Trade, Welfare, and International Labor Market Spillovers

Transcription

1 Trade, Welfare, and Internatonal Labor Market Spllovers Kyu Yub Lee Job Market Paper Abstract Ths paper develops a two-country new trade theory framework wth two types of labor sklled and unsklled) and an mperfect labor market arsng from country-specfc real mnmum wages. It examnes welfare mplcatons of trade lberalzaton and spllover effects of labor market shocks n a global economy. The model dentfes two key forces that shape the results: ) external scale effects generatng employment expanson among unsklled workers, and ) wage effects arsng from ntensve use of sklled workers. The model provdes three clear predctons. Frst, the ntroducton of trade results n a rse of wage nequalty n both countres. Second, trade enhances welfare by lowerng unemployment across countres only when external scale effects domnate. Last, when wage effects outwegh external scale effects, a country wll be better off f the other country rases ts mnmum wage, but both countres wll be worse off under unduly strong external scale effects n the global economy. Keywords: External Scale Effects; Wage Effects; Welfare; Labor Market Spllovers JEL-Codes: F11, F12, F16, L11 1 Introducton Much attenton has been pad to the mpact of trade lberalzaton on wages and unemployment, yet relatvely lttle s known about cross-country adjustments caused by shocks to labor I would lke to express my sncere grattude to Steven Matusz for hs gudance throughout the process of ths work. I am also ndebted to Carl Davdson and Jay Wlson for many useful comments and suggestons. I would lke to thank partcpants, n partcular, Chrstan Ahln, Jon Egua, Tony Doblas Madrd, Arjt Mukherjee at the Theory Brown Bag semnar, held at Mchgan State Unversty, Lansng, 2014, and partcpants at the 2014 Mdwest Internatonal Trade Meetng n Kensas, the 51st Annual Meetng of the Mssour Valley Economc Assocaton n Mssour, and the 2015 Annual Meetng of the Mdwest Economcs Assocaton n Mnnesota. All remanng errors are mne. Department of Economcs, Mchgan State Unversty, 110 Marshall-Adams Hall, East Lansng, MI USA. Phone USA Emal: leekyu8@msu.edu. 1

2 markets lnked by trade for goods. Ths paper s nterested n how trade nteracts wth labor market nsttutons to produce effects on dstrbuton, employment and aggregate welfare. 1 The man queston s: How does varaton of labor market nsttuton, e.g. mnmum wage, n one country affect ts tradng partners? Consder a world comprsed of Europe and the U.S. Well known s that Europe has a more rgd labor market than has the U.S. Davs 1998) and Meckl 2006) ntroduce mnmum wages nto the Heckscher-Ohln model and shed lght on nsghts that European mnmum wages prop up U.S. wages. In other words, tghtenng labor market constrants n one country results n transmsson of a postve labor market effect to the other country. 2 Ths result has been the conventonal vew among scholars and poltcans. Recently, however, the same queston has receved attenton n the monopolstc competton model wth heterogeneous frms and country-specfc mnmum wages. Egger, Egger, and Markusen 2012) overturn the results by the aforementoned models and conclude that European mnmum wages prop up U.S. unemployment. That s, stronger labor market nsttuton n a country results n a negatve labor market spllover effect on ts tradng partners. The model by Egger et al. 2012) hnges on the assumpton of a sngle factor n whch the real wage s subject to an exogenously specfed mnmum-wage. Hence, the assumpton fals to address an adjustment mechansm va factor prces on external shocks. One may conjecture that when both worker types are ndspensable n producton, but sklled workers are used ntensvely, varatons n the mnmum wage would mpact frms varable costs relatvely lghtly, whle varatons n the stock of sklled workers would mpact heavly. To explore ths ssue, ths paper develops a two-country new trade theory framework wth heterogeneous workers and labor market frctons arsng from country-specfc real mnmum wages. 3 The model s novelty s the addton of two types of labor, sklled and unsklled, nto the work by Egger et al. 2012) who emphasze external scale effects generatng employment expanson. In ths extenson, ths paper fnds that ther man result s not necessarly robust. 4 By dentfyng two counteractng forces, namely wage effects and external scale 1 See also Krugman 1995) for detaled dscusson of labor market nsttutons and trade. 2 In the earler work, many models are bult on the classc Heckscher-Ohln model. For nstance, Davdson et al. 1988, 1999) ntroduce search frctons nto that model, whch mples that f labor market frctons tghten n one country, then the unemployment rate rses. However, the tradng partner benefts by a lower unemployment rate due to the terms-of-trade apprecaton. In the sprt of Brecher 1974), Davs 1998) and Meckl 2006) develop a trade model wth a flexble wage U.S. and a rgd wage Europe; they conclude that f Europe rases the mnmum wage, t benefts the U.S. by ncreasng the U.S. wage. The key nsght s that Europe determnes U.S. wages va factor prce equalzaton. 3 Meltz 2003) reles on a sngle factor wth a flexble real wage among symmetrc countres. Accordngly, the model developed heren may be vewed as a varant of Meltz 2003), ncorporatng flexble love-of-varety and multple factors wth an mperfect labor market. 4 External scale effects followng Ether 1982) are known also as love-of-varety, varety gans, ncreasng 2

3 effects, ths paper shows that shocks to a country s labor markets exert ether postve or negatve spllover effects on ts tradng partners. When wage effects domnate external scale effects, the U.S. wll be better off f Europe rases ts mnmum wage. Intutons follow. Consder Europe rases ts real mnmum wage. An ncrease n the mnmum wage drectly ncreases all ntermedate nput frms varable costs. Due to worsened proftablty, margnal frms begn to ext the market. Then, a reduced number of actve frms lead to a fall n sklled workers wage, thus, European unemployment ncreases and welfare falls. Its tradng partner the U.S. s mpacted ndrectly by a rse n European mnmum wage. Two effects compete n ths scenaro. On one hand, potental entrants would beneft from postve wage effects or a lowered sklled workers wage. Lower varable cost enables those frms to enter the market. On the other hand, at the same tme, those frms also encounter negatve external scale effects or decreased demand for nputs by fnal output producers. If wage effects domnate, a rse n the mnmum wage leads potental frms n the U.S. to enter the market. Entry of these frms expands employment thus lowers unemployment for unsklled workers) and results n enhancng the U.S. welfare. When external scale effects domnate wage effects, the model has qualtatvely the same predcton as n Egger et al. 2012). The partcular model consdered here s where, n each country, the fnal output producers assemble varous ntermedate nputs accordng to the generalzed Constant Elastcty of Substtuton CES) producton technology whch captures external scale effects. 5 Each ntermedate nput frm wth some market power has the ablty to produce a unque varety valued by fnal output producers. Producton by ntermedate nput frms nvolves both fxed and varable costs. Fxed costs are ncurred as nvestment n unts of the fnal good; varable costs use sklled and unsklled workers. Unsklled workers face the threat of unemployment due to a country-specfc mnmum wage, whereas sklled workers wth flexble real wages are fully employed. Wage effects derve from ntensve use of sklled workers. It then s possble to solve explctly for autarky equlbrum assumng a Pareto dstrbuton from whch a frm draws random productvty. In addton to focusng on how domestc labor market outcomes are affected by foregn labor market nsttutons, ths paper also studes welfare mplcaton of trade lberalzaton. It shows that the ntroducton of trade ncreases wage nequalty between dfferent skll-type workers n both countres. Thus, ntuton of the result s: Wthout trade mpedments, openreturns to varety, and returns to specalzaton. 5 As Ether 1982) stresses, trade n ntermedate nputs s mportant see Y 2003; Amt and Konngs 2007; and more recently, Amt and Davs 2011). It occurs mostly among developed countres and represents respectvely 56% and 73% of overall trade flows n goods and servces see Mroudot et al. 2009; Sturgeon and Memedovc 2010). 3

4 ng to trade expands market sze for all ntermedate nput frms, compared to autarky. Those frms ncreased aggregate demand for sklled results n a rse of sklled workers wages snce the stock of sklled workers s exogenous. In the model, ncreased wage for sklled workers mples a rse of wage nequalty snce the real mnmum wage for the unsklled s bndng. The result of wdened wage nequalty s consstent wth the lterature on trade lberalzaton and wage nequalty see, e.g., Yeaple 2005; Helpman et al. 2010; Harrgan and Reshef 2015; Bursten and Vogel 2010). The other man result s that trade yelds two opposte forces: postve external scale effects generatng employment expanson, but negatve wage effects arsng from ntensve use of sklled workers. Gans from trade materalze only when the former effects domnate. From the perspectve of ntermedate nput frms, proftablty essentally relant on market demand and varable producton costs would determne f those frms ext or enter the market. Wth strong external scale effects, lberalzed trade leads to entry of potental frms. An ncreased aggregate demand for unsklled workers reduces the unemployment rate. Accordngly, total output and total labor ncome ncrease, thereby mprovng welfare across countres. Although average productvty falls n the product market wth heterogeneous frms, gans from trade rse va postve employment expanson. Adjustment at the extensve margn of frms s crucal n the present paper, snce selecton effects are neutralzed by the assumpton of no trade cost. Interestngly, ths paper shows a possblty that trade worsens both economes f negatve wage effects outwegh postve employment effects. Wth the wage nequalty result, we can say that by the openng to trade, sklled workers always become wnners whereas unsklled workers may be losers due to unemployment or the threat thereof. A long lne of lterature exsts on trade and unemployment. Tradtonal nternatonal trade theory uses full-employment condtons n ts smple and elegant Heckscher-Ohln HO) model. Although contrbutng to our understandng of trade patterns together wth two mportant theorems Stolper-Samuelson and Rybczynsk), the model cannot be reled upon once attenton s drected to unemployment ssues. Many scholars extended the HO model by employng mnmum wages Brecher 1974; Davs 1998; Oslngton 2002; Meckl 2006), mplct contracts Matusz 1985, 1986), search frctons Davdson et al. 1988, 1999), and far wages Kreckemeer and Nelson 2006). However, many economsts have made the pont of clamng that the HO model provdes no explanaton towards ntra-ndustry trade as under the assumptons countres wth dentcal factor endowments would not trade and produce goods domestcally. Krugman s new trade theory 1980) -and ts generalzed verson by Meltz 2003)- successfully explan ntra-ndustry trade patterns by emphaszng love-of-varety. In 4

5 ther models structure, ther choce of consumer preferences s the standard Dxt-Stgltz 1977) specfcaton. As n the HO model, these papers assume perfectly compettve labor markets. Usng varous sources, many economsts began to develop ntra-ndustry trade models wth equlbrum unemployment. Matusz 1996) merges effcency wage theory nto Krugman s model 1980) wth homogeneous frms and homogeneous workers. Davdson et al. 2008) ntroduce search frctons as n Albrecht and Vroman 2002) wth ex ante) homogeneous frms and heterogeneous workers. Based on Meltz 2003), Helpman and Itskhok 2010), Helpman et al. 2010), and Felbermayr et al. 2011) employ search frctons. Davs and Harrgan 2011) and Amt and Davs 2011) embed effcency wages. Egger and Kreckemeer 2009) ncorporate far wages. Egger et al. 2012) use mnmum wages. The above models, usng Meltz s framework, assume ether symmetrc countres or homogeneous workers or both. Ths paper employs heterogeneous workers and heterogeneous frms wth flexble external scale economes to consder labor market lnkages between asymmetrc countres. Ths paper contrbutes to the lterature on labor market nterdependence between asymmetrc countres. In the new trade theory, Matusz 1996) has shed lght on the possblty of postve correlaton of labor market outcomes. He constructs an ntra-ndustry trade framework n the Ether 1982) type model wth homogeneous frms and an effcency wage. Hs concluson mples that relaxng constrants on the effcency wage permts employment expanson n one country, boostng the world economy through trade, thereby expandng employment n the other. Recently, Egger et al. 2012) extends Matusz s 1996) arguments n a varant of the Meltz 2003) model wth country-specfc mnmum wages; they conclude that a fall n a country s mnmum wage has postve spllover effects for the tradng partner va external scale effects. The model developed heren dentfes wage effects and scale effects. In theory, one country s labor market shocks can have both postve and negatve spllover effects on the other country, and ther possble coexstence s demonstrated n ths paper s framework. The present paper relates to earler models examnng the lnk between welfare and trade lberalzaton. A theoretcal possblty of negatve welfare effects due to trade lberalzaton has been rased by Montagna 2001) who develops a monopolstc competton model wth techncal heterogenety among frms and countres. She shows that trade reduces the mnmum effcency to survve n the more effcent country and argues that adverse welfare effects may preval n an advanced technology economy f love-of-varety s suffcently low. The present paper rases such a possblty of losses of trade f external scale effects are suffcently low relatve to wage effects. 5

6 Ths paper s complementary to Egger and Kreckemeer 2009) who examne the effect of trade lberalzaton on a labor market n the presence of postve varable trade costs and external scale effects. They conclude that a negatve employment effect s trggered f varable trade costs are not too low and the external scale effects are moderate, whereas a postve employment effect can be expected f varable trade costs are neglgble and the external scale effect s strong. Ths also s well n lne wth Matusz s 1996) conclusons assumng full external scale effects and no trade cost. It also closely relates to Egger et al. 2012) predctng that wthout trade mpedments, trade lberalzaton always leads both economes to hgher levels of welfare, reducng the unemployment rate due to postve employment effects va external scale economes. In addton, a country s lowered mnmum wage always yelds postve spllover effects to ts tradng partner va the channel of external scale effects. Whle nsghtful, ther model s an ncomplete analyss. Frst, they rely on a sngle factor whose real wage s subject to an nsttutonally-set mnmum, whch shuts down the channel of wage effects. Second, t s mpossble to consder effects of varatons n the stock of sklled workers. Thus, ntroducng a second factor wth flexble real wages complements many parts of the results of Egger et al. 2012). Key fndng of the present paper s that the second factor revves the force of wage effects whch acts to offset the force of external scale effects on external shocks. Eventually, only when external scale effects domnate, do gans from trade materalze and stronger foregn labor market nsttutons harm domestc workers. In addton, varatons n foregn labor stock wth flexble wages also would mpact domestc workers. In the followng secton, ths author develops a baselne model n autarky. Secton 3 characterzes autarky equlbrum n both the product market and the labor market. Secton 4 dscusses trade equlbrum wth asymmetrc labor market nsttutons. Secton 5 examnes the mpact of a country s labor market varatons on the other: mnmum wage shock and factor supply shock. Secton 6 provdes concludng remarks. 2 The Model: Autarky Consder a world economy comprsng two asymmetrc countres ndexed by and j. In each, two types of goods are produced: homogeneous fnal output and dfferentated ntermedate nputs. Assume that both countres share fnal and nput producton technology, but dffer from each other n factor endowments sklled and unsklled workers), sze of real mnmum wages, and mass of potental entrants. All notaton s wrtten n terms of country. For country j, the subscrpt changes from to j. 6

7 2.1 Producton Technology and Frm Behavor In the sprt of Dxt-Stgltz 1975) and Ether 1982), the fnal output used for consumpton as well as nvestment s produced by assemblng wthout the use of labor) varous ntermedate nputs accordng to the generalzed CES producton technology 6 ˆ ) Y = M η σ σ 1 [z v)] σ 1 σ dv v V where V denotes the set of all avalable nput varetes wth measure M, z v) s the quantty of nput varety v employed n the producton of Y. Worth notng are a number of features of fnal goods technology n 1). Frst, σ > 1 s the constant elastcty of substtuton between varetes. Second, ρ = σ 1 σ < 1 captures the degree of complementarty between nput varetes. Thrd, two ndependent parameters, η [0,1] together wth σ, measure the degree of external scale effects. To understand the thrd feature, consder the case where z v) = z, v V. Fnal output becomes Y = M σ 1 σ η σ 1 1) z. Defne y = Y M z, whch measures the fnal output gan derved from spreadng a certan amount of producton among M dfferentated nputs nstead of concentratng t on a sngle nput see wth an elastcty 1 η σ 1 χη,σ). A margnal fnal output gan for addtonal nput varety s called the external scale effect. 7 Benassy 1996). Thus, the fnal output gan s y = M In the borderlne case of η = 0, external scale effects are full,.e., χ0,σ) = σ 1 1 and the expresson n 1) s equvalent to the standard Dxt-Stgltz 1977) specfcaton. As η rses, external scale effects become weaker, whch s nterpreted as an ntermedate nput per se becomng less mportant. 8 If we set η = 1, fnal output s produced under constant returns to scale n the measure of nputs, thereby showng no external scale effects,.e., χ1,σ) = 0. Let Y be the numerare. Takng nput prce p v) as gven, fnal goods producers choose nput quantty z v) n order to maxmze ther profts: max z v) P Y v V p v)z v)dv. We observe that P Y = v V p v)z v)dv n equlbrum snce, n a perfectly compettve fnal 1 η σ 1 6 In the unpublshed verson by Dxt-Stgltz 1975), they nclude the product dversty gan loss) wth measure M, nterpretng as publc good bad). Later, Benassy 1996) and Montagna 2001) redscover t n a consumpton context. See also Neary 2004), Eckel 2008), Acemoglu, Antras, and Helpman 2007), Egger and Kreckemeer 2009), and recently, Egger et al. 2012). 7 If we treat the fnal output technology as a utlty functon, χ s smlarly nterpreted as a margnal utlty gan from addtonal consumpton varety, so called love-of-varety. 8 Usng data, Haveman and Hummels 2004) state that complete specalzaton model consderably overstates ether the extent of specalzaton the degree to whch goods are dfferentated) or the degree to whch consumers value that dfferentaton. In the same ven, Ardelean 2009) reports that love-of-varety s forty two percent lower than s assumed n Krugman s model, whch mples exstng studes may overstate the varety gans from trade lberalzaton. 7

8 output market, free entry drves profts of fnal goods producers to zero. 9 Usng P = 1 due to the choce of numerare, the optmal nput demand for varety v s z v) = Y M η p v) σ. 2) Each ntermedate nput frm wth some market power has the ablty to produce a unque varety valued by fnal output producers. Producton by ntermedate nput frms nvolves fxed and varable cost. To operate, all ntermedate nput frms spend the same fxed nvestment cost f normalzed to one. Varable costs use sklled and unsklled workers wth skll ntensty β [0,1], but vary wth a frm s random productvty φ. The varable cost functon for a frm wth productvty φ to produce z amount of varety v assumes the Cobb- Douglas form: c φ) = z φ sβ w1 β 3) where s s the wage rate for sklled workers and w s the mnmum wage for unsklled workers n country. The cost functon n 3) has the convenence of generatng unt labor demand for sklled and unsklled workers, respectvely, as n Harrgan and Reshef 2015). 10 Orgnal work by Egger et al. 2012) consders only a mnmum-waged worker,.e., β = 0. The homogeneous worker assumpton, n partcular one such as bndng to a mnmum wage, fals to address an adjustment mechansm va factor prces. It naturally s conjectured that dependng on skll ntensty n producton, heterogeneous frms may be nfluenced dfferently by exogenous shocks, such as varatons n mnmum wage or n factor supply. Wth a hgh skll ntensty hgh β), varatons n the mnmum wage would have relatvely lghter mpact on frms varable costs, whle varatons n the stock of sklled workers would mpact heavly. Takng the soelastc demand by fnal goods producers n 2) and aggregate varables, an ntermedate nput frm maxmzes ts proft by settng ts optmal prce p φ) = sβ w1 β ρφ. 4) The revenue and proft generated by an nput frm wth productvty φ are automatcally calculated. Frm proft s then π φ) = r φ) σ 1 where r φ) s frm revenue and r φ) σ s 9 η ) 1 σ 1 Thus, the ndex of ntermedate goods prces s gven as P = M v V p v) 1 σ 1 σ dv. 10 See Romals 2004) who uses Krugman s model n explanng how factor proportons determne the structure of commodty trade. See also Bernard et al. 2007). 8

9 varable proft. 2.2 Input Frm Entry and Aggregate Varables A frm draws a random productvty φ from Pareto dstrbuton functon wth shape parameter κ. 11 Productvty s dstrbuted over [1, ) accordng to Gφ) = 1 φ κ where ts correspondng densty functon s gφ) = κφ κ 1. The shape parameter κ measures the concentraton of the frm s productvty dstrbuton. Wth a hgh κ, the nput sector becomes more homogeneous n the sense that more nput frms are located among the least productve frms. The Pareto dstrbuton not only generates a good approxmaton of the dstrbuton of frm sze see, e.g., Axtell 2001), but also provdes analytcal tractablty, enablng a comparson of results n the closed economy wth those from the open economy. Denote M as the mass of actve frms and φ as a cutoff productvty. Assume that the total mass of potental entrants n the dfferentated nput sector s gven by exogenous N. 12 Thus, only frms drawng productvty above φ engage n producton. The cutoff productvty condton CPC) yelds M = N [1 Gφ )] = N [φ ] κ. 5) By settng π φ ) = 0 r φ ) = σ), the zero-proft cutoff productvty ZCP) ndcates Y M η β ) s 1 σ w1 β ρφ = σ. 6) Next, defne the weghted) average productvty as φ = φ ) 1 φ σ 1 σ 1 µ φ)dφ where µ φ) = gφ) 1 Gφ ) s the productvty dstrbuton of frms n equlbrum. Usng the Pareto dstrbuton, the average productvty condton APC) s See Helpman, Meltz, and Yeaple 2004) and Chaney 2008). 12 The present paper can be seen as a steady-state model or a statc varant model of the dynamc verson n Meltz 2003). In Meltz 2003), there s an unbounded mass of potental entrants and free entry, resultng n expected zero proft n equlbrum. In the present paper, however, the assumpton of exogenous N s adopted to smplfy the analyss throughout wthout losng the man nsghts from Meltz 2003). See also Do and Levchenko 2009) and Chaney 2008). 13 Revenues of an average frm are proportonal to revenues of a margnal frm, r φ ) r φ ) = 9 κ σ+1 κ. Ths fact wll

10 where κ > σ 1 s assumed. s [ φ φ = κ κ σ + 1 ] 1 σ 1 Usng the ndex of ntermedate goods prces, the proft maxmzaton condton PMC) 7) M χ = p φ ). 8) Other aggregate varables are obtaned easly. For example, R = M r φ ) and Π = M π φ ) where R = r φ)m µ φ)dφ and Π = π φ)m µ φ)dφ represent aggregate φ revenue and proft, respectvely. φ 2.3 Labor Market Country s endowed wth H of sklled workers and L of unsklled workers. Labor markets for both types of worker are perfectly compettve. In the sprt of Brecher 1974), we consder here a very stark labor-market nsttuton. Assume that the government sets a mnmum wage w above the market clearng level for unsklled workers. Let U denote unemployment rate for unsklled workers. Let us fnd the labor demand for each type of worker to produce one unt of output wthn a frm. Usng 3), the margnal cost of a frm wth productvty φ s then mc φ) = sβ w1 β φ. 9) Denote h φ) and l φ) as the unt labor demand for sklled and unsklled workers, respectvely. Smlarly to Harrgan and Reshef 2015), applyng Shephard s lemma yelds h φ) = β φ l φ) = 1 β φ s w ) β 1, 10) s w ) β. 11) Wthn a frm wth productvty φ, the unt labor cost s h φ) = β φ sβ w1 β s ncurred when hrng sklled workers and w l φ) = 1 β) φ s β w1 β when employng unsklled workbe used later n the welfare analyss. 10

11 ers. 14 The total unt labor cost a frm wth productvty φ spends s just mc φ) n 9). For a frm to produce z φ) amount of goods, t spends mc φ)z φ) whch equals to ρr φ). Hence, c φ) = ρr φ). 12) Denote W as the total labor cost expendtures: W = c φ)m µ φ)dφ from the sum of wage payments by all ntermedate nput frms. Integratng both sdes n 12) over φ [φ, ), ˆ φ c φ)m µ φ)dφ = ρ ˆ φ φ r φ)m µ φ)dφ. 13) The relaton n 13) mples that W = ρm r φ ) = ρr. Due to the choce of fnal output as numerare, W = ρy. 14) In equlbrum, 1 U ) L unsklled workers wll be employed, whereas H sklled workers wll be fully employed snce the sklled wage s assumed to be flexble. The aggregate labor demand for sklled workers s obtaned by ntegratng over the total labor demand of frms wth productvty φ [φ, ): φ h φ)z φ)m µ φ)dφ. Smlarly, the aggregate labor demand for unsklled workers s l φ)z φ)m µ φ)dφ. φ Usng nput demand n 2), demand for sklled workers n 10), and demand for unsklled workers n 11), the two labor market equlbrum condtons then are H = ˆ φ β φ s w ) β 1) Y M η p φ) σ M µ φ)dφ, 15) 1 U ) L = ˆ φ 1 β φ s w ) β ) Y M η p φ) σ M µ φ)dφ. 16) The sum of wage ncomes for unsklled and sklled workers s equal to total labor cost expendtures,.e., W = 1 U )w L + s H. Manpulatng 14)-16), the unemployment rate s and one smple relaton s obtaned U = 1 1 β)w w L 17) 14 The demand rato of sklled to unsklled workers to produce a unt of nput varety s nversely related to the relatve wage of sklled workers,.e., h φ) l φ) = β w 1 β s. 11

12 β = s H ρy. 18) Equaton 18) states that a fracton β of the total labor cost payments ρy s gven to sklled workers, whch must be equal to the total labor ncome for sklled workers, s H. As β rses, wage payments to sklled workers out of total labor costs rse accordngly. In the present paper, wage effects arse from ntensve use of sklled workers. The magntude of the effects wll be determned by the parameter β. Together wth external scale effects χη,σ), β wll play a sgnfcant role throughout the paper. 3 Analyss of Autarky Equlbrum Equlbrum varables n autarky are characterzed completely by dervng the soluton for cutoff productvty and sklled workers wage φ,s ). Gven the soluton, all the other aggregate varables φ,m,y,w ) n the product market and U n the labor market are determned endogenously. Substtutng CPC 5) and APC 7) nto PMC 8), cutoff productvty s ncreasng n sklled workers wage wth an assumpton of θ 1 κχ > 0 15 [ ) 1 ] where λ = 1ρ κ σ+1 σ 1 θ 1 κ > 0. [ 1 β ] 1 w φ θ β ī = λ s N χ θ, 19) Pluggng CPC 5) and Y of 18) nto ZCP 6), cutoff productvty s decreasng n sklled workers wage wth an assumpton of β 1 σ 1 16 [ 1 β)σ 1) w φ = µ N η ] 1 H ) σ 1 ϑ ϑ β σ 1 1 s 20) 15 The condton 1 > κχ s 0 1 η σ 1 < κ 1. That s, the elastcty of fnal output gan wth respect to the measure of varety χη,σ) = 1 η σ 1 has a upper bound κ 1. Techncally, t s known that f φ s Pareto dstrbuted, then lnφ s exponentally dstrbuted wth standard devaton of κ 1. Recall that κ > σ 1 due to the assumpton of Pareto dstrbuton. Thus, 0 χη,σ) < κ 1 < σ 1 1 whch completes the restrctons of the elastcty. 16 Factor ntensty β should be n [0,1] and elastcty of substtuton σ s larger than one. In a general form, β mn{ σ 1 1 Dependng on σ, factor ntensty has a upper bound 1,1} should be satsfed. When σ > 2, factor ntensty β should decrease to keep 0 β 1 σ 1. If βσ 1) > 1, we are no longer able to consder the case of β = 0 because ths would mply that 0 > 1 contradcton). Lastly, at βσ 1) = 1, the curve n 20) becomes horzontal. 12 σ 1.

13 Fgure 1: Cutoff Productvty and Wage for Sklled Worker n Autarky Equlbrum Equaton 20 Cutoff Productvty Equaton 19) Note: Followng Bernard et al. 2007) and Harrgan and Reshef 2015), t s assumed that κ = 3.4 for Pareto shape parameter, σ = 3.8 for elastcty of substtuton. From Ardelean 2009), I adopt η = 0.42 for external scale parameter. For the rest of parameters, I set w = 7.25 for mnmum wage, N = 100 for the mass of potental entrants, and β = 0.15 for factor ntensty. The mass of sklled workers, H, s assumed to be suffcently small. wth µ = [ βσ 1) ρ σ 1 ] 1 ϑ 0 and ϑ = σ 1 + κη > 0. Proposton 1. A unque autarky equlbrum exsts n whch cutoff productvty and sklled workers wage are determned. [ φ = ψ N β χη,σ) 1 β w ) ] 1 θ+βκ H β 21) wth ψ = λ θ1 βσ 1)) µ βϑ ) 1 θ+βκ > 0 and s = µ ) θϑ [ θ+βκ N λ w 1 β)κ Proof. See Appendx A and Fgure 1. H θ ] 1 θ+βκ. 22) An ncrease n the stock of sklled workers H reduces both sklled workers wage s n 22) and cutoff productvty φ n 21). 17 A rse n mnmum wage w decreases sklled workers wage s n 22) and rases cutoff productvty φ n 21). Clearly, an ncrease n the } 17 A necessary and suffcent condton for φ 1 s N {ψθ+βκ w1 β χ β 1. H β 13

14 exogenous mass of potental frms N rases sklled workers wage s n 22). How does an ncrease n the exogenous mass of potental frms N affect the cutoff productvty level? To answer, we carefully should look at the soluton n 21). An ncreased mass of potental frms N exhbts two adjustment channels: wage effects β and external scale effects χη, σ). Relatve forces between them determne sgn{β χη, σ)} whch ponts to the drecton of the change n cutoff productvty. If wage effects domnate external scale effects,.e., β > χη,σ), cutoff productvty rses as N rses. To understand ths result, we focus on a margnal frm. An ncreased mass of potental frms mples a hgher demand for sklled workers n the labor market, thereby rasng the wage for sklled workers. That ncreased wage means hgher varable costs, forcng margnal frms to ext the market. Thus, wage effects drve cutoff productvty upward. Contrarly, an ncreased mass of potental frms rases M, thereby expandng fnal output through scale economes. Expanded fnal output ndrectly rases demand for ntermedate nputs, resultng n an ncrease n the returns to all ntermedate nput frms. Thus, external scale effects drve cutoff productvty downward. However, f fnal output frms use producton technology that generates weak external scale effects and ntermedate nput frms use skll-ntensve technology,.e., a suffcently small χ relatve to β, margnal frms n the dfferentated nput sector cannot offset ncreased varable costs by larger market demand, thus ext the market. If β < χη,σ), then potental frms enter the market. Egger et al. 2012) show that as N ncreases, cutoff productvty would not change at all f there s no external scale effect. In contrast, cutoff productvty ncreases due to prevalng wage effects even wthout external scale effect, as long as β > 0. In Egger et al. 2012), the effect of an ncrease n N depends only on external scale effects, drvng cutoff productvty downward. Ths results because they only consder mnmum-wage workers. In general, though, an addtonal stablzng force exsts by means of ncreasng factor prces n response to a larger number of potental entrants. 18 In the next secton, to facltate comparson between autarky and trade equlbrum, t s useful to explctly solve for aggregate product market varables. In the goods market, average productvty s derved by pluggng 21) nto APC 7), φ = ψ [ ρλ θ Pluggng 21) nto CPC 5), the mass of actve frms s N β χη,σ) 1 β w ) ] 1 θ+βκ β. 23) H 18 Egger et al. 2012) pont out ths matter n footnote 7 on page 777 but they seem to beleve that the assumpton of a sngle factor s nnocent but helps keep the analyss tractable as stated n footnote 3 on page

15 1 θ+βκ M = N H ψ β κ κσ w 1 β ) κ θ+βκ. 24) Snce Y = M r φ ) = M κ σ+1, the total fnal output produced Y becomes κσ ) N Y = κ σ θ+βκ ψ κ H β w 1 β ) κ θ+βκ. 25) Next, the labor market equlbrum n autarky s brefly dscussed. Usng W = ρm r φ ) and 25), the total labor costs W are W = κσ 1) κ σ + 1 ) N Usng 17), the rate of unemployment s 1 θ+βκ ψ κ H β w 1 β 1 β)κσ 1) [ N H βκ U = 1 κ σ + 1)ψ κ L w θ+κ ) κ θ+βκ. 26) ] 1 θ+βκ. 27) Obvously, the unemployment rate s one when β = 1. The Egger et al. 2012) model s a specal case of the present paper when β = 0. A hgher mnmum wage w or a lower stock of sklled workers H ) lowers the total mass of nput frms M, total output Y, and total labor ncome W from 24)-26) wth a rse n the rate of unemployment U from 27). Ths completes the analyss n autarky Introducton of Trade Consder free nternatonal trade between country and j. Assume both are n all respects dentcal except n the mnmum wage level,.e., w w j, L = L j, H = H j, and N = N j. 20 Ths assumpton wll be relaxed n the next secton. Assume throughout that no trade costs are 19 Examnng the effect of a rse n N s not the prmary focus of our analyss. However, t s nterestng to know that a larger N stmulates entry everywhere n the productvty dstrbuton and thus, a larger number of hgh productve frms operate n the market. If β > χη,σ), then φ n 21) rses. However, t s clear to predct that as N rses, total mass of nput frms, total output, and total labor ncome ncreases from 24)-26). Unemployment rate clearly falls n 27). Consequently, a rse n N wll have a postve mpact on welfare n the long-run. 20 Egger et al. 2012) pont out that Krugman s type model wth homogeneous frm fals to have bndng mnmum wages n both countres after trade. The assumpton of heterogeneous frms, however, enables both countres to have dfferent mnmum wages. 15

16 present, so that all frms are exporters and charge the same prce n both domestc and foregn markets. 21 In each country, fnal goods producers do not dscrmnate among ntermedate nputs produced n dfferent countres. Last, all notaton s wrtten n terms of country. For country j, the subscrpt changes from to j and from j to. 4.1 Frm Behavor between Asymmetrc Countres Denote M t as the mass of actve frms n country where the subscrpt t refers to free trade. Fnal output s produced by assemblng both domestc and foregn nput varetes accordng to the CES producton technology, 22 ˆ Y t = Y jt = M η σ 1 t ˆ [z t v)] σ 1 σ dv + v V ) σ [z jt v )] σ 1 σ 1 σ dv v V j where M t M t + M jt, V j denotes the set of all avalable varetes wth measure M jt, and z jt v ) s the quantty of varety v produced by country j. Takng ntermedate nput demands by fnal goods producers and other aggregate varables, ntermedate goods frms solve ther proft maxmzaton problem. Each frm wth dfferent productvty φ follows the constant mark-up prcng rule: 28) p t φ) = sβ t w1 β ρφ, p jt φ) = sβ jt w1 β j ρφ. 29) Smlar to the closed economy, cutoff productvty condtons CPCs) yeld M t = N [φ t ] κ, M jt = N j [φ jt] κ. 30) Two zero-proft cutoff productvty condtons ZCPs) are r t φ t ) = σ, r jt φ jt) = σ. 31) Usng the common ndex of ntermedate goods prces, proft maxmzaton condtons PMCs) yeld M χ t = p t φ t ), M χ t = p jt φ jt ) 32) 21 By the assumpton of no trade cost, selecton effects n Meltz 2003) are neutralzed n ths paper. It s crucal to focus on the adjustment at the extensve margn of frms throughout the paper. 22 The prce ndces are equalzed across countres. Due to the choce of Y as numerare, we set P = 1. 16

17 where φ t and φ jt APCs) are defned smlarly to n the closed economy case. 23 Equaton 31) mples that the rato of two cutoff productvtes can be expressed as the rato of varable costs from both countres: φ jt /φ t = sβ jt w1 β j /s β t w1 β. 24 In each the government mposes a dfferent mnmum wage so that t affects a frm s prce settng by nfluencng varable costs. In Egger et al. 2012), the rato of two cutoff productvtes equals the rato of two mnmum wages,.e., φ jt /φ t = w j/w. Unlke the Egger et al. 2012) model, the generalzed verson of the model here proposed entals sklled workers wages. In ths case, we take account of endogenously-determned sklled workers wage of each country n computng the rato of two cutoff productvtes. An nterestng fndng s t s unnecessary to do so n the present model because sklled workers wages n open economes are equalzed. Intutvely, ths result makes sense. Suppose country j sets a hgher mnmum wage than that of country. As dscussed n autarky, country j has a smaller goods market than has country. In the autarky equlbrum, s > s j 22). Upon openng to trade, frms n country j encounter a larger foregn market than that n country. Gven the same use of skll ntensty n producton across countres, the ncrease n the magntude of labor demand for sklled workers n country j should be hgher proportonally than n country. Due to the perfectly compettve labor market for sklled workers, wages for sklled workers adjust to clear the labor markets and turn out to be equal between the two countres. Indeed, we can derve ths result usng two zero proft condtons ZPCs) and two proft maxmzaton condtons PMCs). Lemma 1. Sklled workers wages are equalzed n open economes, s t = s jt. 25 [ ) 1 β)κ Lemma 2. M t = 1 + w w j ]M t Proof. See Appendx C. 4.2 Trade Equlbrum Equlbrum varables n free trade between asymmetrc countres are characterzed completely by dervng the soluton for cutoff productvty and sklled workers wage n each 23 As Egger et al. 2012) pont out, n the open economy t s necessary to dstngush between the average productvty of domestc frms, φ t, and the average productvty n the market, ˆφ t, wth domestc producton as well as mports from foregn frms. φ t and ˆφ t are dentcal only f the negatve lost-n-transt effect and the postve export-selecton effect are of the same sze. Snce we abstract from any trade mpedments and all frms export, φ t = ˆφ t. For more detals, see Egger and Kreckemeer 2009). 24 Due to the constant relatonshp between cutoff and average productvty, φ jt / φ t = s β jt w1 β should j /s β t w1 β be satsfed. 25 However, f one country has a hgher mass of sklled workers than the other, factor prce equalzaton fals. See Secton 5. 17

18 country. Gven the soluton, all the other aggregate varables φ t,m t,y t,w t, φ jt,m jt,y jt,w jt ) n product markets and U t,u jt ) n labor markets are determned across countres. Usng CPCs 30), ZCPs 31), PMCs 32), APCs, and Lemma 1-2, two key equatons are derved for each country. Proposton 2. [ 1 β ] 1 w φt θ [ ī w = λ N χ 1 + [ 1 β)σ 1) w φt N η ] 1 = µ H ϑ [ 1 + ) ] 1 β)κ χ θ w j w s β θ t, 33) ) ] ) 1 β)κ η σ 1 ϑ ϑ β σ 1 1 st. 34) w j A unque trade equlbrum exsts n whch cutoff productvty and sklled workers wage are determned n each country, { } 1 β w ) φt 1 [ θ+βκ w ) )] 1 1 β)κ β χη,σ) θ+βκ = ψ N β 1 + H w j wth ψ > 0 as defned n Proposton 1 and s t = 35) µ ) θϑ [ θ+βκ N 1 ) 1 β)κ 1 ) )] 1 1 β)κ θ+βκ +. 36) λ H θ w w j Corollary 1. Usng 21) n Proposton 1 and 35) n Proposton 2, φt [ w ) ] { } 1 β)κ 1 β χη,σ) θ+βκ φ = 1 +. w j Corollary 2. Usng 22) n Proposton 1 and 36) n Proposton 2, s [ t w ) ] 1 β)κ 1 = 1 + θ+βκ Φ. s w j Trade lberalzaton nduces an ncrease of sklled workers wage due to an ncrease of aggregate labor demand for sklled workers Corollary 2). As llustrated n Fgure 2, wth constant external scale effects χ, the dotted lne of sklled workers wage n trade equlbrum s always above the sold lne n autarky equlbrum regardless of β. Moreover, wage nequalty between dfferent skll-typed workers grows after trade lberalzaton at any gven β. Due to the assumpton of bndng mnmum wage, there s no change n real) wage for unsklled workers so that a larger market sze ought to te wth an ncreased wage nequalty. 18

19 Fgure 2: Wage for Sklled Worker and Factor Intensty n Trade Equlbrum Wage for Sklled Worker Autarky Equlbrum Trade Equlbrum Note: The same parameter values are mposed as n Fgure 1. Sold and dashed lnes refer respectvely to autarky and trade equlbrum. s It s easy to show the rato of wage nequalty before and after free trade: t w / s w = Φ > 1 where Φ s defned n Corollary 2. Ths result s consstent wth the lterature on trade lberalzaton and wage nequalty see, e.g., Yeaple 2005; Helpman et al. 2010; Harrgan and Reshef 2015; Bursten and Vogel 2010). Last, one can compare wage nequalty before and after free trade between country and j. Gven an assumpton that both countres are dentcal n all respects other than the mnmum wage level, wage nequalty n country n free trade compared wth one n autarky s less severe than one n country j f and only f w < w j. Ths result s straghtforward n Corollary 2 because w < w j mples Φ < Φ j. Fgure 3 llustrates Corollary 1 n whch wth constant external scale effects χ, the dotted lne of cutoff productvty n trade equlbrum crosses from below the sold lne n autarky equlbrum as β rses. Based on parameter values as noted n Fgure 1, one addtonal parameter s mposed w j = 8.5 for mnmum wage n country j. In Corollary 1, sgn{β χη,σ)} s mportant and governs the scale of φt /φ. Clearly, φ t /φ = 1 at β = χη,σ). If β > χη,σ), then φt /φ > 1 and vce versa. As noted n autarky, postve sgn{β χη,σ)} s nterpreted smlarly on the openng of trade. On one hand, trade lberalzaton expands the goods market va external scale economes, thus leads potental entrants nto the market. On the other, t rases labor demand for both sklled and unsklled workers. Frms have to bear hgher payments to workers, resultng n hgher varable costs negatve wage effect). If the latter effects always domnate the former,.e., β > χη,σ), lberalzed trade nduces 19

20 Fgure 3: Cutoff Productvty and Factor Intensty n Trade Equlbrum 25 Cutoff Productvty 20 Autarky Equlbrum 15 Trade Equlbrum Note: Parameter values are as noted n Fgure 1. Vertcal lne s gven at χ = 1 η 0.207). Sold and dashed lnes refer respectvely to autarky and trade equlbrum. σ 1 = approxmately, margnal frms to ext the market, resultng n φt /φ > 1. If β < χη,σ), then potental frms enter the market, φt /φ < 1. Fgure 4 llustrates how the current paper relates to several others n terms of frm ext/entry, dependng on wage effects and external scale effects. Meltz 2003) assumes both a full love-of-varety 1/σ 1)) and a perfectly compettve labor market β = 1), and predcts that, absent trade costs, cutoff productvty does not change at all after trade lberalzaton. At β = 1, there s no employment for unsklled workers n the world, regardless the exstence of mnmum wages, because nput frms producton technology obvates hrng any. The two countres become symmetrc, thereby producng equal mass of varetes n each. 26 Thus, hs model corresponds to the upper-rght corner n Fgure 4. Matusz 1996) consders a trade model wth effcency wage and full external scale effects 1/σ 1)). He predcts that trade lberalzaton relaxes constrants on effcency wage n the labor market and permts employment expanson n both countres. Although hs model deals wth homogeneous frms, entry of more frms after free trade can be nterpreted as a reducton n the cutoff productvty n the framework of the present paper. Snce hs model has labor market frctons from effcency wage, t corresponds to β = 0 and 1/σ 1) n the upper-left corner n Fgure 4. Egger et al. 2012) explctly consder flexble external scale effects but mnmum-wage workers. They predct that potental frms always enter the market after trade lberalzaton, 26 For example, M t = 2M t = 2M jt. 20

21 Fgure 4: Trade Lberalzaton and Change n Cutoff Productvty Scale Effect χ) Matusz 1996) Meltz 2003) A Egger et al. 2012) B C 0 Wage Effect β) 1 Note: To have the nterval of skll ntensty β [0,1], elastcty of substtuton between varety should be σ 2 whch satsfes one of the stablty condtons see footnote 15). Regon A shows φ t < φ f β < χη,σ) whle Regon C shows φ t > φ f β > χη,σ). Lne B ndcates φ t = φ f β = χη,σ). φ t < φ. Thus, ther model can be located on the vertcal lne at β = 0. The model developed heren llumnates the rest of the area n the parameter space χη,σ),β) of Fgure 4. All other aggregate varables n the trade equlbrum are provded n Appendx B. Usng Φ n Corollary 2, t s convenent to delver the rato of equlbrum varables before and after free trade: φ t φ = φ t = Φ β χ φ and M t M = Y t Y = W t W = Φ κχ β). When wage effects outwegh external scale effects,.e., β > χη,σ), an ncreased cutoff productvty φt trggers the mass of actve frms, total output, and total labor ncome to fall. In contrast, β < χη,σ) mples that potental frms would not worry much about havng to pay sklled-workers wages snce producton technology for ntermedate nput frms less ntensvely uses sklled workers. Thus, potental frms enter the market, thereby rasng the mass of actve frms, total outputs, and total labor costs. 4.3 Unemployment and Welfare From the dscusson n the prevous subsecton, t s clear that sgn{β χη,σ)} determnes frm performance and frm ext/entry. In partcular, β > χη,σ) mples that the most productve frms n the nterval φ t, ) ncrease ts producton volume by servng both domestc and foregn markets, resultng n hgher profts. Relatvely less productve frms n φt, φ t ) serve both markets but have lower profts compared wth ones n autarky, whle all nput frms n φ,φ t ) ext the market Corollary 1). The two types of worker are unevenly affected by 21

22 trade lberalzaton. Regardless of sgn{β χη, σ)}, also clear s that the transton from autarky to free trade results n ncreased returns to sklled workers n both countres Corollary 2). In contrast to the model by Egger et al. 2012), some unsklled workers may face unemployment despte lberalzed trade s postve employment effects. Denote U t and E t, of country n free trade t, as unemployment and employment rate for unsklled workers. By constructon, E t = 1 U t E s defned smlarly n autarky). Usng the defnton of Φ, the followng rato holds: E t E = Φ κ{β χη,σ)} 37) Postve sgn{β χη,σ)} mples that negatve wage effects, dervng from an ncreased wage for sklled workers, outwegh postve employment effects to unsklled workers. Free trade shrnks employment of unsklled workers 37), resultng n a hgher rate of unemployment n each country. Thus, free trade harms some unsklled workers who have worked n less productve frms. 27 If β < χη,σ), then both sklled and unsklled workers become wnners. The model presented heren accords wth the effcency wage model developed by Matusz 1996), analyzng labor market effects of trade lberalzaton wthout varable costs n an Ether-type 1982) framework. He predcts that ntroducton of trade results n establshment of more frms n each country and commensurately-hgher employment levels, thereby lowerng unemployment. That s consstent wth the result under full external scale effects, η = 0 see also Fgure 4). The present paper s complementary to the model by Egger and Kreckemeer 2009). Respectve fndngs by Egger and Kreckemeer 2009) derve from consderaton of the effect of trade lberalzaton on a labor market n the presence of postve varable trade costs and external scale effects. They conclude that a negatve employment effect s trggered f varable trade costs are not too low and external scale effects are moderate, whereas a postve employment effect can be expected f varable trade costs are neglgble and external scale effects are strong. 27 In the borderlne case, η = 1 shows no external scale effects, χ = 0. Then, P t = 1 mples p t φ t ) = 1 = s β t w1 β /ρ φ t. Snce there s no change n prce ndex, no change s made n nomnal wages n both countres. But there s a larger demand for sklled workers n both countres, whch drves sklled workers wage upward. Ths mples that varable cost s β t w1 β /φ ncreases. In order for average frm s prce to be 1, average productvty level should rse compared wth the one n autarky. Ths can be done by the ext of margnal frms. From the perspectve of margnal frms, the unt cost s β t w1 β /φ ncreases so that t cannot bear the costs anymore. A slghtly hgher productve frm s n the same poston. The margnal frm s productvty ncreases up to a certan level at whch average productvty satsfes p t φ t ) = 1. Hence, cutoff and average productvty rses. Ths leads Y t and M t to falls and consequently unemployment U t rses. The same logc apples to the case n country j. 22

23 Next s economy-wde welfare. Defne welfare measure Ω t as the sum of aggregate labor ncome W t and aggregate profts of domestc frms Π t. 28 That s, Ω t = W t + Π t = ρm t r t φ t ) + M t [r t φ t )/σ 1]. Hence, Ω t = M t [r t φ t ) 1]. 38) The welfare measure n 38) s unlke Meltz 2003) whch focuses manly on welfare per worker, represented by the number of varetes consumed and the average productvty. The reason s that hs model assumes free entry condtons so that the present value of aggregate profts equals total entry costs of frms n the productvty draw. Hence, only wage ncome s avalable for consumpton. Meanwhle, the present paper assumes exogenous N potental frms so that the welfare measure also ncludes aggregate profts. Snce an average productvty frm s revenue s constant,.e., r t φ t ) = κ σ+1 κσ, the mass of actve frms M t n 38) determnes economy-wde welfare level n country. The followng proposton summarzes the results. Proposton 3. Economy-wde Welfare) Trade welfare s mprovng f and only f β < χη,σ). Ths paper shows that when β > χη,σ), the possblty exsts that welfare worsens due to trade lberalzaton.e., M t /M < 1). Noteworthy here s that Neary s statement 2004) that Dxt-Stgltz specfcaton mposes too bengn a vew of product dversty. It clearly fals to capture one of the concerns of ant-globalzaton protesters: that lberalzng trade may reduce rather than ncrease varety. In addton, a theoretcal possblty of negatve welfare effects due to trade lberalzaton has been rased by Montagna 2001) who develops a monopolstc competton model wth techncal heterogenety among frms and countres. She shows that adverse welfare effects may preval n an advanced technology economy f love-of-varety s suffcently low. In contrast, Egger et al. 2012) conclude that trade lberalzaton always leads both economes to hgher levels of welfare once external scale effects,.e., η < 1, are n play. In ther model, workers always beneft from free trade because of postve external scale effects thus postve employment effects) and economy-wde welfare always mproves. Ther analyss s ncomplete n the presence of heterogeneous workers. 28 The welfare defnton follows Egger et al. 2012) who explan that total ncome can be used as a utltaran welfare measure n each country, due to assumng one homogeneous fnal good. 23