Market shares and multinationals investment: a microeconomic foundation for FDI gravity equations

Transcription

1 Market sares and multinationals investment: a microeconomic foundation for FDI gravity equations Gaetano Alfredo Minerva November 22, 2006 Abstract In tis paper I explore te implications of te teoretical framework of Baldwin and Ottaviano [NBER Working paper n. 6483] in deriving a partial equilibrium relation for ome and foreign investment stocks of multinational firms. Specifically, te model analyzes te investment and export decisions by two multiproduct multinational firms, eac located separately in one of two countries. Te novel point tis paper addresses is related to a Market Sare Effect, tat is te more tan proportional growt in te stock of investment following te rise in te market sare of a multinational firm. Keywords: Foreign direct investment; JEL Classification: Preliminary and incomplete version. I am indebted to Gianmarco Ottaviano for very detailed and useful suggestions. I tank University Jaume I in Castellón de la Plana for kind ospitality. Tis paper is written in te framework of an Integrated Action Spain-Italy 2005 between te University Jaume I and te University of Bologna. I gratefully acknowledge te financial support from te Italian Ministry for University and Researc. Dipartimento di Scienze Economice, Università di Bologna, Strada Maggiore 45, 4025 Bologna, Italy. minerva@spbo.unibo.it

2 Introduction [to be added] 2 Te model I consider te same setting of Baldwin and Ottaviano (998). Te model is a partial equilibrium framework made of two countries, wit a single factor of production, labour, wose endowment is fixed across countries, and a single differentiated-goods sector, manufacturing. Tese countries are perfectly symmetric apart from te fact tat total expenditure on te manufacturing sector is greater in one country, E > E f, wit E being te size of te ome market, and E f being te size of te foreign market. Tere exist two multinational companies (MNCs) and tey can produce more tan one variety. A fixed cost F in terms of labour must be borne to produce eac single variety. It can be tougt to be te cost necessary to set up a plant. If te MNC wants to produce a variety in an additional plant, it as to bear te fixed cost F again. Tis implies tat MNCs will never find profitable to replicate te production of an existing variety in anoter factory, and tey will opt for establising a brand new variety, wic guarantees iger profits. By coice of measurement units, te wage rate going to labour can be normalized to one, similarly to te unit labour requirement for manufacturing te differentiated good. Tis amounts to saying tat te total cost function for eac variety is F + x(i), were x(i) is total production of variety i. I assume tat eac multinational firm faces additional general costs to co-ordinate its operations at ome and abroad. Tese general expenses stay constant irrespectively of te number of varieties produced, so tat in equilibrium eac multinational firm will find convenient to produce more tan one variety. Te strong assumption I make, for te sake of analytical tractability, is tat only two multinational firms exist, one located wit its eadquarters at ome, and te oter located abroad. In oter terms, te general costs are so ig wit respect to te size of te manufacturing sector, tat only two MNCs are allowed to exist in equilibrium. Eac multinational may set up te production of varieties in bot countries. Te aim of te paper is to model te coice by te MNC concerning te spatial distribution of varieties and teir total number (first stage), and te quantity of eac variety to be produced (second stage). Te FDI decision consists in tis framework of locating te production of some varieties in a different region from te one were eadquarters are located. Anoter key assumption tat is made is tat building a plant abroad is in general more costly tan building a plant at ome. If te MNC makes FDI, te fixed cost to establis a plant abroad is ΓF, wit Γ. Tis is due to barriers to foreign investment. Finally, sipping final goods across countries is also costly. To represent tis fact we introduce iceberg transport costs: in order to sell one unit abroad, τ units must be sipped. Tis is exactly te same logic tat is found in te standard Dixit-Stiglitz monopolistic competition model. 2

3 Turning to te preference side of te model, eac consumer as a utility function equal to U = N i=0 c(i) /σ di () were c(i) is consumption of variety i, N is te total mass of varieties produced in bot countries, and σ > is elasticity of substitution between varieties. If total expenditure on manufacturing in te ome country is E, a ome consumer maximizes () subject to te constraint p(i)c(i)di E i N were p(i) is te price of variety i. Te direct demand function for a generic variety j is c(j) = p(j) σ E i N p(i) σ di (2) and te inverse demand function is p(j) = c(j) /σ i N c(i) /σ di E Te demand for varieties in te foreign country is similarly derived substituting E f to E. We now describe te profit functions. We introduce a sligtly more complicated notation to precisely track te origin-destination pattern of eac commodity. Te ome and te foreign markets are segmented (resale of varieties by unrelated parties is assumed to be proibitively expensive). Eac MNC sets te quantity to be sold for eac variety in eac market, given consumers demand. For instance te ome MNC sets c (i) and c f (i) to maximize profits in te ome market. Profits made by te ome MNC in te ome market will descend from ome-made, Ω, and foreign-made, Ω f, varieties. Home market s profits, π, and foreign market s profits, π f, for te ome MNC are π = πf = i Ω i Ω f [p (i) ]c (i)di + [p f (i) τ]c f (i)di + i Ω f i Ω ff [p f(i) τ]c f(i)di (3) [p ff (i) ]c ff (i)di (4) Te objective is to maximize profits functions in te two segmented markets taking as given te quantities cosen by te oter MNC tat influence market prices. 2. Solving te model Te fully-fledged solution involves calculus of variations. We skip te calculations. Tey can be found in Baldwin and Ottaviano (998). Differently from tem, in te present paper we work wit different manufacturing expenditures in te two countries, E > E f. Te necessary conditions related to te optimality of quantities in te context of profit maximization yield an expression 3

4 for equilibrium prices. In wat follows we write te expressions for te equilibrium prices faced by te ome MNC: p p ff ( ( ɛ ɛ f ) =, p f ) ( =, p f ( ɛ ɛ f ) = τ; ) = τ; ɛ ɛ f ( σ + ) S σ ( σ + ) Sf σ Let us introduce and comment te results: ɛ is te elasticity of demand in te ome market, wile ɛ f is te elasticity of demand in te foreign market. For instance, te iger ɛ te iger elasticity of demand. Tese elasticities depend on two elements: te substitutability parameter σ, and te market sares of te ome MNC, S and S f. Te parameter σ in te Dixit-Stiglitz model is linked bot to increasing returns to scale and to product differentiation. 2 Wen σ =, eac variety enjoys a perfect monopoly power. Substitutability among varieties is nil, te perceived demand elasticity is equal to one, and it is not affected by te market sare enjoyed by te MNC. Wen eac variety becomes a substitute to oter varieties (σ > ), elasticity rises above. Just in tis case, elasticity is inversely related to te market sare of te MNC, because te iger te market sare, te less elastic te demand will be perceived, since te MNC will control te sales of a wider range of differentiated products. Te mark-up of te ome MNC on ome varieties is a quantity rising in te market sare S. /ɛ = ( /σ)( S ) pricing rules of te MNC based in te foreign region. Similar expressions can be obtained for te optimal From (2), te sare over total expenditure of a single variety produced locally by te ome MNC and sold locally, s p c /E, is equal to (p ) σ s = n (p ) σ + n f (p f ) σ + n f (pf ) σ + n f f (pf f ) σ were n is te number of varieties of te ome MNC produced at ome, n f is te number of varieties by te ome MNC produced in te foreign market, n f is te number of varieties belonging to te foreign MNC located in te ome market, and n f f is te number of varieties located in te foreign market and belonging to te foreign MNC. Using te optimal pricing rules, we get: were S f s ( S = )σ (n + n f φ)( S )σ + (n f + nf f φ)( Sf )σ s ( Sf ff = )σ (φn + n f )( S f )σ + (φn f + nf f )( Sf f )σ is te total market sare of te foreign MNC in te ome region. Te formulas for te oter two sares s f, s f are: s f = φs, s f = φs ff 2 On te ambiguity of σ in te CES Dixit-Stiglitz specification see Benassy (996). 4

5 From te definition of total market sares, we get S = n s + n f s f, S f f = nf f sf ff + nf sf f S f = n s f + n f s ff S f = nf f sf f + nf sf so tat we get te following equations S = (n + n f φ)/σ (n f + nf f φ)/σ + (n + n f φ)/σ (5) S f = S (6) S f = (n φ + n f )/σ (n f φ + nf f )/σ + (n φ + n f )/σ (7) S f f = S f (8) Te total sare of te MNCs in te domestic market and in te foreign market can be retrieved as a function of te number of varieties establised in eac market. Let us concentrate for te moment on te profit functions related to te ome MNC. Total profits are Π = σ { E S [ + (σ )S ] + E f S f [ + (σ )S f ] } (n + n f Γ)F and te first order condition for te number of ome based varieties to be optimal is Π / n = 0, and leads to { } E [ + 2(σ )S σ ] S n + E f [ + 2(σ )Sf ] S f n = F (9) wile te condition for te number of foreign based varieties to be optimal is Π / n f = 0, yielding { } E [ + 2(σ )Sf ] S f σ n + E f [ + 2(σ )Sf ] S f f n = ΓF (0) f We can compute S n = σ (n + φn f )/σ (n f + φnf f )/σ [(n + φn f )/σ + (n f + φnf f )/σ ] = S S f 2 σ(n + φn f ) () Sf n S n f Sf n f = φ σ = φ σ = σ (φn + n f )/σ (φn f + nf f )/σ [(φn + n f )/σ + (φn f + nf f )/σ ] = φs f Sf f 2 σ(φn + n f ) (2) (n + φn f )/σ (n f + φnf f )/σ [(n + φn f )/σ + (n f + φnf f )/σ ] = φs S f 2 σ(n + φn f ) (3) (φn + n f )/σ (φn f + nf f )/σ [(φn + n f )/σ + (φn f + nf f )/σ ] = S f Sf f 2 σ(φn + n f ) (4) Te marginal effect on markets sares of an increase in te number of manufactured varieties inges upon markets sares temselves. For instance, in (), te marginal effect of an increase 5

6 in n depends on bot S and Sf. Assume tat S is close to zero and Sf is close to one. Ten te marginal effect of rising n will be small itself, and S will be still close to zero. Te same is true if S is close to one and Sf is close to zero. In tis case, a marginal cange in n will leave S almost unaltered and close to one. Partial derivatives from () to (4) sow tat incentives to introduce new varieties (measured in terms of gains in te market sare) are te igest wen te two firms equally sare te country s market. Substituting te partial derivatives back into (9) and (0) we get E [ + 2(σ )S] S Sf (n + φn f ) + E φs f [ + 2(σ )Sf f ] Sf f (φn + n f ) = σ2 F φs Sf S f Sf f E [ + 2(σ )S] (n + φn f ) + E f [ + 2(σ )Sf ] (φn + n f ) = σ2 ΓF Tis system can be solved to retrieve F n and F n f, te stock of capital, belonging to te ome multinational, invested at ome and abroad. Applying Cramer s rule, I obtain: n + φn f = E [ + 2(σ )S ]S Sf ( φ2 ) σ 2 η F ( Γφ) φn + n f = E f [ + 2(σ )S f ]S f Sf f ( φ2 ) σ 2 F (Γ φ) η (5) were te system allows as admissible an interior solution (n > 0 and n f > 0) if Γ < /φ. Condition. To ave an interior solution, te necessary condition Γ < /φ as to be satisfied. Solving in turn system (5), te solution is n = η φη φ 2, n f = η φη φ 2 Let us substitute back all te parameters in order to get an explicit solution for te ome and foreign stocks of capital: n F = E [ + 2(σ )S ]S Sf σ 2 ( Γφ) n f F = E f [ + 2(σ )S f ]S f Sf f σ 2 (Γ φ) φ E f [ + 2(σ )Sf ]S f Sf f (Γ φ) σ 2 (6) φ E [ + 2(σ )S ]S Sf ( Γφ) σ 2 (7) At tis point we could furter use equations from (5) to (8) to solve te model to simultaneously compute te equilibrium number of varieties in eac region and te equilibrium market sares as a function of all te oter parameters of te model. Given non-linearities, tis approac would require numerical solutions tat we do not perform in te present paper. In (6) and (7) we get te equilibrium stock of investment at ome and abroad as a function of market sares for te ome MNC. Tey are te result of profit maximizing simultaneous coices on te mass of varieties to be located in eac local market, n and n f. In general, MNCs introduce a limited number of varieties due to a cannibalization effect: new varieties decrease operating profits of existing ones. 6

7 MNCs work out were it is more profitable to locate suc a limited number of varieties. Let us concentrate on (7). It is a gravity equation. Te FDI stock of te ome MNC is positively related to manufacturing expenditure in te foreign region, E f, and inversely related to manufacturing expenditure in te ome region, E. It is positively related to total market sare in te foreign region of te ome MNC, Sf, and to tat of te foreign MNC, Sf f = ( S f ). Tere are two forces operating ere. First, tere is te impact of te partial derivative (4). Second, market sare in te foreign market, S f, affects investment abroad troug te term 2(σ )S f as well. Tis force operates wen varieties are substitutes among temselves, σ >. Te economic interpretation is straigtforward, provided tat, wen σ >, te MNC faces an increasingly inelastic demand te iger its market sare is. Tis effect is increasingly important te iger σ, tat is te iger te substitutability among varieties. In tis case te possibility for te MNC to rise its mark-up crucially depends on te overall market sare it enjoys in te market. Te iger te mark-up, te iger operating profits, te iger te stock of foreign varieties introduced in equilibrium. Similarly, te stock of foreign capital negatively depends on ome market sares, S, and Sf. Te investment stocks for te foreign MNC is reported for completeness: n f F = E [ + 2(σ )S f ]Sf S σ 2 (Γ φ) φ E f [ + 2(σ )S f f ]Sf f S f ( Γφ) σ Te Market Sare Effect We can furter use our relations to compute te world amount of FDI stock in te economy, (n f + nf )F : (n f + n f )F = E f S f Sf f σ 2 2Γφ + φ 2 (Γ φ)( Γφ) }{{} Trade and FDI frictions + E S Sf 2Γφ + φ 2 σ 2 (Γ φ)( Γφ) }{{} Trade and FDI frictions [ ( ( + φ)( φ) + 2(σ ) 2Γφ + φ 2 Sf ) + ] 2 2 }{{} Market Sare Effect [ ( ( + φ)( φ) + 2(σ ) 2Γφ + φ 2 S f ) + ] (8) 2 2 }{{} Market Sare Effect Let us comment on te most interesting points in tis expression for world FDI stocks. FDI is positively related to te term representing trade and FDI frictions. (Γ, φ) 2Γφ + φ2 (Γ φ)( Γφ) It can be easily proved tat (Γ, φ)/ φ < 0, so tat wen φ goes down (iger trade barriers) te stock of world FDI grows accordingly. Additionally, (Γ, φ)/ Γ < 0. 3 Te world stock of FDI is decreasing in te barriers to foreign investment. 3 To prove tis result, decompose ( ) in two separate terms: ( 2Γφ + φ 2 )/( Γφ) and /(Γ φ). It is ten easy to ceck tat tey are bot decreasing in Γ. 7

8 Finally notice tat variations in S f and Sf we call te Market Sare Effect terms, MSE ereafter. originates from te fact tat provoke a more tan proportional variation in wat ( + φ)( φ) 2Γφ + φ 2 > Te more tan proportional variation Te MSE is stronger te iger σ is, tat is te lower te market power of eac variety produced by te multinational. Te economic intuition beind te MSE term is te following. A rise in te foreign market sare by te ome MNC, Sf, rises te stock of FDI belonging to te ome MNC. But if it rises, te foreign market sare of te foreign MNC, S f f, goes down. A fall in Sf f pressure upon te foreign MNC to increase its stock of foreign capital (in analogy to wat appens to n f F wit respect to S puts in (7)). In oter terms, market penetration by te ome MNC in te foreign market, will make te foreign MNC more aggressive on te ome market, in response to te ome MNC s action. Te interaction among tese reciprocal effects will determine a more tan proportional rise in te world FDI stock in response to an initial rise of Sf. Tis constitutes te Market Sare Effect. Let us derive te net FDI stock (n f nf )F. It is equal to (n f n f )F = E f Sf { [ Sf f ( + φ)( φ) 2Γφ + φ 2 σ 2 + 2(σ ) (Γ φ)( Γφ) ( + φ)( φ) E S Sf σ 2 ( + φ)( φ) (Γ φ)( Γφ) { + 2(σ ) [ 2Γφ + φ 2 ( + φ)( φ) Te results are just symmetric to tose for total FDI stocks. Since an increase in S f 2Γφ + φ 2 ( + φ)( φ) < ( Sf ) + ]} 2 2 ( S f ) + ]} 2 2 will lead to a less tan proportional increase in te net FDI stock of te ome MNC wit respect to foreign MNC s FDI oldings, since te foreign MNC will increase its FDI stock in te ome region in response to ome MNC s foreign investment. 2.3 Export flows Te trade flows between te two countries can be derived. For example, te value of total flows from te foreign to te ome region, EXP f n f p f c f + nf f pf f cf f, is equal to n f EXP f = φe ( S )σ + n f f ( Sf )σ (φn f + n )( S )σ + (φn f f + nf )( (9) Sf )σ were trade flows EXP is te sum of te exports flows of varieties from to f by te ome MNC, and by te foreign MNC affiliates located abroad. Since we are considering a perfectly symmetric case, (9) is also te flow of exports from f to. 8

9 3 Symmetric countries (E = E f ): more analytical results We now consider te case were E = E f, tat is expenditures in te two markets are exactly te same. Te symmetry simplifies te model, since it implies tat market sares and te number of varieties are also symmetric, S = S f f, n = n f f, S f = S f n f = n f 3. Selection in investment abroad: FDI depending on φ As in Baldwin and Ottaviano (998), we work out wen multinational firms do not find convenient to invest abroad. Tis issue is regulated by a selection condition. 4 In particular, n f > 0 (tere is FDI) as long as Γ < Γ o (φ, σ), were Γ o (φ, σ) ( + φ2 )( + φ /σ ) + 2(σ )(φ 2 + φ /σ ) 2σφ( + φ /σ ) (20) tat is as far as te additional fixed cost for FDI (Γ) is small enoug. Oterwise tere is only twoway trade. Te selection depends on freeness of trade (φ), and on te parameter σ. Concentrating on φ, we notice tat te easier it is to trade, tat is te iger φ, te less likely it is to ave orizontal FDI, since Γ o / φ < 0: te explanation is due to te cannibalization effect of varieties produced abroad. Introducing a variety manufactured abroad always reduces te sales of ome made varieties, bot in te domestic and foreign market. Wen barriers to trade are relevant, te cannibalization effect is compensated by te profits earned by-passing barriers to trade and building a production facility abroad. Wen barriers to trade are low, te cannibalization effect prevails, and te MNC finds more convenient to focus on te export strategy only. 5 A precise taxonomy of te different trade and investment patterns can be now sketced. Wen transport costs are low te MNC cooses te export strategy to serve te foreign market. For ig levels of transport costs export and FDI coexist. 6 4 A selection condition can be found in oter works dealing wit FDI, see Razin, Rubinstein, and Sadka (2005). 5 Te result tat, as trade gets freer, orizontal FDI are less likely is qualitatively similar to Brainard (993) toug te underlying logic is quite different. 6 In te CES Dixit-Stiglitz-Krugman monopolistic competition approac I adopt ere, tere is always some trade, also wen transport costs are very ig. Tis is an admittedly unrealistic feature of te model due to its matematical properties. 9

10 3.2 Market Sare Effect again Rearranging terms in (6) and (7), and using te symmetry of te model, we get te ome stock of capital and te foreign stock of capital for te ome MNC: n F = E S Sf Γ 2φ + φ 2 Γ [ ( Γ( + φ)( φ) σ 2 + 2(σ ) (Γ φ)( Γφ) Γ 2φ + φ }{{} 2 S ) + ] Γ 2 2 }{{} Trade and FDI frictions Market Sare Effect n f F = E f Sf Sf f 2Γφ + φ 2 [ ( ( + φ)( φ) σ 2 + 2(σ ) (Γ φ)( Γφ) 2Γφ + φ }{{} 2 Sf ) + ] 2 2 }{{} Trade and FDI frictions Market Sare Effect In tis derivation we crucially employ te symmetry in te model in saying tat in equilibrium it must be true tat S = S f = S f Te trade and FDI frictions term for ome investment is increasing in φ (i.e. decreasing in trade barriers). Tis implies tat market integration is associated to concentration of production in te ome country. On te oter side, te parameter Γ is positively associated to te domestic capital stock. A fall in Γ, representing FDI liberalization, decreases te ome stock of capital. 7 Wen te market sare S (2) (22) by te ome MNC is greater tan /2, in order to ave a Market Sare Effect te igligted term on te rigt in squared brackets as to be greater tan S itself. Tis appens if Γ( φ)( + φ) Γ 2φ + φ 2 Γ > wic boils down to φγ <, and ten Γ < /φ. We prove ere tat tis condition is compatible wit (20). Lemma. Te FDI tresold Γ o ( ) is suc tat Γ o (φ, σ) < /φ. Proof. See Appendix 5.. We skip te discussion of (22), because it as been done in te context of te asymmetric regions model. It is instructive to compare (8) wit (22). Te first obvious difference is tat wile (8) represents world FDI stocks, (22) stands for FDI stocks just in one country. Apart from tat, tere is a deeper difference. Wile discussing te MSE due to S f in (8), we said tat a rise in te ome stock of foreign capital belonging to te foreign MNC, n f F, appens in response to rise in Sf. But we did not mention tat also Sf will rise in (8). In te discussion of (8) we did not work out tis additional effect analytically. Conversely, wen E = E f, tis is easily done. In suc a case, te cange in S f must be mirrored by an equal cange in Sf due to te perfect 7 To easily prove tis, just separate te trade and FDI frictions expression in two terms, /( Γφ), and (Γ 2φ + φ 2 Γ)/(Γ φ). Bot are increasing in Γ. 0

11 symmetry of te equilibrium. A rise in te foreign stock of capital of te ome MNC will induce te foreign MNC to rise its FDI stock in te ome country by an equal amount. Te ome market sare of te ome MNC, S, becomes lower by exactly te same amount S f as increased. Tis in turn reinforces te ome MNC s incentives to raise te stock of FDI in te foreign country (see (7)). Overall, a rise in S f leads to a more tan proportional rise in te FDI stock n f F. 4 Conclusion [to be written] 5 Appendix 5. Proof of Lemma In order to prove te statement of te Lemma, we ave to sow tat Γ o (φ, σ) ( + φ2 )( + φ /σ ) + 2(σ )(φ 2 + φ /σ ) 2σφ( + φ /σ ) After some manipulation and simplification < φ + φ 2 2σ < σ( φ2 ) + φ 2 + φ /σ σ( + φ /σ ) Remember tat σ >, and φ <. We are left to sow tat + φ 2 < σ( φ 2 ) + φ 2 + φ /σ φ /σ < σ( φ 2 ) were it is straigtforward to sow tat te last inequality is surely verified.

12 References Baldwin R., Ottaviano G.I.P. (998) Multiproduct Multinationals and Reciprocal FDI Dumping, NBER Working Paper, n Benassy J.-P. (996) Taste for variety and optimum production patterns in monopolistic competition. Economics Letters, 52, Brainard L. (993) A simple teory of multinational corporations wit a trade-off between proximity and concentration, NBER Working Paper, n Razin A., Rubinstein Y., Sadka E. (2005) Fixed Costs and Bilateral FDI Flows: Conflicting Effects of Country Specific Productivity Socks, mimeo. 2