FDI and endogenous market shares with multiproduct multinational firms

Transcription

1 FDI and endogenous market shares with multiproduct multinational firms Gaetano Alfredo Minerva April, 04 Abstract This paper is motivated by an interesting empirical regularity: foreign direct investment (FDI) by multinational companies in a host country is inversely related to the market share held by the same multinationals in the market where they are headquartered. In other words, multinational companies react to a decrease in their domestic market share by increasing the number of affiliates in host countries (alternatively, they decrease FDI when they experience a domestic market share surge). I propose a model with multiproduct firms which is consistent with this evidence. I show that, under horizontal product differentiation, a key role is played by the degree of product substitutability. Given the interrelatedness of domestic and foreign markets, the model also delivers simple testable implications related to international trade policy. Policies devoted to attract FDI in a host country by lowering taxes or increasing subsidies on foreign investment end up decreasing market shares and mark-ups of multinationals in their domestic market. Moreover, quite counterintuitively, liberalizing trade between two countries by lowering tariffs ends up increasing the domestic market shares and mark-ups of multinationals. Keywords: Foreign direct investment; Gravity equation; Multiproduct firms; Multinational companies. JEL Classification: F; F3; L3 Preliminary and incomplete version circulated for discussion purposes. I am indebted for very useful suggestions to Mariam Camarero, Robert Feenstra, Antonio Minniti, Peter Neary, Gianmarco Ottaviano, participants to the III Jornadas INTECO in Valencia, the 9th European Trade Study Group conference in Athens, and to seminars in Bologna and UMR THEMA in Cergy-Pontoise. Part of this research was carried out while I was visiting the Department of Economics of the University of California, Davis, whose hospitality is gratefully acknowledged. Department of Economics, University of Bologna, Piazza Scaravilli, 406 Bologna, Italy. ga.minerva@unibo.it Telephone:

2 Introduction The interaction among multinational companies at the world level is essentially strategic in nature. In 00 Lavazza, a well-known Italian manufacturer of coffee, bought a 7% share of Green Mountain Coffee Roasters (GMCR), an American company engaged in the coffee business in the US, to become the first industrial shareholder (other bigger shareholders being pension funds). Lavazza objective was to get into the rich North-American market of coffee pods (where GMCR was the dominant company, being a licensee of a coffee pod system called K-cup) to promote the sales of espresso pods, something GMCR did not pursue, given its focus on a type of coffee more appealing for American consumption. In the US, the strong incumbent for the espresso pods was the brand Nespresso by Nestlé. This move was apparently a reaction to the competitive situation in Itay, Lavazza domestic market, where the espresso pods market had experienced a dramatic surge in the Nespresso sales. From an economic point of view, this simple case study describes a situation where a multinational company (MNC hereafter) reacts to the decrease in the domestic market share due to a competing MNC (Lavazza reacts to the rise of Nespresso sales in Italy) by making foreign direct investment in a host country where the competing MNC is present (Lavazza makes an acquisition of GMCR equities to subtract sales from Nespresso in the espresso pods market in the US). The aim of this paper is to provide a stylized model of the strategic interaction of two multiproduct multinational firms that may give rise to the kind of behavior described above. The model also delivers other simple testable implications related to trade policy. I show that policies devoted to attract foreign direct investment in a host country end up decreasing MNC market share in the domestic market. Moreover, liberalizing trade between two countries ends up increasing the domestic market shares of MNC in both countries. To further motivate the paper, it is instructive to see whether the main message conveyed by the case study (MNC may expand abroad to offset the decrease in the domestic market share) can be confirmed through some simple statistical data. To do this, I consider the empirical link between MNCs total market shares (both at home and abroad) and the average number of foreign affiliates per parent company in the two biggest national economies worldwide, the US and Japan, for the period A detailed description of how the variables are built can be found in Appendix A.. More specifically, I consider an OLS regression where the dependent variable is the average number of Japanese foreign affiliates in the US per parent company in Japan. I then regress this variable on the Japanese host market share in the US (i.e., the foreign market share), and the Japanese source market share (i.e., the domestic market share). The same type of regression is replicated for FDI to Japan. Results are reported in Table. [Insert Table about here] Table shows the strong correlation among the number of foreign affiliates per parent company and Detailed sales data are not available since it is a Nestlé policy not to release sales data for single countries. The expansion of Nespresso in the Italian market is well represented by the increase in the number of boutique shops in Italian cities and the huge expenditure on advertising in the media. Unfortunately, I have only data for the total number of parent companies in each country. The ideal information would be to have in the denominator of the dependent variable the number of Japanese parent companies with affiliates in the US, and the number of American parent companies with affiliates Japan. These data are not available, so I normalize for the total number of multinational companies in each country.

3 the host and source market shares. For example, a rise by 0 percentage points in the Japanese total market share in the US is associated with an increase of 5.6 foreign affiliates per parent company (column ()). Conversely, the domestic market share shows a negative coefficient: a rise by 0 percentage points in the domestic (source) Japanese market induces a decrease, on average, of 0. foreign affiliates per parent company. These correlations survive the inclusion of host and source GDP in column (). This link also exists for US FDI to Japan, where a rise of 0 percentage points in the host share raises the average number of affiliates per parent by 0., while the same rise in the source market share decreases the average number of foreign affiliate per parent company by 0.0. The figures presented above show how strong it is the relationship in each country between the number of foreign affiliates and the market shares enjoyed by MNCs. As to the sign of the coefficients that relate market shares and foreign and domestic plants, the following interpretation can be given. The positive link between host market shares and the number of affiliates is easy to understand. For example, a surge in the number of US affiliates in Japan will be surely associated to a contemporaneous surge in the US host market share. However, assuming that each multinational firm is endowed with market power, any change in market shares in the source or host economy will also affect the relative profitability of foreign investment with respect to domestic investment. A surge in the US host share in Japan, will increase the profitability of the host economy with respect to the source one, and so it will make US FDI in Japan more profitable with respect to domestic investment. Another element to be taken into account is the strategic interaction among MNCs. When a MNC market share rises, this is realized at the expenses of other MNCs share. For example, when the American market share in Japan raises, the domestic market share accruing to a Japanese MNC is reduced. Because of the market power channel outlined above, this will trigger a response by the Japanese MNC in the direction of investing more in the US, since the relative profitability of host and source markets has changed. In a nutshell, the simple correlations in Table may well be the result of a not-so-obvious interaction among market shares and investment decisions. This paper then brings together the two essential ingredients of market power and strategic interaction to properly formalize these issues. In what follows I present a model with two multiproduct multinational firms where the interplay between market shares and the investment activities in both host and source markets is analyzed. The model. Demand side I consider a framework with two countries, and a single factor of production, labour, whose endowment is fixed and immobile in each country. Preferences are defined over the consumption of a horizontally differentiated good. Each consumer has a utility function equal to /( ) M = c(j) ( )/ () j Ω 3

4 where c(j) is consumption of variety j, Ω is the total mass of varieties available to the consumer, and > is elasticity of substitution between varieties. This is the well known Dixit and Stiglitz (977) preferencefor-diversity utility function. If total expenditure on manufacturing in country is E, a consumer that resides in maximizes the utility function () subject to the constraint p(j)c(j) E where p(j) is the price of variety j. The direct demand function for a generic variety i is c(i) = j Ω p(i) E j Ω p(j) ( ) () and the inverse demand function is p(i) = j Ω c(i) / E c(j)( )/. (3) The two countries are perfectly symmetric apart from the fact that total expenditure on the differentiated good is larger in one country, E > E, with E being the size of the market in country. The demand for varieties in country can be derived substituting E to E in () and (3). I treat the two expenditure levels on the differentiated good, E and E, as exogenous parameters.. Supply side Two multinational companies, whose headquarters are located in countries and, respectively, produce more than one variety of the differentiated commodity. Hence, the model is a duopoly with multiproduct firms. Each multinational may set up the production of a given variety in any country. A fixed cost F in terms of labour is needed to produce a single variety if the production takes place in the same country where the MNC s headquarters are located. Otherwise, if production facilities are located in the foreign country, the fixed cost is Γ k F, where k is the index identifying the country where the foreign investment is located, k = {, }, and Γ k. This is due to barriers that may hinder foreign investment. If the MNC wants to produce a variety in an additional plant, it has to bear the fixed cost F again (Γ k F if the plant is abroad). This implies that MNCs will never find profitable to replicate the production of an existing variety in another plant, and they will opt for establishing a brand new differentiated variety, which guarantees higher profits. By choice of measurement units, the wage rate going to labour can be normalized to one, similarly to the unit labour requirement for manufacturing the differentiated good. The game between the two MNCs is modelled in the following manner. The first stage concerns the number of plants to be located in each country. The second stage concerns the quantity of each variety to be produced. When the MNC headquartered in a given country locates some varieties in the other one, the plants producing those varieties will qualify as foreign affiliates. Finally, shipping goods across countries is costly. To represent this fact I introduce iceberg transport costs: in order to sell one unit abroad, τ units must be shipped. I now describe the profit functions. Markets and are segmented. Each MNC sets the quantity to be sold for each variety in each market, given consumers demand. I indicate the origin-destination pattern in the subscript, and the ownership of the variety in the superscript. Let us focus on MNC. The set of 4

5 varieties by MNC that are produced in country is Ω, and that of varieties produced in country by the same MNC is Ω. The objective of the MNC is to maximize profits in the two segmented markets, taking as given the quantities chosen by the other MNC that influence market prices. In order to do so in market, the MNC simultaneously sets, for each i Ω, the quantity produced of variety i in country and then sold in, c (i), and, for each i Ω, the quantity produced in and then re-imported in, c (i). A similar choice concerns quantities sold in market by MNC, c (i) and c (i). Total operating profits of MNC, π, come from the two segmented markets, and, and are thus made up by the components π and π, so that π = π + π, where π = [p (j) ]c (j) + [p (j) τ]c (j), (4) j Ω j Ω π = [p (j) τ]c (j) + [p (j) ]c (j). (5) j Ω j Ω The model is solved in the following manner. First of all, the equilibrium quantities sold of each variety by each MNC are derived. Then, conditional on the equilibrium quantities, the optimal number of varieties in each market by each MNC is obtained. 3 Equilibrium analysis 3. Second stage equilibrium I now characterize the second stage equilibrium. MNC s optimization in each segmented market takes into account the fact that the firm faces a downward sloping demand curve for each variety. The price at which each variety can be sold is inversely related to the quantity sold of that variety, to the quantity of all the other varieties belonging to MNC (which MNC directly controls), and to the quantities sold of the varieties belonging to MNC (which MNC takes as given). The necessary conditions related to the optimality of prices in the context of profit maximization with respect to quantities of each variety are derived in Appendix A.. They yield the following expressions for prices by the MNC headquartered in : p = ( )( S ), p = τ ( )( S (6) ), p = ( )( S ), p = τ ( )( S (7) ). The prices depend on three elements: the substitutability parameter, the total market shares of MNC in markets and, S and S respectively, and the marginal cost, which is equal to in the case of local varieties and τ in the case of varieties shipped from one market to the other. From the definition of total market shares, we get S = n s + n s, (8) S = n s + n s, (9) where s p c /E is the share out of total expenditure E of a single variety produced locally by MNC and sold locally (with similar notations for the other market shares of individual varieties). The mark-up 5

6 of MNC on varieties sold in market, in percentage terms, is p p = p τ p = + S, (0) a quantity rising in the total market share S as long as >. The mark-up of MNC on varieties sold in market is p p = p τ p = + S. () Equations (0) and () show an important property; that is, mark-ups are positively correlated to total market shares in a given segmented market. The economic rationale for this result goes through the decrease in the own and cross elasticities of price with respect to quantity that a higher market share guarantees. In Appendix A. I show that the higher it is the market share commanded by a certain variety, the steeper it is the inverse demand curve. 3 Since, by (8) and (9), total market shares, S and S, are positively associated to the market shares of individual varieties, ceteris paribus, when the MNC enjoys a large total market share, this will be mirrored by large market shares enjoyed by individual varieties, by unelastic inverse demand curves, and, consequently, by high mark-ups. This implies that any change in the total market share in a given market is met by a corresponding variation in the mark-ups charged by a certain MNC. In other terms, looking at total market shares allows to infer the behavior of mark-ups. Another noticeable aspect of equations (0) and () is that the dependence of mark-ups on market shares goes through the substitutability parameter. When is close to one, each variety enjoys an almost perfect monopoly power and its demand is almost independent from the other varieties (substitutability is negligible). In this case, the own and cross elasticities of price with respect to the quantity of variety i tend to a constant (they are and 0, respectively), and they are not affected by the market share enjoyed by i. 4 As increases, varieties become increasingly better substitutes, and the own and cross price elasticities become increasingly more sensitive to the market share. This happens because, with some substitutability, the demand for a certain variety is influenced by the other varieties price, and so the size of the market share commanded by the MNC matters: only with a large market share the MNC can charge a high price (and mark-up) for its varieties, because only with a large share consumers have less opportunity to switch to varieties of the other MNC to escape uncompetitive pricing. The following equations are also true (see Appendix A.3 for the derivation): S = (n + ϕn ) / (n + ϕn )/ + (n + ϕn )/ () S = S (3) S = (ϕn + n ) / (ϕn + n )/ + (ϕn + n )/ (4) S = S (5) where ϕ τ ( ) is an inverse measure of transport costs (ϕ is usually called in the literature freeness of trade). The total market share of each MNC in the two markets is a function of the number of varieties 3 Both the direct and indirect inverse demand curves are affected by the market share of a certain variety i. The direct inverse demand is the price of variety i as a function of the quantity of variety i. The indirect inverse demand is the price of a variety j i as a function of the quantity of variety i. In the Appendix I show that both the direct and indirect prices are steeper (lower elasticity) with respect to a change in the quantity of i when variety i commands a larger market share. 4 Again, see Appendix A.. 6

7 established in each market. It is convenient to express the market shares with the following notation: where S = A A + C S = C A + C S = B B + D S = D B + D A (n + ϕn ) / B (ϕn + n ) / C (n + ϕn ) / D (ϕn + n ) / This allows me to write, for example, S /S = A/C. The equations above will be very useful to solve analytically the model. 3. First stage equilibrium In the first stage MNCs choose the optimal number of varieties to be placed in each market. In doing so, they correctly identify the equilibrium that is prevalent in the second stage of the game. I indicate total profits for MNC as Π. They are equal to total operating profits, π = π + π, minus the fixed costs for building plants. It can be proved (see Appendix A.4) that: Π = { E S [ + ( )S] + E S[ + ( )S] } (n + n Γ )F. (6) The first order condition for the number of varieties located in market to be optimal is Π / n = 0, and leads to { } E [ + ( )S ] S n + E [ + ( )S] S n = F, (7) while the condition for the number of varieties located in market to be optimal is Π / n = 0, yielding { } E [ + ( )S ] S n + E [ + ( )S] S n = Γ F. (8) Given () and (4), the marginal effect of an increase in the number of varieties belonging to MNC on total market shares is: S n S n S n S n = = ϕ = ϕ = (n + ϕn ) / (n + ϕn ) / [(n + ϕn )/ + (n + ϕn )/ ] = S S (n + ϕn ) (9) (ϕn + n ) / (ϕn + n ) / [(ϕn + n )/ + (ϕn + n )/ ] = ϕs S (ϕn + n ) (0) (n + ϕn ) / (n + ϕn ) / [(n + ϕn )/ + (n + ϕn )/ ] = ϕs S (n + ϕn ) () (ϕn + n ) / (ϕn + n ) / [(ϕn + n )/ + (ϕn + n )/ ] = S S (ϕn + n ) () 7

8 Substituting the partial derivatives back in (7) and (8) I get: E [ + ( )S] SS (n + ϕn ) + E [ + ( )S] ϕss (ϕn + n ) = F E [ + ( )S] ϕss (n + ϕn ) + E [ + ( )S] SS (ϕn + n ) = Γ F (3) Another similar system can be derived from the optimization problem of MNC. It turns out that these systems are highly non-linear. For this reason Baldwin and Ottaviano (998) do not pursue further analytical results for the general case 0 ϕ <. In what follows I extend their analysis, to show that new analytical results can indeed be derived, and that they have far-reaching consequences from an economic point of view. The system (3) can be solved applying Cramer s rule, considering as two separate variables the quantities (n + ϕn ) and (ϕn + n ). I obtain: n + ϕn = E [ + ( )S]S S ( ϕ ) F ( Γ ϕ) ϕn + n = E [ + ( )S ]S S ( ϕ ) F (Γ ϕ) where the system allows a positive interior solution if FDI is sufficiently free, Γ < /ϕ. This condition becomes more binding as ϕ goes up; that is, as trade becomes less inhibited. The economic interpretation is that, for an MNC to be profitable to invest abroad, investment costs should be not too high. Moreover, the likelihood of FDI raises with the level of transport costs, because higher transport costs provide a more effective shield against mutual cannibalization between domestic and foreign varieties. Assumption. In order to have a positive interior solution, (n + ϕn ) > 0, the condition Γ < /ϕ has to be satisfied. I can derive a set of conditions similar to (4), but related to MNC, working on the corresponding first order conditions: Similarly to before, I assume the following. n + ϕn = E [ + ( )S]S S ( ϕ ) F ( Γ ϕ) ϕn + n = E [ + ( )S ]S S ( ϕ ) F (Γ ϕ) Assumption. In order to have a positive interior solution, (n + ϕn ) > 0, the condition Γ < /ϕ has to be satisfied. (4) (5) The equations in (4) and (5) taken together lead to the following set of conditions: ] A A AC ϕ = E [ + ( ) A + C (A + C) F ( Γ ϕ) ] C C AC ϕ = E [ + ( ) A + C (A + C) F (Γ ϕ) ] B B BD ϕ = E [ + ( ) B + D (B + D) F (Γ ϕ) ] D D BD ϕ = E [ + ( ) B + D (B + D) F ( Γ ϕ) (6) 8

9 Taking the ratio between the fourth and the third equation in (6), and expressing it in terms of the total market share of MNC in country, S, I get ( ) S S = + ( )( S ) Γ ϕ + ( )S Γ ϕ. (7) This equation implicitly defines the equilibrium market share S. A symmetric equation can be derived for S, working on the first two equations of system (6). Let us prove the following. Lemma. In equilibrium, the value of the foreign market shares S and S is the following. ) When ϕ = 0, S is strictly less than / if and only if Γ > ; S is strictly less than / if and only if Γ >. ) When 0 < ϕ <, both equilibrium foreign market shares S and S are strictly less than / if either Γ > or Γ >, or both Γ and Γ are larger than one; they are equal to / if both Γ and Γ are equal to. Proof. Let us start from the equilibrium condition ( ) S S = + ( )( S ) Γ ϕ + ( )S Γ ϕ (8) which implicitly defines the equilibrium market share S. The domain for S is (0, ), and >. The equilibrium condition can be written as where f(s ; ) = g(s ; ) Γ ϕ Γ ϕ, (9) ( ) S f(s; ) = S, g(s; ) = + ( )( S ) + ( )S. First of all notice that, for every 0 ϕ <, Γ ϕ Γ ϕ with the strict inequality holding when: Γ is greater than one; or Γ =, Γ >, and 0 < ϕ <. The two functions f and g are monotonically decreasing and convex on the domain. Moreover, when S approaches zero f goes to infinity, while g is positive and finite. When S goes to one, f is zero and g is positive and finite. Evaluating f and g for S = /, I get that f(/; ) =, and g(/; ) =. Then, there exists a unique value for S so that (9) is verified, and it must also be that such a unique value is 0 < S /. The same kind of reasoning applies to S. In Figure I provide a graphical representation of the solution. From the figure it is also apparent that in order to have S = / it is needed that both Γ and Γ be equal to one; or Γ = and ϕ = 0. The solution is well-defined provided that 0 ϕ <. [Insert Figure about here] Lemma generalizes what Baldwin and Ottaviano (998) have found for the special case of trade inhibited between countries (what they prove is that, with investment frictions Γ and Γ strictly larger than one, foreign market shares are strictly less than / in the extreme case ϕ = 0). Lemma shows that 9

10 when 0 < ϕ <, it is enough that at least one FDI friction parameter is strictly larger than one to have both foreign market shares strictly less than /. The reason is the following. Let us imagine that the FDI friction parameter is strictly greater than one in country, Γ >, while it is equal to one in country, Γ = (actually, this amounts to having no frictions to foreign investment in country ). This will put at a disadvantage the MNC with respect to MNC in market, and so it will induce S to be strictly less than / and S to be strictly larger than /. But this is not the only effect. A priori, in market the two MNCs are on an equal footing, because Γ =. However, the optimal number of varieties in market to be located by both MNCs depends on the relative magnitude of the market shares enjoyed by them in the two markets. For example, looking at the first order condition (7) and at the related first equation in (3) shows that, for the maximization of Π with respect to n, both the domestic and the foreign market shares are relevant. Even if a priori there are no particular advantages for MNC to invest more in market compared to MNC, and hence to end up with a larger market share there, an incentive exists for both MNCs to invest more in the market where the total market share is larger in relative terms, because in this market MNCs benefit from higher mark-ups and higher profitability. Since Γ > implies that S < / and S > /, this makes in relative terms more attractive market to MNC and market to MNC, even if both MNCs were experiencing equal market shares in market, S = / and S = /, due to the absence of FDI frictions there, i.e. Γ =. The last step needed to convey a precise intuition of what is going on is to acknowledge that the benefits from a larger market share in a given market are reaped more effectively by increasing the amount of investment in that market, more than by increasing the amount of investment in the other market. So, if MNC enjoys a relatively larger market share in country, i.e. S / > S, in order to raise total profits Π it is more effective to increase n up to some point, than to increase n. 5 The increase in n eventually makes S strictly larger than /. All the above reasoning explains why, even with Γ =, it is enough that Γ > in order to have both domestic market shares S and S strictly larger than /, and consequently both foreign market share S and S strictly less than /. The crucial issue is that MNCs balance their relative investment stock in the two markets according to the relative total shares in each market, hence an impediment to FDI in market for MNC leads to a relative advantage to investment in market. The Lemma also implies that MNCs will charge a higher mark-up on the units shipped to the markets where they are headquartered (market for MNC and market for MNC ) than on those shipped to the foreign ones, since mark-ups are increasing in market shares. This will happen independently of whether the units are actually produced at home or abroad: inspection of (0) and () reveals that what matters for the mark-up is the market of destination, rather than the one of origin. Hence, factors affecting market shares will also impact on mark-ups. Moreover, there is reciprocal dumping in trade in the sense of Brander and Krugman (983). 6 5 This point is important because, ceteris paribus, increasing n would also allow to take advantage of the relatively larger market share in country, since the mark-up on exports from market to market for MNC is the same of the mark-up on local sales from market to market and both depend on S, see equation (0). However, my working hypothesis about FDI frictions (Γ = and Γ > ) implies that it is more profitable to increase n than n, because the marginal fixed cost of a variety in market is lower for MNC. 6 Brander and Krugman (983) analyze the case of a duopoly with one identical product without FDI, while here I analyze a duopoly with multiproduct firms and FDI. However, the definition of dumping in trade as the case where mark-up over 0

11 Proposition (Dumping in trade). For 0 ϕ < there is no dumping in trade if investment is free in both countries (Γ = and Γ = ). To generate dumping in trade it is enough to assume that there are some investment frictions in one of the two countries (Γ > or Γ > ). In the presence of some investment frictions in one of the two countries, free trade (ϕ = ) does not inhibit dumping in trade. Proof. The proof is based on the inspection of Figure. When Γ and Γ are one there are no frictions to invest abroad in both countries, and the equilibrium market share in the foreign market, S, is equal to /. When either Γ or Γ is greater than one this is enough to make the term (Γ ϕ)/( Γ ϕ) greater than one, so that S becomes smaller than /. In the Brander and Krugman (983) s framework there is no longer dumping when trade is free (ϕ = in my terminology). This happens because, in that model where there is no FDI, the only way to restore an equal market share in the domestic and foreign markets for a certain firm is to assume that there are no transport costs. On the contrary, in this paper with intra-industry FDI, the only way to restore the equality of market shares in the foreign and domestic markets for a certain MNC (and then to inhibit dumping in trade) is to assume that the investment frictions are zero in both countries. 4 Comparative statics on equilibrium market shares Let us now consider the following propositions which provide comparative statics results. First, I focus on the effects of investment and trade liberalization on the market shares of each MNC. Proposition (Investment liberalization in one country). A lower FDI friction parameter in one single country (either Γ or Γ ) affects negatively market shares and mark-ups in both domestic markets, and positively market shares and mark-ups in both foreign markets. The comparative statics exercise for trade liberalization leads to the following proposition. Proposition 3 (Trade liberalization). A larger freeness of trade parameter, ϕ, affects positively market shares and mark-ups in both domestic markets, and negatively market shares and mark-ups in both foreign markets. Proof. I perform comparative statics analysis on the parameters Γ, Γ, and ϕ. These parameters enter (9) through the last multiplicative term only (a positive constant). Notice that ( )/ Γ ϕ Γ k > 0, with k = {, } Γ ϕ ( )/ Γ ϕ ϕ > 0, Γ ϕ so that rising FDI costs and rising freeness of trade increase the right hand side in (9). Given the shapes of f and g portrayed in Figure, an increase in the right hand side of (9) induces a decrease in the value of S that solves (9). marginal cost is higher in the domestic market than in the foreign one on the sales of the same good applies to both settings. Remember that marginal cost is higher in the case of exports (being τ against of domestic shipping) but what matters for the dumping definition is f.o.b. price, which is lower on exports.

12 The intuition behind these results is the following. Let us consider the impact of a rise in Γ, which is the cost for establishing a plant in country by MNC. The negative impact on S and the positive impact on S are straightforward to understand, since higher FDI frictions in country discourage the establishments of foreign affiliates in country, and this has also a beneficial impact on MNC s market share in its domestic economy. However, this change in market shares leads also to a change in the relative profitability of market and market for the two MNCs, and this creates additional reallocations in market shares. The fall in S makes market relatively more profitable for MNC, so new varieties are established in that market, and S raises accordingly. By the same token, the rise in S makes relatively more profitable to invest in market for MNC, and so S goes down. These reciprocal adjustments in market shares are further analyzed below, where I study the equilibrium relation among the total stock of FDI and MNC market shares. Let us now consider the economic intuition behind the comparative statics for transport costs. It is convenient to start from a situation where trade is completely inhibited (ϕ = 0). In this case, the domestic and foreign market shares depend exclusively on local varieties (n and n, respectively, for MNC and MNC in their domestic markets, and n and n in their foreign markets). When trade is allowed, the domestic market share of MNCs becomes even larger: since the domestic market is more profitable because both MNCs enjoy a larger market share (see Lemma ) the increment of the domestic investment outweighs the foreign one, something which is facilitated by the fact that MNCs are allowed to reach the foreign market through export thanks to the decrease in trade costs. I conclude the comparative statics analyzing how market shares vary according to the degree of product substitutability embedded in consumers preferences. Proposition 4 (Product substitutability). A larger substitutability parameter,, affects negatively market shares in the domestic markets and positively market shares in the foreign markets. This implies that, ceteris paribus, in industries where substitutability is higher, MNCs foreign market shares and mark-ups are higher. Proof. After totally differentiating with respect to S and in (9), the derivative of S with respect to can be expressed as ds d = The denominator in (30) can be written as f g Γ ϕ Γ ϕ f g Γ ϕ S S Γ ϕ ( f g Γ ϕ Γ ϕ two functions. Then, I get that S is monotonically increasing in if and only if ( ) S ( ) S log 4S Γ ϕ > [ + S ( )] Γ ϕ S S. (30) )/ S and is negative given the shape of the I am interested in evaluating the expressions in (3) when (8) is verified; that is, when S = S. Substituting (8) in (3) and rearranging I get a simplified expression: ( ) S log > ( S ) + S ( ) + ( S )( ) (3) S First of all, notice that the right-hand side is decreasing in. Then, if the inequality holds for =, it will hold for every. When =, inequality (3) becomes ( ) S log > ( S) S (3)

13 Through numerical methods, it can be checked that this inequality is always verified if S (0, /). The effect of the substitutability parameter,, can be explained in the following manner. A rise in reduces the profitability in both domestic and foreign markets. However, the reduction is larger for the market where profitability is higher (the domestic), so that it is convenient for the MNC to increase the foreign capital stock with respect to the domestic one. This in turn raises the foreign market share with respect to the domestic one. I summarize the effects of a change in the parameters Γ, Γ, ϕ, and on the MNCs market shares in the table that follows. [Insert Table about here] 5 The equilibrium number of varieties 5. Gravity equations I now derive explicit equilibrium relations between market shares and the number of domestic and foreign varieties. Since I characterized market shares in equilibrium, we can express (4) with the following notation, n + ϕn = η (33) ϕn + n = η where η and η are constant and represent the equilibrium values, and (5) as n + ϕn = θ (34) ϕn + n = θ with θ and θ being other constant representing the other equilibrium values. Solving system (33), the solution is n = η ϕη ϕ, n = η ϕη ϕ If I substitute back market shares, I get an explicit solution for the number of varieties in each market: n = E [ + ( )S ]S ( S ) F ( Γ ϕ) n = E [ + ( )S ]S ( S ) F (Γ ϕ) The corresponding expressions for MNC are: n = E [ + ( )S ]S ( S ) F ( Γ ϕ) n = E [ + ( )S ]S ( S ) F (Γ ϕ) ϕ E [ + ( )S ]S ( S ) F (Γ ϕ), (35) ϕ E [ + ( )S ]S ( S ) F ( Γ ϕ). (36) ϕ E [ + ( )S ]S ( S ) F (Γ ϕ), (37) ϕ E [ + ( )S ]S ( S ) F ( Γ ϕ). (38) Let us concentrate on (36). It is a gravity equation since the number of foreign affiliates located by MNC in country depends on the size of the foreign economy, E, on the size of the domestic one, E, and on freeness of trade, ϕ. Their number is the outcome of two contrasting forces: on the one side there 3

14 is the positive effect on the FDI stock exerted by the attraction of the foreign market (first right-hand side term), on the other side there is the negative effect on FDI exerted by the attraction of the domestic market (second right-hand side term). Since cannibalization among varieties entails that the MNC finds optimal to introduce only a finite number of varieties, the equilibrium FDI stock results from the relative attractiveness of the two markets. Notice the symmetric expression for the equilibrium stock of domestic investment of MNC, given by (35), according to which the attraction exerted by market simultaneously inhibits FDI and boosts domestic investment, while that of market favors FDI and hinders the home stock of capital. Imposing that both n and n are strictly positive I get kϕe < E < (k/ϕ)e, where k is a constant which depends on the parameters of the model and it is defined as follows: k(γ, Γ,, ϕ) Γ ϕ [ + ( )S ]S ( S ) Γ ϕ [ + ( )S ]S ( S ) The values of S and S are those implicitly defined at equilibrium, which are function themselves of the parameters of the model. The condition amounts to say that, in order to have positive investments at home and abroad, market size E should not differ too much from ke. Focusing on the first right-hand side term of (36), the FDI stock by MNC in the foreign country is positively related to expenditure in that market, E. In addition, it is positively related to total market share in region by MNC, S, since in equilibrium S < /. There are two forces operating here. First, there is the dependence of profits of MNC from n through S independently from the fact that varieties are substitutes ( > ) or not ( = ). This effect can be traced back to the partial derivative (8), where marginal revenues from an increase in n depend on S/ n and S/ n. Expressions () and () provide the value of these partial derivatives. Second, market share S affects investment abroad through the term ( )S as well. This force operates only if varieties are substitutes, >. The economic interpretation is straightforward, provided that, when >, the MNC faces an increasingly inelastic demand the higher it is market share. This effect gets stronger the higher it is ; that is, the higher it is the substitutability among varieties. A larger foreign market share raises the mark-up, and the higher it is the mark-up, the higher they are operating profits in that market, and the higher it is the stock of varieties located abroad. Considering the second right-hand side term in (36), the FDI stock by MNC is inversely related to expenditure in the domestic market, E. The overall impact of market shares by MNC in country, S, is a priori ambiguous. On the one side, a larger S makes more inelastic the elasticity of demand in country, raises the profitability of market, and promotes a smaller foreign capital stock with respect to the domestic one. On the other side, provided that S > /, as S goes up n F could also get bigger. This happens as far as is close enough to (substitutability among varieties is small) since a higher domestic market share and, consequently, a higher domestic capital stock do not cannibalize foreign varieties much, but goes instead hand in hand with higher foreign FDI stocks, thanks to the exports from the foreign economy to the domestic one. As a final remark I can say the following. Remark. When is sufficiently larger than, the number of foreign affiliates is a decreasing function of the domestic market share. The model predicts that a strong substitutability between the varieties is matched 4

15 by substitutability between the domestic market share and FDI. 5. The world stock of FDI The total number of foreign affiliates in the economy predicted by the model is: n + n = E S ( S ) F + E S ( S ) F I label the terms (Γ + Γ )ϕ + ϕ (Γ ϕ)( Γ ϕ) }{{} Trade and FDI frictions (Γ + Γ )ϕ + ϕ (Γ ϕ)( Γ ϕ) }{{} Trade and FDI frictions [ + ( ) (Γ Γ )ϕ ϕ ( )] (Γ + Γ )ϕ + ϕ S }{{} Market share effect [ + ( ) (Γ Γ )ϕ ϕ ( )] (Γ + Γ )ϕ + ϕ S. (39) }{{} Market share effect (Γ, Γ, ϕ) (Γ + Γ )ϕ + ϕ (Γ ϕ)( Γ ϕ), (Γ, Γ, ϕ) (Γ + Γ )ϕ + ϕ (Γ ϕ)( Γ ϕ) as trade and FDI frictions terms. It can be easily proved that these two terms are decreasing in ϕ. For example, the derivative of the first term with respect to ϕ is less than zero when the inequalities (Γ ϕ) > ( Γ ϕ) > 0 are verified, which is true under the parameters restrictions of the model. Additionally, they are also decreasing in the cost of investing abroad, i (Γ, Γ, ϕ)/ Γ j < 0, for i = {, } and j = {, }. We can derive the following lemma. Lemma. The terms and are decreasing as the cost of investing abroad goes up and as freeness of trade goes up. Notice that, as far as >, the equilibrium values of S and S are associated in a more than proportional fashion to the world total number of foreign affiliates, n + n, through what I call the market share effect term, MSE hereafter. The more than proportional relation originates from the fact that Λ (Γ, Γ, ϕ) (Γ Γ )ϕ ϕ (Γ + Γ )ϕ + ϕ >, and Λ (Γ, Γ, ϕ) (Γ Γ )ϕ ϕ (Γ + Γ )ϕ + ϕ >. These inequalities are easily verified. One needs to realize that both the numerator and the denominator are greater than zero. For example, in the case of Λ, it is easily checked that the numerator is greater than zero since ( Γ ϕ) + ϕ(γ ϕ) > 0. The denominator is greater than zero under Assumptions?? and??. The MSE term is turned on by : the higher it is the degree of substitutability between varieties, the stronger it is the connection of this term to the equilibrium world number of foreign affiliates. When approaches (varieties are almost independent) this term vanishes. This term is nurtured by the interrelatedness among market shares, mark-ups, and profitability to invest in a given market. We know from previous sections that such interrelatedness depends on. The economic intuition behind the MSE term is the following. An increment in the foreign market share by MNC, S, is positively associated to the stock of FDI belonging to MNC, n, through equation (36). But as S rises, the equilibrium foreign market share of MNC, S, goes down. A fall in S pushes MNC to have a larger stock of foreign capital, n, through the term ( )S in equation (38). 7 In turn, a larger n will be associated to a higher S, a 7 As noted before, the sign of the relationship between n and S is negative only if is sufficiently large. However, what goes in the MSE term is only ( )S. The MSE channel unambiguously relates a decrease in S to a rise in n. 5

16 lower S, a higher n, etc. The cumulation of these reciprocal adjustments explains the presence of the MSE term; that is, a term that links in a more than proportional fashion the foreign market share of MNCs to the total number of affiliates worldwide. Obviously, the MSE term does not explain alone the total number of foreign affiliates. It is evident from equation (39) that the world stock of FDI is also related to the terms S ( S ) and S ( S ), which are linked to overall MNCs profitability. We can prove the following Lemma. Lemma 3. The terms Λ and Λ are increasing as the cost of investing abroad goes up and as freeness of trade goes up. It can be easily checked that the derivative of the MSE terms with respect to Γ and Γ are greater than zero. Imposing that the derivative of Λ with respect to ϕ is positive boils down to Γ ϕ ϕ( Γ ϕ) > 0, which is true provided that (Γ ϕ) > ( Γ ϕ). Lemma 3 implies that there is a magnification of the MSE when investment frictions are high and trade costs are low. To better understand the economic rationale underlying magnification let us consider the impact of raising the cost of investing in country, and how this changes at different levels of the investment cost in, Γ, keeping fixed freeness of trade. Raising Γ by a certain amount will make less attractive the investment in country for MNC. For this reason S will go down and S will go up. I have argued that this triggers, through the MSE term, further reallocation in market, where MNC will decrease investment, since market has become relatively more attractive, and where MNC will increase investment, since market has become relatively more attractive for her. 8 The extent of the decrease of FDI by MNC will in turn depend on Γ : as shown by equation (36), the larger Γ the more sizeable will be the reallocation. This explains why the MSE term is magnified by large investment frictions, as the MNCs are more reactive to the differential in attractiveness of the two markets. Turning to the magnification induced by low transport costs, let us see what happens for a certain increase in the cost of investing in country, and how this changes at different levels of ϕ, keeping Γ constant. Raising Γ will make less attractive the investment in country for MNC. For this reason S will go up and S will go down. These changes will determine, through the MSE term, a reallocation of market shares also in country, with S going down and S going up. The intensity of these reallocations depends on freeness of trade, because the easier it is to trade, the more sensitive MNCs are with respect to the relative profitability of the two countries, since it becomes increasingly more convenient to expand investment in one market and reach the other one by export. This is evident from equations (35) and (36), where ϕ affects both the domestic and the foreign terms in such a way that a freer trade magnifies the changes in market shares ceteris paribus. Relying on the lemmas above, we can then assess what is the effect of a change in FDI frictions and freeness of trade on the world FDI stock. Proposition 5 (Comparative statics on the world FDI stock). The world FDI stock is decreasing as the cost of investing abroad in one of the two countries, Γ or Γ, go up, and as the degree of freeness of trade, ϕ, goes up. 8 It is true that a change in Γ will impact on the world number of foreign affiliates in equation (39) through the terms 6

17 Proof. The proof follows directly from Lemmas, and 3. Lemma shows that foreign market shares go down when FDI frictions and freeness of trade goes up. Hence also the two terms S( S) and S( S) are decreasing. The terms and are also decreasing, according to Lemma. Finally, Lemma 3 states that Λ and Λ are increasing in FDI frictions and freeness of trade. This implies that the whole MSE term is decreasing (remember that S and S are decreasing). The combination of these effects unambiguously points toward an decrease of the world FDI stock (n + n )F. 6 Conclusions and future work This paper is motivated by an interesting empirical regularity: foreign direct investment (FDI) by multinational companies in a host country seem to be inversely related to the market share held by the same multinationals in their domestic market. In other words, multinational companies react to a decrease in their domestic market share by increasing the number of affiliates in host countries (alternatively, they decrease FDI when they experience a domestic market share surge). I propose a model with multiproduct multinational firms and horizontal product differentiation which is consistent with this evidence. In particular, I retrieve a gravity equation for the number of foreign affiliates located in each country, and I also get an equation for the total number of affiliates in the two countries. I show that a key role is played by the degree of product substitutability. The model also delivers simple testable implications related to international trade policy. Policies devoted to attract FDI in a host country by lowering taxes or increasing subsidies on foreign investment end up decreasing market shares and mark-ups of multinationals in their domestic market. Moreover, liberalizing trade between two countries by lowering tariffs ends up increasing the domestic market shares and mark-ups of multinationals in both countries. Finally, my opinion is that a promising direction for future research on the issues touched in this paper is to deepen the empirical investigations. For example, one may test with wider and more comprehensive data sets the substitutability among domestic and foreign market shares of multinational companies, or he may estimate the gravity equation for the number of foreign affiliates. These estimates may add valuable insights on the economics of multinational companies and FDI. References Anderson J. E. (979) A Theoretical Foundation for the Gravity Equation. American Economic Review, 69, Anderson J. E., van Wincoop E. (003) Gravity with Gravitas: A Solution to the Border Puzzle. American Economic Review, 93, Baldwin R., Ottaviano G.I.P. (998) Multiproduct Multinationals and Reciprocal FDI Dumping, NBER Working Paper, n Behrens K., Picard P. M. (007) Welfare, home market effects, and horizontal foreign direct investment. Canadian Journal of Economics, 40,

18 Benassy J.-P. (996) Taste for variety and optimum production patterns in monopolistic competition. Economics Letters, 5, Dixit A., Stiglitz J. E. (977) Monopolistic competition and optimum product diversity. American Economic Review, 67, Feenstra R., Ma H. (008) Optimal Choice of Product Scope for Multiproduct Firms under Monopolistic Competition, in E. Helpman, D. Marin and T. Verdier, (eds.), The Organization of Firms in a Global Economy. Cambridge, MA: Harvard University Press. Head K., Ries J. (006) FDI as an Outcome of the Market for Corporate Control: Theory and Evidence. Journal of International Economics, 74, -0. Neary, J.P. (00) Of Hype and Hyperbolas: Introducing the New Economic Geography. Journal of Economic Literature, 39, Razin A., Sadka E. (007) Foreign Direct Investment: Analysis of Aggregate Flows. Princeton: Princeton University Press. 8

19 f( ) 0 S / g( ) Γ ϕ Γ ϕ g( ) S Figure : Graphical representation of the solution S. 9

20 Table : Comparative statics results for domestic and foreign market shares of a change in the parameters of the model Domestic market shares (S, S ) Foreign market shares (S, S ) Domestic mark-ups Foreign mark-ups Γ + Γ + ϕ + + E 0 0 E 0 0 Table : Dependent variable: Average number of foreign affiliates in the host country per parent company () () (3) (4) FDI to US FDI to US FDI to Japan FDI to Japan Coef./se Coef./se Coef./se Coef./se Host market share 56.09*** *** ** (7.50) (0.6) (0.55) (0.498) Source market share -.9** -.886* *** -0.37*** (0.934) (0.938) (0.0) (0.079) Host GDP (0.44) (0.009) Source GDP *** (0.0) (0.09) Constant *** 0.60*** (0.56) (.37) (0.03) (0.078) Linear time trend -0.03** *** 0.03*** (0.00) (0.098) (0.00) (0.008) Median of dep. variable R Obs. 9 9 Note: The table reports the results of ordinary least squares regressions. Robust standard errors are in parentheses. ***, ** and * denote significance at the, 5 and 0 per cent level. 0