1 Profit Taxatio, Moopolistic Competitio ad Iteratioal Relocatio of Firms Wataru Johdo This paper presets a two-coutry moopolistic competitio trade model to aalyze how the profit taxatio determies the locatio of firms ad atioal welfare. Profit tax cuts may icrease or decrease the umber of firms i a coutry, depedig o the elasticities of substitutio betwee domestic ad foreig goods ad betwee goods produced i the same coutry. Accordigly, profit tax cuts may icrease or decrease domestic cosumptio ad welfare, depedig o these elasticities. The paper provides parameter coditios uder which a decrease i the domestic profit tax attracts foreig firms ad icreases domestic welfare. Keywords: Profit tax, Locatio, Moopolistic competitio, Two coutry model JEL Classificatio: F2, H2 I. Itroductio I the last two decades, profit tax competitio amog OECD coutries has icreased. This is because uder greater iteratioal firm mobility, lowerig profit tax attracts foreig firms, creates ew busiesses, ad thereby icreases atioal icome. Accordigly, OECD coutries have icreasigly lowered profit taxes to attract foreig firms (see, e.g., Haufler 1999; Fuest ad Huber 2002). The purpose of this paper is to Associate Professor, Faculty of Ecoomics, Tezukayama Uiversity, 7-1-1, Tezukayama, Nara 631-8501, Japa, (Fax) +81-742-46-4994, (E-mail) johdo@ tezukayama-u.ac.jp. Substatial improvemets i this paper were made possible by helpful commets ad costructive suggestios from two aoymous referees. Fiacial support by Tezukayama Uiversity is gratefully ackowleged. [Seoul Joural of Ecoomics 2010, Vol. 23, No. 3]
366 SEOUL JOURNAL OF ECONOMICS ivestigate the effects o welfare of a reductio i the profit tax i a world i which productio is globalized so that firms ca relocate easily, usig a two-coutry moopolistic competitio trade model. The relatioship betwee profit taxatio ad firm locatio (or foreig direct ivestmet) has bee studied extesively at a game theoretic level (Jaeba 1995; Koa 1997; Haufler ad Wooto 1999; Haufler ad Schjelderup 2000; Kid, Midelfart, ad Schjelderup 2000, 2005; Fuest ad Huber 2002; Huiziga ad Nielse 2002). Of particular iterest is the issue whether or ot each coutry will levy positive profit taxes from the viewpoit of household welfare. For example, Jaeba (1995) shows how the locatio of foreig direct ivestmet ad atioal icomes are iflueced by ocooperative profit taxatio policies uder capital mobility usig a game theoretic tax competitio model where two govermets compete by strategically settig profit tax rates to attract ew foreig capital. Jaeba (1995) foud that the equilibrium atioal icome pair is idepedet of profit taxatio policies. As a result, optimal tax rates uder the exemptio ad the credit method are both zero, while uder the deductio method the positive profit tax rate does ot impact upo the capital locatio. As metioed above, over the past few decades, i the game theoretic tax competitio literature, umerous attempts have bee made by researchers to show that tax competitio leads to a race to the bottom. 1 I cotrast, Baldwi ad Krugma (2004) exted the tax competitio aalysis to ecoomic geography models ad cosider how agglomeratio exteralities which iduce mobile firms to prefer to stay together create a race to the top i capital taxes. I their core-periphery model with icreasig returs to scale ad iceberg trade costs, they show that greater itegratio may lead to a race to the top i taxes i the presece of agglomeratio i the core regio. 2 This is because i the presece of agglomeratio, mobile firms ca ear more agglomeratio ret i the core regio ad therefore the govermet i the core regio ca attract mobile firms to the domestic coutry, eve if the profit tax is set at a high level. I additio, usig a ecoomic geography model, Borck ad Pflu ger (2006) show the race to the top i capital taxes 1 See Wilso (1999) for a comprehesive survey of the tax competitio literature. 2 See Krugma (1991) ad Krugma ad Veables (1995), who show how trade itegratio (fallig trasport costs) may produce a cocetratio of firms i a moopolistic competitio model with icreasig returs to scale ad trasport costs.
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 367 geeralizes to a framework with partial agglomeratio. Thus, i cotrast to the results i the tax competitio literature, the above studies i the ew ecoomic geography reveal how the sigificace of agglomeratio leads to a race to the top. Although a large umber of studies have bee made o the effects of capital mobility o tax competitio based o a ocooperative game theoretic approach, little is kow about the effects of chagig a exogeous profit tax rate o the welfare of each coutry uder free movemet of firms based o a two-coutry moopolistic competitio trade model. The exceptio is Johdo ad Hashimoto (2005), who ivestigate the welfare effects of a profit tax i a world i which firms ca relocate easily across coutries ad the terms of trade effect is cosidered. Johdo ad Hashimoto (2005) showed that the welfare impacts of a profit tax icrease ca be positive or egative, depedig o the relative share of owership of firms betwee the two coutries. However, the followig questio remais uresolved: how does the relatioship betwee profit taxatio ad firms choice of locatio chage whe we take ito accout two types of elasticity of substitutio: that is, the elasticity of substitutio betwee home ad foreig goods ad the elasticity of substitutio betwee goods produced i the same coutry? 3 Further, how do chages i the profit tax i oe coutry affect aother s welfare whe we take ito accout the two types of elasticity of substitutio? 4 We emphasize that oe of the existig literature focuses o the profit tax, firms locatio ad the two types of elasticity of substitutio, or how the iteractios betwee these affect welfare at home ad abroad. 5 I order to address these issues, we propose a two-coutry moopolistic trade model, ad examie i detail the relatioship betwee profit taxes, firms locatio ad the two types of elasticity of substitutio. The results idicate that the likage betwee 3 Tille (2001) defied the former as the cross-coutry substitutability ad the latter as the withi-coutry substitutability. 4 Oe differece betwee the profit tax competitio literature ad the curret aalysis is whether the profit tax rate is optimized or fixed. This paper attempts to examie the welfare effect of a reductio i a fixed profit tax rate cosiderig both firms locatio ad the two types of elasticity of substitutio. 5 A umber of other factors affectig firms locatio choices other tha profit taxatio have also bee examied i the literature. These iclude: commodity taxes (Haufler ad Pflu ger 2004); emissio taxes (Pflu ger 2001); firm specific fixed (suk) costs (Hosoe ad Sugeta 1995); trade liberalizatio i itermediate iputs (Wag 1994); public ifrastructure (Marti ad Rogers 1995); ad wage taxes (Pflu ger 2004). See Ricci (1999) for a extesive survey of locatio theories.
368 SEOUL JOURNAL OF ECONOMICS firms locatio ad the two types of elasticity of substitutio ca play a importat role i determiig how profit taxes affect welfare i each coutry. 6 Two iterestig results arise from this aalysis: 1) whe the elasticity of substitutio betwee home ad foreig goods is relatively small, a decrease i domestic profit tax rate ca decrease domestic welfare ad raise foreig welfare; ad 2) whe the elasticity of substitutio betwee home ad foreig goods ad betwee goods produced i the same coutry are both large, ad a large proportio of the firm profits accrue to domestic residets, the a decrease i the domestic profit tax rate will effectively icrease domestic welfare ad decrease foreig welfare. The remaider of this paper is structured as follows. Sectio II outlies the features of the model. Sectio III describes the equilibrium. I Sectio IV, we examie the impact of a profit tax reductio o the spatial distributio of firms across the two coutries, the terms of trade, wage rates, cosumptio ad welfare i each coutry. The fial sectio summarizes the fidigs ad cocludes the paper. II. The Model We assume a two-coutry world ecoomy, with a home ad a foreig coutry, i which the overall umber of firms is exogeously give, but firms ca relocate freely ad without ay cost betwee two coutries. Moopolistically competitive firms exist cotiuously i the world i the [0, 1] rage. Firms i the iterval [0, ] locate i the home coutry, ad the remaiig (, 1] firms locate i the foreig coutry, where is edogeous. Firms charge mark-up prices based o product differetiatio, each producig a uique variety i a sigle locatio to serve world demad. Labor is the oly iput with costat margial productivity ad o fixed costs are required. There is free trade betwee two coutries that share idetical prefereces, ad have a predetermied size i terms of labor edowmet. Departig from the covetioal free etry set-up, profits are ot wiped out i equilibrium. Istead, the key ad- 6 This paper is also related to work by Melitz (2003) who ivestigated the welfare effects of trade liberalizatio uder moopolistic competitio with heterogeeous firms. The paper differs i their aalysis of govermet istrumets, but shares may of the cocers about the welfare cosequeces via geeral equilibrium effects.
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 369 justmet is a relocatio of firms betwee the two coutries drive by the equilibrium coditio that profits are equalized across coutries. This aalysis further assumes that firms are mobile iteratioally, but their owers are ot. Hece, all profit flows are distributed to the immobile owers accordig to the respective holdig shares. Fially, we assume that the home govermet imposes a profit tax rate τ o the profits of domestically located firms, ad all tax reveue are shared equally by correspodig residet households i a lump sum fashio. A. Households The size of the world populatio is ormalized to uity. We assume that the shares of households i the home ad foreig locatios are s ad s ( 1-s), respectively. 7 Each household is edowed with oe uit of labor. Every household supplies oe uit of labor to domestic firms at the real domestic wage, ad receives profits from the iteratioally mobile firms. The households i each coutry cosume a group of differetiated goods. The model s cetral assumptio is that domestic ad foreig goods affect cosumer welfare i a differet way although firms are perfectly mobile across coutries. This implicitly assumes that households receive a differet level of utility from a product depedig o whether it is produced i the home coutry or i the foreig coutry (e.g., wie from Frace, whiskey from the Uited Kigdom, rice from Japa). The utility maximizatio problem i a typical household i the home coutry is the: maxu=log C, c hj,c fj π 0 j subject to α((1-τ) dj + π j dj)/s+w+z=c, 1 (1) where ( 1)/ c θ θ 0 hj C=(C h (σ -1)/σ +C f (σ-1)/σ ) σ/(σ-1), σ>0 (2) 1 c ( θ 1)/ θ fj C h =( dj) θ/(θ-1), C f =( dj) θ/(θ-1). θ >1 (3) I (1), the cosumptio idex, C, is a costat-elasticity-of-substitutio (CES) fuctio composed of two types of goods, home ad foreig, ad σ is the elasticity of substitutio betwee the home ad the foreig 7 Foreig-coutry variables are idicated by a asterisk.
370 SEOUL JOURNAL OF ECONOMICS goods. 8 The secod equatio i (1) is the household s budget costrait per capita, ad α (1-α) deotes the share of the total profit flows of firms repatriated to the home (foreig) agets. 9 Throughout the paper, we also use the idex j [0, 1] to refer to the product of firm j. There 1 fore, π dj ( π j dj) represets the total profit flows of home- (foreig-) 0 j located firms. I additio, i (1), w( W/P) deotes the real wage rate i terms of the cosumptio idex where W is the home coutry s omial wage rate ad P is the price idex of the home coutry correspodig to C, ad z is the lump-sum trasfer per capita. I (2), C h ad C f represet the cosumptio of the home ad foreig goods, respectively, ad are defied by a CES fuctio across goods i the same coutry as defied by (3). I (3), θ is the elasticity of substitutio amog goods produced i the same coutry, c hj ad c fj represet the cosumptio of a particular good j produced i the home ad the foreig coutry, respectively. We divide household decisios ito two stages: first, cosumers allocate their cosumptio betwee two types of goods, C h ad C f ; ext they allocate their cosumptio across various goods, c hj ad c fj, withi each type. I the first stage, households solve the followig problem: max U=log C=log [(C h (σ-1)/σ +C f (σ -1)/σ ) σ/(σ-1) ] C h,c f subject to E=P h C h +P f C f 1 p θ 1 p 1 θ where P h = [ dj] 1/(1-θ) ad P f =[ dj] 1/(1-θ) are the price idexes 0 hj fj of the home ad foreig goods, respectively, ad E is the total cosumptio expediture. We the obtai the followig demad fuctios: C h =(P h /P) -σ C, C f =(P f /P) -σ C (4) where P=[P 1-σ h +P 1-σ f ] 1/(1-σ) is the price idex correspodig to the cosumptio idex C. I the secod stage, households solve the followig two problems: 8 I what follows, we maily focus o the descriptio of the home coutry because the foreig coutry is described aalogously. 9 I other words, α deotes the extet to which firms are domestically owed. Huiziga ad Nielse (1997, 2002) ad Fuest ad Huber (2002) studied the feasibility of profit taxatio i the presece of foreig owership of the domestic firm.
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 371 ( 1)/ c θ θ 0 hj p 0 hj max C h =( dj) θ/(θ-1), subject to P h C h = c hj d j c hj 1 c ( θ 1)/ θ fj 1 p fj maxc f =( dj) θ/(θ-1), subject to P f C f = c fj d j c fj where p hj ad p f j are the prices of good j maufactured i the home ad foreig coutries. From these, we obtai the followig demad fuctios of the home coutry: c hj =(p hj /P h ) -θ C h, c fj=(p f j /P f ) -θ C f (5) Combiig (4) ad (5) yields the followig demad fuctios of the home coutry: c hj =(p hj /P h ) -θ (P h /P) -σ C, c fj =(p f j /P f ) -θ (P f /P) -σ C (6) Similarly, the demad fuctios of the foreig coutry are: c h j =(p hj /P h ) -θ (P h /P ) -σ C, c fj =(p f j /P f ) -θ (P f /P ) -σ C (7) where P =(P 1-σ h +P 1-σ f ) 1/(1-σ) (=P) is the price idex correspodig to the cosumptio idex C. Substitutig (6) ito C, ad (7) ito C =(C (σ-1)/σ h +C (σ-1)/σ f ) σ/(σ -1), respectively, yields C=e ad C =e, where e=e/p ad e =E /P represet the home ad foreig household s expediture i terms of the cosumptio idex. I a symmetric equilibrium, the price idexes, P= P =(P 1-σ h +P 1-σ f ) 1/(1-σ ) are rewritte as: P h /P=P h /P =ω -1 [ω σ -1 +1] -1/(1-σ), P f /P=P f /P =[ω σ-1 +1] -1/(1-σ ) (8) where w=p f /P h is the relative price idex betwee home ad foreig coutries. Accordigly, the terms of trade (the price of home goods relative to foreig goods) are 1/ω for the home coutry, ad ω for the foreig coutry. I other words, the terms of trade of home (foreig) coutry is defied by the relative price of home (foreig) exports to 1 home (foreig) imports. Furthermore, from P h =[ p θ dj] 1/(1-θ) ad P f = [ dj] 1/(1-θ) 0 hj 1 1 θ, we obtai the followig symmetric price ratios: p fj p hj /P h = -1/(1-θ), p f j /P f =(1-) -1/(1-θ) (9)
372 SEOUL JOURNAL OF ECONOMICS Summig the demad fuctios (6) ad (7) across all households, ad equatig the resultig equatio to the output of good j produced i the home coutry, y j, yields the followig market clearig coditio for ay product j: y j =sc hj +s c h j =(p hj /P h ) -θ (P h /P) -σ s w j [0, ] (10) where sc hj (s c h j ) is aggregate home (foreig) cosumptio demad for product j ad s w (se+s e ) is global cosumptio expediture idex. Similarly, the market clearig coditio for ay good j produced i the foreig coutry is y j =sc fj +s c f j =(p f j /P f ) -θ (P f /P) -σ s w, j [, 1]. B. Firms We assume that ay moopolistically competitive firm that operates i either of the two coutries employs the same productio techology. These firms use costat returs-to-scale techology to produce the differetiated cosumptio products, accordig to y j =l j, where l j represets labor iput. Sice the home-located firm j hires labor domestically, give W, P h, P ad s w, ad subject to (10), the home-located firm j faces the followig profit-maximizatio problem: max Π j =(p hj -W)y j, subject to y j =sc j +s c j=(p hj /P h ) -θ (P h /P) -σ s w (11) p hj Give the above, the price mark-up is chose accordig to: p hj =(θ/(θ-1))w (12) Sice W is give, (12) yields p hj =p h, j [0, ]. These relatioships imply that each home-located firm supplies the same quatity of goods. Similarly, the price mark-ups of foreig-located firms are idetical, sice p f j =p f, j (, 1]. Droppig the firm idex because of symmetry ad deotig the maximized profit flows of the home- ad foreig-located firms i terms of the cosumptio idex, respectively, by π h ( Π h /P) ad π f ( Π f /P ), ad substitutig (10) ad (12) ito Π j of (11) yields: π h =(1/θ )(p hj /P h ) 1-θ (P h /P) 1-σ s w, π f =(1/θ )(p f j /p f ) 1-θ (P f /P) 1-σ s w (13)
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 373 III. Equilibrium A. Profit-equalizatio Coditio We assume that firms do ot face ay relocatio costs such that it does ot take ay time to relocate to aother coutry. For a firm to be idifferet betwee home ad foreig locatios after locatio arbitrage, the returs from the two locatios must be equalized. Hece, for a equilibrium where moopolistic firms are located i both coutries, the followig profit-equalizatio coditio must be satisfied. 10 (1-τ )π h =π f (14) This coditio eables us to determie the equilibrium spatial distributio of firms across the two coutries. B. Labor Market Clearig Coditios The equilibrium coditios for the labor market of each coutry are, respectively, give by: l j =s, (1-)l j =s (15) I (15), the left-had sides deote total labor demad ad the righthad sides deote total labor supply, respectively. C. Equilibrium Values Usig the price mark-up, the profit-equalizatio coditio, product ad labor market-clearig coditios for domestic ad foreig coutries yield the equilibrium relative price, the distributio of firms ad real cosumptios of both coutries, ω e, e, e e, ad e e. a) The Distributio of Firms Equatios (8), (9), ad (13) ca be rewritte as: 10 I the direct foreig ivestmet literature (e.g., Jaeba 1995; Koa 1997; Rhee 1998; Huiziga ad Nielse 2002), locatios take the form of fiacial portfolio ivestmet. The distributio of foreig direct locatios is the determied so as to equalize the et retur o domestic ad foreig ivestmets for capital owers.
374 SEOUL JOURNAL OF ECONOMICS π h =(1/θ ) -1 ω (σ-1) [ω σ -1 +1] -1 s w, π f =(1/θ )(1-) -1 [ω σ-1 +1] -1 s w (16) Substitutig (16) ito (14) yields the followig relatioship betwee ω ad i locatio-equilibrium: ω =(/[(1-)(1-τ )]) 1/(σ -1) (17) From (17), whe 0<σ 1, we obtai d/dω <0, which idicates that the domestic share of mobile firms is iversely related to the relative price ω. We ituitively explai this relatioship as follows: whe 0<σ 1 is assumed, a exogeous rise i ω decreases π h ad icreases π f, sice 0<σ 1 implies that the cross-coutry price elasticity for each product is smaller tha uity. Therefore, some firms relocate to the foreig coutry from the home coutry. Also, d/dω >0 holds whe σ>1. This is because whe σ >1 it implies that the cross-coutry price elasticity for each product is larger tha uity, so the iverse mechaism occurs i (17). By substitutig (8) ad (9) ito (10), ad usig y j =l j ad (15) yields: 1/(1-θ) ω σ [ω σ-1 +1] σ/(1-σ) s w =s (18) The govermet budget costrait i the home coutry is τπ h =sz (19) From (8), (9), ad (12), real wages are w=(w/p hj )(p hj /P h )(P h /P)=((θ-1)/θ ) -1/(1-θ) ω -1 [ω σ-1 +1] -1/(1-σ) (20) w =(W /p fj )(p f j /P f )(P f /P)=((θ-1)/θ )(1-) -1/(1-θ) [ω σ-1 +1] -1/(1-σ ) (21) From (1) ad (16), combiig the budget costraits of each coutry yields: 11 s w se+s e =s -1/(1-θ) ω -1 [ω σ-1 +1] -1/(1-σ ) +s (1-) -1/(1-θ) [ω σ-1 +1] -1/(1-σ) Substitutig this ito (18) yields: 11 See the Appedix for derivatio of s w.
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 375 sω σ-1 (ω σ -1 +1) -1 +s (/(1-)) 1/(1-θ) ω σ (ω σ -1 +1) -1 =s (22) From (22) ad /(1-), we obtai d /dω =σ (θ-1)( /ω )>0, which idicates that the domestic share of mobile firms is positively related to the relative price ω (d/dω >0). From (17) ad (22), we obtai the equilibrium distributio of firms: e =[1+(s/s ) [(1-θ)(σ -1)]/[1-σ (2-θ)] (1-τ ) σ(1-θ)/[1-σ(2-θ)] ] -1 (23) From (23), whe either 0<σ 1, or 1>σ (2-θ) ad σ>1, the profit tax decrease (dτ <0) will lead firms to relocate ito the home coutry, i.e., d e /dτ <0. I cotrast, whe 1<σ (2-θ) ad σ>1, the relocatio effect of decreasig the profit tax rate i the home coutry is d e /dτ>0. The mechaism of d e /dτ>0 is explaied as follows. First, from (17) ad σ>1, a decrease i the profit tax rate reduces the relative price ω for a give, or icreases for a give ω because the decrease i τ leads to (1-τ)π h >π f, ad thereby iduces some firms to relocate ito the home coutry (hereafter we call this the first relocatio effect ). However, the reductio i ω i tur stimulates firm relocatio from the home to the foreig coutry because d/dω >0 holds from (22) (hereafter we call this the secod relocatio effect ). Hece, the et outcome of the spatial distributio of firms by decreasig the profit tax rate depeds o the relative stregth of these first ad secod pressures. I order to establish the et outcome, it is worthwhile to ote that the positive relatioship betwee ad ω (d/dω >0) is icreasig i the size of σ because d /dω =σ (θ -1)( /ω )>0( /(1-)) holds from (22). This implies that a chage i ω have larger (smaller) effect o the larger (smaller) is σ. Hece, the larger (smaller) is σ, the larger (smaller) is d/dω >0 ad the larger (smaller) is the secod relocatio effect. I the latter coditio, 1<σ (2-θ ) ad σ >1; here, θ is restricted to be relatively small, but σ is restricted to be large. This reiforces the secod relocatio effect. Thus, i the case of 1<σ (2-θ ) ad σ>1, the secod relocatio effect domiates the first relocatio effect, ad thereby makes firms relocate to the foreig coutry, that is, d e /dτ>0. Similarly, we ca also cosider the case of 1>σ (2-θ ) ad σ>1, that is, σ is relatively small. As show i the above, this reduces the secod relocatio effect, ad hece, the secod relocatio effect is domiated by the first relocatio effect, ad thereby makes firms relocate to the home coutry, i.e., d e /dτ <0. I additio, from (17), whe 0<σ 1, a decrease i the profit tax rate raises the relative price ω for a give,
376 SEOUL JOURNAL OF ECONOMICS or icreases for a give ω (the first relocatio effect). The rise i ω stimulates firm relocatio from the foreig to the home coutry because d/dω >0 holds from (22) (the secod relocatio effect). Therefore, i this case, the secod relocatio effect reiforces the first relocatio effect, ad hece, d e /dτ <0. b) The Equilibrium Relative Price Next, substitutig (23) ito (17) yields the followig equilibrium relative price: ω e =(s/s ) -(1-θ)/[1-σ (2-θ)] (1-τ ) 1/[1-σ(2-θ)] (24) From (24), dω e /dτ<0 if either 0<σ 1, or 1>σ (2-θ ) ad σ>1 are satisfied. Thus, a decrease i the home coutry s profit tax rate icreases the equilibrium relative price, P f /P h, ad hece the terms-oftrade for the home coutry decreases for the chage dτ <0. By cotrast, if 1<σ (2-θ ) ad σ>1, dω e /dτ>0. I sum, from (23) ad (24), we obtai the followig relatioships: d e /dτ<0, dω e /dτ<0 whe 0<σ 1 (25) d e /dτ>0, dω e /dτ>0 whe 1<σ(2-θ ) ad σ>1 (26) d e /dτ<0, dω e /dτ<0 whe 1>σ(2-θ ) ad σ>1 (27) c) Real Cosumptios ad the Ret Redistributio Effect From (23) ad (24), the symmetric equilibriums pair, e =1/2 ad ω e =1, are always a solutio whe the populatio size of home ad foreig coutries is equal, i.e., s=s ad τ =0. Fially, substitutig (8), (9) ad (12) first ito (13), ad the alog with (14) ad (19) ito (1) ad its foreig couterpart, respectively, ad solvig for the equilibrium levels of cosumptios of both coutries gives: e e =(α /(θ-1))(w+w )+w+(1-α)τ(ω σ-1 /(ω σ-1 +1))(1/(θ-1))(w+w ) (28) e e =((1-α)/(θ-1))(w+w )+w -(1-α)τ (ω σ-1 /(ω σ-1 +1)) (1/(θ-1))(w+w ) (29) where w=((θ-1)/θ ) -(1-θ) e ω -1 e [ω σ-1 e +1] -1/(1-σ) ad w =((θ-1)/θ )(1- e ) -1/(1-θ) [ω σ-1 e +1] -1/(1-σ) from (20) ad (21). The first terms i the
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 377 above equatios are the ret icome. The secod term is the labor icome. The third term deotes the tax trasfer from the foreig coutry to the domestic coutry. Therefore, the tax decrease leads the domestic govermet to shift part of the tax reveue from home coutry to foreig coutry as a ret icome repatriatio to foreig households (hereafter we call this the ret redistributio effect ). Therefore, we obtai the followig lemma. Lemma 1: The ret redistributio effect is always egative for the domestic real cosumptio, ad positive for the foreig real cosumptio. I what follows, we assume that the umeraire is the labour of homelocated households makig W=1. IV. The Impacts of the Profit Tax Rate A. Wage Effects, the Labor Shiftig Effect, ad the Terms-of-trade Effect I this sectio, we ivestigate the impact o the wages of both coutries of a decrease i the home coutry s profit tax rate (dτ <0). From (20) ad (21), the chages i home ad foreig wages are give by differetiatig w ad w with respect to τ : dw/dτ =w{(1/(θ-1)) -1 d/dτ-(ω -1 /(ω σ -1 +1))dω /dτ } (30) dw /dτ =-w {(1/(θ-1))(1-) -1 d/dτ-(ω σ -2 /(ω σ-1 +1))dω /dτ } (31) From (23) ad (24), the effect o e ad ω e of τ are obtaied explicitly as d e /dτ= e 2 (s/s ) [(1-θ)(σ-1)/[1-σ(2-θ)]] [σ(1-θ )/[1-σ(2-θ )]] (1-τ ) [σ (1-θ)/[1-σ(2-θ)]]-1 (32) dω e /dτ =-ω e [1/[1-σ (2-θ )]](1-τ) -1 (33) From (25), (27), (30), ad (31), if either 0<σ 1 or 1>σ (2-θ ) ad σ> 1, the impacts of the profit tax have two opposig effects o each coutry s wage icome. O the oe had, from d e /dτ<0, a decrease i the profit tax rate brigs more differetiated products produced i
378 SEOUL JOURNAL OF ECONOMICS the home coutry due to relocatio from the foreig coutry. This the leads to a shift i labor demad away from the foreig coutry towards the home coutry, thereby icreasig w ad decreasig w (hereafter we call this the labor demad shiftig effect ). Therefore, we obtai the followig lemma. Lemma 2: The labor demad shiftig effect raises (lowers) domestic real wage, ad lowers (raises) foreig real wage whe d e /dτ<(>)0. O the other had, from dω e /dτ<0, a decrease i the profit tax rate leads to a icrease i the ω required for the after-tax profits to be equalized betwee the two coutries, ad this iduces a egative (positive) wage respose i the home (foreig) coutry (hereafter we call this the terms-of-trade effect ). Therefore, we obtai the followig lemma. Lemma 3: The terms-of-trade effect lowers (raises) domestic real wage, ad raises (lowers) foreig real wage whe dω e /dτ<(>)0. Thus, as stated i (30), the first elemet i the brace is the positive effect of a tax decrease o domestic wage ad the secod elemet is the egative effect due to deterioratio of terms of trade. Also, from (26), (30), ad (31), whe 1<σ (2-θ ) ad σ >1, the opposite causal relatioships i both firm locatio ad the terms of trade materialize. Substitutig (32) ad (33) ito (30) ad (31), respectively, the yields: dw/dτ=-[w(1-τ ) -1 /[1-σ(2-θ )]] { e s 1 σ(1-τ ) [σ(1-θ)/[1-σ(2-θ)]] -(1/(ω σ-1 +1))} dw /dτ=[w (1-τ ) -1 ω σ-1 /[1-σ(2-θ )]] { e s 1 σ(1-τ ) [σ (1-θ)/[1-σ(2-θ)]]+1 -(1/(ω σ-1 +1))} where s 1 =(s/s ) [(1-θ)/(σ -1)]/[1-σ (2-θ)]. Here we ca simplify the otatio without affectig ay of our mai results by assumig that the two coutries are idetical i labor edowmet such that s=s, ad therefore s 1 =1 holds. Evaluatig the sigs of dw/dτ ad dw /dτ at τ =0 yields: dw/dτ τ=0 =(w/2){(1-σ)/[1-σ(2-θ )]}, (34) dw /dτ τ=0 =-(w /2){(1-σ)/[1-σ(2-θ )]}, (35)
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 379 where w=w =((θ-1)/θ )2 (θ-σ )/(1-θ)(1-σ) >0. I sum, from (34) ad (35), we obtai the followig relatioship: dw/dτ τ=0 >0, dw /dτ τ=0 <0 whe 0<σ 1 (36) dw/dτ τ=0 >0, dw /dτ τ=0 <0 whe 1<σ (2-θ ) ad σ>1 (37) dw/dτ τ=0 <0, dw /dτ τ=0 >0 whe 1>σ (2-θ ) ad σ>1 (38) dw/dτ τ=0 +dw /dτ τ=0 =0 (39) From (39), the wage effects of a small decrease i the profit tax rate are exactly offset betwee the two coutries. B. Cosumptio Effects We ow examie the impact of a reductio i the home coutry s profit tax o the cosumptio levels of both coutries. I what follows, we divide the cross-coutry price elasticity ito two cases, the case of 0<σ 1 ad the case of σ>1. a) The Case of 0<σ 1 Here, we cosider the case of 0<σ 1, where the cross-coutry price elasticity is relatively small. From (28), (29), (36), ad (39), evaluatig the sigs of de/dτ ad de /dτ at τ=0 yields: de e /dτ τ=0 =(w/2){(1-σ)/[1-σ (2-θ )]+2(1-α)/(θ-1)}>0 (40) de e /dτ τ=0 =-(w /2){(1-σ)/[1-σ (2-θ )]+2(1-α )/(θ-1)}<0 (41) where 1>σ(2-θ) holds from 0<σ 1 ad θ>1. 12 To explai the above, we examie the two terms collected i the brackets i (40). From (39), dw/dτ τ=0 +dw /dτ τ=0 =0. Therefore, the first term i the brackets i (40) is derived by differetiatig the secod term i Equatio (28) with respect to τ ad the cosiderig (30), (32), ad (33). As stated i (30), from (25), the impacts of the profit tax have two opposig effects o the domestic real wage, w. O the oe had, from d e /dτ<0, the tax decrease leads to a shift i labor demad away from the foreig coutry 12 See the Appedix for derivatio of (40) ad (41).
380 SEOUL JOURNAL OF ECONOMICS towards the home coutry, thereby icreasig w ad decreasig w (see Lemma 2). O the other had, from dω e /dτ <0, the tax decrease iduces a egative wage respose i the home coutry, ad a positive wage respose i the foreig coutry (see Lemma 3). Hece, the first term i the brackets i (40) deotes the compositio of the positive labor demad shiftig effect ad the egative terms-of-trade effect. I additio, the secod term i the brackets i (40), which is derived by differetiatig the third term i Equatio (28) with respect to τ, deotes the ret redistributio effect of the domestic profit tax decrease. The tax decrease leads the domestic govermet to shift part of the tax reveue from home coutry to foreig coutry as a ret icome repatriatio to foreig households. Hece, the ret redistributio effect is egative for the home coutry, ad positive for the foreig coutry (see Lemma 1). I sum, the egative effect of a margial decrease i the domestic profit tax rate is the sum of the terms-of-trade effect ad the ret redistributio effect, while the beefit of the domestic profit tax decrease is the labor demad shiftig effect. Therefore, the et effect depeds o the relative stregth of these pressures. However, if 0<σ 1, the former effects always domiate the latter, so we obtai the followig propositio. Propositio 1: Whe 0<σ 1 is assumed, a decrease i the home coutry s profit tax rate lowers home coutry cosumptio C=e. Coversely, the tax decrease raises foreig coutry cosumptio C =e. The above mechaism ca be ituitively explaied as follows: A decrease i τ leads to (1-τ)π h >π f ad thereby iduces some firms to relocate ito the home coutry. Sice 0<σ 1, this implies that the cross-coutry price elasticity for each product is smaller tha uity. Thus, a decrease i the profit tax rate leads to a icrease i the ω required for the after-tax profits to be equalized betwee the two coutries from dω e /dτ <0 (see Equatio (25)). Sice a icrease i ω implies fall i the home coutry s terms of trade, this has a egative effect for home cosumptio ad a positive effect for foreig cosumptio. I additio, the reductio i the profit tax rate raises the wage rate of the home coutry because of relocatio of firms away from the foreig coutry toward the home coutry from d e /dτ <0 (the labor demad shiftig effect i (25)). Furthermore, the profit tax decrease shifts partial ret icomes from the home to the foreig owers (the ret redistributio effect ). Thus, we obtai ambiguous effects of a margial profit
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 381 tax reductio o cosumptio i each coutry. However, 0<σ 1 implies that the available goods are less substitutable for each other globally, so that a relatively large icrease i ω is required for the after-tax profits to be equalized followig the profit tax reductio. This is why the egative terms-of-trade effect domiates the positive labor demad shiftig effect i the home coutry uder 0<σ 1 (see Equatios (30) ad (36)). Thus, from (40) ad (41), a reductio i the profit tax rate lowers home coutry cosumptio ad raises foreig coutry cosumptio uder 0<σ 1. b) The Case of σ>1 Next, we cosider the case of σ>1, where the cross-coutry price elasticity is relatively large. I additio, this case is divided ito two cases by otig the size of θ; 1<σ (2-θ ) ad 1>σ (2-θ ). I the case of σ>1 ad 1<σ (2-θ ) where the cross-coutry price elasticity is large ad the withi-coutry price elasticity is small, from (40) ad (41), the cosumptio impacts of the profit tax reductio are the same as the results i the Propositio 1. Therefore, we obtai the followig propositio. Propositio 2: Whe 1<σ(2-θ) ad σ>1 are assumed, a decrease i the home coutry s profit tax rate lowers home coutry cosumptio C=e. Coversely, the tax decrease raises foreig coutry cosumptio C =e. This result is explaied ituitively as follows. I the home coutry, whe 1<σ (2-θ ) ad σ>1, the terms-of-trade effect is positive from dω e /dτ>0, while the labor demad shiftig effect is egative from d e /dτ>0 (see Equatio (26)). I additio, i this case, from (30) ad (37), the egative labor demad shiftig effect always domiates the positive terms-of-trade effect. This is because the coditio, 1<σ (2-θ) ad σ>1, implies that σ is restricted to be relatively large, so that available goods are required to be more substitutable for each other globally. Therefore, the coditio, 1<σ (2-θ ) ad σ>1, reduces the impact of the positive terms-of-trade effect, because a relatively small decrease i ω is required for the after-tax profits to be equalized followig the profit tax reductio. This is why the egative labor demad shiftig effect always domiates the positive terms-of-trade effect uder 1<σ(2-θ ) ad σ>1. I additio, recall that a decrease i the profit tax rate redistributes ret icomes partially from the home to the foreig coutry, i.e., the ret redistributio effect. This leads to a reductio i
382 SEOUL JOURNAL OF ECONOMICS total icome i the home coutry, thereby reducig home coutry cosumptio. Therefore, this effect reiforces the egative labor demad shiftig effect, ad hece, de/dτ τ=0 >0. The opposite mechaism is valid for the foreig coutry, so that de e /dτ τ=0 <0. I cotrast, whe 1>σ(2-θ) ad σ>1, for the home coutry, the terms-of-trade effect is egative from dω e /dτ <0, while the labor demad shiftig effect is positive from d e /dτ<0 (see Equatio (27)). I this case, from (30) ad (38), the positive labor demad shiftig effect domiates the egative terms-of-trade effect. This is because the coditio, 1>σ(2-θ) ad σ>1, implies that σ ad θ are both large, so that available goods are required to be more substitutable for each other globally. Therefore, the coditio, 1>σ(2-θ) ad σ>1, reduces the impact of the egative terms-of-trade effect, because a relatively small decrease i ω is required for the after-tax profits to be equalized betwee the two coutries. This is why the positive labor demad shiftig effect always domiates the egative terms-of-trade effect uder 1>σ (2-θ ) ad σ>1. However, there is yet aother effect, the ret redistributio effect, as a additioal egative effect. Therefore, we obtai ambiguous effects of the margial profit tax reductio o cosumptio of each coutry. However, de e /dτ τ=0 <0 ad de e /dτ τ=0 >0 are obtaied if α is close to 1. This is because if α is close to 1, the egative ret redistributio effect approaches zero. Thus, whe the cross-coutry price elasticity ad the withi-coutry price elasticity are both large, ad a large proportio of the firm profits accrue to domestic residets, the a decrease i the domestic profit tax rate will effectively icrease domestic real cosumptio ad decrease foreig cosumptio. Hece, we obtai the followig propositio. Propositio 3: Whe 1>σ (2-θ) ad σ>1 are assumed ad whe α is sufficietly large (close to 1), a decrease i the home coutry s profit tax rate raises home coutry cosumptio C=e. Coversely, the tax decrease lowers foreig coutry cosumptio C =e. If α is relatively small, we may get the opposite results. This propositio shows that whe θ ad σ are both large such that whe 1>σ(2-θ ) ad σ >1 ad α is close to 1, the cosumptio impacts of the profit tax reductio of oe coutry are couter to the results of Propositio 1 ad 2.
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 383 C. Welfare Effects I the previous subsectio, it was show how a margial profit tax decrease affects cosumptio. We ow cosider the impact of a decrease i the home coutry s profit tax rate o the welfare of both coutries. The utility of a home household is U=log e e. Differetiatig this with respect to τ ad evaluatig the resultig equatio at τ=0 yields: du/dτ τ=0 =( U/ e e )(de e /dτ) τ=0 =e e -1 (de e /dτ) τ=0 Similarly, the margial impact of a decrease i the corporatio tax rate o the foreig household s utility is du /dτ τ=0 =e e -1 (de e /dτ) τ=0. As show, the sig depeds solely o the sig of de e /dτ ad de e /dτ, because U ad U are strictly icreasig fuctios of e e ad e e, respectively. Hece, we obtai the followig Propositio 4: du/dτ τ=0 >0 ad du /dτ τ=0 <0 whe 0<σ 1 du/dτ τ=0 >0 ad du /dτ τ=0 <0 whe 1<σ(2-θ) ad σ>1 du/dτ τ=0 <0 ad du /dτ τ=0 >0 whe 1>σ(2-θ), σ>1 ad α closes to 1 The above results are similar to those of the propositios obtaied i the previous subsectio. I particular, the third results i Propositio 4 imply that the home coutry will have a icetive to ehace firm relocatio ito the home coutry by reducig the domestic profit tax rate. Thus, it is better if a reductio i the profit tax rate takes place i the home coutry as it leads to a icrease i domestic welfare whe the cross-coutry price elasticity ad the withi-coutry price elasticity are both large, ad most firms are domestically owed. V. Coclusios This paper has preseted the impact of chagig profit tax rate o iteratioal firms locatios ad o coutries welfare usig a twocoutry moopolistic competitio trade model. I such a model, it was foud that two types of elasticity of substitutio offer the key to uderstadig the potetial impacts of the profit tax: 1) whe the crosscoutry price elasticity is relatively small, or whe the withi-coutry price elasticity is small ad the cross-coutry price elasticity is large, a
384 SEOUL JOURNAL OF ECONOMICS decrease i domestic profit tax rate ca decrease domestic welfare ad raise foreig welfare; ad 2) whe the withi-coutry price elasticity ad the cross-coutry price elasticity are together large, ad a large proportio of the firm profits accrue to domestic residets, the a decrease i the domestic profit tax rate will effectively icrease domestic welfare ad decrease foreig welfare. The results the idicate the followig policy implicatio: if the aim of profit tax policy is to attract foreig firms to the domestic coutry ad icrease domestic welfare, the taxes must be reduced if the cross-coutry price elasticity ad the withi-coutry price elasticity are both large ad if most firms are domestically owed. The model developed here is rather simple i a umber of respects. This suggests may directios for future research. Firstly, this paper focused o aalyzig the effects of chagig profit tax rate o several key variables uder the assumptio that the coutries i the model are of the same size. Aalyzig the effects of differet coutry size might be importat. Secodly, the firms decisio to relocate is rather simplistic i this framework as it postulated that firm relocatio depeds o crosscoutry profit differeces. This formulatio may be urealistic because the iteratioal relocatio of firms is also determied by may other factors besides the relative price ad the profit tax rate. Icorporatig other factors affectig relocatio (wage tax, cosumptio tax, trasport costs, tariff, ad public goods) may be importat. Thirdly, this paper assumed implicitly that each household exogeously ows a equity portfolio that is perfectly diversified across all firms. However, this assumptio may be urealistic because real-world portfolios exhibit home bias, as the home households ivest most of their wealth i local firms. 13 Therefore, icorporatig the home bias issue i the aalysis might be iterestig. Furthermore, as the mai purpose of this paper is to aalyze the effects of a decrease i a exogeously fixed profit tax, iteractios betwee the two govermets i settig optimal profit taxes are ot cosidered i the model. Therefore, extedig the preset model to a ocooperative game theoretic aalysis ad takig the profit tax as a strategic variable may be iterestig. Fially, this paper has attempted to shed light o the theoretical aspects of the effects of profit taxes uder perfect mobility of firms. Therefore, whether the results of this paper are cosistet with empirical evidece is the questio that we must 13 For a discussio o the puzzle of home bias i equity portfolios, see Obstfeld ad Rogoff (2000).
A TWO-COUNTRY MONOPOLISTIC COMPETITION TRADE MODEL 385 cosider ext. These issues remai for future research. (Received 13 September 2008; Revised 4 Jue 2009; Accepted 5 Jue 2009) Appedix Derivatio of s w : Substitutig C=e ito the household s budget costrait i the home coutry (1) yields 1 0 j α((1 τ) π dj + π dj ) + sw + sz = se. j (A.1) Similarly, i the case of the foreig coutry, 1 0 j (1 α)((1 τ) π dj + π dj) + s w = s e. j (A.2) Combiig (A.1) ad (A.2) yields 1 τ π 0 j π j se + s e = (1 ) dj + dj + sw + s w + sz. (A.3) Substitutig the govermet budget costrait, τ π, ito (A.3) 0 j dj = sz yields 1 w + = π 0 j + π j + + (A.4) s se s e dj dj sw s w. Furthermore, substitutig (16) ito (A.4) yields s w =(θ/(θ-1))(sw+s w ). (A.5) Fially, substitutig (20) ad (21) ito (A.5) yields s w =s -1/(1-θ) ω -1 [ω σ-1 +1] -1/(1-σ ) +s (1-) -1/(1-θ) [ω σ -1 +1] -1/(1-σ). (A.6) Derivatio of (40) ad (41): From the household s budget costrait i the home coutry (1) ad the govermet budget costrait, τπ h =
386 SEOUL JOURNAL OF ECONOMICS sz, we obtai e=(α/s)(π h +(1-)π f )+w+(1-α )(τπ h /s). (A.7) Similarly, i the case of the foreig coutry, e =((1-α)/s )(π h +(1-)π f )+w -(1-α)(τπ h /s ). (A.8) Summig the real profit flows (16) across all firms yields π h +(1-)π f =(1/θ)s w. (A.9) I additio, substitutig (A.5) ito (A.9) yields π h +(1-)π f =(1/(θ-1))(sw+s w ), (A.10) Substitutig (A.5) ito π h i (16) yields π h = -1 ω (σ -1) [ω σ -1 +1] -1 (1/(θ-1))(sw+s w ) (A.11) The, substitutig (A.10) ad (A.11) ito (A.7) ad (A.8), respectively, yields e=(α /s)(1/(θ-1))(sw+s w )+w+((1-α)/s)τω (σ-1) [ω σ-1 +1] -1 (1/(θ-1))(sw+s w ), (A.12) e =((1-α )/s )(1/(θ-1))(sw+s w )+w -((1-α)/s )τω (σ-1) [ω σ -1 +1] -1 (1/(θ-1))(sw+s w ). (A.13) Whe s=s, (A.12) ad (A.13) ca be rewritte as e=(α/(θ-1))(w+w )+w+((1-α)/(θ-1))τω (σ-1) [ω σ-1 +1] -1 (w+w ), (A.14) e =((1-α)/(θ-1))(w+w )+w -((1-α)/(θ-1))τω (σ-1) [ω σ-1 +1] -1 (w+w ). (A.15) Differetiatig (A.14) with respect to τ ad evaluatig the resultig at τ=0 ad the cosiderig (24), (34), ad (39) yields de e /dτ τ=0 =(w/2){(1-σ)/[1-σ(2-θ)]+2(1-α)/(θ-1)}, (A.16)
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