Kiel Institute for World Economics. On the Coexistence of National Companies and Multinational Enterprises

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1 Kiel Institute for World Eonomis D 2400 Kiel Kiel Working Paper o. 8 On the Coexistene of ational Companies and Multinational Enterprises by Jörn Kleinert September 2003 The responsibility for the ontents of the working papers rests with the author, not the Institute. Sine working papers are of a preliminary nature, it may be useful to ontat the author of a partiular working paper about results or aveats before referring to, or quoting, a paper. Any omments on working papers should be sent diretly to the author.

2 On the Coexistene of ational Companies and Multinational Enterprises* Abstrat ational and multinational ompanies oexist in many setors of all developed ountries. owever, eonomi models fail to reprodue this fat beause of the assumption of symmetry between ompanies. To show that the symmetry assumption is the reason for this failure, a two-ountry general equilibrium model is set up where multinational enterprises emerge endogenously in reation to exogenously indued market integration. In a model version with symmetri ompanies, stable mixed equilibria with national and multinational ompanies do not exist, beause all ompanies deide to internationalize prodution at the same onditions. In ontrast, if ompanies are allowed to differ, there exist a wide range of eonomi onditions where national and multinational ompanies oexist. Keywords: Globalization, Multinational Enterprises, Exports, Market Struture JEL-Classifiation: F2, F23, L22 Jörn Kleinert Kiel Institute for World Eonomis 2400 Kiel, Germany Tel : Fax : j.kleinert@ifw.uni-kiel.de * The author thanks the partiipants of the 5 th Passau workshop on International Eonomis for lively disussion and valuable omments.

3 . Introdution There is no doubt that national and multinational ompanies oexist in many setors and many eonomies. Although the number of multinational enterprises (MEs) has inreased signifiantly in reent years, there are no signs of exporting national ompanies (Cs) dying out. Almost all industries are haraterized by a stable struture onsisting of both, Cs and MEs. Moreover, Cs oexist in many industries with two groups of MEs: with MEs based in the same ountry and with affiliates of MEs based in foreign ountries. Models of MEs an, generally, not reflet this oexistene. This is troubling beause the analysis of market strutures is thus restrited to orner solutions whih reflet observed market struture in many industries not very well. Brainard (993) disusses oexistene for a knife-edge solution of her model. Markusen and Venables (998) laim that both types of ompanies oexist in their model, beause under partiular onditions there might be Cs or MEs in equilibrium. owever, the market struture is not expliitly given, and the existene of a partiular type of ompany might depend on the prevailing market struture. Moreover, ompanies do not ompare profits from exporting and from produing abroad, the two possible strategies for foreign market supply. There is, therefore, no hek in the model whether it would be profitable for a ompany to swith the strategy. Whether the oexistene result prevails if suh a omparison is made was unlear.

4 2 The symmetry assumption of all ompanies yields the diffiulty for theoretial models to generate stable mixed equilibria. Idential ompanies fae the hoie between ating as an C or as an ME that depends on exogenous parameters. Sine all ompanies are symmetri, they all internationalize prodution at the same exogenous parameter onstellation. To show this, a two-ountry general equilibrium model with symmetri ompanies is set up. Companies an hoose between exports and prodution abroad to serve the foreign market. Their deision is dependent on their prodution tehnology, demand harateristis, and the degree of separation of the two eonomies, i.e. the level of distane osts. ene, the deision is effeted by exogenous parameters. The effet of an exogenous hange in distane osts on the internationalization deision is partiularly important in this framework, beause falling distane osts drive the endogenous emergene of MEs in this model. With suh a setting the model resembles the globalization proess. Exogenously falling distane osts, whih result in hanging onditions of ompetition, are the soure of eonomi integration of the two ountries in this model. Eonomi integration hanges inentives of ompanies to internationalize their prodution. In the initial situation, distane osts are assumed to be high. The distane osts an be thought of as border effets (MCallum 995). They separate the two markets in this two-ountry model but do not apply to domesti transations. Border effets have fallen over the last

5 3 two deades (itsh 2000). By assumption, distane osts here our only in the manufaturing setor but not in the agriultural setor. With falling distane osts, an eonomy with symmetri ompanies swithes from hosting only Cs to hosting only MEs when distane osts have fallen below a partiular threshold. An equilibrium with Cs and MEs (mixed equilibrium) is a knife-edge solution. It is restrited to the adjustment proess between the pure C equilibrium and the pure ME equilibrium at one partiular level of distane osts. ene, the model annot resemble stable mixed equilibria. owever, we observe mixed equilibria. I argue that laking differenes between ompanies hinder the model to resemble this empirial fat. To show this, the model struture is hanged to inorporate differenes between ompanies. Then, the manufaturing setor onsists of one industry whih hosts several groups of different ompanies. These are symmetri within their group but two ompanies from different groups have at least one different harateristi. A onsumer hooses his/her most preferred version of the differentiated good in a two-stage proess. First, the onsumer hooses one of the different groups depending on the prie indexes of the groups. Seond, he/she selets the most preferred version from the hosen group. Companies whih differ in their tehnology or in the demand harateristis for their produts hange their optimal supply strategy of the foreign market at a different distane ost level. Mixed equilibria

6 4 result. In ontrast to the symmetri ompany model, these mixed equilibria are stable. 2. Related Literature and Model Struture elpman et al. (2002) presented a model of ompanies faing the hoie between three alternatives: not serving the foreign market, serving it by exports or by prodution abroad. After market entry, ompanies draw their produtivity level from a known distribution. Depending on the produtivity, one of three strategies dominates the other two (exept for the indifferene points, whih have a probability of zero). In equilibrium, the most produtive ompanies hoose to produe at home and abroad, i.e. they beome MEs, the least produtive ompanies serve only the home market and ompanies in between export to serve the foreign market. ene, MEs and Cs oexist. Companies asymmetry is the key to this mixed market struture. Coexistene of MEs and Cs in the model I present here depends also on asymmetry among the ompanies. owever, ompanies do not differ in their produtivity but in harateristis suh as fixed osts, produt differentiation and the omplexity of their prodution proess. The model stands in the tradition of Brainard (993). It has two setors, agriulture and manufaturing, two ountries, home and foreign, and one fator, labor. The perfet ompetitive agriultural setor produes a homogenous good. In the manufaturing setor, two groups of ompanies are ative: final goods

7 5 produers and intermediate goods produers. Final good produers produe a bundle of differentiated goods, whih onsists of many varieties. Final good produers engage in monopolisti ompetition within their group. It is profitable to produe a single variety of the bundle of differentiated goods in only one ompany beause the final good produers in the manufaturing setor use fixed input fators in prodution. They produe in a multi-stage proess, whih inlude fixed inputs at the orporate level (R&D, marketing, finaning) and at the plant level (equipment). Furthermore, final good produers use a speifi intermediate good, whih is also produed in the manufaturing setor. Final goods produer hoose between exports and prodution abroad to serve the foreign market. Exporting saves on additional fixed osts at the plant level, while prodution abroad saves on distane osts. All goods in both eonomies are produed by using labor, the only prodution fator. The model goes beyond Brainard (993) in modeling the usage of the speifi intermediate good in the prodution proess of the final good. Reent empirial work (Feenstra 998, Campa and Goldberg 997) has alled attention to the inreasing use of imported intermediate goods in various developed eonomies and has related this to rising ativities of MEs (ummels et al. 998). Intermediate goods ompanies in the model presented here are assumed to produe a homogenous good in a single stage without using fixed input fators. Their market is perfetly ompetitive. The intermediate good is speifi either to

8 6 the final goods or to the prodution proesses, or to both. Final goods produers use, therefore, the intermediate good exlusively from their home ountry, even if they produe abroad. Intermediate good produers and final good produers of the same ountry ompose a network. A good example is a ar produer s prodution in a foreign ountry whih relies on the same omponent inputs as at home. These inputs must be imported by the foreign affiliate. on-speifi intermediate goods ould be modeled as labor. There would be an additional prodution fator whih is taken from the ountry where prodution takes plae. For simpliity, non-speifi intermediate goods are exluded here. on-speifi intermediate goods do not add new insight to the analysis, while speifi intermediate goods do. Table gives a short summary of the model struture. Table : Model Struture Agriultural good Intermediate good Final good Produt harateristi homogeneous homogeneous differentiated many varieties Competition perfet ompetition perfet ompetition monopolisti ompetition Input fators labor labor labor, intermediate goods Prodution stages one stage one stage headquarter servie and prodution stage using fixed osts at plant level Foreign market servie trade without inurring distane osts exports to foreign affiliates of home-based ME, inurring distane osts exports with inurring distane osts or foreign prodution umber of ompanies endogenous

9 7 Exogenous falling distane osts hange the optimal onsumption bundle, pries, optimal output levels, the number of ompanies in equilibrium and the preferred strategy for supplying the foreign market. ene, market struture hanges with the level of distane osts. For very high and very low distane osts, equilibria with only Cs prevail. For high distane osts, variable profits of the foreign affiliate are not high enough to over the additional fixed ost at the plant level. For small distane ost levels, savings of distane ost are not large enough to make up for the additional fixed ost at the plant level. Companies then always prefer exports to prodution abroad. For intermediate distane ost levels, however, profits of foreign affiliates might be suffiient to over the additional fixed osts at the plant level. There is, therefore, only a limited range of (intermediate) distane osts where MEs may exist. ene, there is only a limited range of distane osts, where oexistene is possible. The analysis onentrates on this range studying neessary onditions for the emergene of mixed equilibria with Cs and MEs. In models with symmetri ompanies, mixed equilibria are an instable knife-edge solution. In the model with different groups of ompanies varying in their harateristis, however, stable mixed equilibria may exist over a wide range of distane osts.

10 8 3. The Basi Model There are two symmetri ountries, home and foreign F, eah with two setors of prodution. The output of the agriultural setor is denoted Q A. Companies in agriulture produe a homogenous produt with onstant returns to sale under perfet ompetition. Companies in the manufaturing setor produe a variety of final goods under monopolisti ompetition and a homogeneous intermediate good under perfet ompetition. The aggregate output of the final goods in the manufaturing setor is Q M. An individual final good produer s output is denoted q i. The final goods produer, whih an serve the foreign market through exports or prodution abroad, uses the intermediate good. The output of the intermediate good is Z. Z is used as input exlusively by the final goods produer headquartered in the same ountry. The assumption is, therefore, that the intermediate good is tradable. Foreign affiliates of the MEs import it from the home ountry. But the intermediate good is not used by foreign ompanies. Beause of the symmetry of the two ountries, it is suffiient to desribe the eonomy of the home ountry. All definitions, onditions and derivations apply to the foreign ountry F in the same way. It is assumed that every individual in is endowed with one unit of labor, L. The individual is free to hoose any job in his/her ountry. There is no rossborder mobility of labor. The labor market equilibrium gives wage level, w, in ountry. Full employment is assumed.

11 9 3. Consumption L inhabitants live in. They have idential preferenes. Their utility funtion is inreasing in the agriultural produt and the aggregate manufaturing produt. U = Q µ A, Q µ M, µ ( 0, ) () µ gives the inome share spent on manufaturing goods. The aggregate Q M is a CES-funtion onsisting of λ different produts λ qi, i= Q M, = ( 0, ) (2) where defines the degree of differentiation among the manufaturing goods. The produts are poor substitutes for eah other if is small, leaving the ompanies with more market power. The CES-funtion (2) implies that onsumers love variety. It yields a onstant elastiity of substitution σ, with σ=/(-), between any two varieties of the final goods in the manufaturing setor. Individuals maximize their utility () subjet to budget onstraints Y = P A, Q A, λ i, i= + q p i, (3) to obtain the optimum quantities of agriultural and manufaturing goods Q = ( µ ) Y / P, (4) A, A,

12 0 Q = µy M, / PM,. (5) P A, is the prie of agriultural goods, P M, is the prie index of the varieties of manufaturing goods. This prie index depends on the pries, p i,, of eah individual produt i. Sine agriulture is the perfetly ompetitive setor in the eonomy and sine the agriultural good an be traded without inurring osts, the prie of the agriultural produt is the same in both eonomies. It is set one (p A =). The agriultural good is, therefore, used as a numeraire throughout the paper. 3.2 Prodution 3.2. The Agriultural Good Produer Companies in the agriultural setor produe under onstant returns to sale. Beause agriulture is a perfetly ompetitive setor, the wage, w, is paid aording to the marginal produts of the prodution fator labor. Q L A, A, = w (6) Perfet mobility of workers aross setors assures idential wages in all setors of the eonomy. Prodution osts in agriulture, C A,, are given by C = w A, QA,. (7) The Manufaturing Goods Produer Final good produers in the manufaturing setor engage in monopolisti ompetition. Consumers view the differentiated produts as imperfet

13 substitutes for one another. Eah ompany produes a single variety. ene, the number of differentiated goods equals the number of firms produing the final good in the two ountries. There are two groups of ompanies in the manufaturing setor, intermediate goods produers and final goods produers. Eah final goods produer uses the intermediate good as input in final good s prodution. Sine the intermediate good is speifi to a prodution proess or a final good, the prodution of the final good in the foreign ountry depends on the supply of intermediate goods from the home ountry. For the sake of simpliity, it is assumed that MEs exlusively use intermediate goods produed in their home ountry, irrespetive of whether prodution of the final good ours in the home or in the foreign ountry. Intermediate Good Produers The intermediate good is a homogenous good. It is used by all final good produing ompanies in the manufaturing setor for their prodution. Costs of prodution of the intermediate good, C Z, are given in (8) by Z C = z w. (8) Prodution of the intermediate good requires only labor. Costs of prodution are proportional to output. The marginal osts equal the wage rate, w, in

14 2 ountry. Sine the intermediate good is a homogenous good produed under perfet ompetition its prie equals marginal osts, w. pz = w (9) Equation (9) gives the prie of the intermediate good at home, i.e. without distane osts. The prie, pz M, pereived by affiliates in the foreign ountry, however, must take distane osts, τ, into aount. Foreign affiliates of -bases MEs have to pay.i.f. pries (whih inlude distane osts) for the intermediate goods they use. The prie of the intermediate good inreases to pz M = w e τ. (0) Distane osts are modeled in Samuelson s ieberg form: a part of the value of every produt must be paid for transportation. To buy one unit of the imported intermediate good, the affiliate of the final good produer in the foreign ountry must pay e τ (>) units, e τ - units being distane osts. For very high distane osts, τ, the prie of the intermediate good used as input in the foreign ountry, M pz, goes to infinity. For very small distane osts, it approahes pz. Final Good Produer There are two possible types of final goods produers in every ountry: (i) the C, produing in their home market and serving the foreign ountry through exports and (ii) the ME, produing domestially and abroad. Given the

15 3 symmetry of both ountries in this model, exports of MEs affiliates to the home ountry annot be profitable. Final good produers produe in a multi-stage proess. In the first stage, eah ompany produes headquarter servies. These headquarter servies, like R&D or marketing, an be used non-rivalry within the ompany. In the seond stage, prodution takes plae at the plant level. eadquarter servies and intermediate goods are used as inputs. The ost funtion of an C is given by C i, = w r + w f w + θ θ pz θ θ q i, θ (0,) () The first term represents fixed osts at the ompany level, the seond term the fixed osts at the plant level. Fixed osts inrease in wages, w, and in r and f. r and f are the levels of headquarter-servies produed and the amount of fixed input neessary at the plant, respetively. r and f are tehnology parameters and exogenous to the ompany. Variable osts, the third term in equation (), inrease in the fator prie of labor at home, w, the prie of the intermediate goods, pz, and the output level q i,. Marginal osts, (w/θ) θ (pz (-θ)) -θ, are denoted by. Costs of an ME s produing in its home-ountry are denoted C are given by M i,,. They C M i,, = w r + w f w + θ θ pz θ θ q M i,, θ (0,). (2)

16 4 The first subsript stands for the ompany, the seond for the home ountry of the ME, and the third for the loation of the prodution plant. An ME s prodution osts differ from prodution osts of an C only in the third term, the variable osts. Fator pries and tehnologies used are the same but the ME produes at its home ountry plant only to meet demand in the home market and not for export. The quantities produed in ountry by an -based C and an -based ME differ ( q M i, q i,, ). Marginal osts are the same ( = M ), but variable osts differ beause the quantities differ. The two plants of an ME have different variable osts beause the pries of the intermediate good ( pzm pz ) differ in both ountries. In the foreign ountry, the affiliate pays the.i.f. prie. An affiliate s osts in the foreign ountry F, C M i,, F, are given by C M i,, F = w F f F w + θ F θ M pz θ θ q M i,, F θ (0,). (3) Costs of prodution in the foreign ountry do not inlude osts at the orporate level. The ME produes the headquarter servies at home and uses them nonrivalry in both plants. Prodution osts of the foreign affiliate depend on the wage rate, w F, in F, the amount of fixed inputs used in prodution, f F, the elastiity of prodution, θ, and on the prie of the intermediate good, pz, (inluding distane osts). Prodution osts of the foreign affiliate inrease in M

17 5 distane osts, beause the prie of the intermediate good inreases in distane osts. For very high distane osts, affiliate s prodution osts in the foreign ountry approah infinity. Output, k q i,, (k=, M) differs between Cs and MEs based in the same ountry as well as between the ME s home ountry plant and its affiliate in the foreign ountry. In equilibrium, ompanies produe the amount of goods they an sell at an optimal prie. Given the utility funtion () and the omposition of the aggregated final manufaturing good (2), equation (4) gives the demand for a single produt, qi,, of an C, whih serves the foreign market through exports. ( + γ ) ( + γ ) p ( ) i, pi, e + γ τ q i, = µ Y + µ Y γ γ F PM, PM,F γ=/(-) (4) The optimal quantity of good i produed in depends on: its prie, p i,, the prie-indexes, P M,, P M,F, in both markets, the size of the markets, µy, and the distane osts, τ. The lower the prie of good i is relative to the prie index in both ountries, the higher is the optimal output of this good. igh distane osts derease the optimal output by inreasing the good s prie in the foreign market. Consumers in the importing ountry F must pay the distane osts and, therefore, reat by partially substituting imported goods by goods produed in their ountry F. For very high distane osts, exports approah zero.

18 6 An ME headquartered in produes in both ountries. The optimal output from the domesti plant, M i,, M ( + γ ) i,, γ PM, p q = µ Y, (5) equals the demand in the home ountry (no re-exports). The output of the foreign affiliate, M i,, F M ( + γ ) i,, F γ PM,F p q = µ Y F, (6) is lower, sine the prie of a good of an ME from ountry in the foreign market F is higher than at home beause of the more expensive intermediate good. owever, the affiliates output, q M i,, F, is larger than export volumes of an exporting C, beause the affiliate s prie is lower than the prie for an imported good. Consumers do not have to pay distane osts for the affiliate s good. The quantity of the intermediate good used by a single final goods produer an be alulated from the ost funtions (4 6) by taking the partial derivatives with respet to the prie of the intermediate good, pz (Shephards lemma). Quantities used by an C, z, and by an ME, z, differ. M z C = pz i, w = θ θ θ θ pz q i, (7)

19 7 z M M i,, C = pz w = θ θ C + M P,i,,F pzm θ θ pz q M i,, = z M, w + θ + z F θ M, F θ pz M θ q M i,, F (8) In equilibrium, aggregate demand for intermediate goods equals aggregate supply, Z. The amount spent on intermediate goods, I, equals total osts of the intermediate good produers. Every final good produer sets his/her prie to maximize profits. The solution to this maximization problem is a fixed mark-up fator over marginal osts, k PV,i, {k=,m}. p k i, = k / k=, M (9) The prie of a single final good depends only on the good s marginal osts, k i, and on, the parameters of differentiation. Marginal osts an be obtained from variable osts in ( 3). Marginal osts differ only if the fator pries differ. But fator pries annot differ within one ountry, beause of intersetoral mobility. ene, the pries of the different varieties i produed in the same ountry are the same (p, =p i,, ). In eah ountry, there are four different potential suppliers of final manufaturing goods: (i) ountry s Cs produing for their home ountry, (ii) foreign Cs serving ountry through exports, (iii) MEs, with headquarters

20 8 in ountry produing at their plant in, and (iv) MEs with headquarters in ountry F produing at their affiliate in ountry. F.o.b. pries (net of distane osts) set by ompanies loated in and F do not differ. By assumption, the eonomies are symmetri. Thus, ompanies do not differ in their ability to use eonomies of sale, they all operate at the same sale in their home market. owever, pries set by Cs and MEs from the same ountry differ in their foreign market but not at home. There are, therefore, up to three different pries, k p j,, (j=,f and k=,m) for different varieties of the final good in eah market depending on the strategy by whih the market is served: the prie of goods produed by -based firms (Cs and MEs), the prie of imported goods and that of goods produed by an F-based ME affiliate s plant in. The prie of an C s good in the foreign market,,, F = e τ, equals the home-market prie multiplied by distane osts, p p. p, F From equations () and (2), the prie index, P M,, for eah market an be alulated: λ γ µ Y γ P = M, = pi Q. (20) M, i= Using the different produt pries, equation (20) hanges to

21 9 P M, µ Y = Q = M, n nf, i= i= m γ γ γ ( p ) + ( p ) + ( p ) + ( p ) F, i= M, mf i= M F, γ γ (2) n is the number of Cs loated in, n F the number of Cs loated in F, and m and m F are the numbers of MEs headquartered in and F, respetively. n, n F, m, and m F, add up to equal λ. The prie index, P M,, inreases in the pries of eah kind of ompany and therefore in distane osts. Sine there is free market entry and exit, the zero-profit ondition holds in equilibrium for both, Cs and MEs: Π Π M ( ) pq w ( r + f ) = 0 = ( )( p q + p q ) w ( r + f ) + w f = 0 = M M M M,,, F, F F F (22) (23) The zero-profit-onditions (22) and (23) are suffiient to determine the number of Cs, n, and the number of MEs, m, in ountry in equilibrium. The numbers depend on the market share of the total market µ(y +Y F ) eah group holds, whih is endogenous. 3.3 Distane Costs and Fator Demand From the ieberg-form assumption of distane osts follows, a loss of the fration t of the final goods when an C exports its good. tz is the loss of the intermediate good due to distane osts when the intermediate good is shipped.

22 20 τ ( + γ ) ( ) ( p ) e t = eτ µ YF (24) P γ M,F ( e ) m M M z, F pz tz = τ (25) Labor demand is derived by using Shepard s Lemma. The ost funtions (7), (8), and () through (3) are differentiated with respet to the fator prie w. ote that the goods that melting away when exported (t and tz from 24 and 25) are also produed using labor input. 3.4 Market Equilibrium I assume full employment of all resoures in both eonomies. For a given endowment of labor in, L, equation (26) gives the labor market learing ondition. L = L + m A, + n ( r + f + L + L t, ) + ( z + Ltz, ) ( r + f + L ) + m ( f + L ) M, F M F, with (26) L =(θ/(-θ)) -θ (pz /w ) -θ q, L t, =(θ/(-θ)) -θ (pz /w ) -θ t, L tz, =(θ/(-θ)) -θ (pz /w ) -θ * tz, L M, =(θ/(-θ)) -θ (pz /w ) -θ q M,, and L M F, =(θ/(-θ)) -θ (pz M F /w ) -θ q M F,. The labor market lears if fixed labor supply in ountry, L, equals the sum of labor demand of the agriultural setor, L A, of all stages of prodution of s Cs and MEs produing final goods, of the intermediate good produers in, of the affiliates in of MEs headquartered in F, and of the transport of final and intermediate goods.

23 2 Wages are set in order to lear fator markets. The wage level determines the size of the agriultural setor. In both ountries, the prie of agriultural goods equals marginal osts. P = = w A, A, (27) Inome Y in eah ountry is given by the sum of the inomes of all individuals. Y = w L (28) The demand funtions (4) and (5), the inome equation (28) and the budget onstraint (3) ensure that goods markets lear. Equation (26) ensures learane of the fator market. The marginal produt of labor (6) determines the wage in eah eonomy. The priing rule (9) and equations (4) to (6), (22) and (23) determine the output of Cs and MEs and their number in eah ountry. The demand equations for the intermediate good [(7) and (8)] determine its prodution level. The prie of the intermediate good equals marginal osts whih are set to one. The priing rule (27) determines the agriultural goods output in eah eonomy and, therefore, together with demand equation (4), the level of inter-industry trade. Free of ost one-way trade of the homogeneous agriultural good, Ex A, leads to its prie equality in both eonomies. Beause of the assumed symmetry between the two ountries, there is only intra-industry trade; Ex A is zero in any equilibrium. If the ountries are symmetri, there is no

24 22 trade in the agriultural good. Eah ountry satisfies its own demand for this good. There is always intra-industry trade of final manufaturing produts, Ex MF, in this model beause final goods are not perfet substitutes for eah other. Trade in servies depends on the existene of MEs, sine trade in servies in this model is trade in headquarter servies. It rises with the number of MEs, the wage rate, and the level of headquarter servies, whih is neessary for prodution. Trade in intermediate goods is also bound to MEs. In total, trade must always be balaned. 4. The Strategi Deision: Trade or Prodution Abroad in the Model with Symmetri Companies All final goods produers deide whether to serve the foreign market through exports or to beome an ME and produe abroad. If there are no restritions to prodution abroad, a ompany internationalizes its prodution if it is profitable to do so. Whether the internationalization of prodution is profitable depends on tehnologial parameters whih enter the prodution funtion (fixed osts on plant and ompany level, f and r, and the share of the intermediate good used in prodution, -θ), on the degree of differentiation,, on the degree of ompetition, Γ, whih is affeted by the type of ompanies in equilibrium (and defined below) and on the distane ost level, τ, whih separate the two markets.

25 23 The prie of a good in the foreign market depends on the strategy of its supply. An exporting ompany s good is more expensive abroad than a good produed in a foreign affiliate, beause onsumers in the foreign ountry pay distane osts on an imported good but not on an affiliate s good. A foreign affiliate s good, in turn, is more expensive than a good produed by a foreign ompany (in its home market), beause the affiliate s good is more ostly. The higher osts result from the higher (.i.f.) pries whih must be paid for the intermediate good the affiliate uses in prodution. The quantity of a final good produed by a foreign affiliate is therefore larger than its export volumes would be. ene, variable profits of an ME are larger than those of an exporting C. An C deides to produe abroad if the gains in variable profits are at least as high as the additional fixed osts at the plant level. Then it pays to beome an ME. w F f F ( )( pm M M M, q, + p, F q, F p q ) (29) Condition (29) is essential for the resulting equilibrium. It shows whether it is more profitable for a ompany to serve the foreign market by exports or by prodution abroad. Condition (29) depends on the level of distane osts. ene, it hanges in the globalization proess. It is easy to see, that the lower are the fixed osts at the plant level, w F f F, the more likely is it that an C deides to build a plant abroad. Furthermore, the internationalization deision depends only on the profits earned in the foreign market sine pries, quantities and mark ups,

26 24 and therefore profits, of Cs and MEs at home are the same. But foreign profits differ. Rewriting (29) yields ( pm M ) D( pm ) ( p ) D( pe ) wf ff Φ = τ or Φ = M ( M ) ( eτ ) Γ Γ µ Y F w F f F (30) For onveniene, let p, p M, and M stand for p,f, p M,F,,F, and M,F, respetively. For any given distane ost level, τ, profitability of exports or prodution abroad depends on the market struture whih affets the degree of ompetition Γ. Γ stands for the weighted prie index in the manufaturing setor whih an be interpreted as a measure for the degree of ompetition. Γ is defined τ = n + n e + m + m M as ( ) ( ) ( ) ( ) Γ. The trigger funtion (30) gives the inentive of an C to beome an ME. If Φ is negative it is profitable to be an exporting C, given the exogenous parameters and the market struture. An ME an inrease its profits by swithing to exports for the supply of the foreign market. Trigger funtion (30) shows that ompanies refrain from establishment of a foreign affiliate if distane osts are very high. Then, the term in brakets beomes very small, although it always remains positive, beause ( M /)^(-/(-))> ( e τ /)^(-/(-)) and M > for any τ>0. For very high distane osts, demand for home ountry s goods in the foreign market is too small to generate enough variable profits to

27 25 make up for the additional fixed osts at the plant level, w F f F. For very low distane osts, foreign prodution is not a profitable alternative either, sine the term in brakets approahes zero and Φ is negative. Thus, the trigger urve is heavily affeted by hanges in distane osts. This an be seen in equation (3) whih shows the derivative of Φ with respet to distane osts, τ. ( ) Y e e n e Y e e n M M µ Γ µ Γ θ τ Φ τ τ τ τ τ > + + = (3) The first line of (3) shows the effet of hanging distane osts on the (variable) profits of prodution in the foreign ountry, the seond line shows the effet on variable profits of exports. For onveniene, the first line is denoted Φ M (for ME), the seond Φ (for C, defined without the minus sign). Φ M is negative for all distane osts levels, τ, whih are not too low, given that the share of intermediate good input in prodution of the final good, -θ, is not too low either. Then, falling distane osts result in larger profits of foreign prodution. For very high distane osts, the term in brakets approahes -(-θ). For a prodution funtion whih does not require the use of the intermediate good, (-θ=0), the first line turns positive. At any distane ost levels,

28 26 dereasing distane osts are then related to dereasing profits of prodution abroad. The seond line of (3) is always positive, sine the minus sign in front of the term hanges the negative sign of Φ. Variable export profits rise with falling distane osts. To see this note that the term in brakets is always negative beause is defined as 0<<. The total effet of falling distane osts on the strategi deision is determined by the differene of the two effets (Φ M - Φ ). For most parameter onstellation (distane ost levels not too low, intermediate good share not too low), both, Φ M and Φ, have the same sign, they are negative. ene, the sign of the differene depends on the size of the effets whih falling distane osts have on variable profits of prodution abroad, Φ M and exports, Φ. For very low distane ost levels and intermediate good s shares, however, the total effet must be positive, beause Φ M is positive: Φ inreases with rising distane osts and dereases with falling. For an intermediate good share of zero, this results for all distane ost levels. The model onverges to the Brainard (993) model. For intermediate goods shares whih are higher than zero, the total effet is not easily alulated sine it depends on various exogenous parameters in a non-linear manner. Table A in the Appendix gives the level and urvature of the trigger funtion. The emergene of an ME is parameter dependent. For a range of realisti parameter onstellations, MEs may emerge in a globalization proess suh as

29 27 the one modeled here, where falling distane osts drive international integration. In this proess, ompanies rely on exports to serve the foreign market until distane osts have fallen below a ertain threshold. Then, internationalization of prodution beomes profitable. owever, the parameters are industry or even ompany speifi. This may explain the observed pattern of internationalization of prodution with strong onentration on some industries and some industries preeding others in this proess. In addition to the exogenous parameters, the deision about the optimal internationalization strategy depends on the market struture in the final good segment. This struture is represented by Γ. It an be seen from (30) that Φ/ Γ=-(/Γ)[.]µY F <0. This derivative is smaller zero, sine the term in brakets is always positive. Competition yields different equilibrium outomes for a Γ that inludes MEs than for a Γ whih does not. As long as deviating is not profitable, the omposition of Γ does not hange (although pries and numbers of ompanies hange). owever, with the emergene of the first ME, omposition and level of Γ hange. For a given number of ompanies, λ, in equilibrium, Γ inreases in the number of MEs, m. This an be seen by differentiating Γ with respet to m for a given number of ompanies λ=2m+2n (with m=m =m F and n=n =n F ).

30 28 ( ) ( ) τ τ Γ = = e e m M M Plugging in ( ) τ θ = e M yields ( ) ( ) ( ) ( ) 0 > = τ θ τ Γ / e e m. (32) An inrease of the number of MEs in an eonomy affets the weighted prie index positively. That results from the fat that although the prie of an affiliate s produt is lower than the import prie of the same good would be, demand of the good is expanded so that its weight in the onsumption bundle inreases. Sales of this good inrease in the foreign ountry, onsumers substitute this good partly for all other goods. Sales of the other goods fall. That holds for domesti as well as foreign (imported or affiliate s produt) ompanies goods in this market. All ompanies inur losses. Some must drop out, sine the zero profit ondition holds in the long run. The new equilibrium with one more ME and an endogenous number of Cs settles if no (negative) profits are made. In total, home sales fall relative to foreign ompanies sales. owever, home sales generate more variable profits per unit sales, beause the part of the sales in the foreign market whih overs distane osts is not profit-relevant (Kleinert

31 ). ene, total variable profits fall with the establishment of the foreign affiliate. In equilibrium with free entry and exit, variable profits equal the sum of fixed osts of the ompanies. This sum inreases in the number of MEs in an equilibrium with a fixed number of ompanies, λ, sine MEs have higher fixed osts than Cs beause they run two plants. Given the lower variable profits and the higher fixed osts in equilibrium, the number of ompanies must fall when foreign affiliates are established. The degree of ompetition, Γ, inreases in the number of ompanies. Comparison of Γ with the prie index in (2) gives Γ=P -γ M,j. Sine P M,j falls in λ, as an be seen by solving the partial derivative of (2) with respet to λ, Γ must rise. There are, therefore, two opposing effets from the inrease in the number of MEs on the degree of ompetition, Γ, whih push in opposite diretions in symmetri free entry and exit equilibria: Γ Γ Γ = + m m 2( m+n) = λ λ The first term is known from equation (32). It shows the inrease in the degree of ompetition whih results from the deision of one C to internationalize prodution (holding onstant the number of ompanies). With free entry and exit however the resulting market struture is not stable, sine ompanies inur losses. Some ompanies drop out. The redution in the number of ompanies lowers ompetition, whih is seen in the seond term on the right hand side. The

32 30 term is negative, sine Γ falls with a falling number of ompanies in equilibrium, λ. In total, Γ stays onstant in the internationalization of prodution, sine the two opposite effets anel eah other out in this symmetri model. To see this, reall that the zero-profit ondition (22) implies that the redution in the degree of ompetition through market exit of ompanies must be large enough to ensure that ( /)^(-/(-))/Γ is as high after the adjustment as before the internationalization deision of the ompetitor. Total inome spend on final goods, µ(y +Y F ), does not hange, fixed osts of a single ompany, w f, w F f F, w r, w F r F, and the mark-up, /, remain unhanged. Thus, adjustment must ome through the degree of ompetition, Γ. The ratio of ompany sales over the degree of ompetition, ( /)^(-/(-))/Γ, must be the same before and after the ompetitor internationalized its prodution. Sine the marginal osts,, and the degree of differentiation, /, are unhanged, Γ must also remain unhanged. The trigger urve is therefore not affeted by the internationalization deision of other ompanies in the long run, beause Γ is unhanged in the long run if the zero-profit ondition holds. That lets the last C with the same inentive to internationalize prodution as the first. Thus, all ompanies internationalize prodution at the same distane ost level. A mixed equilibrium of Cs and MEs is therefore not stable in this symmetri setting. Both eonomies jump from an equilibrium with only Cs to an equilibrium with only MEs. This result does ertainly not reflet the empirial pattern of the proess of

33 3 internationalization of prodution. It stems from the strong simplifiation that was made by assuming all ompanies to be symmetri. 5. Coexistene in Equilibria with Different Groups of Companies Real-world ompanies differ in harateristis suh as fixed osts, f and r, the degree of the differentiation of their produts, / or the omplexity of their prodution proess, here haraterized by the importane of the intermediate good, -θ. Therefore, I give up the symmetry assumption in this setion. Asymmetry in ompany harateristis leads thereby to asymmetry in the internationalization deision. Companies that differ in at least one of the harateristis internationalize their prodution at different levels of distane osts, τ. At some τ, there might exist equilibria in whih Cs and MEs oexists. While it is profitable for some ompanies to internationalize prodution, it is not profitable for others. For some exporting Cs, it might never beome profitable to internationalize prodution or only later, i.e. at a lower level of distane osts. Thus, the mixed equilibrium is stable. At given onditions, there is no inentive for any ompany to hange its strategy to serve the foreign market. To show this, the model struture from setion 3 is hange slightly to reflet differenes of ompanies within an industry. I use a model with different groups of ompanies belonging to the same industry to analyze ompetition within this industry. Companies within a group are symmetri but ompanies belonging to

34 32 different groups differ in at least one harateristi. The final goods segment of the manufaturing setor onsists, therefore, of a single industry hosting several groups of ompanies. To give onsumers a hane to hoose among the different groups, I use a utility funtion whih allows for the possibility of substitution among produts of ompanies from different groups. Individuals hoose their most preferred version of the differentiated final good in a two-stage proess. First, one of the different groups is hosen depending on the prie indexes. Seond, the most preferred version from the hosen group is seleted. The CD- CES struture utility funtion in () and (2) hanges to a CD-nested CES struture in (33) and (34) µ µ A, j M, j U = Q Q with µ ( 0, ) ; j=,f (33) j λ h= ς ς Q M, j = Q j with Mh, where ς, h ( 0, ) ; j=,f. λh h h h Q Mh, j = q i, j (34) i= Individuals hoose a group h of produts from the whole set of different groups of differentiated final goods. Groups of produts are formed by similar ompanies, whih stand in tougher ompetition among eah other than final goods from two different groups. The idea is, that within an industry like the automobile industry, for instane, there are different groups, like ompat ars, sports ars, pik-ups, whih ompete for ustomers. Although there ertainly is

35 33 ompetition between a produer of a pik-up and a produer of a sports ar 3, the ompetition between two sports ar produers is tougher. That requires the degree of differentiation / h between different members of a group h to be lower than the degree of differentiation /ς between different groups. After having hosen their preferred group, individuals hoose the most preferred variety among the group members in the seond stage. Given the hange in the utility funtion, demand of the representative onsumer hanges. She/he hooses among goods of the different groups depending on their pries. The inome share spent on eah group h varies with pries. It inreases in the prie index of manufaturing goods (the weighted sum of the prie indexes of all groups of differentiated final goods), P M,j, with the share of inome spend on manufaturing goods µ and with total inome Y j, and dereases in its own prie index, P M h, j. Equation (35) gives the demand for eah group of final goods, Q. Equation (36) gives the prie index of manufaturing goods, PM,j, whih an be alulated from (34). Mh ( + χ ) PM h, j Q Mh, j = µ Y χ j PM, j with χ=ς/(-ς); j=,f; h= κ (35) κ χ PMh, j h= χ P M, j = with χ=ς/(-ς); j=,f; h= κ (36) 3 It is hard to maintain the single produt ompany approah in this example, but for simpliity, I ontinue to base the argument on a single produt ompany.

36 34 P M,j inreases in the prie indexes, P M h, j, of the different groups and dereases in their number, κ. Eah group onsists itself of different (symmetri) ompanies whih produe imperfetly substitutable final goods. The prie indexes of these groups inrease in the (within-group idential) pries of the final goods and derease in the number of goods in eah group, λh. Pries of goods in different groups may differ. Within eah group, pries are idential beause ompanies are symmetri. The prie index, P M h, j, of group h in the industry is shown in (37). λh γ h γ h P M h, j = pi,h, j j,l=,f; j l;h=,2, κ; γ h = h /(- h ) (37) i= Demand for a single variant of the differentiated good depends on the variable market size, Ω (Ω = P Q ), of eah group of goods. Demand for a h, j h, j Mh, j Mh, j single variant i of the differentiated final good in group h inreases in the market size for its group s goods, Ωh,j, and in the group s prie index and dereases in its own prie. Demand may differ for ompanies from different groups. Within a group, demand differs for Cs and MEs in the foreign market beause they are differently affeted by distane osts. At home, Cs and MEs fae the same demand. Output of an individual ompany, whih equals demand in equilibrium, is given in (38 40). The output of an C (38) inludes the supply of home and foreign demand, sine the foreign market is served through exports. Prodution takes plae exlusively at home. An ME produes in both ountries to satisfy

37 35 the loal demand at home (39) and abroad (40). I omit the subsript i for the individual ompany beause all ompanies within a group are symmetri. The first subsript stands for the group the ompany is in, the seond for its home ountry, the third for the ountry of prodution. The third subsript applies only to MEs. q ( + γ h ) ( + γ h ) p ( h ) h, j ph, j e + γ τ M h, j = Ω γ h, j + P h γ h Mh, j PMh,l j,l=,f; l j; γ h = h /(- h ) (38) where Ω = P Q, h, j Mh, j Mh, j Ω h,l q M h, j, j = p M ( + γ h ) h, j, j γ P h Mh, j Ω h, j j=,f; γ h = h /(- h ) (39) q M h, j, l = p M ( + γ h ) h, j, l γ P h Mh,l Ω h,l j,l=,f; l j; γ h = h /(- h ) (40) Output of an C, q h,j, is larger than output of the home plant or the foreign plant of an ME. Output of an ME s home plant, q M h,j,j, is larger than output in the foreign plant, beause its prie abroad, pm h, j, l, is higher than its prie at home, pm h, j, j, beause of the higher osts for the intermediate good abroad. Final goods produed by an ME at home sell at the same prie as goods of a M h, j, j domesti C, p = p. h, j Changes in the prie index of the group affet the number of ompanies in eah group in this multi-group model version. Market shares of the groups are

38 36 variable. The size of the market for eah group s goods is important for the number of ompanies entering eah group. In equilibrium, the zero profit ondition determines the number of final goods produers in eah group. For a speial ases (zero distane osts, symmetry between the two ountries), the number of ompanies in group h an be alulated as the produt of the market share, Ω h,j, and the share of variable profits in total revenue of a ompany, - h, divided by the sum of the fixed osts, w j (f j +r j ) or w j (f j +r j )+w l f l. The number of ompanies hanges with the variable market share. The number of Cs and MEs in a group h are given, respetively, by n h, j m h, j ( h ) Ωh, j = w jrh, j + w j fh, j ( h ) Ωh, j = w r + w f + w f j h, j j h, j l h,l j=,f; h= κ j,l=,f; j l; h= κ The model with different groups of ompanies has the advantage to allow for more general substitution patterns aross alternatives than the basi model in setion 3. The main drawbak of using a nested CES struture is that the results are quite sensitive to the grouping and it is not always lear how the industry should be partitioned. That poses a problem mainly to empirial analyses but not to the analysis presented here. I fous on mixed market strutures. Coexistene of Cs and MEs emerges within the industry, beause not all ompanies but only those belonging to the same group internationalize prodution at the same time. To see this, look at the

39 37 trigger urve, Φ, whih shows the profitability of exports relative to the profitability of prodution abroad for a ompany i in group h. h, j ( )( M M h p q + p q p q ) wl fh, l h, j, j h, j, j M h, j, l M h, j, l Φ = (4) h, j h, j j,l=,f; j l. The trigger urves are group speifi. It is easy to see that differenes in the level of fixed osts on the plant level between two groups leads to different trigger urves. Lower plant level fixed osts favor prodution abroad. The trigger urve shifts upward. Prodution abroad beomes profitable at a higher level of distane osts, τ. Fixed osts on the ompany level enter not so obviously. They affet the output of the ompanies via the degree of ompetition, Γ. igher fixed osts on the ompany level lead to fewer ompanies in equilibrium. That dereases Γ, and hene, inreases Φ h as known from setion 4. ene, higher fixed osts on the plant level also lead to an upward shift in Φ h. The degree of differentiation within a group, / h, also affets the trigger urve. h enters the deision between exports and prodution abroad in several ways. First, it defines the share of (variable) profits in sales. Seond, it enters the prie of both, the exported good and the good of the foreign affiliate, as fixed mark-up over osts. Third, it enters the demand (and therefore the output) of the good under both strategies of supplying the foreign market in a highly non-linear