stage these are referred to as atioal ecooies of scale ad are equivalet to a fir ovig dow its average cost curve as productio rises. I the secod stage, the ecooies to variety are referred to as iteratioal returs. hey occur because with trade i iterediate products, fial good producers gai access to a wider rage of iterediate varieties Cosuptio ad Welfare With oe good beig cosued, Y, atioal welfare is directly related to total

9 8 cosuptio of this good ad egatively related to the level of pollutio. I odellig welfare we use Stokey s (998 fuctioal for to odel the utility of our represetative cosuer: U δ ( Y / L = βz δ where, β>0 ad δ>0. (6 he paraeter β is the argial disutility of pollutio; the higher is β the larger the disutility of pollutio. Utility is decreasig i pollutio, Z, but icreasig with per capita cosuptio. Further, utility is positive for ay value of δ>0 as log as (Y/L -δ > ad βz is sufficietly sall. 6 o coplete the odel it is assued that cosuers do ot save ad thus sped their etire icoe o cosuptio of Y. he budget costrait is therefore: wl + τz = PY, (7 where, P is the price of the fial good. otal icoe is coposed of labour icoe, wl, ad eviroetal tax reveue, τz, as the reveue is fully rebated to cosuers. he eviroetal tax,τ, is levied o the pollutio arisig fro productio of Y. Give the pollutio ad productio relatioship described above, ad assuig perfect iforatio, firs otice that the goveret iplicitly taxes the use of iterediate good X i fial productio. 2.3 Pollutio We ow cosider how dirty iterediates geerate pollutio i fial good productio. I Sectios 3, 4 ad 5 of the paper it is assued that pollutio is proportioal to the aout of the dirty iterediate used i fial good productio specify. For a closed ecooy the pollutio fuctio is specified as Z = X = /(- x. With this fuctio, the geeratio of pollutio exhibits icreasig returs with respect to the uber of varieties, : usig a larger uber of varieties, but a proportioally saller quatity of each dirty variety, leads to a icrease i output ad pollutio. Oe such exaple could be a textile factory that uses a greater uber of differet

10 9 cheicals, dyestuffs etc., but a saller quatity of each of variety, which produces both a larger aout of fiished textiles ad wastewater discharge or pollutio. Likewise, a far that uses ore fertilizers ad pesticides geerates ore output ad pollutio. A secod possibility, discussed i Sectio 6 of the paper, is that the pollutio fuctio exhibits costat returs with respect to the uber of varieties of the dirty iterediate so that Z=x<X. his iplies that with greater variety the iterediates becoe ore highly specialized so that ore output is produced but less waste or pollutio is geerated per uit of output. With ore varieties of dyestuff for exaple, there is a icrease i the degree of absorptio of dyes i the fabric. A greater variety of iputs thus, allows producers to ore accurately tailor the use of each iput to their eeds. Less goes to waste ad fial good productio rises faster tha pollutio. 3. Autarky Equilibriu hroughout the paper we deote the foreig coutry by * ad assue both coutries levy a eviroetal tax o pollutio. We allow for the possibility that the coutries are idetical but also cosider the case where the tax rates are ot equal across coutries. 3. Exogeous ax Rate I order to derive the equilibriu level of pollutio ad output i autarky, we deterie total dead for each group of iterediates ad the set total dead equal to supply. otal derived dead for the two iterediates is deteried by the profit-axiizig coditios for fial good productio. Give the productio fuctio, firs sped a costat shareα of their total costs o X ad ( α o X 2. akig ito accout the coutry's budget costrait fro equatio (7, the derived dead fuctios for X ad X 2 at Hoe ad abroad are give by:

11 αpy α( wl + τx X D = = ad p + τ p + τ 0 ( α PY ( α( wl + τx X D 2 = =, (8 p p αpy α( wl * + τ * X * X * D = = ad p + τ * p + τ * ( α PY ( α( wl * +τ * X * X * D 2 = =. p p where tax reveue is τ X ad τ * X *, respectively. Assuig both coutries face the sae cost fuctios, their dead fuctios are the sae with the exceptio that the tax rate, the size of the labour force ad the uber of varieties produced. Supply of the two iterediates is deteried by the optial quatity of each variety, equatio (5, ad the edogeous uber of varieties, ad. I the hoe coutry we fid: ( ( a X S ( ( a = x = ( ad X S 2 = x = (. (9 b b otal supply for the foreig coutry is derived i the sae aer. o deterie the uber of varieties of X ad X 2, equate dead, (8, ad supply, (9, for the two iterediates ad use (4 for the profit-axiizig price. With a give eviroetal tax, τ, the equilibriu uber of varieties, ˆ ad ˆ, for the hoe coutry are: αlp ˆ = ( τ ( α a + p ( α L( τ + p ˆ = ( τ ( α a + p ( - ( - αl = a ( αl = a p ( τ ( α + p ( τ + p - ( τ ( α + p, - (0 he equilibriu ubers are aalogous i the foreig coutry. he uber of varieties depeds positively o the share of each iterediate i fial good productio, α ad ( α, ad the size of the coutry, L or L*. It egatively depeds o fixed costs, a. he ratio of clea varieties,, to dirty varieties,, is larger i the coutry with a higher tax. Differetiatig equatio (0 with

12 respect to τ shows the chage i the uber of varieties for a give chage i the tax rate: ˆ ( αl( α p = τ a τ [ ( α + p] ˆ ( αl( α p = τ a τ [ ( α + p] 2 2 ˆ ˆ < 0, > 0. ( A argial icrease i the eviroetal tax reduces (icreases the uber of dirty (clea iterediates used i the ecooy. otal pollutio thus, decreases. Due to the syetry i productio costs across the two varieties however, the total aout of the two iterediates, the su of X ad X 2, is idepedet of the eviroetal tax. Substitutig the optial uber of varieties (0 ito supply (9, ad the suig the derivatives of X as well as X 2 with respect to the tax rate yields: X X 2 + τ τ αl( α px + ( α Lαpx = = 0 2. (2 a[ τ ( α + p] I spite of the fact that the su of the iterediates reais costat, output decreases. here is a trade-off betwee eviroetal quality ad productio of the fial good i autarky. his is show by differetiatig the productio fuctios, equatios ( ad (2, with respect to τ, substitutig for ad fro equatio (0 ad for / τ ad / τ fro equatio (: Y τ ( α py = τ( α + p p + τ < 0. p (3 If the goveret raises the eviroetal tax, fial good producers face a higher price for pollutio ad, therefore, substitute clea varieties for the dirty iterediate. By chagig the productio techique, producers caot fully copesate for the higher eviroetal tax; the cost of producig the fial good rises ad total productio declies.

13 2 Propositio : A eviroetal tax (τ>0 raises a coutry s relative cost of usig the dirty iterediate ad thus icreases relative derived dead for clea iterediate products. Ceteris paribus, this techique effect leads to a decrease i pollutio ad output of the fial good. 3.2 he Optial ax Rate We ow deterie the hoe coutry's optial eviroetal tax i autarky. o derive the tax, axiize aggregate utility with respect to Y ad Z, subject to the coutry s budget costrait. he solutio to the axiizatio proble yields the optial pollutio tax which is give by the failiar coditio that the price of pollutio,τ, is equal to the argial daage of pollutio: τ = β δ δ δ Y PY L = PY (4 β L he pollutio tax is directly related to the argial disutility of pollutio, β, ad total icoe, PY. For values of δ> it is also positively related to per capita cosuptio of the fial good, Y/L. As δ approaches, the optial tax rate coverges to that foud i Copelad ad aylor (997, τ=βpy, ad thus oly depeds o the argial disutility of pollutio ad total icoe. 3.3 Pollutio Supply ad Dead akig ito accout Hoe's budget costrait (wl+τz=i, the pollutio supply fuctio, Z S, ca easily be derived by substitutig i for the tax rate: Z S τ : = w ( Y ( Y βl S L L ad thus Z =. (5 δ βz β τ / w L he pollutio supply curve correspodig to equatio (5 is depicted i Figure by Z SA. he itercept of the pollutio supply curve is equal to βl(y/l δ-. δ

14 3 Supply of pollutio is a icreasig fuctio of the relative price of pollutio, τ/w. With a higher price of pollutio, cosuers are willig to supply, or accept, a greater aout of pollutio because they are copesated by icreased icoe ad cosuptio of Y. he pollutio supply curve shifts to the left with icreases i β because there is greater disutility cost of pollutio ad a lower supply at ay give pollutio price. If δ> the pollutio supply fuctio shifts to the left as per capita icoe rises. he effect of a chage i L o the positio of the pollutio supply curve depeds o the value for δ. If <δ<2, the pollutio supply curve shifts upwards with higher L. A icrease i the willigess to pay for eviroetal quality caused by a higher L, leads to a reductio i pollutio supply. 7 For δ>2, a icrease i L shifts the supply curve dowwards. o deterie the pollutio dead curve take ito accout the fact that total dead for pollutio by producers of the fial good i equilibriu is equal to the derived dead for X. Usig equatios (0, (5 ad (4 the pollutio dead fuctio, Z D, is give as: Z D IRS τ : = w αl b D αl ; Z IRS =. (6 Z( α ( α( ( α τ / w + b /( he pollutio dead curve, Z DA, is dowward slopig, see Figure. Pollutio dead is decreasig i τ/w because with a higher relative price of pollutio, firs substitute X 2 for X ad decrease their dead for pollutio. Dead shifts to the left with icreasig b sice a rise i argial costs lowers output ad dead for both iterediates ad pollutio. Dead shifts to the right with a icrease i α or L. A rise i α, causes productio of the fial good Y to becoe ore pollutio-itesive, whereas a icrease i L raises total icoe ad dead for good Y ad pollutio. he optial level of pollutio, Z A, ad the eviroetal tax, τ A, i autarky are the foud by equatig pollutio supply ad dead as i Figure. 8

15 4 I the reaider of the paper we cosider the effects of iteratioal trade o pollutio levels i each coutry. Iteratioal trade will affect pollutio through a chage i pollutio dead, ad possibly supply. Give that pollutio is geerated i fial good productio, fial good producers pay the tax for the use of iterediate X regardless of where the iterediate good is produced. While the tax alters each coutry s dead for the iterediate, it has o effect o either the cost of producig X or its price. rade is beeficial because with oopolistic copetitio ad icreasig returs i iterediate goods productio, each variety of the iterediate will oly be produced i oe coutry. 9 Gais fro trade are geerated because, as i Ethier (982 ad Meade (952, the extet of the arket is expaded with trade thereby allowig producers of the fial good to beefit fro the icreased variety of iterediates available to each coutry. 4. Free-rade Equilibriu with a Exogeous Pollutio ax I this sectio we cosider the effects o atioal pollutio levels ad welfare whe the two coutries freely trade iterediates with oe aother. We assue that there is o trade i the fial good ad that trasactio costs are zero. While the patter of productio ad trade is ideteriate, the uber of varieties produced i the world, fial good productio, the level of pollutio ad welfare i each coutry are ot. Moreover, it is iportat to ote that the pollutio tax is levied oly o the aout of X that is used i fial good productio, Y, ad ot o the aout of X that is produced i a coutry. I the tradig equilibriu, the total uber of varieties produced i the itegrated arket will equal the su of the varieties produced i autarky. his occurs for two reasos: (i the eviroetal tax rate is costat so that there is o techique effect, ad (ii the elasticity of substitutio is costat ad does ot chage with a risig uber of varieties. 0 he equilibriu

16 5 uber of varieties produced for X ad X 2 uder free trade ca thus, be easily foud fro (0: + * = αlp ( τ ( α a + p ( α L( τ + p + * = ( τ ( α a + p. ( - ( - αl * p + ( τ * ( α a + p ( α L * ( τ * + p + ( τ * ( α a + p ( - ( -. (7 he hoe ad foreig coutry each use +* varieties of X ad +* of X 2 i the tradig equilibriu. Fial good producers i each coutry therefore, use ore varieties of each iterediate good, though world dead for ay idividual variety of the iterediate goods, x, does ot chage. I the hoe coutry, the derived dead for each iterediate is X = x ( + * x ad X 2 = ( + * ( + * ( + *, (8 whereas i the foreig coutry it is: X * = x * * ( + * x ad X 2 = ( + * ( + * * ( + *. (9 Derived dead for each variety is thus, equal to x j = x ad x 2 j = x i ( + * ( + * hoe ad * * * * x j = x ad x 2j = x abroad. he share of each variety deaded ( + * ( + * by a coutry is equal to the coutry s share of the total uber of varieties produced i autarky, for exaple (/(+* for X i the hoe coutry. he shares are positively related to coutry size, ad i the case of clea (dirty varieties positively (egatively related to the tax rate. he free-trade level of fial good productio, Y, is obtaied by substitutig equatios (8 ad (9 ito equatios ( ad (2. For the hoe coutry this is give by

17 6. ( ( ( ( ( * ( * * ( * α α = x x Y (20 Dividig Y by the output i autarky, Y A = α/(- x α (-α/(- x (-α, shows that fial good productio relative to autarky output rises with free trade:. * * > + + = α α Y Y A (2 A aalogous result ca be foud for the foreig coutry. otal pollutio ad welfare ca the be coputed. With icreasig returs with respect to variety i the pollutio fuctio, total pollutio rises with trade i both coutries. his ca easily be see by takig the ratio of pollutio i free trade, Z, with pollutio i autarky, Z A : ( ( * * * > + = + + = x x Z Z A. (22 A aalogous equatio ca be derived for the foreig coutry. he questio reais as to whether pollutio per uit of output rises or falls with trade. o aswer this questio we take the ratio of output to pollutio i free trade versus the ratio i autarky ad ake use of equatios (2 ad (22:. * * * ( * ( * * * / / / / + + = + + = = = α α α α Z Z Y Y Z Y Z Y A A A A (23 Whether, pollutio per uit of output rises, falls or reais costat with trade depeds o the value of the last ter i the brackets of equatio (23. his sig, i tur, depeds o whether the

18 7 ratio of clea to dirty iterediates at hoe copared to the foreig coutry i autarky, (*/(* is greater tha, less tha or equal to oe. Substitutig ito equatio (23 for (*/(* fro the equatios for the equilibriu uber of varieties, equatios (0 ad (7, yields: * * = p + τ * p + τ > * = * < iff τ < τ * τ* = τ. τ > τ * (24 his shows that for τ>τ*, (*/(*< ad (Y /Z /(Y A /Z A <. Equatio (24 iplies that pollutio per uit of output ca rise, fall or stay the sae with trade depedig o the relative tax rates i the two coutries. If the tax rate is higher (lower at hoe, the trade will cause pollutio per uit of output to rise (fall at hoe. he reaso is that a higher tax rate is associated with a higher ratio of clea to dirty varieties of the iterediates used i fial good productio i autarky. With trade, however, the hoe coutry gais access to the relatively larger uber of dirty varieties used i the foreig coutry. It therefore, eploys a higher ratio of dirty to clea iterediate products with trade thereby raisig pollutio per uit of output. he opposite is true whe hoe has the lower tax i autarky. his copositio effect of itra-idustry trade causes the coutry that is dirtier (cleaer i autarky to becoe coparatively cleaer (dirtier after trade. With itra-idustry trade a coutry iports its tradig parter s eviroetal quality through chages i the ratio of the dirty to clea iterediate. Pollutio per uit of output, cosequetly, falls i the dirty coutry ad rises i the clea coutry so that the gap i pollutio per uit of output for coutries with differet eviroetal taxes declies. his stads i sharp cotrast to the results foud i the trade literature i which, coutries with weaker eviroetal stadards have a coparative advatage

19 8 i pollutio-itesive goods ad becoe pollutio haves through the copositio effect. o derive the chage i welfare for the represetative residet of each coutry cosider the fact that both pollutio ad output rise with trade. Whether welfare icreases or decreases depeds o the level of pollutio per uit of output i autarky versus free trade. he total differetial of the utility fuctio, equatio (6, yields the chage i welfare: Y du = L = ( δ ( δ ( Y α β dx + ( Y L dx α X X dx + ( α X L 2 2 ( δ βdx dx ( α X 2 2. (25 As show above, the use of each iterediate rises with trade so that dx ad dx 2 are positive. Whether welfare icreases with trade the depeds o the value of ( β L X Y ( δ α. Give that β adα are costat, a sufficiet but ot ecessary coditio for welfare to rise with trade is Y L ( δ that ( α βx. With both α ad β costat while Y as well as X (=Z are icreasig with trade the beefit of greater fial good productio declies as pollutio levels rise withi a coutry. Propositio 2: With a exogeous eviroetal tax, trade i iterediate products icreases output ad pollutio whe the pollutio fuctio exhibits icreasig returs with respect to varieties of the iterediate good. Pollutio per uit of output at hoe coutry rises (falls with trade if τ>τ* (τ<τ*. Welfare uabiguously rises if the level of pollutio is sufficietly low. Oe ca separate the effects of pollutio ito a scale, techique ad copositio effect. With a exogeous tax rate there is o chage i the relative price of X to X 2 ad thus, there is o techique effect. he scale effect is however, positive because with a greater variety

20 9 of iterediates both iterediate ad fial good productio expads. his scale effect thus, leads to higher pollutio. I Figure, the pollutio dead curve would shift to the right (scale effect, whereas the pollutio supply curve would be perfectly elastic at the give tax rate (o techique effect. he copositio effect depeds o the relative tax rates betwee the two coutries, equatio (24. If the tax rates are equal, τ * = τ, the there is o copositio effect sice both coutries have the sae ratio of clea to dirty iterediates i autarky ad free trade. Whe τ* τ however, there is a copositio effect. A higher (lower tax rate i the foreig coutry iplies that the hoe coutry will use a lower (higher proportio of dirty iterediates i the tradig equilibriu, the pollutio dead curve shifts to the left (right. Pollutio per uit of output cosequetly falls (rises with trade, partially offsettig (reiforcig the scale effect. rade causes coutries to iport the eviroetal quality of their tradig parters. 5. Free rade with a Optial (Edogeous Pollutio ax I this sectio we allow the optial eviroetal tax to be deteried edogeously. I autarky, A, it is assued that the tax is set at its optial level, τ A A = βp Y Aδ δ L A A Aδ adτ * = βp * Y * L * δ. he questio the arises as to whether ad to what extet the optial tax rate will chage whe we allow for iteratioal trade i iterediate products? I Sectio 4 it is show that whe the tax rate is fixed, trade leads to a icrease i fial good productio, per capita icoe, ad pollutio i both coutries. With a edogeous tax however, higher per capita output will put upwards pressure o the tax rate, see Sectio 3.3. he questio the reais as to whether pollutio will still rise with trade? I the curret sectio we eploy the pollutio dead ad supply aalyses to exaie how iteratioal trade affects the optial pollutio tax, total pollutio, pollutio per uit of output, ad welfare. I cotrast to

21 20 Sectio 4, the pollutio supply curve ow eters the aalyses because of the existece of a techique effect: the effect of a chage i the eviroetal tax o pollutio. he pollutio supply curve, Z S, describes the trade-off betwee icreasig the relative price of pollutio ad the willigess to accept higher pollutio. It reflects aggregate prefereces i the ecooy, which for values of δ are affected by chages i per capita icoe as show i Sectio 3.3. Whe ovig fro autarky to free trade the horizotal shift i the pollutio supply fuctio ca be deteried by the first derivative of equatio (5 with respect to output: Z S ( Y δ = ( δ L. (26 Y βy With δ> the positio of the pollutio supply curve will shift to the left as Y or per capita icoe icreases. 2 It is assued throughout this paper that the value of δ is ot so large as to cause Y to decrease with trade. his iplies that while the eviroetal tax rate will adjust to chages i fial good productio, it is ot so sesitive to chages i Y as to outweigh the beefits of trade. he pollutio dead curve, Z D, represets the trade-off betwee chages i the relative price of pollutio versus dead for dirty iterediates. With icreasig returs i the pollutio fuctio, the pollutio dead curve will shift to the right with a trade-iduced icrease i fial good productio, sice trade leads to higher derived dead for dirty iterediate products. With a greater uber of varieties of the dirty iterediate, both coutries experiece greater ecooies i fial good productio. Pollutio dead will, therefore, rise. I the tradig equilibriu, the pollutio dead curve is derived by substitutig (0 ad (7 ito the pollutio fuctio with icreasig returs ad usig (4 for p:

22 Z D IRS a( = ( + * αlb x = ( + * ( + * + 2 x = a( [( α τ / w + b /( ] αl * b αlb [( α τ / w + b /( ] a( [( α τ * / w + b /( ] he directio ad extet of the shift i the pollutio dead curve caused by trade is ost easily deteried by the chage i the horizotal itercept of the curve. Settig τ / w = 0 i (27 ad D DA takig the ratio of Z IRS with the itercept i autarky, Z [ ]x ( τ / w= 0 IRS = αl/(a, leads to: ( τ / w= 0 D Z αl αl αl * b ( τ/w= 0 = + > 0. (28 Z DA ( a a ( [( * / /( ] a α τ w + b Equatio (28 shows that with trade, the pollutio dead curve shifts to the right fro Z DA to Z D i Figure. his occurs solely because of the icreasig returs i the geeratio of pollutio. he directio of chage i fial good productio is foud by coparig the total aout of each iterediate i autarky versus the tradig equilibriu. Fial good producers gai access to a greater variety of iterediate iputs with trade. here are ( + * varieties of the dirty iterediate ad ( + * varieties of the clea iterediate used i each coutry, with a x (27 share ( + * ad ( + * of each iterediate x used i doestic productio ad the reaider i the foreig coutry. Output of good Y i free trade versus autarky is

23 Y Y A ( ( * + 22 ( ( * + ( ( + * + * = ( ( ( A A ( α ( α. (29 Give that the higher eviroetal tax causes a icrease i the uber of clea varieties i A A each coutry, > ad * > *, X > X ( α A( α 2 2 ( ad X * 2 > X * α A( α 2, a sufficiet though ot ecessary coditio for output of good Y to icrease with trade at hoe is that α Aα X X ad i the foreig coutry α Aα X X * *. Fro equatio (29 this requires that: ( ( + * ( + * A ( (. (30 A siilar coditio exists for the foreig coutry. Recall that it is assued that the eviroetal tax does ot rise by such a degree that output of Y will fall with trade. Give equatio (30 this iplies that the total uber of dirty iterediates i the world, the su of the varieties at hoe ad abroad, will ot shrik below the autarky value i either coutry i the tradig equilibriu, > A + * ad * A + * >. 3 If the opposite were the case, pollutio would always be lower i the tradig equilibriu relative to autarky due to the fact that eviroetal taxes would be very sesitive to icreases i output. Whe equatio (30 holds, the differece betwee ad A is relatively sall so that α Aα X X > ad A X X * * >, ad fial good productio rises i both coutries. 4 With the pollutio dead ad supply curves shiftig i opposite directios, the equilibriu level of pollutio depeds o the relative agitude of these shifts. With icreasig returs i the pollutio fuctio ad assuig that ( ad > * A A + * > ( + *, pollutio ust rise fro Z A to Z i the tradig equilibriu i spite of the higher pollutio tax,

24 23 τ A / w < τ / w, see Figure. he ituitio behid this result is as follows. Give that trade raises atioal icoe i both coutries, a edogeous tax rate leads to higher tax rates i each coutry. A higher tax rate, i tur, puts dowward (upward pressure o the derived dead for iterediate X (X 2 i both coutries. Fial good productio ad the aout of pollutio geerated by each coutry evertheless expad with trade because each coutry gais access to a larger uber of varieties of both iterediates. With icreasig returs to variety i both fial good productio ad the pollutio fuctio, both pollutio ad output ust rise. Oce agai we ca decopose the effects of trade ito a scale, copositio ad techique effect. he scale effect uabiguously raises the level of pollutio sice higher output requires greater use of the dirty iterediate. I ters of the copositio effect the coutry with the lower tax i autarky will experiece a relative shift towards cleaer iterediates with trade. 5 he techique effect, coversely, uabiguously lowers pollutio levels by reducig the ratio of dirty to clea iterediates i the world. he overall effect is, however, a higher aout of pollutio tha i autarky, with total pollutio risig fro Z A to Z i Figure. As i the exogeous tax case pollutio per uit of output ay or ay ot icrease with trade depedig o the relative tax rates i the two coutries i autarky. Equatios (0 ad ( show that copared to the tradig equilibriu with a exogeous tax, there are ow fewer dirty varieties, (+* exogeous > (+* edogeous, ad ore clea varieties, (+* exogeous < (+* edogeous. With fewer dirty varieties, pollutio will be lower i the edogeous tax tradig equilibriu copared to the exogeous tax case. otal output of fial good Y cosequetly, icreases by a relatively saller aout i the edogeous tax tradig equilibriu (equatio (3. Natioal welfare evertheless, rises copared to the exogeous tax case. By allowig the tax rate to adjust to its optial level welfare is axiized as show by equatio (25, whe the

25 24 ratio of X 2 used i fial good productio icreases copared to X welfare iproves. With higher tax rates, the ratio of the clea to the dirty iterediates used i fial good productio is higher ad pollutio per uit of output lower i the edogeous versus the exogeous tax case. Propositio 3: With icreasig returs i the pollutio fuctio iteratioal trade i iterediate products leads to a higher optial eviroetal tax ad greater total pollutio tha i autarky for both coutries. Pollutio icreases by a saller aout ad welfare is higher copared to the exogeous tax case. As stated above satisfyig equatio (30 is a sufficiet though ot ecessary coditio for fial good productio to rise. Eve if equatio (30 does ot hold, fial good productio could still icrease. I this case, the chage i the tax rate would be large eough to cause X to declie below its autarky levels but ot by a sufficiet aout to cause Y to fall. he ipact of X X 2 the techique effect is such that + = 0 τ τ (equatio (2, whereas the scale effect causes both X ad X 2 to icrease i both coutries. If α < 0. 5, the the clea iterediate akes up a larger share of fial good productio ad it is possible for equatio (30 to ot hold but productio of Y to icrease Costat Returs to Scale i the Pollutio Fuctio he results discussed above represet the case where the icreasig returs i productio also exted ito the geeratio of pollutio. hat is, as X productio rises, pollutio also ecessarily icreases. his case however, does ot allow for the possibility that the icreasig returs i productio ay ot fully be trasferred to the geeratio of pollutio. As etioed above, it ay be the case that icreasig the variety of iputs ito the productio process will cause output to rise at a faster rate tha pollutio. I this sectio we cosider the effects of trade

26 25 o pollutio whe the pollutio fuctio exhibits costat returs with respect to variety. Uder this sceario total pollutio is give by Z = x. If the uber of varieties,, doubles pollutio will double, but X will icrease by a factor greater tha two. 6. rade-equilibriu with a Exogeous Pollutio ax With costat returs i the pollutio fuctio, total pollutio i either coutry is equal to the uber of varieties used i fial good productio ultiplied by the aout of each iterediate eployed, Z=x at hoe. Give a exogeous tax rate, output, give by equatios (20 ad (2, rises i the tradig equilibriu. Both coutries gai access to a greater uber of A varieties of each iterediate, + * >, * A + * >, > A + * ad * A + * > with trade so that output of good Y rises. Pollutio o the other had is equal to: * Z = ( + x = x, (3 * ( + A aalogous equatio ca be derived for the foreig coutry. Whereas productio of good Y is higher i both coutries, there is o chage i the level of pollutio with trade. his occurs because both the tax rate ad are fixed so that the total uber of varieties of either good with trade, X ad X 2, are the sae as i autarky, * A A + * = + ad * A A + * = +. 7 With total pollutio uchaged, pollutio per uit of output declies. Welfare i both coutries cosequetly, ust icrease. Propositio 4: A exogeous eviroetal tax ad itra-idustry trade i iterediate products icreases output without raisig pollutio whe the pollutio fuctio exhibits costat returs to the varieties of iterediates. Welfare uabiguously rises.

27 26 he differeces i the results derived i Sectios 4. ad 6. are due to the ature of how pollutio is geerated. With costat returs i the pollutio fuctio, the icreasig returs oly affect fial ad iterediate good productio ad ot pollutio. his is cosistet with additioal varieties leadig to either less waste i productio or allowig for a ore efficiet ix of iputs thereby geeratig less pollutio per uit of output as explaied above i referece to pulp ad paper, textile dyig, ad agriculture. 6.2 rade-equilibriu with a Edogeous Pollutio ax o fid the level of pollutio whe eviroetal taxes are edogeous ad the pollutio fuctio exhibits costat returs, oe siply eeds to deterie the uber of varieties of good X used i fial good productio i the tradig equilibriu. With costat returs to scale i the pollutio fuctio, pollutio uder free trade is less tha i autarky i both coutries. his occurs because as icoe rises, the eviroetal tax rate icreases. A higher eviroetal tax, i tur, iplies that, i total, the uber of varieties of across both coutries will be saller i free trade rather tha autarky. At hoe this is show as follows: A A Z = ( + * x = x < x = Z, (32 ( + * where A <. With costat returs to scale i the pollutio fuctio, the ipact of higher eviroetal taxes, the techique effect, is sufficiet to cause pollutio to declie sice the uber of dirty varieties i either coutry will fall fro its autarky level as the tax rate rises, A < ad * A * <. As with the case of icreasig returs i the pollutio fuctio, the su of the uber varieties for either iterediate good across both coutries with trade however, still exceeds the autarky aout i either coutry. hat is > A + * ad * A + * >, whereas

28 > A + * ad 27 A + * > * he directio of chage i fial good productio is foud by coparig the total aout of each iterediate i autarky versus the tradig equilibriu ad is qualitatively the sae as i Sectio (5 (see equatios (29 ad (30. Fial good productio rises because as show above, producers of the fial good gai access to a greater variety of both iterediate iputs with trade ad therefore, output of X, X 2 ad Y all expad. Welfare uabiguously icreases i both coutries. With higher fial good productio, cosuptio expads ad, coupled with lower pollutio, welfare rises i each coutry. he odel thus, provides a additioal theoretical explaatio for the epirical results foud i Atweiler, Copelad ad aylor (200. Itra-idustry trade with costat returs i the pollutio fuctio ca lead to a reductio i pollutio with higher output. Propositio 5: With a edogeous eviroetal tax rate, trade i iterediate products icreases total output due to ecooies i the uber of varieties. Whe the pollutio fuctio exhibits costat returs to scale, however, pollutio is reduced due to the techique effect. 7. Coclusio his paper ivestigates the relatioship betwee itra-idustry trade i iterediate goods ad the eviroet. Iterediate products are produced i a oopolistically copetitive arket ad pollutio arises fro the use of dirty iterediates i the productio of the fial good. here are however, iteratioally icreasig returs with respect to the uber of iterediate products available i the fial good idustry. While, both coutries ipose eviroetal taxes o the use of the dirty iterediate i fial good productio, we allow for the possibility that tax rates ay differ across the two coutries. hough the odel is highly stylized, we derive a uber of iterestig results. he odel shows that whether pollutio icreases or ot depeds o the ature of the pollutio geeratio

29 28 fuctio. I particular, itra-idustry trade expads the uber of varieties of both iterediate products available to producers of the fial good ad allows the fial good idustry to icrease its total output. Siilar to Ethier (979, 982, we fid that the larger uber of varieties of the iputs akes productio of a fial good ore efficiet. Icreased output however, eed ot coe at a cost of higher pollutio. If the geeratio of pollutio exhibits costat returs to variety, pollutio will either reai costat, the exogeous tax case, or declie, the edogeous tax case. Whe the geeratio of pollutio exhibits icreasig returs to variety ad the iitial pollutio taxes i autarky differ across the two coutries, total pollutio will rise due to the scale effect, though pollutio per uit of output will declie i oe of the two coutries. I particular, the coutry with lower tax i autarky realizes a decrease i its pollutio per uit of fial good productio, i.e. the copositio effect egatively affects pollutio. he other coutry experieces the opposite effect. he directio of the copositio effect thus, depeds o the iitial relative levels of the eviroetal tax i autarky. Fially, we show that with edogeous taxes, trade leads to a icrease i the eviroetal tax i both coutries which puts dowward pressure o total pollutio ad pollutio per uit of output i each coutry. hat is, the techique effect works to lower pollutio. Europea Itegratio ay represet a iterestig applicatio of our odel. With the expasio of the Europea Uio towards Easter Europe, the questio arises whether existig ebers are iportig the eviroetal quality of the ew ebers. Our odel provides a potetial explaatio o the effects of Europea itegratio i which producers gai access to ew iterediates of differet eviroetal quality used to produce fial products. A alterative iterpretatio of our odel would be to view pollutio as cosuptiogeerated pollutio. Idividual cosuers purchase goods X ad X 2 ad cobie the to ake

30 29 a fial good Y that eters their utility. Pollutio is geerated whe cosuers eploy the dirty good X. he geeratio of pollutio uder this fraework is therefore, differet fro that foud i ost of the literature because it occurs through cosuptio. Dirty varieties could geerate larger aouts of waste or they ay cotai greater aouts of cheicals that daage the eviroet whe cosued. Uder this sceario the potetial of exportig pollutio oto a foreig coutry is reduced sice it occurs i cosuptio rather tha productio. I tur, iportig pollutio ca becoe a bigger dager as a coutry ay gai access to ore pollutioitesive goods eterig doestic cosuptio with trade.

31 Bibliography: 30 Atweiler, Werer, Bria R. Copelad, M. Scott aylor (200, Is Free rade Good for the Eviroet, Aerica Ecooic Review, 9 (4, Birdsall, Nacy ad David Wheeler (992, rade Policy ad Idustrial Pollutio i Lati Aerica: Where are the Pollutio Haves? i Patrick Low (ed., Iteratioal rade ad the Eviroet, World Bak Discussio Papers 59. Berhofe, Daiel M. (999, Itra-Idustry rade ad Strategic Iteractio: heory ad Evidece, Joural of Iteratioal Ecooics, 47, Boer, Rolf (999, Eviroetal Policy ad Idustrial Copetitiveess: he Pollutio Have Hypothesis Recosidered, Review of Iteratioal Ecooics, 7 (2, Copelad, Bria M. ad M. Scott aylor (994, North-South rade ad the Eviroet, Quarterly Joural of Ecooics, 09, Copelad, Bria M. ad M. Scott aylor (995, rade ad the Eviroet: A Partial Sythesis, Aerica Joural of Agricultural Ecooics, 77, Copelad, Bria M. ad M. Scott aylor (997, he rade-iduced Degradatio Hypothesis, Resource ad Eergy Ecooics, Vol. 9, Copelad, Bria M. ad M. Scott aylor (2003, rade ad the Eviroet: heory ad Evidece, Priceto: Priceto Uiversity Press. Dixit, Aviash K. ad Joseph E. Stiglitz (977, Moopolistic Copetitio ad Optiu Product Diversity, Aerica Ecooic Review, 67, 3, Eright, Michael J. ad Rolf Weder (eds.(995, Studies i Swiss Copetitive Advatage, Ber: Peter Lag. Ethier, Wilfred J. (979, Iteratioally Decreasig Costs ad World rade, Joural of Iteratioal Ecooics, February, 9, -24. Ethier, Wilfred J. (982, Natioal ad Iteratioal Returs to Scale i the Moder heory of Iteratioal rade, Aerica Ecooic Review, 72, 3,