School of Economics and Management

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1 School of Economics and Management TECHNICAL UNIVERSITY OF LISBON Deartment of Economics Carlos Pestana Barros & Nicolas Peyoch José Pedro Pontes A Comarative Analysis of Productivity Change in Italian and Vertical Linkages Portuguese and Multinational Airorts Plant Size WP 30/009/DE/UECE WP 006/007/DE WORKING PAPERS ISSN Nº

2 Vertical linkages and multinational lant size José Pedro Pontes Setember 009 Abstract This aer deals with the location of inut suly in a two country satial economy. A duooly sulies intermediate goods to a erfectly cometitive consumer good industry that oerates with a quadratic roduction function insired in PENG, THISSE and WANG (006). Since the consumer good is non-tradable, the downstream industry locates in both countries and can be viewed as made by a set of multinational firms. On the one hand joint location of the ustream firms is caused by a localization economy and by the intensity of the demand addressed to the industry. On the other hand roduction and transort costs of the inut lead to disersed locations by the ustream firms. If the inut suliers agglomerate, the neighboring downstream lant oerates with a larger size that the distant one. Keywords: Vertically-linked industries; Location; Oligooly; Transort Costs. JEL classification: F; L3;R. Affi liation: ISEG (School of Economics and Management) of the Technical University of Lisbon and UECE (Research Unit on Comlexity and Economics). Address: Rua Miguel Lui, 0, Lisboa, Portugal. Tel Fax <ontes@iseg.utl.t> UECE is financially suorted by FCT (Fundação ara a Ciência e Tecnologia), Portugal. This article is art of the Multi-annual Funding Project (POCI/U0436/)006). Acknowlegements: The author wishes to thank Armando Pires and Joana Pais for helful comments. Secial thanks are due to Jacques Thisse, who suggested the use of the linear quadratic roduction function to shed light on vertical linkages. The usual disclaimer alies.

3 Vertical linkages and multinational lant size. Introduction It is common sense (see MARKUSEN and VENABLES, 999) that the success of Foreign Direct Investment (FDI) deends critically on the existence of inut suliers which are close enough to the subsidiary of the multinational firm. In order to get a full understanding of this, a deeer analysis of the oeration of vertical linkages in sace is necessary. In this aer, with a two country setting, an imerfectly cometitive ustream industry manufactures an intermediate good and sells it to a downstream industry. This industry rocesses it into a consumer good which is sold to final customers. Agglomeration follows from the interlay of the transort costs of intermediate and consumer goods. The existing literature has shown this result assuming different secifications of market structure for both industries. VENABLES (996) assumes that both industries are Dixit-Stiglitz monoolistic cometitive. FUJITA and THISSE (00,. 3-36) make the assumtion that the ustream industry is Dixit-Stiglitz monoolistic cometitive while the downstream industry oerates under erfect cometition. BELLEFLAMME and TOULEMONDE (003) assume that both industries work under Cournot oligooly. This aer addresses the same issues of the revious literature with a different focus. First, there is an emirical evidence that a large share of consumer goods are non-tradable so that they must be offered in each location. The non-tradable character of consumer goods stems from the fact that roduction entails two successive vertically-related activities, namely manufacturing and distribution, the outut of distribution being usually a non-tradable good. The aer kees this asect in its

4 Vertical linkages and multinational lant size 3 assumtions. Second, the technology of firms, which is usually described as the sum of a fixed cost and a marginal roduction cost, is often more comlex than this secification. In this aer, following PENG, THISSE and WANG (006), we assume that the consumer good industry works under a technology described by a quadratic roduction function with decreasing returns to scale, substitution across inuts and a ositive imact of inut variety on outut. Finally, another difference consists on the fact that both ecuniary externalities and technological externalities, through a localization economy, as in BELLEFLAMME, PICARD and THISSE (000), are introduced. The aer finds that the economy of localization and the intensity of the demand addressed to the ustream industry foster the clustering of the inut suliers while roduction and transort costs of the intermediate good lead to disersion. Hence, as the growth of industry involves both an increase of the intensity of the demand and a decrease of costs, it determines a transition from a disersion to the agglomeration of the ustream firms. If the inut suliers agglomerate, the neighboring downstream lant has a larger size than the distant one.. The model.. Assumtions A satial economy is made by two countries (or regions): H(ome) and F(oreign). Two ustream firms, U and U, suly differentiated inuts to firms roducing an homogeneous consumer good under erfect cometition. The downstream industry is made by symmetric firms, so that it can be reresented by a erfectly cometitive firm, D. Thisfirm sets the arametric rice w.l.g.. The consumer

5 Vertical linkages and multinational lant size 4 good is non-tradable, so that the firm D has two lants, each one being located in a different country. Hence firm D can be regarded as a multinational firm. Firms U and U have a unit constant roduction cost c if they locate in different countries and a unit cost c θ if they agglomerate, where θ stands for a (Marshallian) localization economy. The intermediate good is shied across the countries at a transort rate t and at a rate zero inside each country. The trade between an ustream lant in a country and a downstream lant in the same country is labelled a "local flow". The trade between units located in different countries is named a "cross flow". The locational atterns and flows are deicted in Figures and. (See Figures and ) Firms U and U suly amounts of differentiated inuts x and x that are transformed by the downstream firm into an homogeneous consumer good according to the quadratic roduction function: Y (x,x )=α (x + x ) µ β x + x δx x () where α > 0,β > δ 0. The meaning of these conditions is the following. α>0 stands for the intensity of final roduction in intermediate goods, i.e. the intensity of demand addressed to the ustream industry. β δ is a measure of sohistication of the downstream roduction rocess, i.e. an inverse measure of the degree of substitution between inuts. δ>0means that the inuts are substitutes instead of comlements (see PENG, THISSE and WANG, 006). It is assumed that the demand addressed to the ustream industry is high in relation to the unit

6 Vertical linkages and multinational lant size 5 roduction cost of the inut suliers, so that we have α c>0. Eachustream firm charges a fob mill rice, so that its rofit function is π i =( i c) q i,i=,, where i stands for the mill rice and q i is total outut. The oeration of the economy can be modelled by a three-stage game where: Stage : Firms U and U select locations in H and F. Stage : Firms U and U select rices and. Stage 3 Firms D determine demands for x,x. The equilibrium is SGPE found through backward induction. Given the mill rices of the inuts and, delivered rices d and d are formed (see Figures and ). Then the downstream firm determines the demands of the the inuts x and x by maximizing its rofit function: π d = Y (x,x ) d x d x () where Y (x,x ) is given by (). Maximizing π d with relation to x and to x,we obtain the inverse demand functions for the inuts by the downstream firms: d i = α βx i δx j,i,j =,,j 6= i (3) The direct demand functions for the inuts are: x i = a b d i + d d j d i,i,j =,,i6= j (4)

7 Vertical linkages and multinational lant size 6 where a = b = d = α β + δ β + δ δ β δ (5) Given the symmetry of this framework, the inut suliers U and U charge identical mill rices and for the differentiated intermediate goods in each locational setting (disersion or agglomeration). Then, using inut demand functions (4), it is easily seen that, in the disersed locational setting of Figure, the downstream lants are equally sized and each lant uses more intensively the inut that is sulied locally. By contrast, in the clustered attern of Figure, both downstream lants use the inuts in the same roortion although the "distant" lant roduces a smaller amount of outut than the lant that lies close to the inut suliers.

8 Vertical linkages and multinational lant size 7.. Results The results of the aer can be summarized in a roosition. Proosition Agglomeration of the inut suliers is an equilibrium iff θ +α c + t Proof. The first stage location game is a two erson, doubly symmetric game where the ayoff matrix of firm U is Firm U H F Firm U H π A π S F π S π A where π A stands for the rofit ofanustreamfirm in an agglomeration and π S reresents the rofit of an isolated inut sulier. Then it is obvious that the outcome of this game deends on the sign of π A π S. If the sign is ositive, there are two symmetric location equilibria, where both ustream firms locate in the same country. If π A π S is zero, each locational attern is an equilibrium. If π A π S < 0, the inut suliers will locate in different countries in equilibrium. We deal first with case where firms U and U are geograhically searated, deicted in Figure. We assume that all trade flowsofinutsareositive. In the Aendix, necessary and sufficient conditions for this to haen are derived.

9 Vertical linkages and multinational lant size 8 Then, the rofit functions of the inut suliers are (see Figure ) π U = ( c)[x (, + t)+x ( + t, )] (6) π U = ( c)[x ( + t, )+x (, + t)] where x (, ) are direct demands for the inuts as given by (4). The Nash equilibrium rices associated with ayoffs (6) are: S = S = a +bc +cd bt 4b +d (7) Then we consider the rofit functions for the case where the ustream firms agglomerate (see Figure ). By using the demand functions for the inuts (4), rofit functions become: π U = ( (c θ)) [x (, )+x ( + t, + t)] (8) π U = ( (c θ)) [x (, )+x ( + t, + t)] The Nash equilibrium rices following from ayoffs (8) are A = A = a +bc +cd bt bθ dθ 4b +d (9) Equilibrium rices (9) hold only if the cross flows of the inut are ositive. We derive in the Aendix a necessary and a sufficient condition for this to be true.

10 Vertical linkages and multinational lant size 9 Substituting rices (7) in the rofit function (6) of the disersed locational attern, we obtain the ayoffs of the location game: π S = π S = (b + d)(bc a + bt) (b + d) (0) Performing the same oeration for the agglomerated attern, with rices (9) and rofit function (8), we obtain: π A = π A = (b + d)(bc a + bt bθ) (b + d) () Comaring (0), and (), we conclude that this location roblem is nontrivial iff θ>0. If this condition is met, agglomeration is at least as rofitable as locational searation iff : θ +α c + t () Clearly for a given value of the localization economy, agglomeration is fostered by the intensity of the demand addressed to the ustream industry and is stoed by the roduction and transort costs. As it brings about the increase of the demand and a decrease of costs, the evolution of the ustream industry causes a transition from disersion to agglomeration of the inut suliers. A corollary of Proosition follows. Corollary A sufficient condition so that agglomeration of the ustream firms holds is that θ t. Proof. This follows directly from Proosition and α c>0 by assumtion.

11 Vertical linkages and multinational lant size 0 3. Conclusions This analysis has enabled us to conclude that agglomeration is fostered by the localization economy and the intensity of the demand addressed to the ustream industry and is revented by the roduction and transort costs of the inut. A sufficient condition for this to hold is that the localization economy outweighs the transort cost of the inut. Hence we can exect the evolution of the ustream industry to bring about a transition from disersion to agglomeration as it entails usually an increase of the intensity of demand and a decrease of costs. Moreover the evolution of the ustream industry entails the arise of some kind of fragmentation of roduction since a downstream lant is sulied by an ustream firm located in a different country. This "distant" downstream lant roduces a smaller amount of outut than the lant that lies aside the inut suliers. Hence the size of a multinational firm subsidiary deends inversely on the distance to the clustered inut suliers. This aer reresents only a first ste in the assessment of the location of two inut suliers to downstream firms working with a quadratic roduction function. A natural extension of the aer is to assume that there are many (or a continuum) of ustream firms. This extension is in line with the revious research by BELLEFLAMME, PICARD and THISSE (000) and PENG, THISSE and WANG (006). Aendix. It can be roved that there exists a situation with trade rovided that the transort cost of the inut is low enough. We need only to derive necessary and sufficient conditions for the cross flows to be ositive.

12 Vertical linkages and multinational lant size If the ustream firms are disersed, the condition that x i ( i + t, j ) > 0,i,j =,,i6= j (withrices7)isequivalentto t< (a bc)(b + d) 6bd +3b +d (3) On the other hand, if the inut suliers agglomerate, the cross flow x i ( i + t, j + t),i=,,i6= j (with rices 9) is ositive iff t< (a bc + bθ)(b + d) b (3b +d) (4) If θ =0, the right hand side (r.h.s.) of (4) is larger than the r.h.s. of (3). As the former increases with θ while the latter is a constant function of θ, t< (a bc)(b + d) 6bd +3b +d is a single sufficient condition for the existence of trade is both locational configurations. A necessary condition for this to hold is that α c>0, thatismetby assumtion. References BELLEFLAMME, Paul, Pierre PICARD and Jacques-François THISSE (000), "An economic theory of regional clusters", Journal of Urban Economics, 48, BELLEFLAMME, Paul and Eric TOULEMONDE (003), "Product differentia-

13 Vertical linkages and multinational lant size tion in successive vertical oligoolies", Canadian Journal of Economics, 36(3), FUJITA, Masahisa and Jacques-François THISSE (00), Economics of Agglomeration Cities, Industrial Location and Regional Growth, Cambridge, Cambridge University Press. MARKUSEN, James and Anthony VENABLES (999), "Foreign direct investment as a catalyst for industrial develoment", Euroean Economic Review, 43, PENG, Shin-Kun, Jacques-François THISSE and Ping WANG (006), "Economic integration and agglomeration in a middle roduct economy", Journal of Economic Theory,3,. -5. VENABLES, Anthony J. (996), "Equilibrium locations of vertically linked industries", International Economic Review, 37(),

14 Vertical linkages and multinational lant size 3 Y H Y F (, t) x ( + t, ) x + ( t) x +, ( t ) x +, U U Figure : Searated locations

15 Vertical linkages and multinational lant size 4 H Y F Y,U U ( ) ( ),,, x x ( ) ( ) t t x t t x ,,, Figure : Agglomerated locations