Subsidy Competition and the Relocation Choice of MNCs∗ Facundo Albornoz† University of Birmingham Gregory Corcos Norwegian School of Economics and Business (NHH) October 19, 2006

Abstract Regional integration makes relocation a more attractive option for MNCs, influencing in turn the provision of investment incentives by member countries. We examine in this context whether subsidy competition increases as integration proceeds. To do so, we model the strategic interaction between two governments offering subsidies and an MNC facing different location alternatives. Our welfare analysis shows that the combination of integration and subsidy competition may lead to an excess of subsidization. We also discuss how the desirability of harmonizing subsidies and the net gains from integration crucially depend on technological differences, ownership, and on corporate tax rates. Lastly, we find that the gain from supranational subsidy coordination increases with integration. JEL-Classification: F15, F21, F23 Key-words: Multinational Corporations, Regional Integration, FDI, Subsidy Competition, Location Choice

∗

We gratefully acknowledge helpful suggestions and comments from Antonio Cabrales, Hector Calvo Pardo, Jayasri Dutta, Yannick Kalantzis, Philippe Martin, Thierry Mayer, Peter Neary, Bernard Salani´e, Jean-Philippe Trop´eano, and Thierry Verdier, as well as seminar participants at LACEA 2004 (San Jos´e), ETSG 2004 (Nottingham), Universit´e Libre de Bruxelles (CEPR workshop), Paris-Jourdan School of Economics, CREST-LEI, University of Birmingham and the ADRES Journ´ees Doctorales. All errors remain ours. † [email protected] (Corresponding author), University of Birmingham, Edgbaston, B15 2TT, UK.

1

Introduction

The relationship between trade integration and competition for foreign direct investment, and consequently the location of Multinational corporation (MNC) subsidiaries, has attracted the attention of both academics and policy makers. Numerous theoretical models of tax and subsidy competition have focused on the location strategies of MNCs, discussing the positive and normative aspects of incentive provision1 . However, this literature has almost overlooked the impact of incentives on the relocation of existing operations, rather than the location of new activities. This should matter for two reasons. First, a thorough analysis of the determinants of relocation should take into account the possibility of keeping existing subsidiaries as an alternative to relocation. Second, the threat of relocation may trigger a specific type of subsidy wars, whose welfare effects have to be assessed. This question is made particularly relevant by the proliferation of regional trade agreements. We contend that the new trade environment modifies the reasons for the existence of different subsidiaries, which impulses new location strategies involving relocation. We study competition for FDI in that context. We can illustrate the importance of the problem with a few examples. For instance, Mercosur offers many illustrations of the coincidence between regional integration, changes in location patterns and intense subsidy competition. Before integration, MNCs operated subsidiaries in both Brazil and Argentina (Anll`o and Ramos, 2006), mostly to ”escape” from trade protection and high transportation costs. More often than not, the subsidiaries had similar operations, used similar technologies, and sold similar products (Gatto, Kosacoff, and Sourrouille, 1984) on each national market. Regional integration, taking the form of a Customs Union in 1995, encouraged MNCs to use one of the member countries as an export platform to serve the region (Kosacoff, 2000), relocating either part of the production or even a full plant2 . Facing the possibility of relocation, member governments, either national or local, increased the provision of investment incentives, most notably in Argentina and Brazil3 . We may even mention the case of Delphi, a producer of electronic car parts, that relocated from Argentina to Brazil in 1998 and back to Argentina in 2000, influenced by subsidy schemes (Ambito financiero, September 20, 2001 issue). Interestingly, subsidies are routinely offered to induce as well as to prevent relocation. For instance, in 1998, Siemens maintained its activities in Brazil, declining production subsidies worth $2 million conditional on installing a plant in Cordoba, Argentina (La Nacion, April 26, 2000). Similarly, Piqueras, a producer of medical tools had contemplated relocation after an offer of a 10-year subsidy scheme by the Brazilian government. The company finally gave up its plans, as the Argen1

The next section offers a literature review. According to the financial newspaper Ambito financiero (September 20, 2001 issue), several MNCs relocated their production from Argentina to either Brazil or Uruguay between late 1998 and 2000. Examples range over several industries, such as the car parts (ZF, Echlin, THA), electrical equipment (Enertec), or metallic components industries (Amp, Cablesa, Dynacast SA). 3 With, respectively, 22% and 40% of FDI in the manufacturing sector being subject to incentives from the central State. Some sectors were more specifically targeted by authorities, especially the automobile and the computer industry, as suggested by the creation of state-funded programmes dedicated to these industries (Chudnovsky and L´opez, 2001, 2002). 2

tinean government quickly countered the Brazilian initiative by offering a renewable purchase of the annual production (La Nacion, March 17, 2000). This issue goes beyond Mercosur. In 2000 Nissan threatened to relocate the production of some car models between two of its existing plants, from Sunderland (UK) to Barcelona (Spain). The relocation was avoided thanks to a 58-million-dollar subsidy from the British government (Financial Times, September 21, 2000). In 1997, VW received a 180,000 dollar/worker job subsidy from the German State of Lower Saxony to avoid relocation to the Czech Republic (Oman, 2000, p. 71). Finally, in France, the highly-publicized threat of relocation exerted by Hewlett Packard motivated the adoption of a general ’defensive’ incentive package in the 2006 budget. All these examples show (1) that the relocation of MNC activities within a region triggers competition among governments and (2) that this process is reinforced by trade integration. We offer a positive and normative analysis of the matter. To tackle the problem of subsidy competition in the shadow of MNC relocation, we consider a region consisting of two countries, A and B, that are served by a multinational firm. The multinational may operate production facilities in both A and B (the ”ubiquity” regime), or may concentrate production in A, supplying B through exports from A (the ”concentration” regime). The former will prevail in situations where the main motive for location is to jump over tariffs and avoid transport costs. The latter involves setting an export platform. A trade agreement will reinforce the export platform motive. Welfare-maximizing governments may offer production subsidies to the multinational should it produce locally. We then investigate how these subsidies and the multinational’s location choice change as trade barriers between A and B are reduced. To understand the logic behind our model, assume first that trade barriers between A and B are prohibitively high so that the multinational operates plants in each country. Suppose further that each government can capture the multinational’s profit from local operations. In this case, each government will subsidize production so as to offset the distortion caused by the multinational’s monopoly power. Next, suppose that trade barriers are eliminated. In the absence of production subsidies, the multinational would concentrate production in the country that has the lowest production cost, namely A. The threat of losing the plant may induce B to offer a higher production subsidy than it would do otherwise, and this may force A to also raise its subsidy. We investigate the outcome of such subsidy competition, and examine the associated welfare effects. We find that, first, a country not too backward technologically may manage to block potential relocation by offering high subsidies. However, this should lead to welfare losses for the region. Second, competition should be more intense between symmetric countries, resulting in excessively high amounts of subsidies. Third, the choice of subsidies by competing governments typically overlooks a positive externality on foreign consumers and a negative externality on foreign producers. The perception of welfare losses associated with subsidization is a cause of concern, for this may jeopardize the benefits from regional integration processes. The communication from the EU commission (Official Journal C 70 of 19.03.2002) provides a clear example of a recent increase in the EU effort to control subsidy wars within the region. On the other hand, the implementation of some sort of coordina-

tion on subsidies belongs to the current agenda of talks on Mercosur’s future4 . In this respect, our model allows for two alternative forms of subsidy coordination: one in which A and B commit to laissez-faire, in the form of zero subsidies (”harmonization”), and one in which A and B offer subsidies that maximize their joint welfare (”regionally optimal subsidies”). We show that the advantage of setting regionally optimal subsidies increases with trade liberalization. Indeed, as integration proceeds, more efficient relocation opportunities are distorted away. Moreover, we identify circumstances under which a zero-subsidy regime dominates subsidy competition. More specifically, we find the following results. First, subsidy competition entails excessive subsidization. The combination of regional integration and subsidy competition leads to an excess of subsidization, even in an imperfect competition framework where subsidies improve allocative efficiency. Second, subsidy competition gives scope for regional coordination. Conflicts of interest between integrating countries create a potential gain from regional policy coordination. Such a need for coordination depends on intra-regional trade barriers. We find the gains from coordination to be magnified by regional integration. Third, harmonization is potentially welfare improving. Under certain conditions, a weak form of regional coordination, such as the harmonization of production subsidies to zero within the region, is enough to improve welfare compared to subsidy competition. Finally, Regional characteristics matter. Our results depend on regional asymmetries, profit repatriation rates, and MNC ownership. Hence policy implications of our analysis need not be the same in regional unions that differ along these dimensions. The remainder of this paper is organized as follows. Section 2 discusses the related literature. We introduce the model and discuss properties of the equilibrium in section 3. In Section 4 we apply our model to a simple case of subsidy competition for the location of an extra-regional MNC. Section 5 presents the case of an MNC originating from the region. Section 6 concludes.

2

Related Literature

There has been a great deal of interest in the effects of competition among countries for the location of MNC operations. First, several studies converge in finding that FDI flows and multinational activity are influenced by taxation (for a review, see Devereux and Griffith, 2002). In a meta-analysis of this literature, Ederveen and de Mooij (2003) report that according to the median estimation, a one percentage point increase in the tax rate results in a decrease of FDI flows by 3.3%. Investment incentives are also found to be influential. Beyond the abundant case-study evidence mentioned in the introduction, Head, Ries, and Swenson (1999) also find supporting quantitative evidence for the role of investment incentives in the location decisions of Japanese MNCs across US states. Interestingly, their simulation results also suggest some neutralization between State-level incentive packages. More generally, some studies assess how strategic interaction between jurisdictions has led to some fiscal 4 As reported by P´ agina 12, an Argentinean newspaper (June 28, 2005 issue). Pol´onia Rios, 2003.

See also

convergence, for example in the EU (Devereux, Lockwood, and Redoano, 2004). Governments may have various motives to offer fiscal or investment incentives to MNCs, which allows for different theoretical approaches. The tax competition literature, as reviewed by Wilson (1999), seeks to explain the effects of intergovernmental competition for mobile capital on the provision of public goods and overall efficiency. Basic tax competition models predict sub-optimally low tax rates and under-provision of public goods, due to either negative pecuniary externalities, or strategic behavior, between jurisdictions (Zodrow and Mieszkowski, 1986; Wilson, 1986). While these central results have been found to hold in a variety of contexts, and to lead to global social losses, some elements relevant for FDI may have been overlooked. First, the effects of fiscal competition may differ between countries, notably for countries of different market sizes. Haufler and Wooton (1999) analyze two-country ’auctions’, in lump-sum profit tax bids for foreign investment, and show that, due to a home market effect, the largest country typically wins the auction. The size advantage may even allow that country to levy a tax on the MNC. Going further, two strands of literature offer a more nuanced normative assessment of fiscal competition: agglomeration effects may create locational rents, part of which may be captured by taxing jurisdictions; local positive externalities may raise the social return on FDI above its private return, counteracting the negative inter-jurisdictional externality. The New Economic Geography literature has emphasized the role of agglomeration effects to explain governments’ willingness to reduce taxes on mobile capital in an integrated region5 . In these papers, agglomeration rents give an edge to one jurisdiction above its rivals, as that jurisdiction may induce location while taxing part of the agglomeration rent. Two useful insights from this literature are worth mentioning. First, further integration makes firms even more responsive to profit differentials resulting from incentive provision, as long as full agglomeration has not yet been reached. Second, a core or geographically-advantaged (be it first or second nature) country may be able to set a limit tax, deterring investment in the periphery. These two features will be present in our model. However, our focus will be on MNCs potentially operating several subsidiaries in potentially several countries, as opposed to single-plant firms as in the above mentioned papers. The other strand of literature has built on the simple idea that the social and private return of FDI may differ because of local positive externalities to the presence of an MNC (for a review, see Blomstr¨om and Kokko, 2003). For instance Barros and Cabral (2000) focus on the reduction of unemployment allowed by the presence of FDI6 . Fumagalli (2003) applies a similar argument to horizontal technological externalities, and obtains a similar result7 . However, assuming horizontal externalities 5

See inter alia the core-periphery models of Ludema and Wooton (2000) and Baldwin and Krugman (2004), and footloose capital models by Ottaviano and van Ypersele (2005) and Dupont and Martin (2006). 6 In their model, this is an assumption rather than a result, justifiable in their partial equilibrium setting. As an implication, competition is positive as the country suffering the most from unemployment wins the bidding contest for the MNC. The gain in employment for this country outweighs the expense in subsidies, and competition has a positive effect on allocative efficiency. 7 With sufficiently large technological differences between countries, the least advanced country

is not exempt of controversy, especially in developing countries (on this debate, see the contributions by Aitken and Harrison (1999), Chudnovsky and L´opez (2004) and Kugler (2006)). Summarising, the two mentioned papers find investment incentives may be welfare enhancing even in the presence of subsidy competition between potential and mutually exclusive host countries. How integration modifies investment decisions has also been extensively studied in the literature. Norman and Motta (1996) and Neary (2002), for instance, show that economic integration not only increases FDI, but may also shape location patterns. Further integration towards the completion of a single market may cause MNC location decisions to be determined by the interplay between a ’tariff-jumping motive’ and an ’export-platform motive’. The tariff-jumping motive biases the location decision towards operating as many subsidiaries as there are countries in the single market, while the export-platform motive pushes for serving the whole market from a single member country. Building on these insights, Raff (2004) investigates the exports vs FDI decision of an extra-regional MNC in a two-country region, after the formation of a Free Trade Agreement or a Customs Union. He shows that trade integration never leads to a reduction in FDI when governments use bilateral tariffs in conjunction with proportional profit taxes. He also finds that a regional FTA may lead to lower external tariffs and a reduction in the tax rates levied by member countries on the profits of multinational firms. Our approach is complementary to his in the sense that the fiscal instrument we study, production subsidies, affects output and hence allocative efficiency, creating a role for strategic subsidization by governments8 . Besides we relax the implicit assumption of costless profit repatriation. All this leads to different conclusions. In particular, we obtain a wider array of location possibilities, including duplication of plants under perfect integration, and find a determining role for ownership in shaping nationally optimal policies towards FDI. We also examine the impact of regional coordination. Indeed, the above discussion on fiscal competition suggests that a case for regional coordination may straightforwardly be made. Haufler and Wooton (2006) investigate the effects of a regionally coordinated profit tax or location subsidy to a monopolistic and globally mobile firm. In their model, optimal regional coordination depends on the relative desirability of extracting rents from existing investors with respect to attracting new investors9 . We address a complementary question: how do the gains from coordination depend on the level of regional integration? This question deserves some attention, especially for policy purposes, since regional coordination should win the contest, as opposed to what would happen without incentives, and that should improve overall welfare. Besides, subsidies also bias the export vs. (extra-regional) FDI decision towards FDI, again improving regional welfare. 8 Janeba (1998) explores subsidy competition in a Brander-Spencer rent-shifting context, and finds laissez-faire as the equilibrium outcome. However, his result depends on a ’third market’ assumption, and would not be robust to more general welfare concerns, as in this paper. 9 For investments whose realization does not rely upon any kind of coordination, a coordinated tax allows for appropriating location rents from the firm. On the other hand, a coordinated tax reduction will attract investment that would not take place when countries act non-cooperatively. Depending on which motive dominates, regional coordination may result in an increase or reduction in tax levels.

might be costly to implement. We identify conditions on regional characteristics for integration to increase the benefits of regional coordination, or, put another way, the net gains from building regional institutions. Our model features several points of departure from the literature that might be summarized as follows. First, we study the interplay between regional integration and competition for firms that already produce in the region10 . When investments are made in a non-integrated region and sunk at the time of regional integration, the creation of a regional export platform in one of the countries may be worthwhile. Our study therefore complements the literature discussed above, which mainly analyses pure auctions for new investments. We obtain a wealth of possible equilibria. Some of them display limit-subsidization, that is excessive by a welfare criterion that will be explained below. This normative assessment of subsidy competition allows us to identify under which circumstances gains from regional integration exceed losses from fiercer subsidy competition. Second, we include the geography of capital in the analysis by allowing for two different types of ownership (intra- or extraregional) and taxation of MNC repatriated profits. Note that the tax rate parameter could also be seen as a particular measure of the social value of MNC investments, as will be discussed below. We will obtain qualitatively different results for both types of MNCs, which we will discuss. Lastly, we put the normative discussion on subsidy competition into perspective by measuring regional welfare in alternative policy settings, such as mutual interdiction (harmonization) of subsidies and perfect regional coordination. We also study how welfare differences vary with the extent of regional integration and assess the potential net gains to coordination.

3 3.1

The Subsidy Game Setup of the model

Formally, the region consists of 2 countries, A and B, whose markets are assumed to be segmented with a linear inverse demand function: DA (p) = DB (p) = A − p An extra-regional MNC has monopoly power over both markets. Consistent with our discussion of location decisions, the firm faces two location alternatives, reflecting the conflicting influences of the tariff-jumping motive and the exportplatform motive. On the one hand, the MNC may want to operate one subsidiary in each country, jumping over tariff barriers: we call this location choice Ubiquity (U for short). On the other hand, it may prefer to build an export platform in a single country, to serve the other country through exports: we call this Concentration (C). Without loss of generality we will only allow for Concentration in country A, which amounts to calling A the country that ’wins’ the bidding game. Because we focus on relocation decisions, the location strategy U will be the original choice of the MNC, 10

Some studies assess potential losses from the relocation of manufacturing operations from Northern to Southern countries, as in Fontagn´e and Lorenzi (2005). However, work on relocation within regional unions seems to be lacking.

while trade integration may lead to a switch to location regime C. Consistent with that view, we assume that fixed production costs are already sunk when the MNC decides whether to relocate. How we model subsidies matters for the analysis. We choose to focus on unit production subsidies. It is worth noting that there is no natural candidate in this respect. First and foremost, in practice, a variety of tax and subsidy instruments are used to influence location and relocation decisions (for an overview, see UNCTAD, 1996 and Oman, 2000, , pp. 26-27). Incentive packages typically rely on several fiscal instruments, which in turn have various tax bases: profits, sales, investment, wage bill, exports... Consequently, lump-sum profit tax reductions cannot straightforwardly be treated as representative subsidies. The study of lump-sum and unit subsidies should rather be seen as complementary tasks. Second, this complementarity is partly reflected in the existing literature. While some papers focus on the more tractable case of lump-sum profit tax reductions (Haufler and Wooton, 1999; Barros and Cabral, 2000), some others study the effect of marginal-cost-reducing subsidies (Janeba, 1998; Hanson, 2001). Dupont and Martin (2006) actually offer a comparative analysis of both instruments in a footloose capital model. Third, in terms of the modeling, choosing lump-sum instruments offers substantial gains in tractability. But this comes at the cost of introducing discontinuity in the variables of interest. This makes the discussion less transparent and more dependent on functional forms11 . Moreover, unit subsidies capture governments’ ability to reduce market power distortions. Finally, lump-sum subsidies can be interpreted as unit subsidies if their amount is conditional on the amount invested (Hanson, 2001). Indeed, the choice of output can be seen as a reduced form of a sequential choice of production capacity and price12 . The two countries are assumed to be identical except in one dimension, that is production costs. With constant returns to scale, cost differences and an intraregional tariff t, the costs of serving the home market j, and the export market k, respectively, equal: Cj (qj,D ) = (αj − sj ) qj,D Cj (qj,X ) = (αj − sj + t) qj,X where sj ’s denote unit production subsidies from host government j, qj,D denotes production in j for the local market, and qj,X denotes production in j for the export market. offered by government j if the MNC is located there. Our assumption on production costs simply amounts to αA ≤ αB . Notice that non-negativity of outputs requires subsidies to be bounded below by −(A − αA ). With linear demand and cost functions, monopoly profits in each market j will simply be equal to π j = (qjj )2 = 41 (A − αj + sj )2 if the market is served by regional production and π j = (qjk )2 = 14 (A − αj + sj − t)2 when market k is served by means of exports from j. As markets are segmented, regional profits (Π) are simply the sum of profits made in each market. 11 12

This applies particularly to demand and welfare functions. This applies to our monopoly model but can also extend to a Kreps-Scheinkman oligopoly.

Denote by φ the corporate tax rate in both countries. We take this variable as exogenous in the analysis. This assumption is consistent with the partial equilibrium nature of the model. Our focus is on subsidies offered in a particular industry, rather than general corporate tax rate levels in host countries. In the context of relocation of existing activities, we see exogeneity as a relatively realistic assumption. Note that other interpretations of the φ variable are possible. First, this could be the share of profits that are reinvested in the host country. This is quantitatively important for developing countries with imperfect capital markets where a significant part of investment is self-financed. Second, it may represent the distribution of part of the affiliate’s profits to local residents13 . This variable therefore captures the share of the MNC’s profit captured by the host government. From the MNC headquarters’ viewpoint, (1 − φ) measures the profit repatriation rate. A second assumption we make, for the sake of simplicity, is that corporate tax rates be equal between the two countries. This assumption seems simplistic but may find support from evidence of convergence in corporate tax rates, for example in the EU (Devereux, Lockwood, and Redoano, 2004). Still, this will allow us to focus on competition in subsidies. Regional MNC profits are reported in Table 1. The relative advantage of a location over the other depends on the internal tariff (t), technological differences (α’s) and subsidies (sj ). Table 1: Regional MNC profits by location and ownership Loc.

Profits

U C

2 2 ΠU (sA , sB ) = (1−φ) 4 [(A − αA + sA ) + (A − αB + sB ) ] 2 2 ΠC (sA , sB ) = (1−φ) 4 [(A − αA + sA ) + (A − αA + sA − t) ]

We now turn to the determination of subsidies. As governments’ decisions depend crucially on their objective functions, we measure national welfare by the sum of consumer surplus (CS), some part of the MNC’s producer surplus (PS), and government surplus (GS), i.e. tariff revenue minus subsidy expenditure. Table 2 displays welfare functions for each type of location and ownership. Note that when φ = 0, the government simply maximizes consumer surplus and net fiscal revenues. By contrast, when φ = 1, the government maximizes total surplus, including fiscal revenues. Given our assumptions on market structure and demand, concavity of total welfare functions with respect to subsidies is always assured. Therefore, a welfare maximizing subsidy for each location choice exists. We model the interaction between governments and the MNC as a two-stage non-cooperative game. The timeline goes as follows: 13

In another interpretation, φ could represent a non-appropriable (proportional to profit) externality to the host country, whose generating process we do not model. For instance, φπ j could be the benefit from an investment in training j’s local workforce. In this interpretation, profit functions would be slightly different, but their comparison would not be affected.

Table 2: Welfare functions by location and ownership

Country

A A B B

Loc.

U C U C

Welfare CS

PS

GS

1 A−αA +sA 2 ) 2( 2 1 A−αA +sA 2 ( ) 2 2 1 A−αB +sB 2 ) 2( 2 1 A−αA +sA −t 2 ( ) 2 2

φ( A−α2A +sA )2 A−αA +sA 2 φ[( ) + ( A−αA2+sA −t )2 ] 2 φ( A−αB2 +sB )2

−sA ( A−α2A +sA ) −sA ( 2A−2αA2+2sA −t ) −sB ( A−αB2 +sB ) t( A−αA2+sA −t )

0

• In the first stage, governments A and B choose their subsidy levels sA and sB . • In the second stage, the MNC chooses a location R between alternatives U and C. This formalization captures both the non-cooperative aspect of subsidy competition and the ability enjoyed by governments to credibly commit to a certain amount of subsidies14 . Notice that, due to the shape of the objective functions, decisions on subsidies exhibit neither strategic substitutability nor strategic complementarity. A rival subsidy will constraint a government’s offer simply because it will affect the MNC’s second-stage location incentives. Formally, the solution to the subsidy game will be denoted by a triple composed of a location regime chosen by the MNC and two amounts of unit subsidies offered by the governments {R, sA , sB }. We now turn to the governments’ objective function to characterize the set of optimal subsidies.

3.2

Characterization of equilibria

The two-stage game is solved by backward induction, looking for sub-game perfect equilibria. 3.2.1

In the second stage

The MNC chooses its location R so as to maximize its regional profits, which we may write as the best-reply function R∗ = R (sA , sB ) satisfying ΠM N C (sA , sB , R∗ ) ≥ ΠM N C (sA , sB , R) for all R 6= R∗ in {U, C}. This best-reply function may be illustrated by a straight line in {sA , sB } space. In general, the profit differential between Ubiquity and Concentration, conditional on subsidies sA and sB , is given by (see Table 1): 14

Credibility is an important assumption, as in one case government A would gain from reneging on its commitment. In real economic situations, reputational concerns with respect to potential investors (beyond the scope of this paper) may arguably be enough to alleviate the credibility problem.

Figure 1: The MNC’s location choice according to first-stage subsidies ~

sA

sA(sB)

C is preferred

U is preferred

sB



1 1 ∆Π(sA , sB ) = (1 − φ) (A − αB + sB )2 − (A − αA + sA − t)2 4 4



We may express this basic comparison between profits from home-based exports and local operations by computing subsidy pairs that leave the MNC indifferent between locations. Denote by sf A (sB ) the function plotting the indifference subsidy from government A for a given sB , and sf B (sA ) the inverse function. Straightforward calculations yield: sf A (sB ) = sB + αA − αB + t Figure 1 represents the graph of this function15 . 3.2.2

In the first stage

Governments choose their subsidy levels simultaneously. At a sub-game perfect equilibrium, a government’s subsidy maximizes its continuation payoff given the other government’s subsidy. Note that when subsidies make the MNC indifferent, we consider Ubiquity as the status quo, consistent with our focus on relocation. Recall that each government’s objective function is composed of:

Wj (sj , sk , R(sj , sk )) = CSj (sj , sk , R(sj , sk ))+P Sj (sj , sk , R(sj , sk ))+GSj (sj , sk , R(sj , sk )) (1) 15

The function is defined over the real interval, thus allowing for negative subsidies (taxes). For expositional simplicity we choose to plot them in the positive quadrant.

Government B’s best reply By defining sopt B (U ) = arg max{WB (sA , sB , U )} we obtain sB

sopt B (U ) =

2φ − 1 (A − αB ) 3 − 2φ

opt This is government B’s best-reply to all sA lower than sf A (sB (U )), which, it should be noted, does not depend on the other government’s subsidy. That is, some opt part of the best-reply function will be vertical. Whenever sA ≥ sf A (sB (U )), B should choose between facing relocation or setting a limit subsidy inducing Ubiquity. The latter must be sf B (sA ), since this is the lowest subsidy inducing Ubiquity and above opt sB (U ) we are on the decreasing part of the bell-shaped welfare curve. Lastly, above a certain subsidy set by government A, it may well be that country B prefers Concentration since high subsidies from A increase consumer surplus in B. To see this in more detail, let us compute the subsidy from government A that makes government B indifferent between Concentration and Ubiquity. Denote it by s0A . Using Table 2, the particular subsidy level such that WB (sopt B (U ), U ) = WB (sA , C) is given by:   p 2 0 (A − αB )2 + (3 − 2φ)t2 − (A − αA ) − t sA = √ 3 − 2φ

Any subsidy higher than s0A makes Concentration more desirable than Ubiquity for government B. Summarizing, we have the following best-reply schedule for government B, pictured in Figure 2 :  opt sopt f  A (sB (U )) B (U ) if sA ≤ s opt 0 s∗B (sA , R∗ (sA , sB )) = f sf B (sA ) if sA ≥ sA > s A (sB (U ))  0 0 any sB s.t. sB < sf B (sA ) if sA > sA Government A’s best reply We proceed in a similar manner by defining 2φ − 1 (A − αA ) 3 − 2φ 4φ − 3 1−φ sopt (A − αA ) + 2t A (C) = 7 − 4φ 7 − 4φ sopt A (U ) =

Notice that in the special case where φ = 1, the government maximizes total surplus, and therefore the optimal subsidy equals the marginal cost. Otherwise, the objective function takes only part of the MNC’s rent into account. It is more difficult to determine government A’s best-reply function. This is because technology and ownership differences make the model asymmetric. In general, the shape of A’s best-reply function will depend on welfare comparisons between

Figure 2: Government B’s best-reply schedule ~

sA

sA(sB)

s’A sB*(sA)

C is preferred

U is preferred

sBoptU

sB

locations U and C16 . We show below that in general government A’s best-reply schedule has a three-part structure. First, against that interval of sB where sopt A (C) yields Concentration, that subsidy is clearly a best-reply to sB if it welfare-dominates Ubiquity with suboptimal subsidies.   opt opt Second, consider the interval sf f B (sA (C)); s B (sA (U )) . Government A’s bestreply depends on the comparison between welfare under U and C. Because welfare functions are bell-shaped, WA (·, sB , C) decreases in sA above sopt A (C). Similarly, opt WA (·, sB , U ) increases in sA below sA (U ). Recall also that when profits are equal across location alternatives, U is chosen. Therefore, sf A (sB ) + ε dominates all other (greater) subsidies conducive to C, while sf A (sB ) dominates all other (lower) subsidies conducive to U. Government A’s best-reply must therefore be one of these subsidies. By continuity, there must be a switch at sA > sopt A (C) such that WA (sA , C) =  opt maxsA WA (sA , sB (U ), U ) . This threshold subsidy may be equal to sopt A (U ), or to another level, leading to a discontinuity in the best-reply schedule. This defines the second part of the three-part best-reply schedule. Lastly, consider that interval of sB where sopt A (U ) yields Ubiquity. By construction, that subsidy is clearly a best-reply to sB as it welfare-dominates Ubiquity with suboptimal subsidies. Intuitively, the three-part structure comes from the fact that no location regime unambiguously welfare-dominates the other for all possible subsidy levels. The shape of the optimal subsidy therefore depends on the rival’s subsidy. In the following section, we will enumerate conditions on welfare functions and subsidies that put opt Both welfare functions are bell-shaped, and take their maximum values at sopt A (U ) and sA (C). As may be seen from (2) and (2), the comparison between these subsidies hinges on parameter opt values. To save space, we will only address here the case where sopt A (C) is lower than sA (U ). The opposite case lends itself to a similar reasoning. 16

Figure 3: Government A’s best-reply schedule ~

sA

sA(sB)

sAoptU

sA*(sB)

C is preferred

U is preferred

sAoptC

sB

more structure on best-reply schedules and allow for a precise characterization of equilibrium. Summarizing, we obtain the following best-reply function for government A: sopt A (C) s∗A (sB , R∗ (sA , sB )) = sf (s )−ε  A Bopt sA (U )  

if if if

opt sB ≤ sf B (sA (C)) opt f sf B (sA ) ≥ sB > s B (sA (C)) sB > sf B (sA )

where ε may be arbitrarily small. Figure 3 shows government A’s best-reply map. We now turn to the conditions for existence of an equilibrium in the sequential game. 3.2.3

Existence of equilibrium

Careful examination of the potential intersections of both best reply schedules leads us to investigate the existence of the four following types of candidate equilibria : • A U 1 equilibrium yielding Ubiquity where the vertical part of B’s reply intersects the horizontal part of A’s reply in the Ubiquity zone. • A C1 equilibrium yielding Concentration where the vertical part of B’s reply intersects the horizontal part of A’s reply in the Concentration zone. • A C2 equilibrium yielding Concentration, with both governments bidding higher subsidies than in the C1 equilibrium levels, where the part of A’s best reply line closely parallel to the MNC indifference line (f sA (sB )) intersects B’s reply curve in its vertical component.

• A U 2 equilibrium yielding Ubiquity, with government B bidding a higher subsidy than in the U 1 equilibrium in order to prevent relocation in country A. Figure 4 illustrates how best-reply curves intersect, leading to four types of equilibria.

sB*(sA)

sA

sB*(sA)

sA

s’A

sAopt(U)

U sBopt(U)

U1 Equilibrium

sA*(sB)

U

sAopt(C) s’A

sB

sB*(sA)

sA

sBopt(U)

sB

C1 Equilibrium sB*(sA)

sA s’A

s’A

sAopt(U)

C

sA*(sB)

C

sA*(sB)

C

sAopt(U)

sA*(sB)

C U

U sBopt(U)

U2 Equilibrium

sB

sBopt(U)

C2 Equilibrium

sB

Figure 4: The four types of equilibria of the subsidy game

Let us now identify the conditions for existence of subgame-perfect equilibria in the subsidy game. Proposition 1 There exists a unique equilibrium in the subsidy game, for a given set of parameter values. The actual equilibrium type depends on the logically sufficient set of conditions described in Appendix A1, particularly in Figure 5. Proof. See Appendix A1. We now discuss the intuition behind and the implications of our first Proposition.

3.3

Discussion

We have now fully characterized the equilibria of this game. As can be seen in Appendix A1, Conditions 1 − 6 and the tree diagram enable us to easily determine the prevailing equilibrium for different levels of regional integration, ownership, tax rates and regional technological differences.

Despite a simple formalization, with the property that for a given location regime welfare-maximizing subsidies do not depend on the other government’s subsidy, we have ended up with a wealth of subgame-perfect equilibria. This results from the sequential game setup. In a simultaneous game, only U1 and C1 equilibria would appear. To make this clearer, notice that at equilibria U1 and C1, no player has an incentive to deviate in a unilateral way. Indeed, for the MNC the location is optimal given the subsidy pair; for governments, by construction, the equilibrium subsidies maximize welfare conditional on the chosen location regime. By contrast, at equilibria U2 and C2 at least one player has an incentive to deviate. Indeed, at equilibrium C2, government A would rather post a lower subsidy (equal to sopt A (C)), if it were guaranteed that government B posts a low enough subsidy and that the MNC chooses Concentration. Government A’s capacity to commit to the subsidy is essential to the existence of such an equilibrium outcome. Similarly, at equilibrium U2, government B would rather set a lower subsidy (equal to sopt B (U )), if it were guaranteed that government A plays its optimal subsidy and that the MNC chooses Ubiquity. In that sense, the existence of equilibria U 2 and C2 stems from governments’ capacity to make credible offers to mobile investors. We define the subsidies offered at each of these equilbria as excessive, in the sense that they exceed the levels maximizing national welfare. As we will argue, trade liberalization makes the emergence of these equilibria likelier, causing subsidization to increase substantially. Indeed, deepening integration favours the export-platform motive, increasing governments’ willingness to subsidize beyond their optimal levels, resulting in an efficiency loss. In our view, this concurs with an observed rising trend of subsidy spending from governmental agencies, mentioned in the Introduction. In what follows, which equilibrium eventually obtains will depend on three features of the regional union: technological asymmetries between countries (αi ), the corporate tax rate (φ), and internal trade barriers (t). For instance, an equilibrium with Concentration is more likely to occur whenever asymmetries are substantial, tax rates are high, and trade barriers are low. To focus on regional integration, it also straightforwardly appears that sufficiently high levels of t imply an equilibrium with Ubiquity (U 1 to be more specific). In Appendix A1, we discuss in more detail how threshold tariffs depend on parameter values (see Table 3 in particular). What is interesting to keep in mind is that deepening regional integration is likely to make the region switch to another equilibrium. A final remark concerns the costs of operating subsidiaries. In our model, fixed production costs are sunk when the MNC decides whether to relocate. Therefore, Ubiquity does not entail any duplication, while Concentration does not entail any additional fixed costs. This should be thought of as a focus on relocation decisions. In addition, we do not take liquidation costs into account. However, as will become clear later, introducing liquidation costs would only reinforce our result of excessive ubiquity from Proposition 2. More generally, these simplifying assumptions allow our conclusions not to rely on the comparison between arbitrary values of these fixed costs. We are now in a position to study the effect of regional integration and subsidy

coordination on the decision to relocate, using our general framework.

4

Applications

We seek to establish MNC location in equilibrium and its welfare consequences under different regional policy schemes. Public policy towards FDI may take various forms, according to the degree of regional coordination. We define the following alternative policy options : • Decentralized integration, under which countries compete in subsidies to influence the MNC’s location choice. • Harmonized integration, under which governments commit themselves to a weak form of coordination, namely zero subsidy. This situation amounts to the mutual interdiction of investment incentives. • Coordinated integration, under which countries cooperatively set subsidy levels that maximize regional welfare, mimicking a benevolent supranational social planner. ’Regionally optimal’ subsidies, conditional on each regime R, are denoted by sreg j (R) and maximize the sum of both countries’ national welfare for a given location regime (a formal treatment is given in Appendix A2). We can turn now to our analysis of the location equilibrium. Intuitively, in the absence of trade, a MNC would set up an affiliate in each nation17 : for a large enough tariff, the tariff-jumping motive dominates the export platform motive. Lower tariffs allow the MNC to concentrate production in the most convenient country and serve both markets from there. When subsidy competition is avoided by either regional harmonization or coordination, it straightforwardly follows that full regional integration (t = 0) implies Concentration. The case of subsidy competition requires careful analysis of the set of equilibria. This leads us to determine the MNC location choice at full integration, as summarized in the following Proposition. Proposition 2 Under perfect trade integration, subsidy competition prevents efficient relocation, except for the special case of large regional asymmetries and high levels of repatriation rates. Proof. The result follows from evaluating conditions 1 − 6 expressed in Table 3 at t = 0, which we defer to Appendix A2. The intuition lies in the fact that the subsidy that country B has to pay to avoid relocation is higher the greater the regional asymmetries and that the gain from preserving the MNC activities decreases in the repatriation rate. It is interesting to note that in the case of a symmetric region, the equilibrium would be U 1, or the status quo location. The slightest difference in technologies leads to a U 2 equilibrium, and excessive subsidies. 17

Remember that we do not consider the possibility of exports from outside the region.

Does this result imply that countries should necessarily avoid offering subsidies? To answer this question, we compare subsidy competition and the weakest form of coordination we consider (harmonization) from a regional welfare point of view. According to the literature we should expect subsidy competition to be welfare-improving with respect to no intervention. However, we find that this is not necessarily the case. Corollary 1 Harmonization is generally welfare-improving over subsidy competition. Proof. The proof is referred to Appendix A3. Competitive (decentralized) subsidization enables the high-cost country’s government to influence location decisions. We have just shown that, in a vast spectrum of cases, the MNC will not relocate production even under perfect integration (U 2 equilibrium). This entails two potential sources of welfare loses: the cost of excessive subsidization and the inefficient allocation of production in the region. Whether the decentralized outcome (equilibrium U 2) welfare-dominates the harmonized outcome (C1) depends on local production cost differences. We show in the proof that a moderate difference suffices for harmonization to improve on decentralized competition. For intermediate levels of profit repatriation, the result holds even for negligible differences in technology. The result also suggests that subsidy competition may jeopardize the gains from regional integration as this process would invigorate competition for MNC location. We need now to have a closer look at whether the cost of subsidy competition may offset the benefits of regional integration. Corollary 2 Subsidy competition reduces the gains from regional integration, potentially leading to welfare losses. Proof. See Appendix A4. The result simply assesses that the cost of subsidy competition may induce losses from integration. Recall that the welfare comparison involved perfect integration with subsidies and autarky with subsidies. This ’sophisticated’ autarkic benchmark might be more relevant for governments considering regional integration while being aware of potential losses from subsidy competition. Integration creates a possibility of relocation off the equilibrium path, leading to higher subsidy levels, and welfare losses. Another consequence of the fact that harmonization may be a better policy than subsidy competition is that even weak coordination rules between partner countries may be required in order to fully enjoy the benefits from trade integration. This is undoubtedly interesting for policy matters. Harmonization seems to be a focal point from a policy point of view; however, this should only be a natural first step in a broader three-policy comparison. Indeed, in a theoretical analysis of MNCs enjoying market power in sub-regional markets, the zero subsidy benchmark is no reference from a welfare viewpoint. In our model, a non-zero subsidy level maximizing regional welfare always exists. This leads us to

examine the admittedly extreme case of both governments coordinating on regionalwelfare maximizing subsidy levels. This will provide an upper bound on the extent of potential gains from coordination. Having defined a measure of these gains from coordination, we may now examine how they vary with trade integration, recalling that trade barriers are exogenous to our model. We do this in two steps: first, we consider a move from autarky to freer trade; second, we examine how the gains from coordination vary with further integration. Proposition 3 The regional welfare gains from coordination increase monotonically with trade integration: • starting from autarky, a tariff decrease that is sufficient to affect the location choice creates a gain from coordination, i.e. a positive difference in regional welfare between subsidy coordination and competition; • welfare gains from coordination decrease monotonically with the internal tariff. Proof. See Appendix A5 for the first part and Appendix A6 for the second part. As we know, the U 1 equilibrium prevails under autarky, while all other equilibria are conditional on trade integration. Therefore, there is no scope for gains from coordination under autarky. In contrast, integration may cause a welfare change due to the divergence between national governments’ and a supranational authority’s welfare objectives, be it simply a change in subsidy levels or even a change in location. In other words, we know that a reduction of trade barriers starting from autarky raises the extent of welfare gains from coordination. The second part of the Proposition states that the derivative of the regional welfare differential between coordination and subsidy competition with respect to t, the internal tariff, is negative. Therefore the gains from coordination take their maximum at perfect integration. The intuition behind the result and its implication for economic policy are the following: the gain to the coordination of subsidization policies increases as regional integration proceeds. Intuitively, an export platform strategy becomes more attractive with deeper regional integration, which raises the payoff to reorganizing the extra-regional MNC’s regional production facilities into a single location through subsidies. But we have already discussed that government intervention under subsidy competition generally induces the MNC to choose Ubiquity, so that regional welfare does not depend on trade openness. In that sense, subsidy competition eliminates new location possibilities made possible by integration. The creation of a supranational institution coordinating subsidy expenses among member States should be all the more desirable as regional integration proceeds. Considering trade policy in conjunction with related policies such as investment incentives, this result confirms that the interaction between both policies may raise the payoff to implementing one particular policy.

5

Extension: competition for a regional MNC

We now examine whether the origin of the multinational matters for the outcome of subsidy competition. Indeed, we expect subsidization behavior to differ when the MNC comes from within the region. We therefore expect different predictions according to MNC ownership. The welfare effects for the EU and Mercosur, for instance, should be different, as the former has more ’regional’ MNCs than the latter. In this section, we consider a version of our model where the MNC comes from country A. We shall compare this ’regional MNC’ scenario to that of the previous section. The model presented in section 3 is straightforwardly extended to the case of a regional MNC. Appendix A7 displays MNC profits and national welfare functions. The subsidy game in the regional MNC case is solved in exactly the same way as before, implying that Proposition 1 also holds. As in the previous section, we analyze the location outcome of that game, and the potential gains from coordination. We defer to Appendix A7 the evaluation of Conditions (1)-(6). As before, the location outcome of the game depends on the extent of profit repatriation and production cost differences. The equilibrium is C2 whenever the repatriation rate and and the cost difference are low enough (high value of φ) (low αB ), in a sense defined in Appendix A7. In that case, government B’s willingness to subsidize is high enough and the cost disadvantage of producing in B is low enough to make government A commit to large subsidies. Compared to the extra-regional MNC case, government A has an additional interest in hosting the MNC, which translates in a greater ability to ’win’ the subsidy contest. In the case of a greater repatriation rate (lower φ) or a more asymmetric region, the C1 equilibrium obtains. In other words, subsidy competition never hinders efficient relocation, unlike in the extra-regional case, but it can make governments offer subsidies in excess of their welfare-maximizing level. It is interesting to compare gains from trade integration in the extra-regional and regional MNC cases. In the former case subsidy competition can prevent relocation, while increasing subsidy expenditure compared to a prohibitive tariff regime (U 2 equilibrium). When this occurs, the region incurs a welfare loss, as shown in the previous section. In the latter case subsidy competition does not prevent relocation, while it increases subsidy expenditure. We show in Appendix A7 that this increase does not jeopardize the gains from trade, as defined in our model. This important result reinforces the case for cooperation in regions like Mercosur where the presence of out-of-bloc MNCs is relatively more important. Finally, we study how the gains from supranational coordination vary with the degree of trade integration. As in the previous section, a decrease in the tariff starting from autarky will lead to a change in location outcomes, creating a gain from coordination for the region18 . We show in Appendix A7 that this gain from coordination increases with the tariff at the neighborhood of perfect integration. This non-monotonicity of the gains from coordination contrasts with our results in 18

Notice that the reasoning behind the first part of Proposition 3, shown in Appendix A5, does not depend on the origin of the MNC.

the extra-regional case. To gain some intuition about this result, let us distinguish the C1 and C2 equilibria. In the former case, the only difference between subsidy competition and coordination is the concern for B’s consumers by the fictitious social planner. This implies that tariff reductions allow for smaller coordination subsidies, while competitive subsidies are unaffected, lessening potential gains from coordination. In the case of a C2 equilibrium, a tariff reduction has more complex effects on governments’ best responses. Straightforward calculations show that C2 subsidies are decreasing with the level of tariff barriers compared to regionally optimal subsidies, while the latter are consistently higher and increasing. This is intuitive since the C2 subsidy makes B indifferent between locations, which is less costly with low trade barriers ; in contrast, as explained above, regionally optimal subsidies increase with trade barriers. Therefore under subsidy competition, the deviation from the regional optimum benchmark gradually vanishes in the course of trade integration.

6

Conclusion

We have investigated the effects of subsidy competition in situations where regional integration makes relocation a more attractive strategy for MNCs. Our starting point has been the analysis of a subsidy game in a two-country model where the reduction of trade barriers enhances national incentives to offer production subsidies. While this game admits a unique equilibrium, its nature changes according to the extent of trade integration. In particular, a low enough tariff causes a switch to an equilibrium characterized by an excess of subsidization compared to autarky. For the two types of MNCs that we consider, one government commits to subsidy levels beyond those which maximize national welfare, causing either too little or too much relocation. MNC location under free trade within the region depends on ownership. In equilibrium, an extra-regional MNC will serve the region from existing subsidiaries in each country. A regionally-owned MNC will relocate its operations and serve the region from an export platform. Both cases involve excessive subsidization. An excess of subsidization does not necessarily mean that countries are not to gain from regional integration. Only in the case of an extra-regional MNC does intense subsidy competition prevent the region from specialization. In that case, removing trade barriers intensifies subsidy competition, leading to excessively high subsidies, but this does not lead the MNC to concentrate its operations. Lower trade barriers create welfare losses because of an increase in subsidies and subsequently an inefficient location. In contrast, when the MNC is regional and for a relatively low level of technological asymmetry, excessive subsidization also occurs. However, it does not prevent relocation, which is efficient for the region. Gains from trade offset the cost of increased subsidies. We find mixed results for the welfare gains from subsidy harmonization in an integrated region, depending on MNC ownership and regional characteristics. We show that for the case of an extra-regional MNC, harmonization generally dominates subsidy competition in terms of regional welfare. This result is conditional on the

level of regional asymmetry and profit repatriation. Harmonization makes the region better off when regional asymmetry is sufficiently high. For low levels of asymmetry, repatriation must be in an intermediate range for harmonization to dominate subsidy competition. This is an original result, as well as an interesting one for policy purposes, as it shows that simple harmonization may be the relevant second best policy when regional coordination is difficult to implement. While we do not discuss the political feasibility of coordination, we still show that building the appropriate regional institutions may be crucial for the region to enjoy gains from regional integration. Moreover, we show how a reduction of trade barriers, starting from autarky, raises the extent of welfare gains from coordination. This is so since integration causes a divergence between national governments’ and a supranational authority’s welfare objectives, or even a change in location choices that results in regionally suboptimal outcomes. In addition, when the MNC is extraregional, we show that the highest gain to regional coordination is achieved when integration is fully completed. The monotonicity of this gain from coordination with respect to trade costs is interesting, from the point of view of integrating processes among developing countries, often characterized by the presence of extraregional MNCs. Our result suggests that in a gradual integration process, the cost of building institutions may later be recouped by gains from further integration. Our theoretical framework is sufficiently general to adapt to be applied to the specificities of various regions and economic unions, such as Mercosur (which resembles our extra-regional MNC case in a heterogenous region with incipient efforts of harmonization), the former 15-country European Union (a relatively homogenous region, with both regional and extraregional MNCs, and some coordination between partner countries), the 25-country EU (relatively more asymmetric), and the NAFTA (an asymmetric region with no explicit regional coordination). Our findings are sensitive to firm ownership, regional technological heterogeneity, corporate taxation, and, furthermore, to the kind of agreement between countries. No analysis of the role played by country size has been carried out. Nor have we analyzed the case in which repatriation levels are endogenously determined by governments or extended our framework to the case of multiple firms (as we do in Albornoz and Corcos, 2004). We leave these complementary tasks to future research.

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¨ m, M., and A. Kokko (2003): “The Economics of FDI Incentives,” NBER Blomstro Working Paper No 9489. ´ pez (2001): “Las Pol´ıticas de Promoci´on de Inversiones Chudnovsky, D., and A. Lo Extranjeras en el MERCOSUR,” in El Desaf´ıo de Integrarse para Crecer. Balance y Perspectivas del MERCOSUR en su Primera D´ecada, ed. by D. Chudnovsky, and J. M. Fanelli. Siglo XXI, Buenos Aires. (2002): “Policy Competition for FDI : the Global and Regional Dimensions,” in The Promise and Problems of Trade Negotiations in Latin America, ed. by D. Tussie. Palgrave. (2004): “Transnational Corporations’ Strategies and Foreign Trade Patterns in MERCOSUR Countries in the 1990’s,” Cambridge Journal of Economics, 28(5), 635– 652. Devereux, M. P., and R. Griffith (2002): “The Impact of Corporate Taxation on the Location of Capital: A Review,” Swedish Economic Policy Review, 9, 11–33. Devereux, M. P., B. Lockwood, and M. Redoano (2004): “Do Countries Compete over Corporate Tax Rates?,” mimeo University of Warwick. Dupont, V., and P. Martin (2006): “Subsidies to Poor Regions and Inequalities: Some Unpleasant Arithmetic,” Journal of Economic Geography, 6, 223–240. Ederveen, S., and R. de Mooij (2003): “Taxation and Foreign Direct Investment: a Synthesis of Empirical Research,” International Tax and Public Finance, 10, 673–693. ´, L., and J.-H. Lorenzi (2005): “D´esindustrialisation, d´elocalisations,” RapFontagne port 55, Conseil d’Analyse Economique. Fumagalli, C. (2003): “On the Welfare Effects of Competition for FDI,” European Economic Review, 47(6), 963–983. Gatto, F., B. Kosacoff, and J. V. Sourrouille (1984): “Inversiones Extranjeras en Am´erica Latina - Pol´ıtica Econ´omica, Decisiones de Inversi´on y Comportamiento Econ´omico de las Filiales,” Discussion paper, INTAL/Banco Interamericano de Desarrollo (BID). Hanson, G. H. (2001): “Should Countries Promote Foreign Direct Investment ?,” G-24 Discussion Paper Series 9, UNCTAD. Haufler, A., and I. Wooton (1999): “Country Size and Tax Competition for Foreign Investment,” Journal of Public Economics, 71, 121–139. (2006): “The Effects of Regional Tax and Subsidy Coordination on FDI,” Journal of Public Economics, 50, 285–305. Head, C. K., J. C. Ries, and D. L. Swenson (1999): “Attracting Foreign Manufacturing : Investment Promotion and Agglomeration,” Regional Science and Urban Economics, 29, 197–218. Janeba, E. (1998): “Tax Competition in Imperfectly Competitive Markets,” Journal of International Economics, 44, 135–153.

Kosacoff, B. (2000): Corporate Strategy under Structural Adjustment in Argentina. Responses by Industrial Firms to a New Set of Uncertainties, St. Anthony’s - Macmillan. Macmillan Press UK. Kugler, M. (2006): “Spillovers from FDI: Within or Between Industries?,” Journal of Development Economics, In Press. Ludema, R. D., and I. Wooton (2000): “Economic Geography and the Fiscal Effects of Regional Integration,” Journal of International Economics, 52(2), 331–357. Neary, J. P. (2002): “Foreign Direct Investment and the Single Market,” University College Dublin. Norman, V., and M. Motta (1996): “Does Economic Integration Cause Foreign Direct Investment?,” International Economic Review, 37(4), 757–783. Oman, C. (2000): “Policy Competition for Foreign Direct Investment,” Development center studies, OECD. Ottaviano, G. I. P., and T. van Ypersele (2005): “Market Size and Tax Competition,” Journal of Public Economics, 67, 25–46. ´ nia Rios, S. (2003): “MERCOSUR: Trade Agenda Dilemmas and Alternatives,” Polo Discussion paper, INTAL/Banco Interamericano de Desarrollo (BID). Raff, H. (2004): “Preferential Trade Agreements and Tax Competition for Foreign Direct Investment,” Journal of Public Economics, 88(12), 2745–2763. UNCTAD (1996): “Incentives and Foreign Direct Investment,” Current Studies, Series A 30, Division on Transnational Corporations and Investment, New York and Geneva. Wilson, J. D. (1986): “A Theory of Interegional Tax Competition,” Journal of Urban Economics, 19(3), 296–315. Wilson, J. D. (1999): “Theories of Tax Competition,” National Tax Journal, 52(2), 269–304. Zodrow, G. R., and P. Mieszkowski (1986): “Pigou, Tiebout, Property Taxation and the Underprovision of Local Public Goods,” Journal of Urban Economics, 19, 356–370.

Appendix A1: Proof of Proposition 1 Consider the following set of conditions. 0 1. sopt A C ≥ sA opt opt 2. WA (sopt A U, sB U, U ) ≥ WA (sA C, C) opt 0 3. WA (sopt A U, sB U, U ) ≥ WA (sA , C) opt opt opt 4. Π(sopt A U, sB U, U ) > Π(sA U, sB U, C) 0 5. sopt A U ≤ sA 0 0 6. WA (s0A , sf B (sA ), U ) ≥ WA (sA + , C)

We will show that these conditions are logically sufficient to characterise the equilibrium of the subsidy game, using the diagram in Figure 5:

e tru e tru

Condition 4 fal

Condition 2 ue tr

fal

se

se

U1 e tru

Condition 5 fal

C1

U2 C1

se

e tru

Condition 1

fa ls e

e tru e tru

Condition 4 fal

Condition 3 fal

se

C2

se

U1 U2

e tru

Condition 2 fal

se e tru

U2

fal

e tru

Condition 5 fal

Condition 6

se

C2 se

U2

Condition 6 fal

se

C2

Figure 5: Conditions 1-6 and the existence of equilibrium The above mentioned seven conditions fully characterize best-reply functions and their intersections in {sA , sB } space. The tree diagram follows from careful inspection of all possible intersections. We pause now to give some intuition on Proposition 1 and the determination of equilibria in the subsidy game. The most important condition is Condition 1, that determines whether Concentration/relocation with optimal subsidies for country A is acceptable to country B. In this model, governments will generally compete for investment, since the social benefit to the MNC’s presence is higher consumer surplus plus a share of profits. However, Concentration/relocation may be a good option for the ’losing’ country if it implies large efficiency

gains that are passed through to the consumers, and ultimately depends on the amount of subsidy spent by the ’winning’ government. Hence the role of s0A . In graphical terms, this means that government B’s best-reply schedule will always have a vertical component. To summarize, Condition 1 tells us where governments’ best-reply curves intersect in the subspace where Concentration obtains. When Condition 1 holds, then either government A may not increase welfare under Concentration (Condition 2 does not hold and we have the simple C1 equilibrium), or government A may reach a higher welfare level under Ubiquity, despite higher subsidies from the rival government (U2 equilibrium). When Condition 1 does not hold, then a C1 equilibrium is not possible, but all other types of equilibria exist, depending on government A’s comparison between welfare under Concentration with suboptimal subsidization, and welfare under Ubiquity. Table 3 displays Conditions 1 − 6 expressed in parameter values.

Table 3: Conditions for existence of different equilibria in the Subsidy Game expressed in parameter values No. 1

Condition t≥

(A−αB )(7−4φ) √ −2(A−αA ) 3−2φ

1−φ r

(A−αA )2 (1−2φ)2 (7−4φ) 2 −3(A−αA ) 12−8φ 2φ2 −3φ−2 (A−αA )2 1 t 2

2

t≥

3

1 2 3−2φ q≥ ( 2 + φ)(Ω(t) (A−αB )2 + t2 o` u Ω(t) = 3−2φ 2 t ≥ 3−2φ (αB − αA ) √

4 5 6

A − αA ≤

t≥ t≤

− 2 ) − (Ω(t) − 2t )(2Ω(t) − (A − αA ) − t)

3 − 2φ(A √ − αB )

4−(A−αA )2 (3−2φ)2 −16(A−αa )2 (3−sφ)2 (1−φ)φ 2(3−2φ)2 φ √ 2(A−αA )(3−2φ)+ 4−(A−αA )2 (3−2φ)2 −16(A−αa )2 (3−sφ)2 (1−φ)φ 2(3−2φ)2 φ

2(A−αA )(3−2φ)−

In this proof, we will go through some steps to characterize necessary conditions for the existence of qualitatively different types of equilibria. opt U1 equilibrium (sopt A U, sB U, U )

•

MNC

By backward induction, it must be optimal for the MNC to choose U in the second stage, i.e. given these subsidies, Ubiquity profits must be higher than Concentration profits. Hence Condition 4 : opt opt opt Π(sopt A U, sB U, U ) > Π(sA U, sB U, C)

(Condition 4)

Under this condition, choosing Ubiquity indeed maximises the MNC’s secondstage payoff. But when does our candidate equilibrium belong to governments’ best replies ? •

Government A

Let us start with government A, facing sopt B U . By construction, no subsidy conducive to Ubiquity could dominate this candidate equilibrium subsidy. Recall now that s0A is the exact subsidy from A that makes government B indifferent between Concentration and U 1 Ubiquity. In order to induce Concentration, Government A could thus offer a subsidy equal to max{s0A , sopt A C}, knowing that it will be unmatched by the rival government. We should now check whether this strategy pays off more for A than the candidate equilibrium strategy. If not, then against sopt B U no other subsidy may dominate the candidate equilibrium subsidy. To achieve this, we first need to examine Condition 1: 0 sopt A C ≥ sA

(Condition 1)

If Condition 1 is met, then for U 1 to be an equilibrium it is necessary that the following condition, Condition 2, hold : opt opt WA (sopt A U, sB U, U ) ≥ WA (sA C, C)

(Condition 2)

If, to the contrary, Condition 1 is not met, then for U 1 to be an equilibrium it is still necessary that Condition 2 be met, and also that the following condition, Condition 3, hold opt 0 WA (sopt A U, sB U, U ) ≥ WA (sA , C)

(Condition 3)

Conditions 2 and 3 ensure that against sopt B U , no subsidy conducive to Concentration (even outside the equilibrium set) may be preferred by government A. Hence under these conditions the candidate equilibrium subsidy is government A’s best-reply to sopt B U. •

Government B

To complete the proof of existence of equilibrium U 1, we need to examine govopt ernment B’s best-reply to sopt A U . Again, by construction, sB U dominates any other subsidy conducive to Ubiquity. It must therefore be checked that setting an sB conducive to Concentration, against sopt A U , does not yield a higher payoff. This simply amounts to Condition 5 (recall that it is implied by Condition 4): 0 sopt A U ≤ sA

(Condition 5)

Hence, if either Conditions 4, 2 and 1 are met, or Conditions 4, 2 and 3 are met and 1 is not met, then a U 1 equilibrium also exists.

C1 equilibrium (sopt A C, Ø, C) • MNC The MNC will choose Concentration with subsidy sopt A C if country B’s subsidy is below the profit indifference level. This obviously depends on government B deciding to post a subsidy consistent with this location choice.

• Government B Since the sub-game between governments is simultaneous, a C1 equilibrium only obtains whenever government B is better off with Concentration at government A’s equilibrium subsidy level, i.e. sopt A C is sufficient for government B to prefer Concentration. Hence the necessity of Condition 1: 0 sopt A C ≥ sA

(Condition 1)

• Government A For C1 to be an equilibrium it is sufficient that Condition 2 does not hold, since then the candidate equilibrium subsidy payoff-dominates all other subsidies conducive to either Concentration (by construction) or Ubiquity (by the Condition). However, this condition is not necessary. Whenever Condition 2 holds, it is sufficient that Condition 5 fails to hold for a C1 equilibrium to occur. Indeed, the invalidity of Condition 5 implies that against sopt A U government B will always choose sB so as to induce Concentration. Given that Concentration with sopt A C is feasible, it must be government A’s best reply.

C2 equilibrium19 (s0A , Ø, C) A C2 equilibrium obtains when a subsidy higher than sopt A C is necessary to make government B accept Concentration. Obviously, A would prefer it to be the smallest amount required by B not to ’compete’, hence we may talk about a limit-subsidy equilibrium. Given our assumption that Ubiquity should be the status quo location in case of equal profits, it is sufficient for government A to offer an infinitesimal quantity over the limit subsidy to secure location of the MNC. 20 For the MNC, as in the previous subsection, sB must be sufficiently low for the MNC to choose Concentration. Rather straightforwardly, for government B, Condition 1 must be invalid for a C2 equilibrium to exist else the C1 subsidy would be available for and preferred by A. Examining government A’s best-reply strategy, we find that the invalidity of Condition 3 rules out any subsidy leading to Ubiquity, as the candidate subsidy must payoff-dominate it. Alternatively, when Condition 3 is met, the invalidity of Condition 6 guarantees that the limit-subsidy strategy be payoff-dominant. Hence, a C2 (limit-subsidy) equilibrium exists whenever Conditions 1 and 3 are not met, or whenever Conditions 1 and 6 are not met but Condition 3 is met, excluding the above-mentioned U 1 equilibrium. opt U 2 equilibrium (sopt f B (sA U ), U ) A U, s

Loosely speaking, a U 2 equilibrium obtains when government A reaches a high level of welfare with Ubiquity and government B is able to ’compete’ for high enough 19

To save space, we will refer to Conditions 1 − 6 as presented in Table 3. In the next section, we will consider that this infinitesimal amount tends to zero in our calculations. 20

amounts of subsidies. This results in government B offering the exact amount of subsidy that leads to the status quo (Ubiquity, by assumption). Formally, a U 2 equilibrium occurs whenever it is in both governments’ interest to offer subsidy levels that exactly induce the MNC to keep the status quo, i.e. on the profit indifference line. First consider the case where Condition 1 is met. Condition 5 being true implies a ranking of the three reference subsidy levels. If Condition 4 is false, then the U 1 equilibrium is not feasible, but if Condition 2 holds, then by continuity government A’s best-reply curve should intersect with government B’s on the profit indifference line. This result derives from the shape of government B’s best-reply function, as explained in the main text. Now consider the case when Condition 1 is not met. As explained before, Condition 3 rules out one instance of the C2 equilibrium. Suppose first that Condition 4 does not hold, implying that neither U 1 nor C1 is feasible. Then by a continuity argument again, government A’s best-reply must have a ’knife-edge’ shape, lying on the profit indifference curve or away by an infinitesimal amount (inducing Concentration). Condition 6 then ensures that a U 2 equilibrium is reached. Lastly, suppose that Condition 4 holds, namely that a U 1 equilibrium would be feasible for the firm but does not exist. Notice that Condition 4 implies Condition 5 (the reciprocal is not true). If Condition 2 fails to hold, government A will not be satisfied with U 1, hence playing again along the profit indifference line, therefore Condition 6 will again determine which equilibrium will occur. To summarize, a U 2 equilibrium occurs when Conditions 1, 2 and 5, but not 4, are met ; or, when Conditions 1 and 2 are not met, but 4, 3 and 6 are met ; or when Conditions 1, 4 and 5 are not met, but 3 and 6 are met ; or else when Conditions 1 and 4 are not met, but 3 and 5 are met. All these cases exhibit rivalry between the two governments, as government B is not willing to settle for Concentration, and government A has to offer more than it would without competition.

Appendix A2: MNC location under perfect integration In this appendix, we establish the MNC location choice for the 3 types of regional integration. From table 1, we know the MNC regional profits. The location decision of the MNC amounts to choosing R such that Π = M ax(ΠU , ΠC )

Harmonization Let’s begin by considering the case of harmonization (sA = sB = 0). We need to show is that regional integration involves a new location by the MNC so as to run a single subsidiary (location C). To see this, define, for simplicity, a = A − αA and b = A − αB . ΠU = 1−φ [a2 + b2 ], and ΠC = 1−φ [a2 + (a − t)2 ]. Let us call χ the 4 4 profit differential (ΠU − ΠC ). Then χ = b2 − (a − t)2 . Observe that χ increases with t so that, for sufficiently high values of t, χ is positive (U is preferred by the MNC). When t decreases, the chances for a MNC to choose Concentration increase.

Consider now the extreme case of full integration. In such a case, χ = b2 − a2 . Note that a > b and therefore χ < 0 which implies that the preferred location will be Concentration.

Regional subsidies Let’s proceed now with the limit case of governments coordinating on subsidy levels that maximize regional welfare, replicating the decision of a fictitious regional social planner. Consistent with our framework, the timing of the game is now the following: • first, the fictitious regional planner sets sA and sB • second, the MNC chooses a location Notice that the social planner may always set sreg B (C) so as to induce the MNC to choose Concentration with the desired sreg (C). Hence any candidate equilibrium A subsidy pair should be compared to the one leading to a welfare maximum under Concentration. For a start, let us determine ’regionally optimal subsidies’, i.e. subsidies that maximize the sum of both national welfare functions conditional on the MNC choosing a given location. We obtain 2φ − 1 (A − αA ) 3 − 2φ 2φ − 1 sreg (A − αB ) B (U ) = 3 − 2φ 2φ − 1 t sreg (A − αA ) + A (U ) = 3 − 2φ 2 sreg A (U ) =

with obvious notations. It is easy to check that such subsidies bring prices down to marginal cost, totally removing the market power inefficiency. For {sreg A (C), 0, C} to be the equilibrium triplet, it must hold that it welfare-dominates {sreg (U ), sreg A B (U ), U }, let alone any other subsidy pair under Ubiquity. This is true whenever √ p 2 2 2 2 (αA − αB ) + A(αB − αA ) e t< 3 − 2φ It is easy to see that for any t ≤ e t Concentration will be the prevailing equilibrium. To check that Ubiquity is indeed an equilibrium we need to verify that the reg MNC will choose Ubiquity when receiving sreg A (U ), sB (U ). Put another way, we reg reg reg need to show that ΠU (sA (U ), sB (U )) − ΠC (sA (U ), t) ≥ 0 for t > e t which is clear after simple inspection. Summarizing, in the absence of trade within the region, the prevailing equilibrium is U 1. Under perfect integration, C1 prevails.

Subsidy competition To establish location in the case of subsidy competition in an integrated region, we need to evaluate Conditions 1 − 6 for t = 0. We normalize for commodity φ = 0

when repatriation is high, φ = 1 when repatriation is low. At this point, it is also technically convenient and innocuous to assume αA = 0. Recall that αB > 0. Using Tables 2 and 1, and Figure 5, straightforward calculations show that: • When repatriation is high, Condition 1 is satisfied for αB > A2 . In this particular case, as Condition 2 is never satisfied independently of repatriation, the prevailing equilibrium is C1. • In all other cases, Condition 1 is never satisfied. Note that, for all values of φ, Condition 3 holds and Condition 4 is never satisfied. When repatriation is high, Condition 5 holds. When repatriation is low, Condition 5 is not satisfied while Condition 6 is satisfied. Both situations correspond to U2 as the prevailing equilibrium.

Appendix A3: Harmonization as a welfare-improving policy option We start by the case where the prevailing equilibrium under full integration is U 2. opt In this case, country A offers sopt f B (sA (U )). Conversely, A (U ) and country B offers s the equilibrium associated with harmonization is C1. Define ∆ = W reg (C, 0, t) − opt W reg (U, sopt f B (sA (U ))) as the difference in regional welfare with harmonization A (U ), s and subsidy competition. Recalling that αA = 0 and αB > 0, we obtain ∆=

A(4αB − A(1 − 2φ)2 ) 12 − 8φ

Observe that ∆ is positive for αB > 41 A(1−2φ)2 . This means that for sufficiently high levels of regional asymmetry, harmonization dominates subsidy competition. How high φ must be, depends on the level of repatriation. For intermediate levels of φ (i.e. φ = 12 ) this result holds even for tiny differences between the countries. For extreme values of φ, harmonization dominates subsidy competition for intermediate levels of regional asymmetry. Note that for low repatriation U 2 is always obtained and therefore this condition always holds. For the case of high repatriation we need the additional condition that guarantees U 2 be an equilibrium (αB < A2 ). This implies that when repatriation is high, subsidy competition reduces regional welfare for αB ∈ [ 14 A(1 − 2φ)2 , A2 ]. In the case where subsidy competition does not prevent relocation, subsidy competition dominates harmonization for, by construction, subsidies are optimal.

Appendix A4: Net gains from trade We know so far that the reduction of regional tariffs may lead to an excess of subsidization. In the case under which subsidy competition prevents the region from enjoying gains from trade, the effect of integration consists in a switch from a U 1 to a U 2 equilibrium. Simple investigation of regional welfare under both equilibria shows that

opt reducing trade barriers within the region reduces welfare (W reg (U, sopt A (U ), sB (U ))− 2 αB opt W reg (U, sopt f B (sA (U ))) = 6−4φ , which is always positive). A (U ), s

Appendix A5: Gains from trade and coordination We prove here the first part of Proposition 3. First, a brief inspection of nationally and regionally optimal subsidies (Appendix A2) shows that they coincide only at a U 1 equilibrium. Second, regionally optimal subsidies must induce the MNC to choose Ubiquity for U1 to be a subgame-perfect equilibrium. This implies that an analog of Condition 4 with regional subsidies must be met. This analog condition is given by: reg reg reg Π(sreg A U, sB U, U ) ≥ Π(sA U, sB U, C)

Define t1 as the threshold tariff such that the inequality in Condition 4 just holds, and similarly t2 for the analog condition. Then t ≥ min{t1 , t2 } is a sufficient condition to obtain different equilibria under subsidy competition and coordination. Note that it is straightforward to compute these threshold tariffs using Table 3 and show that they exceed prohibitively high tariffs. Since regional coordination achieves a regional welfare maximum by assumption, a gain from coordination always occurs for a low enough tariff.

Appendix A6 : Gains from coordination and trade integration We prove here the second part of Proposition 3. Recall that at a full-integration subgame-perfect equilibrium, the MNC chooses Ubiquity with U 2 subsidies. On the contrary, a social planner would prefer Concentration with C1 subsidies. The welfare differential between coordination and competition is given by:

opt reg opt W reg (sreg (sA U, sf B (sA (U ), U ) = A C, t, C)−W

(A − αA )2 3 − 2φ 2 (A − αA )2 + (A − αB )2 − t− 3 − 2φ 16 2(3 − 2φ)

Taking the derivatives of these welfare differentials with respect to t yields:   opt reg opt ∂ W reg (sreg (sA U, sf 3 − 2φ 2 αB − αA B (sA (U ), U ) A C, t, C) − W =− t − ∂t 8 2 It is straightforward to see, that evaluated in the neighborhood of a zero tariff, these derivatives are always negative, proving the second part of the Proposition.

Appendix A7: Regional MNC MNC profits are given by: 1 ΠU (sA , sB ) = [(A − αA + sA )2 + (1 − φ)(A − αB + sB )2 ] 4 1 ΠC (sA , sB ) = [(A − αA + sA )2 + (A − αA + sA − t)2 ] 4 so that: sf A (sB ) =

p  p 1 − φ sB − (A − αA ) + ( 1 − φ) (A − αB ) + t

which can be represented by a graph similar to that of Figure 1. The following Table display welfare functions. Table 4: Welfare functions in the case of a regional MNC.

Country

A A B B

Loc.

U C U C

Welfare CS

PS

GS

1 A−αA +sA 2 ( ) 2 2 1 A−αA +sA 2 ( ) 2 2 1 A−αB +sB 2 ( ) 2 2 1 A−αA +sA −t 2 ( ) 2 2

( A−α2A +sA )2 + [1 − φ]( A−αB2 +sB )2 ( A−α2A +sA )2 + ( A−αA2+sA −t )2 φ( A−αB2 +sB )2 0

−sA ( A−α2A +sA ) −sA ( 2A−2αA2+2sA −t ) −sB ( A−αB2 +sB ) t( A−αA2+sA −t )

The next Table expresses Conditions (1)-(6) at t = 0 in the regional MNC case. Table 5: Conditions for existence of different equilibria in the Subsidy Game expressed in parameter values.

No. 1 2 3

4 5 6

Condition A−αB √ q3−2φ 2 B ) (1−φ) t ≤ A − αA − 13 (A − αA )2 + 4 (A−α (3−2φ)2 A−αB 2 1 3 t 2 2 A ) + (1 − φ)( 3−2φ ) ≥ 2 (Ω(t) − 2 ) 2 (A − αq 2 (A−αB ) o` u Ω(t) = + t2 3−2φ √ 1−φ t ≥ 2(A − αA ) − 23−2φ (A − αB ) A−αB √ A − αA ≤ 3−2φ √ 1−φ(αB −1))2 A− √ t ≤ (2A−α 2A−αA −2 1−φ(αB −1) 2 3 (A

− αA ) ≤

− (Ω(t) − 2t )(2Ω(t) − (A − αA ) − t)

Only Conditions 1 and 6 are satisfied when repatriation is high (φ = 0), implying the equilibrium is C1. When repatriation is low (φ = 1), the validity of Condition 1

depends on regional asymmetry. If αB < A3 Condition 1 is not satisfied and therefore the equilibrium is C2. The prevailing equilibrium is C1 otherwise. We can identify the value of φ that is sufficient to make the region switch to a C2 equilibrium. As Conditions 3 and 2 are never satisfied, we simply have to find the value of φ that makes Condition 1 be satisfied21 . Simple inspection of Condition 3(A2 +6AαB −3α2B ) 1 at t = 0 shows that this condition is satisfied whenever φ < . For 8A2 instance in a region made up of similar countries, Condition 1 would be satisfied for φ > 38 . With greater regional asymmetry, the existence of a C2 equilibrium, and therefore of excessive subsidization, depends on lower levels of repatriation. Let us now evaluate the gains from regional trade integration. Given location outcomes, they amount to: opt reg W reg (C, sopt (U, sopt A (C), 0) ≥ W A (U ), sB (U ))for high repatriation opt W reg (C, s0A , 0) ≥ W reg (U, sopt A (U ), sB (U ))for low repatriation

(2) (3)

In other words, we must sign the following expressions: opt reg • ∆4 = W reg (U, sopt (C, s0A , 0) for low repatriation and αB ≤ A (U ), sB (U ))-W A 3

opt reg • ∆5 = W reg (U, sopt (C, sopt A (U ), sB (U ))-W A (C), 0) otherwise

Note that s0A is evaluated at a zero tariff. Simple calculations yield: p 2 • ∆4 = 21 (4A2 − 4A (A − αB )2 − 6AαB + 3αB ) • ∆5a =

5α2B −10αB A−2A2 18

• ∆5b =

A2 9

− AαB +

α2B 2

for a high repatriation rate and for the special case of low repatriation and αB >

A 3

which are always negative. Finally, we evaluate the derivative of the gain from coordination with respect to t in the neighborhood of zero. When C1 is an equilibrium, the gain from coordination is given by   reg opt ∂ W reg (sreg (sA C, t, C) A − αA t A C, t, C) − W = + ∂t 6 4 which is positive at any relevant value of t, and in particular at t = 0. When C2 is an equilibrium, the gain from coordination is given by a similar though substantially more cumbersome calculation. We display here the value of this derivative at the neighbourhood of a zero tariff.  
√ reg opt ∂ W reg (sreg C, t, C) − W (s C, t, C) 3 (A − α ) 3 − 2φ − (A − α ) A B A A √ = ∂t 2 3 − 2φ which is strictly positive. Hence potential tariff increases from full integration may cause higher gains from coordination, suggesting that the maximum gain occurs at a positive tariff level. 21

Remember from our previous discussion (see Figure 5) that should this happen, the prevailing equilibrium would be C1.