Horizontally-integrated MNE and plant heterogeneity

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1 Bank Kredyt 44 (6), 203, Horzontally-ntegrated ME and plant heterogenety Andrze Ceślk Submtted: 5 January 203. Accepted: 28 July 203. Abstract In the paper we develop a monopolstcally compettve general equlbrum model of horzontally- -ntegrated multnatonal enterprse (ME) wth heterogeneous plants. We demonstrate that smaller productvty dfferences between domestc and foregn plants ncrease the level of multnatonal actvty. We also show that the level of multnatonal actvty s the most ntensve between countres of the smlar sze. Fnally, we show that the relatve wage ncreases (decreases) wth relatve productvty of workers and the degree of product dfferentaton when the home country s smaller (bgger) compared to the foregn country. Keywords: horzontal ntegraton, ME, plant heterogenety JEL: F23 Unversty of Warsaw, Department of Economcs; e-mal: ceslk@wne.uw.edu.pl.

2 606 A. Ceślk. Introducton The late 970s and early 980s saw the frst wave of maor developments n the theory of nternatonal trade. A number of authors, ncludng Krugman (979; 980; 98), Dxt and orman (980), Lancaster (980), Helpman (98), Brander (98), Ether (982), and Brander and Krugman (983) started ntroducng elements of ndustral organzaton nto the study of nternatonal trade. These developments were the response to growng dssatsfacton wth the neoclasscal trade theory that was unable to explan the actual foregn trade and nvestment patterns. Ths led the emergence of the frst strand n the so-called new trade theory (TT). The tradtonal trade theory was crtczed because of relyng on the set of very extreme assumptons such as constant returns to scale (CRS), perfect competton and product homogenety. The frst strand n the TT relaxed these assumptons and added ncreasng returns to scale (IRS), mperfect competton and product dfferentaton to the tradtonal trade models based on the concept of comparatve advantage. Accordng to the TT, trade and the gans from trade can arse ndependently of any pattern of comparatve advantage as frms explot economes of scale and pursue strateges of product dfferentaton. These early developments n the TT provded a set of models that proved extremely useful n studyng the emergence of multnatonal enterprses (MEs) and foregn drect nvestment (FDI). Ths resulted n the development of the new theory of multnatonal enterprse (TME) n the md 980s and the 990s. The TME was a response to the neoclasscal theory of factor movements. The early theoretcal studes of FDI such as Mundell (957), MacDougall (960) or Kemp (962) vewed the expanson of multnatonal frms as the transfer of fnancal or physcal captal. However, as argued by Krugman (995) wth the development of the TT lterature t turned out that the expanson of MEs descrbed as FDI and tracked va balance-of-payments statstcs was a conceptual msunderstandng. Lpsey (2004, p. 334), n hs survey paper noted that accordng to the new concept FDI s rather a set of economc actvtes or operatons carred out n a host country by frms controlled or partly controlled by frms n some other (home) country. These actvtes are, for example, producton, employment, sales, the purchase and the use of ntermedate goods and fxed captal, and the carryng out of research. Thus, n ths new concept of FDI no movement of physcal or fnancal captal s necessary, although t mght take place. Whle many models n the lterature were proposed to study nternatonalzaton of producton two dstnct reasons why a frm should go multnatonal were dentfed: effcency seekng and market seekng. Accordng to the frst one frms nternatonalze producton and become multnatonals n order to get access to nputs at lower costs. Foregn drect nvestment undertaken wth the am of reducng producton costs s often called vertcal FDI as t nvolves fragmentng producton processes and locatng each stage n the country where the factors used ntensvely n that partcular stage In terms of the theory t was Caves (97) who, buldng on the neoclasscal specfc factor model, frst argued that FDI s assocated wth the transfer of frm-specfc captal rather than physcal or fnancal captal, although the dea that multnatonal frms are vehcles for the transfer of frm-specfc assets goes back at least to Hymer (960). Accordng to Markusen and Maskus (2003) the approach proposed by Caves (97) can be regarded as a crucal step n dfferentatng FDI assocated wth the nflow of frm ntangble assets from the portfolo flows of homogenous captal n the earler neoclasscal models. However, the approach proposed by Caves (97) was stll neoclasscal n many respects and assumng perfect competton, constant returns to scale and product homogenety was unable to adequately address the determnants of FDI. See recent extensons of ths approach n Ceślk (2008; 202).

3 Horzontally-ntegrated ME are relatvely cheap. Accordng to the second one multnatonal frms are vehcles to overcome dstance and lower costs of foregn markets access. Foregn drect nvestment undertaken to serve local markets s often called horzontal FDI and refers to producng abroad roughly the same goods and servces as n the parent country. Horzontal FDI consttutes the largest fracton of multnatonal actvty n the contemporary world economy and occurs mostly between developed countres that are smlar both n terms of ther relatve factor endowments and economc sze. To explan ths phenomenon several models of horzontally ntegrated ME have been developed. Typcally, these models employed the tools used prevously n the TT lterature that allowed addressng explctly the ssues of ncreasng returns and market structure. Intally, these models were extremely smple assumng dentcal factor endowments across countres and/or were based on partal equlbrum frameworks. Probably, the most frequently cted early example of ths approach s the partal equlbrum model of olgopolstc competton developed by Markusen (984) that assumes the exstence of frm-level scale economes as the drvng force for FDI. The multnatonal frm s headquarter produces a servce of a frm-specfc asset that can be smultaneously used n multple plants n a non-rval manner. Therefore, two-plant frms have lower fxed costs than those of two sngle plants and ths motvates multnatonal producton. The orgnal Markusen (984) model was later extended by Horstmann and Markusen (987), Markusen and Venables (998; 2000) and Markusen (2002) and allowed for endogenous market structure and dfferent forms of competton between frms wthn the partal as well as general equlbrum frameworks. In these frameworks frms have dfferent potental channels of enterng a foregn market and each of these channels ncurs dfferent costs. A frm faces a choce between concentratng producton n the home country and servng foregn markets exportng to acheve scale economes and producng abroad to beneft from proxmty to consumers. General-equlbrum extensons of the Markusen (984) model allow relatng the extent of multnatonal actvty to country characterstcs. They predct that gven moderate to hgh trade costs, multnatonal frms wll preval n equlbrum when countres are smlar n sze and n relatve factor endowments. If countres were of dfferent szes but smlar n relatve factor endowments horzontal multnatonals would be at a dsadvantage relatve to natonal frms producng n the large country and servng the small country market through exportng as they would have to nstall costly capacty n the small market. If countres were of smlar sze but dffered n terms of ther relatve factor endowments multnatonal frms would be at a dsadvantage relatve to natonal frms as they would have to ncur a substantal part of ther costs n a hgh-cost locaton, assumng that human captal was ntensvely used n both fxed and varable costs n the multnatonal sector. Another early attempt to ntegrate MEs nto the TT was made by Krugman (983) who extended hs prevous models of nternatonal trade based on monopolstc competton. He consdered a smple model wth only one factor of producton labor and assumed that labor forces of two countres were equal. The perfect symmetry of the model setup resulted n wage equalzaton across countres whch greatly smplfed the analyss. In contrast to the Markusen (984) model whch assumed the same producton technologes both n home and foregn countres, Krugman (983) made an mportant contrbuton to the lterature by allowng the productvtes of labor to dffer between domestc and foregn plants of the same ME.

4 608 A. Ceślk Ths early contrbuton was almost completely overlooked n the subsequent TME lterature but t seems especally mportant n the lght of second wave of maor developments n the trade theory lterature ntated n the early 2000s by Meltz (2003) and Helpman, Meltz and Yeaple (2004) who focused on the role of frm heterogenety and created a new strand n the TT. 2 Ther models, however, allowed for heterogenety among frms n terms of ther productvty but not among the plants belongng to the same frm. Therefore, t s useful to restate and extend the orgnal model of ME proposed by Krugman (983) focusng on an mportant aspect of frm heterogenety to a more general settng and rentegrate t nto the manstream lterature on frm heterogenety and FDI. Hence, the man goal of ths paper s to generalze Krugman (983) model by relaxng the equal country sze assumpton and to derve a broader set of conclusons. In partcular, we endogenze the relatve wages and derve them as a functon of three key model parameters: the relatve labor force, productvty dfferences between domestc and foregn plants and the degree of product dfferentaton. Moreover, we demonstrate that multnatonal sales relatve to domestc sales are maxmzed when countres are of equal sze. Ths fndng s n lne wth the prevous studes by Markusen and hs coauthors. However, n contrast to more complex monopolstc competton models proposed by Markusen and Venables (998) and Markusen (2002, Chapter 8) ths model can be solved analytcally and there s no need to rely on numercal methods to study the propertes of the equlbrum soluton. The structure of ths paper s organzed as follows. In Secton 2 we dscuss the man assumptons of the monopolstcally compettve framework used by Krugman (980; 983) whch s based on the earler model developed by Dxt and Stgltz (977). In Secton 3 we restate equlbrum propertes n the closed economy that would consttute a useful benchmark for the nterpretaton of the results obtaned for the open economy wth multnatonal frms. In Secton 4 we ntroduce the possblty of multnatonal producton allowng for productvty dfferences between domestc and foregn plants. In Secton 5 we determne the equlbrum relatve wages and multnatonal sales. Fnally, Secton 6 summarzed and concludes wth drectons for further study. 2. Man assumptons In ths secton we dscuss the man assumptons underlyng the model of monopolstc competton orgnally developed by Krugman (980) and later extended n Krugman (983) to ncorporate the MEs. Followng hs prevous studes we consder a world that conssts of two countres named Home and Foregn that may dffer n ther sze. Each country has only a sngle homogenous factor of producton called labor. Labor supply n each country s fxed and does not respond to changes n wage rates. Wthn each country labor can produce any of a potentally large number of goods. However, n equlbrum the number of goods actually produced n Home and Foregn countres, 2 In partcular, Meltz (2003) relaxed the key assumpton of the frm symmetry n the Krugman (980) model and ntroduced frm heterogenety n terms of labor productvty. In hs model productvty dfferences among frms are exogenously gven and each frm has to pay fxed costs of entry nto domestc and foregn markets. The model predcts that the most productve frms wth lowest margnal costs can cover the fxed cost of entry and become exporters. Ths model was later extended by Helpman, Meltz and Yeaple (2004) to allow for horzontal FDI.

5 Horzontally-ntegrated ME denoted respectvely by and, wll be smaller than the potental number. Ths s because of the exstence of fxed costs n producton. The technology of producton s assumed to be the same n both countres. To produce a good requres a fxed startup cost and a constant margnal cost afterwards. For smplcty, the same cost functon for all goods produced wthn each country s assumed. Thus, the labor requrements for producton of partcular goods and n Home and Foregn countres are respectvely: l = α + x () l = α + where l and l are respectvely the amounts of labor used n producng the -th good n Home country and -th good n Foregn country; x and x are the outputs of the -th n Home country and the -th good n Foregn country, respectvely; α > 0 s the fxed cost (expressed n terms of labor) and > 0 s the constant margnal cost that s ndependent of the volume of output. x (2) In Home and Foregn countres full employment s assumed, so that the total labor forces n ther economes must be exhausted by employment n producton of partcular goods: l = x L = = ( α + ) = (3) + + l ( α x ) (4) L = = + = + = + where and are the numbers of goods produced n Home and Foregn countres, respectvely; and L and L are the szes of the labor forces n Home and Foregn countres respectvely. Fnally, all resdents n both countres are assumed to have the exactly the same utlty functon nto whch all goods enter symmetrcally: U ( c) = c = (5) + = U ( c ) = c + (6) where c s the consumpton of the -th good and ( 0,) s a fxed parameter that measures the elastcty of substtuton between partcular goods whch s the same n both countres. Each good yelds dmnshng margnal utlty so that consumers would always prefer to have one unt of each good nstead of two unts of ether.

6 60 A. Ceślk Consumers are at the same tme workers. 3 The economy-wde budget constrants for Home and Foregn countres can be wrtten, respectvely, as: = p x = = + p x = + p c L = wl + = p c L = w L = + (7) (8) 3. Benchmark: equlbrum n the closed economy In ths secton we restate the man propertes of the market equlbrum n the closed economy for Home and Foregn countres wth natonal frms only. Ths yelds the optmal prcng condtons ( p, p ), the equlbrum outputs of each frm ( x, x ) and the equlbrum number of goods produced under autarky n each country beng at the same tme the equlbrum number of frms (, ). These results wll consttute a useful benchmark for the nterpretaton of the results obtaned from the model of horzontally-ntegrated MEs developed n the subsequent sectons of the paper. The analyss proceeds as follows. Frst, we analyze consumer behavor n both countres to derve demand functons. Then we derve the proft maxmzng behavor of frms treatng the number of frms as gven. Fnally, we use the free entry assumptons to derve the equlbrum number of frms. Consumers n both countres maxmze ther utlty functons (5) (6) subect to ther budget constrants (7) (8) whch yelds the demand functons for -th and -th goods n Home and Foregn countres, respectvely: c = p wl p = (9) c = p w L + p = + (0) It can be noted that for the large number of goods produced n each country the demand facng an ndvdual frm n each country becomes soelastc and equals ε = ε = ( ). Frms n Home and Foregn countres maxmze the proft functons wth respect to ther sales x and x, respectvely: Π ( x ) = p ( x ) x ( α + x ) w () Π 3 Accordng to Krugman (980, p. 95): output of each good must equal the sum of ndvdual consumptons. If we dentfy ndvduals wth workers, output must equal consumpton of a representatve ndvdual tmes the labor force. α

7 Horzontally-ntegrated ME... 6 Π ( x ) = p ( x ) x ( α + x ) w (2) Gven the constant elastcty of demand n each country Home and Foregn frms charge the proft maxmzng monopoly prces: p = p = w (3) p = p = w (4) The proft maxmzng prces are derved by the standard mark-up prcng rules from equatng margnal costs to margnal revenue. It can be noted that snce α, and w are the same for all frms n Home country prces are the same for all goods, hence ndex can be dropped because of symmetry. Smlarly, snce α, and w are the same for all frms n Foregn country prces are the same for all goods, hence ndex can be dropped. ext, gven the optmal prcng strateges of frms n Home and Foregn countres we need to determne the volume of output for each good. For ths we can use the free entry assumptons. Free entry wll drve down profts to zero n both countres so that n equlbrum prces wll equal average costs. Substtutng (3) (4) nto () (2), respectvely, and equatng to zero yelds the long-run equlbrum outputs of representatve goods n Home and Foregn countres: α x = x = = x = ( ) x (5) It can be noted that the break-even outputs per frm n both countres are exactly the same snce parameters determnng technologes and preferences α, and are the same for all frms n both countres. Fnally, the number of goods actually produced n each country can be determned from the full employment condtons (3) (4): L ( L ) = = αα + (6) x αα L ( L = = α + x α ) (7) 4. Multnatonal enterprses To explan horzontally-ntegrated MEs we modfy the closed economy model descrbed n the prevous secton. For smplcty, suppose that trade costs are prohbtvely hgh but frms n both countres can engage n cross-border FDI by establshng producton subsdares abroad to explot

8 62 A. Ceślk economes of scope. 4 ote, however, that ths s FDI only n the sense of establshng effectve manageral control over producton unts located n dfferent countres and there s no transfer of captal as by assumpton labor s the only factor of producton n ths model. As argued by Krugman (990, p. 277) n hs survey paper on the TME the dea of economes of scope s key for understandng ( ) multnatonal modern frms. Accordng to Panzar and Wllg (977) economes of scope arse when a frm that undertakes two actvtes wll have lower ont costs than two frms undertakng the actvtes separately. We assume that fxed costs do not occur n producton but rather n head quarter actvtes such as research and development (R&D). Accordng to Krugman (983, p. 6) the asset acqured by the fxed cost mght be technology n the usual sense, or t mght be less easly specfed know-how n management, marketng, etc. Ths means that these fxed costs are not ted to the locaton of producton and once they have been ncurred they do not have to be repeated even f producton takes place n more than one locaton. At the same tme t s assumed that there are also addtonal costs of producng abroad related to unfamlarty wth local language, customs, tax or legal system, etc. Typcally, such costs are modeled as addtonal fxed costs of foregn market entry (Markusen 984; Markusen, Venables 998; Markusen 2002; Helpman, Meltz, Yeaple 2004). However, n contrast to that strand n the lterature we follow an alternatve approach proposed by Krugman (983) and consder only those costs that rase average varable costs of producton. In partcular we assume that n producton plants located abroad labor s only a fracton k < tmes as productve as t s n producton at home. Therefore, the total costs ncludng the R&D and producton costs for a representatve Home country multnatonal frm producng for both domestc and foregn markets are: C ( x, x ' ) = αw + x w + ( / k) x ' w < C ( x, 0) + C (0, x ' ) (8) where x ' α s the extra output produced n Foregn country, C ( x, 0) = ( α + x ) w s the cost of producng only for the Home country market whle C ( 0, x ') = ( α + ( / k) x ') w s the cost of producng only for the Foregn country market. α It can be noted that due to economes of scope resultng from the common R&D fxed cost the ont cost of producng for two markets together s lower than the costs of producng for each market separately. Thus, the multnatonal frm wll have lower costs than the sngle country frms. Smlarly, for the representatve foregn country multnatonal frm we have: C ( x, x ') = αw + x w + ( / k) x ' w < C ( x, 0) + C (0, x ') (9) where, x ' s the extra output produced n Home country, C = α ( x, 0) ( + x ) w s the cost of producng only for the Foregn country market whle C α (0, x ' ) = ( + ( / k) x ' ) w s the cost α of producng only for the Home country market. Π 4 The assumpton on prohbtvely hgh trade costs s made here for analytcal convenence and not because t s realstc. If the trade costs were not prohbtve both trade and FDI as alternatve modes of nternalzaton would have to be consdered as, for example, n Markusen (2002) or Helpman, Meltz and Yeaple (2004).

9 Horzontally-ntegrated ME The proft functons for home and foregn country multnatonal frms can be wrtten, respectvely, as: Π ( x, x ') = p ( x ) x + p '( x ') x ' ( α + x ) w ( / k) x ' w (20) Π ( x, x ') = p ( x ) x + p '( x ') x ' ( α + x ) w ( / k) x ' w (2) where p ' ( x ') s the prce of the extra output produced by the Home country multnatonal frm n the producton subsdary located n Foregn country whle p '( x ') s the prce of the extra output produced by the Foregn country multnatonal frm n the producton subsdary located n Home country. Proft maxmzaton of the representatve Home country multnatonal frm wth respect to ts domestc and foregn sales x and x ' yelds the optmal prcng strateges for Home and Foregn country markets, respectvely: p = p = w (22) p ' = p' = w k (23) Smlarly, proft maxmzaton of the representatve Foregn country multnatonal frm wth respect to ts domestc and foregn sales x and x ' yelds the optmal prcng strateges for Foregn and Home country markets, respectvely: p = p = w (24) p ' = p ' = w k (25) It can be noted that n the case of the open economy αwth multnatonal frms prces charged by multnatonal frms n ther own markets are exactly the same as n the case of the closed economy wthout multnatonal frms. However, due to lower effcency n producton n subsdares located abroad prces charged by multnatonal frms n ther overseas markets can be hgher compared to prces charged n ther own markets dependng on the relatve wages. Free entry condtons for the representatve Home and Foregn country multnatonal frms can be used to determne the volumes of output produced by each frm for each market. Substtutng solutons for equlbrum prces (22) (23) for the Home country multnatonal frm nto ts proft functon (20) and settng t to zero yelds: α x = x = w x ' ( ) k ( w ) (26)

10 64 A. Ceślk Smlarly, substtutng solutons for equlbrum prces (24) (25) for the Foregn country multnatonal frm nto ts proft functon (2) and settng t to zero yelds: x = x = α ( ) k x w ' (27) ( w ) It can be noted that equatons (26) (27) determne sales of multnatonal frms n ther own markets n Home and Foregn countres, respectvely, gven ther sales n overseas markets. Ths leaves us wth four unknowns and two equatons only. However, we know from the consumer utlty maxmzaton problems for Home and Foregn countres (5) (6) the relatve demands for goods produced by Home and Foregn country multnatonals for the Home country market as well as the relatve demands for goods produced by Home and Foregn country multnatonals for the Foregn country market. Ths gves us two addtonal equatons. The structure of consumer preferences descrbed by the love of varety approach mples that consumers n both countres wll consume all the avalable goods. Gven the symmetrc frm prcng strateges n both countres (22) (25) the modfed economy-wde budget constrants for Home and Foregn countres can be wrtten, respectvely, as: wl = px + p ' w L = p' x' + x ' p x (28) (29) However, snce goods produced n overseas ME afflates are more expensve the amounts consumed wll be smaller. The solutons to consumer utlty maxmzaton problems for both countres (5) (6) wth respect to the modfed economy wde budget constrants (28) (29) yeld now relatve demands for goods nvented n Home and Foregn countres: c c p = ( p ' ) ' c ' c p ' = ( p ) w Therefore, substtutng (30) (3) nto (26) (27) yelds solutons for equlbrum sales n each market as functons of relatve wages w/w and productvty dfferental k: = k = k (30) (3) α x = ( ) ( w w ) k k 2 (32)

11 Horzontally-ntegrated ME x α = ( ) w ( w ) 2 k k (33) α k x ' = ( ) αk x ' = ( ) k ( ) 2 w w k w k ( w ) k 2 (34) (35) α It can be noted that the hgher Home country wage rate relatve to the Foregn country wage rate ncreases output produced by the Home country multnatonal frm for the Home country market and reduced output produced for the Foregn country market. The reverse s true for the Foregn country multnatonal whch reduces ts output for the Home country market and ncreases output for the Foregn country market when the relatve wage rate ncreases. In the extreme case of the model when wages across countres are equal and there s no productvty dfference between domestc and Foregn producton subsdares the volumes of output for each frm n each country are the same and equal to the half of the total volumes produced n the closed economy (5). The numbers of multnatonal frms n each country expressed as a functon of the volumes of output for each market can be determned usng the full employment condtons. Equatng labor supply to labor demand n each country yelds: L = ( α + x) + ( / k) x ' α L = ( α + x ) ( / k) x' (36) (37) Solvng for and we obtan: L( α ) k + x xl = 2 2 ( α )( ) k + x α + x xx α α L α k x L L ( ) k α + x x L = 2 2 ( α + x)( α + x ) k xx (38) (39)

12 66 A. Ceślk 5. Equlbrum relatve wages and multnatonal sales The last thng that we need to determne to be able to solve the open economy model wth MEs s the relatve wage. Ths can be done usng the economy-wde budget constrants for both countres (28) (29). Dvdng (28) by (29) and substtutng solutons for prces (22) (25), quanttes (32) (35) and the number of domestc and foregn multnatonal frms (38) (39), we obtan the followng quadratc equaton: 2 2 ( k ) ( ) k k + ω + ω k + k + k = 0 (40) where ω = w w s the relatve wage and = L L s the relatve country sze. Ths quadratc equaton has two roots: one postve and one negatve. The postve root s the only meanngful soluton as the relatve wage cannot be negatve. Therefore, the equlbrum relatve wage s gven by the followng relatonshp: + ω = + k k (4) It turns out that the relatve wage (ω) depends on three exogenously gven parameters of the model: the relatve country sze ( ), the degree of product dfferentaton () and the relatve productvty of workers n plants located abroad and at home (k). The relatve wage s an ncreasng functon n the relatve country sze. Moreover, the relatve wage ncrease (decreases) wth relatve productvty of workers and the degree of product dfferentaton when the Home country s smaller (bgger) compared to the Foregn country. Fnally, t can be noted that wages n both countres are equalzed when ether: ) countres are of equal sze L = L (.e. = ), ) products are very dfferentated and no substtuton between dfferent varetes s possble (.e. = 0) and/or ) workers n plants located at home and abroad are equally effcent (.e. k = ). Substtuton of the equlbrum relatve wage (4) nto (32) (35) allows us to obtan equlbrum output volumes for domestc and local sales for the Home country and Foregn country frms. Then, substtutng the equlbrum output volumes nto (38) (39) the total number of multnatonal frms orgnatng from each country can be obtaned. Fnally, we can also determne the degree of multnatonal actvty defned by the rato of multnatonal to domestc sales (RMDS) for both Home and Foregn country frms. The sales of the Home country frms n Foregn and Home markets can be respectvely defned as: ' x' w x k = (42) px = wx (43) p

13 Horzontally-ntegrated ME Smlarly, the sales of the Foregn country frms n Home and Foregn markets can be defned as: p ' x p ' wxk = (44) = w x (45) x It can be noted that multnatonal sales are the sum of (42) and (44), whle domestc sales are the sum of (43) and (45). Hence, the rato of multnatonal to domestc sales can be wrtten as: w x + wx RMDS = k (46) wx + w x Dvdng the numerator and denomnator of (46) by w x allows us to express the RMDS as the functon of the relatve country sze: RMDS = n( ) + n( ) + k (47) where n ( ) = s the relatve number of frms whch s an ncreasng functon of the relatve country sze. Takng the dervatve of (47) wth respect to the relatve country sze t s possble to demonstrate that the rato of multnatonal to domestc sales s maxmzed when countres are of equal sze. Then, the RMDS smplfes to: max RMDS = k (48) It can be noted that when countres are of equal sze RMDS depends only on two parameters: the degree of product dfferentaton () and the relatve productvty of workers n plants located abroad and at home (k). The hgher degree of product dfferentaton (.e. the lower value of ) the hgher the rato of multnatonal to domestc sales. Smlarly, the lower the productvty dfference between domestc and foregn plants (.e. the hgher the value of k) the hgher the rato of multnatonal to domestc sales. When workers n plants located at home and abroad are equally productve (.e. k = ), or/and goods are very dfferentated (.e. = 0) the rato of multnatonal sales to domestc sales equals. Ths means that the volume of multnatonals sales s equal to the volume of domestc sales. 6. Conclusons Followng the new strand n the trade lterature that focuses on frm heterogenety, n the paper we developed a monopolstcally compettve general equlbrum model of horzontal foregn drect

14 68 A. Ceślk nvestment that s a generalzaton and extenson of the early work of Krugman (983). However, n contrast to ths strand new that assumes productvty dfferences between frms wthn each country, we allowed for productvty dfferences between producton plants located at home and abroad belongng to the same multnatonal enterprse. We endogenzed the relatve wages and expressed them as the functon of the relatve country sze, the degree of product dfferentaton and the productvty dfference between the domestc and Foregn plants of multnatonal frms. We showed that the relatve wage s an ncreasng functon n the relatve country sze. Moreover, the relatve wage ncreases (decreases) wth relatve productvty of workers and the degree of product dfferentaton when the Home country s smaller (bgger) compared to the Foregn country. Furthermore, we demonstrated that the multnatonal actvty s the most ntensve between countres of the smlar sze. Ths fndng s n lne wth predctons of the studes by Markusen and hs coauthors and emprcal evdence on FDI patterns quoted n ther studes. We also showed that smaller productvty dfferences between domestc and foregn plants ncrease the level of multnatonal actvty. The proposed theoretcal framework should be complemented wth future emprcal studes amed at verfyng the predctons of the model based on the frm and plant level data. An especally promsng research area would be to test whether ndeed there are sgnfcant productvty dfferences between plants that belong to the same ME that are located n dfferent countres. Moreover, t would also be nterestng to test study the behavor of productvty dfferences between domestc and foregn plants over tme to see whether these dfferences are permanent or declnng over tme wth technology standardzaton across all plants n the long run. References Brander J.A. (98), Intra-ndustry trade n dentcal commodtes, Journal of Internatonal Economcs, (), 4. Brander J., Krugman P. (983), A recprocal dumpng model of nternatonal trade, Journal of Internatonal Economcs, 5(3 4), Caves R.E. (97), Internatonal corporatons: the ndustral economcs of foregn nvestment, Economca, 38(49), 27. Ceślk A. (2008), Multnatonal frms, nternatonal knowledge flows and dual labor markets n developng economes, Revew of Development Economcs, 2(), Ceślk A. (202), Multnatonal enterprses, foregn knowledge spllovers and host country wages, Equlbrum. Quarterly Journal of Economcs and Economc Polcy, 7(), Dxt A.K., Stgltz J.E. (977), Monopolstc competton and optmum product dversty, Amercan Economc Revew, 67(3), Dxt A.K., orman V. (980), Theory of nternatonal trade. A dual general equlbrum approach, Cambrdge Unversty Press, Cambrdge. Ether W.J. (982), atonal and nternatonal returns to scale n the modern theory of nternatonal trade, Amercan Economc Revew, 72(3),

15 Horzontally-ntegrated ME Helpman E. (98), Internatonal trade n the presence of product dfferentaton, economes of scale and monopolstc competton: a Chamberln-Heckscher-Ohln approach, Journal of Internatonal Economcs, (3), Helpman E., Meltz M.J., Yeaple S.R. (2004), Export versus FDI wth heterogeneous frms, Amercan Economc Revew, 94(), Horstmann I., Markusen J.R. (987), Strategc nvestments and the development of multnatonals, Internatonal Economc Revew, 28(), Kemp M.C. (962), Foregn drect nvestment and the natonal advantage, Economc Record, 38(8), Hymer S.H. (960), The nternatonal operatons of natonal frms: a study of foregn drect nvestment, MIT, Department of Economcs, Cambrdge. Krugman P. (979), Increasng returns, monopolstc competton, and nternatonal trade, Journal of Internatonal Economcs, 9(4), Krugman P. (980), Scale economes, product dfferentaton, and the pattern of trade, Amercan Economc Revew, 70(5), Krugman P. (98), Intra-ndustry specalzaton and the gans from trade, Journal of Poltcal Economy, 89(5), Krugman P. (983), The new theores of nternatonal trade and multnatonal enterprse, n: D.B. Audretsch, Ch.P. Kndleberger (eds.), The multnatonal corporaton n the 980s, MIT Press, Cambrdge. Krugman P. (990), Multnatonal enterprse: the old and the new n hstory and theory, orth Amercan Revew of Economcs and Fnance, (2), Krugman P. (995), Increasng returns, mperfect competton and the postve theory of nternatonal trade, n: G. Grossman, K. Rogoff (eds.), Handbook of nternatonal economcs, orth-holland, Amsterdam. Lancaster K. (980), Intra-ndustry trade under perfect monopolstc competton, Journal of Internatonal Economcs, 0(2), Lpsey R.E. (2004), Home- and host-country effects of foregn drect nvestment, n: R.E. Baldwn, A.L. Wnters (eds.), Challenges to globalzaton: analyzng the economcs, The Unversty of Chcago Press, Chcago. MacDougall G.D.A. (960), The benefts and costs of prvate nvestment from abroad: a theoretcal approach, Oxford Bulletn of Economcs and Statstcs, 22(3), Markusen J.R. (984), Multnatonals, mult-plant economes and the gans from trade, Journal of Internatonal Economcs, 6(3 4), Markusen J.R. (2002), Multnatonal frms and the theory of nternatonal trade, MIT Press, Cambrdge. Markusen J.R., Maskus K. (2003), General equlbrum approaches to the multnatonal enterprse: a revew of theory and evdence, n: E.K. Cho, J. Harrgan (eds.), Handbook of nternatonal trade, Blackwell Publshng, Malden. Markusen J.R., Venables A.J. (998), Multnatonal frms and the new trade theory, Journal of Internatonal Economcs, 46(2),

16 620 A. Ceślk Markusen J.R., Venables A.J. (2000), The theory of endowment, ntra-ndustry and multnatonal trade, Journal of Internatonal Economcs, 52(2), Meltz M.J. (2003), The mpact of trade on ntra-ndustry reallocatons and aggregate ndustry productvty, Econometrca, 7(6), Mundell R.A. (957), Internatonal trade and factor moblty, Amercan Economc Revew, 47(3), Panzar J.C., Wllg R.D. (977), Economes of scale n mult-output producton, Quarterly Journal of Economcs, 9(3),

17 Horzontally-ntegrated ME Techncal appendx. Dervaton of the demand functons To derve the demand functon facng an ndvdual frm n Home country we need to solve a decson problem of a representatve consumer: maxu( c) = c c = s. t. c p = wl = To solve ths problem we set up a standard Lagrangan: = c + λ wl c p = = c λp where λ denotes the shadow prce (margnal utlty of ncome). Ths yelds the frst order condton (FOC) that can be wrtten as: c λp c = λ p = λ c λ λ = ( ) p λ Then, we substtute the FOC nto the budget constrant to obtan: = λ = c p ( p ) p = wl = λ ( p ) = wl = = λ λ = wl wl = p Fnally, we substtute ths back nto the FOC to elmnate λ and obtan the demand functon (9): c = p wl p In a smlar manner we can also derve the demand functon facng an ndvdual frm n Foregn country (0).

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