Investments in public infrastructure and fdi 12th sept 2012
1Investments in Public Infrastructure andForeign Direct InvestmentbyKate HynesNational University of Ireland, MaynoothETSG Conference LeuvenSeptember 2012JEL Codes: F13, F23, H41Key words: Public infrastructure, MNE, Domestic firms, Trade liberalisationCorrespondence: Department of Economics, Finance and Accounting, National University ofIreland, Maynooth, Co. Kildare, Ireland; Email: Kate.firstname.lastname@example.org
21. IntroductionThe world is becoming increasingly integrated. One way increased integration is shown, isby increased foreign direct investment (FDI).1Governments tend to welcome FDI: itpotentially generates employment, creates gains from technology transfer, increases homeproduction, and stimulates economic growth. It has been well documented that countries areactively pursuing policies designed to attract inward direct investment. The most commonpolicy tools governments tend to use to attract FDI are tax incentives and subsidies.2Daviesand Eckel (2010) examine tax competition between governments. Janeba‟s (1998, 2000)papers study tax competition between governments using a duopoly framework. Haufler andWooton (1999) consider two countries competing for a monopolist. They show that, even ifthe larger country ends up imposing higher taxes, it nonetheless wins the competition sincetrade costs give it a location advantage due to better market access. Barros and Cabral (2000)investigate subsidy games between governments and determine the welfare implicationsthereof.With Ireland being one of the OECDs smallest and most open economies, Ireland welcomesFDI and offers grants and tax incentives to attract investors. FDI plays an exceptional role inthe Irish economy, accounting for a larger part of its manufacturing output, employment andexports than in most other OECD countries.3As the EU becomes more integrated andgovernments within the EU are restricted in how they can compete on corporate tax rates,other policies may come to the fore as an alternative or complementary method to attract1The literature on FDI is vast. In pioneering work, Hirsch (1976) and Dunning (1977) argue that firms choose tobecome MNE’s to fully exploit competitive advantages. Dunning proposed that a firm must have ownership,location or an internalization advantage in order to have strong incentive to undertake FDI. Ensuing workfocused on the interdependence of MNE’s location decisions, Smith (1987) was the first to explore FDI in aduopoly framework2Literature surveys on FDI and tax competition have been regularly written and updated (for instance, Caves(1996), Wilson (1999) and Markusen (2002)).3OECD Reviews of Foreign Direct Investment: Ireland
3FDI.4The financial instability within the EU has led to increased pressure from Germany andFrance for tax harmonisation.5In the future, government’s hands may be tied with regard tothe policies they can actively use to entice firms to locate in their country. The cost ofattracting foreign investment in Ireland has come under greater scrutiny and questions havebeen raised about whether too much emphasis has gone to promoting foreign investment andnot enough to developing local enterprises.6In the empirical literature on the determinants of FDI.7Coughlin et al (1991) find that moreextensive transportation infrastructures were associated with increased FDI. Wheeler andMody (1992) report infrastructure quality has a large significant and positive impact (1.57 to2.24) on investment.Whilst a substantial amount of empirical work has been carried out to examine whetherinvestments in infrastructure is a determinant of FDI, to my knowledge, governmentinvestments in public infrastructure has received relatively little attention in the theoreticalliterature on FDI. In this paper I theoretically determine optimal investments in publicinfrastructure, when the government invest in infrastructure to attract FDI.Infrastructure is a broad term, including physical, educational, legal and institutional featuresof an economy, which are direct or, more typically, indirect inputs into firm‟s production andcost functions. In this paper I model an investment in public infrastructure as a reduction infirms marginal production cost. Public infrastructure reduces the marginal cost of the MNEand also the domestic firms that exist in the country providing this public good.4Motta and Norman (1996) and Neary (2002) examine how investment decisions are determined wheneconomies become more integrated.5Stated in ‘The Economist’ November (2010)6Reported in OECD Review of FDI in Ireland7Goodspeed, Martinez-Vazquez and Zhang (2006) find that lower taxes, lower corruption and betterinfrastructure attract FDI.
4In section 2, the model is set up. Section 3 determines optimal public infrastructureinvestments and discusses welfare. Section 4 extends the analysis by relaxing some of theassumptions and investigates the strategic interation between two competing governments.Section 5 concludes.2. The ModelA MNE decides to locate in one of two potential host countries, country 1 and country ,aiming to serve both markets. The MNE is a monopolist in each host market. The twomarkets are segmented; when exporting from its chosen production location to the othercountry, the firm incurs a trade cost, The inverse demand function for country is givenby,( (1)where denotes the price of the MNE‟s good in country and is the quantity of theMNE‟s good in country withwhere denotes country ‟s market size. I assume country 2 has a larger market size thancountry 1 ( since The fixed cost, , of setting up a plant abroad is assumedto be identical in both locations. Without government intervention, the marginal productioncost is the same in both countries and is denoted by . Hence the MNE‟s natural locationchoice is to locate in the country with the larger market, i.e., country 2.However, I assume that country 1 has a policy active government.8This government investsin public infrastructure, denoted by , which lowers locally producing firms‟ marginal cost ofproduction. Public infrastructure is a broad term, which can include physical infrastructure,education and the legal or institutional environment of an economy. One can think of8We relax this assumption and allow both countries’ governments to be policy active in section 9
5improvements in any of the above mentioned infrastructures as lowering the marginal costdoing business within that country.So, if it locates in country 1, the MNE‟s cost function is given by:(2)where λ represents the effectiveness of public infrastructure. Hence the MNE‟s respectiveprofit functions from locating in country 1 and country 2 are given by:(3)(4)Subscripts denote the country of destination and superscripts refer to the country of origin.Although the MNE is a monopolist in both markets, each country also has a number ofdomestic firms. For simplicity, I assume for now that there are exogenously givensymmetric domestic monopolist firms in countryDomestic firms also benefit from investments in public infrastructure. Again, to keep thingssimple, it is assumed that public infrastructure lowers the marginal cost of production ofdomestic firms to the same extent as the MNE‟s. Domestic firms serve the domestic marketonly and their location is fixed. The inverse demand function and profit function for each ofthe domestic firms are respectively given by,(5)where denotes the price of a good produced by a representative domestic firm and is theassociated quantity.(6)
6As mentioned earlier, determining the marginal cost of production in country 1 cruciallydepends on the government‟s investment in public infrastructure. This is chosen by thegovernment by maximising domestic welfare, which is given by:, (7)The first and second terms in expression (7) are the consumer surplus generated byconsumption of the product produced by the MNE and domestic firms respectively. Thethird term stands for domestic industry profits. The fourth term in the welfare functionrepresents the cost of investment in public infrastructure. Parameter is a positive constant.The weight attached to government expenditure, , can be interpreted as the social cost ofpublic funds and can be thought of as reflecting the deadweight loss of raising taxes in theeconomy to fund public infrastructure investment.The timing of the game is as follows. In stage 1, the government of country 1 chooses itsinvestment level in public infrastructure. In stage 2, the multinational decides whether toestablish its production facility in either country 1 or 2. In stage 3, the multinational anddomestic firms choose their levels of output. The three-stage game is solved by backwardsinduction.2.1 Stage 3: OutputsIn the final stage of the game, the MNE and domestic firms choose their output levels. If theMNE locates in country the MNE determines optimal outputs for each market bymaximising expression (3) with respect to public infrastructure yielding respectively:(8a)(8b)
7For each domestic firm in country 1 optimal output is given by:(9)where and are defined as andIf the MNE locates in country 2, the optimal output for each market is obtained bymaximising expression (4) with respect to public infrastructure and is given by:(10a)(10b)while optimal output for each domestic firm in country 1 when the MNE locates in country 2is given by:(11)The larger the market size, the more investment in public infrastructure, the larger the outputsof the MNE and of domestic firms.2.2 Stage 2: The MNE’s location decisionIn the second stage the monopolist MNE selects the country in which to locate. The firm‟smaximised profits when it locates in country and country are, respectively, given by:(12)(13)At , since country 2 has a larger market size. In fact, there is a criticallevel of investment at which the MNE is indifferent between locating in country 1 and 2
8denoted by Formally, at we have Using expressions (12) and (13), thevalue of this critical threshold is equal to:(14)The MNE values market size and the effectiveness of public infrastructure when decidingwhere to locate. Figure 1 depicts as a function of the relative market size of country 1. Tothe left of the firm‟s location-indifference locus, the firm decides to invest in country 2. Tothe right of the locus the firm invests in country 1.2.3 Stage 1: Optimal Public InfrastructureGiven that the MNE locates in country , government determines its optimal investments inpublic infrastructure by maximising welfare (see expression ( ) with respectto .(15)The optimal level of public infrastructure given that the MNE locates in country 2, denotedby , is given by:(16)Alternatively, given the MNE locates in country , government ‟s optimal investment inpublic infrastructure is obtained by maximising welfare with respect to publicinfrastructure. This yields the following first-order condition for welfare maximisation:(17)
9The optimal investment level in public infrastructure given that the MNE locates in country1, denoted by is given by:(18)The government invests more in public infrastructure if the MNE locates in its country thanwhen it is not, i.e., The optimal levels for derived so far treated the decision ofthe MNE as given. However as the policy active government moves prior to the MNE makesits location choice, it can compel the MNE to locate in its country by investing , if itwishes to do so. However, the government is not willing to invest an infinite amount offunds on public infrastructure. It has a threshold of investment in public infrastructure, abovewhich, it is no longer worthwhile trying to attract FDI. The maximum level of investmentgovernment is willing to invest in order to attract FDI, denoted by , is obtained by lettingthe welfare for country when the MNE locates in country equal the welfare for countrywhen the MNE locates in country , .If the government is willing to invest more in public infrastructure than the minimum amountrequired by the MNE, i.e., if , government has influenced the MNE in investing inits country, and has thus actively attracted FDI. In that case, the optimal investment in publicinfrastructure is given by:(19)On the other hand, if the minimum amount of public infrastructure required by the MNE isgreater than the maximum the government is willing to invest, , government is notwilling to invest the amount required to attract FDI, its optimal investment in publicinfrastructure is given by,
10(20)3. Determinants of optimal public infrastructure investment and welfare3.1 Social cost of public fundsFigures 2a and 2b depict optimal investment in public infrastructure and welfare levels as thesocial cost of public funds change. For values of less than the government finds itrelatively cheap to invest in public infrastructure; hence, it invests the optimal unconstrainedlevel, and attracts the MNE. As rises, it becomes costlier to raise taxes elsewhere in theeconomy to fund investments in public infrastructure; for this reason optimal investments andwelfare levels fall as increases. For values of between and , the government mustinvest the amount of public infrastructure required by the firm, , and will thus attract theMNE. For values of greater than , the deadweight loss of raising taxes in the economy istoo high to fund investments to attract the MNE; hence, the government invests andwelfare levels continue to fall.3.2 Relative effectiveness of public infrastructureDefine as the relative effectiveness of investment in public infrastructure with withheld constant and allowing λ to change for different values of Figures 3(a) and 3(b)respectively depict optimal investment levels and welfare levels for country for differentvalues of . For low values of , i.e., , it is relatively costly for the government toinvest in public infrastructure, therefore, the government does not try to attract FDI; theoptimal investment level is and the welfare level of country is As investments inpublic infrastructure become relatively more effective, i.e., , the governmentattracts FDI; hence, investment levels immediately increase to the government‟s constrainedoptimal level, , the minimum level required by the MNE to do FDI in country Welfare
11levels for country continue to increase as η increases. For even higher values of , ,the government invests its unconstrained optimal level of public infrastructure given by,and obtains a welfare level of . Summarising, as public infrastructure is relatively moreeffective, the government invests more in public infrastructure, the government has a higherwillingness to attract FDI and, as a result, the government is more likely to obtain FDI.3.3 Number of domestic firmsFigures 4(a) and 4(b) illustrate the optimal investment in public infrastructure and welfarelevels for country as the number of domestic firms‟ increases.9For the governmentdoes not attract FDI and invests The welfare of country is given by As domesticactivity increases to intermediate levels, it is optimal for the government toattract FDI, therefore increasing investment levels to its constrained optimal given by ,welfare levels continue to rise. As increases beyond this value, the optimal level of publicinfrastructure increases and the government invests As a result, the welfare level incountry increases to . As there is more domestic activity, the government invests morein public infrastructure, has a higher willingness to attract FDI and is more likely to obtainFDI.3.4 Trade liberalisationFigure 5(a) illustrates the non-monotonic relationship between trade liberalisation andoptimal investment. Figure 5(b) shows the welfare level for country for different possibletrade costs. When trade costs are prohibitively high, , the firm requires high levels ofpublic infrastructure to be compensated for the high trade costs. The government does notattract FDI; optimal investment in public infrastructure is given by . Welfare in country9Similar result holds as the size of domestic firms increase
12is given by As the trade cost fall and approach , the firm exports more to countryand thereby increasing country 1‟s welfare.When trade costs lie between and , it is optimal for the government to attract FDI.Hence, the government invests , the amount required by the firm. As the two countriesbecome even more integrated and approach , welfare levels rise. The government doesnot need to compensate the MNE with as much public infrastructure, thus is falling. Thegovernment moves closer in investing its optimal unconstrained level of investment, thusincreasing welfare.As we move even closer to zero trade costs where lies in between and , the optimalpublic infrastructure is and welfare is The welfare level remains the same for valuesof in between 0 and as the firm is now located in country , therefore the trade cost doesnot affect how much the MNE will produce to serve the host market.4. ExtensionsThe key message remains relevant even when the basic model is extended in a number ofways. I briefly discuss the effects of competition between MNE and domestic firms,endogenous number of domestic firms and two policy active governments.4. 1. Extension - Competition between MNE and domestic firmsLet us now suppose the MNE and domestic firm are in competition in country1.10I model product differentiation using Shubik-Levitan demandfunctions.1110It is assumed the domestic firm does not export and the MNE serves both markets.11The alternative method using Bowley linear demand functions has the property that that the size of themarket increases as product differentiation increases. Shubik-Levitan demand functions do not have thismarket size effect as the degree of product differentiation increases.
13The demand functions for the products of the MNE and domestic firm incountry 1 are, respectively, given by:(21)(22)The degree of product differentiation is represented by ranging from zerowhen products are independent to one when the products are perfectsubstitutes.As increases, the benefit of attracting the MNE falls since the presenceof the MNE results in lower profits for domestic firms. Therefore asincreases the government is less willing to invest in public infrastructureto try attract the MNE and the MNE is more likely to locate in the largermarket.4.2. Endogenous number of domestic firmsSo far, I have assumed that the number of domestic firms in the model isexogenous. Assume domestic firms compete à la Cournot. Assuming the MNEdoes not compete with domestic firms. When domestic firms are faced withfixed costs of entry into the industry, the number of domestic competitorsis endogenously determined within the model, imagining that firms enter inthe market until their profits are zero. The demand for domestic firms isgiven by
14(23)Each firm has the same cost function given by:(24)where represents the fixed cost of entry into the industry. The zeroprofit condition in the domestic industry is(25)Assuming free entry, from expression (25), we obtain that the equilibriumnumber of domestic firms in the industry is:(26)The policy tool investing in public infrastructure induces more competitionamong domestic firms. As rises, optimal public infrastructureinvestment increases making it more likely the government attracts FDI. Asincreases, less domestic firms exist resulting in the governmentinvesting less in public infrastructure.4.3 Two policy active governmentsOne could assume that the government of country 2 is policy active too. Assume bothgovernments simultaneously invest in public infrastructure and the MNE and domestic firmsare not in competition. Government and government ‟s investments in public
15infrastructure are respectively denoted by and The MNE‟s cost functions if it locatesin country and are respectively given by:(27)(28)The MNE‟s profit function from locating in country and country 2 are respectively givenby,(29)(30)There are domestic firms in country and there are domestic firms in country4.3.1. Stage 3: OutputsIf the MNE locates in country the MNE determines its optimal output by maximising profitwith respect to output, yielding the following:(31a)(31b)The domestic firm‟s optimal output is given by,(32a)(32b)If the MNE locates in country the MNE‟s optimal output is given by,(33a)(33b)The domestic firm‟s optimal output is given by,
16(34a)(34b)4.3.2. Stage 2: Location decisionThe location decision of the monopolist will be influenced by the difference between theprofits in the two locations. This depends on relative country sizes, the trade cost anddifferences in investment levels in public infrastructure between them.4.3.3. Stage 1: Optimal Public InfrastructureGovernment 1 and government ‟s best response functions are illustrated in figure 7. 12, is the minimum investment in public infrastructure government has to offer in orderto attract the MNE, given . If the MNE locates in country government ‟s optimal policyis to invest , the corresponding value for country will be denoted by . It is ingovernment ‟s best interest to overbid country only up to the level where is equalto , that is, the level that country is indifferent between trying and not trying to attractthe MNE. Let be the corresponding critical value of . For higher values of ,government „s best response is to offer . If then government is willing to investmore in public infrastructure than government Let be denoted as . Inequilibrium the monopolist locates in country and . Also, let be thecorresponding value of for which country is indifferent between trying and not trying toattract FDI, where Define . The parameter is an index of therelative size of the two countries. Assuming country 2 has a larger market sizeThe government best response functions are given by,12Figure 7 illustrates best response functions where n1=n2
17(35)(36)Another case can arise when markets are very different in size. This results in a very lowlevel for . In this case the asymmetry is so large between the countries, is very low suchthat resulting in the smaller country not competing for the investment of the foreignfirm.5. ConclusionIn this paper I have developed a theoretical model to examine how optimal investments inpublic infrastructure may influence a MNE‟s location decision. I have discussed thedeterminants of optimal public infrastructure and welfare. A non monotonic relationshipexists between trade liberalisation and optimal investment. For high trade costs thegovernment does not attract FDI. However there exists a threshold value for the trade costbelow which the government attracts FDI. An important relationship exists between thenumber of domestic firms and optimal public infrastructure. As there are more domesticfirms in the country, the government invests more in public infrastructure, the governmenthas a higher willingness to attract FDI and the government is more likely to obtain FDI.
18Section 5. GraphsFigure 1 Location trade off for MNEMNE locate in country 1MNE locates in country 2
190Figure 2a) Social cost of funds and optimal public infrastructure(A=1) (b1=1) (τ=0.05) (λ=0.2) (n=10) (B=1) (H=0.1) (b2=0.2)Figure 2b) Social cost of funds and welfare analysis
20(A=1) (b1=1) (τ=0.05) (λ=0.2) (n=10) (B=1) (H=0.1) (b2=0.2)Figure 3a) Relative effectiveness of public infrastructure and optimal investment(A=1) (b1=1) (τ=0.05) (δ=1.02)(n=3) (B=1) (H=0.1) (b2=0.4)Figure 3b) Relative effectiveness of public infrastructure and welfare analysis
21(A=1) (b1=1) (τ=0.05) (δ=1.02)(n=3) (B=1) (H=0.1) (b2=0.4)Figure 4a) Number of domestic firms and optimal public infrastructure(A=1) (b1=1) (τ=0.05) (λ=0.1) (δ=1.02) (B=1) (H=0.22) (b2=0.4)Figure 4b) Number of domestic firms and welfare analysis
22(A=1) (b1=1) (τ=0.05) (λ=0.1) (δ=1.02) (B=1) (H=0.22) (b2=0.4Figure 5a) Trade liberalisation and optimal public infrastructure(A=1) (b1=1) (δ=1.02) (λ=0.1) (n=4) (B=1) (H=0.1) (b2=0.4)Figure 5b) Trade liberalisation and welfare analysis
23(A=1) (b1=1) (δ=1.02) (λ=0.1) (n=4) (B=1) (H=0.1) (b2=0.4)Figure 7. Equilibrium when governments compete in public infrastructure investment(Asymmetric countries )
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