Investments in Public Infrastructure and Foreign Direct Investment

byKate Hynes

National University of Ireland, Maynooth

ETSG Conference Leuven

September 2012

JEL Codes: F13, F23, H41

Key words: Public infrastructure, MNE, Domestic firms, Trade liberalisation

Correspondence: Department of Economics, Finance and Accounting, National University of Ireland, Maynooth, Co. Kildare, Ireland; Email: Kate.v.hynes@nuim.ie

1

1. Introduction

The world is becoming increasingly integrated. One way increased integration is shown, is

by increased foreign direct investment (FDI).1 Governments tend to welcome FDI: it

potentially generates employment, creates gains from technology transfer, increases home

production, and stimulates economic growth. It has been well documented that countries are

actively pursuing policies designed to attract inward direct investment. The most common

policy tools governments tend to use to attract FDI are tax incentives and subsidies.2 Davies

and Eckel (2010) examine tax competition between governments. Janeba’s (1998, 2000)

papers study tax competition between governments using a duopoly framework. Haufler and

Wooton (1999) consider two countries competing for a monopolist. They show that, even if

the larger country ends up imposing higher taxes, it nonetheless wins the competition since

trade costs give it a location advantage due to better market access. Barros and Cabral (2000)

investigate subsidy games between governments and determine the welfare implications

thereof.

With Ireland being one of the OECD's smallest and most open economies, Ireland welcomes

FDI and offers grants and tax incentives to attract investors. FDI plays an exceptional role in

the Irish economy, accounting for a larger part of its manufacturing output, employment and

exports than in most other OECD countries.3 As the EU becomes more integrated and

governments 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 attract

1 The literature on FDI is vast. In pioneering work, Hirsch (1976) and Dunning (1977) argue that firms choose to become 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 work focused on the interdependence of MNE’s location decisions, Smith (1987) was the first to explore FDI in a duopoly framework2 Literature surveys on FDI and tax competition have been regularly written and updated (for instance, Caves (1996), Wilson (1999) and Markusen (2002)). 3 OECD Reviews of Foreign Direct Investment: Ireland

2

FDI.4 The financial instability within the EU has led to increased pressure from Germany and

France for tax harmonisation.5 In the future, government’s hands may be tied with regard to

the policies they can actively use to entice firms to locate in their country. The cost of

attracting foreign investment in Ireland has come under greater scrutiny and questions have

been raised about whether too much emphasis has gone to promoting foreign investment and

not enough to developing local enterprises.6

In the empirical literature on the determinants of FDI.7 Coughlin et al (1991) find that more

extensive transportation infrastructures were associated with increased FDI. Wheeler and

Mody (1992) report infrastructure quality has a large significant and positive impact (1.57 to

2.24) on investment.

Whilst a substantial amount of empirical work has been carried out to examine whether

investments in infrastructure is a determinant of FDI, to my knowledge, government

investments in public infrastructure has received relatively little attention in the theoretical

literature on FDI. In this paper I theoretically determine optimal investments in public

infrastructure, when the government invest in infrastructure to attract FDI.

Infrastructure is a broad term, including physical, educational, legal and institutional features

of an economy, which are direct or, more typically, indirect inputs into firm’s production and

cost functions. In this paper I model an investment in public infrastructure as a reduction in

firms marginal production cost. Public infrastructure reduces the marginal cost of the MNE

and also the domestic firms that exist in the country providing this public good.

4 Motta and Norman (1996) and Neary (2002) examine how investment decisions are determined when economies become more integrated.5 Stated in ‘The Economist’ November (2010)6 Reported in OECD Review of FDI in Ireland7 Goodspeed, Martinez-Vazquez and Zhang (2006) find that lower taxes, lower corruption and better infrastructure attract FDI.

3

In section 2, the model is set up. Section 3 determines optimal public infrastructure

investments and discusses welfare. Section 4 extends the analysis by relaxing some of the

assumptions and investigates the strategic interation between two competing governments.

Section 5 concludes.

2. The Model

A MNE decides to locate in one of two potential host countries, country 1 and country2,

aiming to serve both markets. The MNE is a monopolist in each host market. The two

markets are segmented; when exporting from its chosen production location to the other

country, the firm incurs a trade cost, τ . The inverse demand function for country i is given

by,

Pi=a−b iQi (i=1,2¿ (1)

where Pidenotes the price of the MNE’s good in country i and Qi is the quantity of the

MNE’s good in country i , with b i=1S i,

where Si denotes country i’s market size. I assume country 2 has a larger market size than

country 1 (S1<S2 , since b1>b2¿ . The fixed cost, F, of setting up a plant abroad is assumed to

be identical in both locations. Without government intervention, the marginal production

cost is the same in both countries and is denoted by c. Hence the MNE’s natural location

choice 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.8 This government invests

in public infrastructure, denoted byX , which lowers locally producing firms’ marginal cost of

production. Public infrastructure is a broad term, which can include physical infrastructure,

education and the legal or institutional environment of an economy. One can think of

8 We relax this assumption and allow both countries’ governments to be policy active in section 9

4

improvements in any of the above mentioned infrastructures as lowering the marginal cost

doing business within that country.

So, if it locates in country 1, the MNE’s cost function is given by:

c1=c−λX (2)

where λ represents the effectiveness of public infrastructure. Hence the MNE’s respective

profit functions from locating in country 1 and country 2 are given by:

П 1=( P1−c+ λX ) Q11+ ( P2−c+λX−τ ) Q2

1−F (3)

П 2=( P1−c−τ )Q12+( P2−c )Q 2

2−F (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 of

domestic firms. For simplicity, I assume for now that there are n1 exogenously given

symmetric domestic monopolist firms in country 1.

Domestic firms also benefit from investments in public infrastructure. Again, to keep things

simple, it is assumed that public infrastructure lowers the marginal cost of production of

domestic firms to the same extent as the MNE’s. Domestic firms serve the domestic market

only and their location is fixed. The inverse demand function and profit function for each of

the domestic firms are respectively given by,

p=α−β q1 (5)

where p denotes the price of a good produced by a representative domestic firm and q is the

associated quantity.

π=( p−c+λX )q1 (6)

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As mentioned earlier, determining the marginal cost of production in country 1 crucially

depends on the government’s investment in public infrastructure. This is chosen by the

government by maximising domestic welfare, which is given by:

W =b1Q2

2+

n1 β q2

2+n1 π−δ

γ X2

2, δ ≥ 1 (7)

The first and second terms in expression (7) are the consumer surplus generated by

consumption of the product produced by the MNE and domestic firms respectively. The

third term stands for domestic industry profits. The fourth term in the welfare function

represents the cost of investment in public infrastructure. Parameter γ is a positive constant.

The weight attached to government expenditure, δ , can be interpreted as the social cost of

public funds and can be thought of as reflecting the deadweight loss of raising taxes in the

economy to fund public infrastructure investment.

The timing of the game is as follows. In stage 1, the government of country 1 chooses its

investment level in public infrastructure. In stage 2, the multinational decides whether to

establish its production facility in either country 1 or 2. In stage 3, the multinational and

domestic firms choose their levels of output. The three-stage game is solved by backwards

induction.

2.1 Stage 3: Outputs

In the final stage of the game, the MNE and domestic firms choose their output levels. If the

MNE locates in country 1 , the MNE determines optimal outputs for each market by

maximising expression (3) with respect to public infrastructure yielding respectively:

Q11= A+λX

2b1

(8a)

6

Q21= A+λX−τ

2 b2

(8b)

For each domestic firm in country 1 optimal output is given by:

q11=H + λX

2 β

(9)

where A and H are defined as A ≡ a−c and H ≡α−c .

If the MNE locates in country 2, the optimal output for each market is obtained by

maximising expression (4) with respect to public infrastructure and is given by:

Q12= A−τ

2 b1

(10a)

Q22= A

2 b2 (10b)

while optimal output for each domestic firm in country 1 when the MNE locates in country 2

is given by:

q22=H + λX

2 β

(11)

The larger the market size, the more investment in public infrastructure, the larger the outputs

of the MNE and of domestic firms.

2.2 Stage 2: The MNE’s location decision

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In the second stage the monopolist MNE selects the country in which to locate. The firm’s

maximised profits when it locates in country 1 and country 2 are, respectively, given by:

П 1=b1 (Q11)2

+b2 (Q21 )2−F (12)

П 2=b1 (Q12 )2+b2 (Q2

2 )2−F (13)

At X=0, П 1 ( X )<П 2 since country 2 has a larger market size. In fact, there is a critical level

of investment at which the MNE is indifferent between locating in country 1 and 2 denoted

by X . Formally, at X we have П 1 ( X )=П 2 . Using expressions (12) and (13), the value of this

critical X threshold is equal to:

X ( λ , b1 , b2 , τ)=τ ( b1−b2 )λ (b1+b2 )

(14)

The MNE values market size and the effectiveness of public infrastructure when deciding

where to locate. Figure 1 depicts X as a function of the relative market size of country 1. To

the left of the firm’s location-indifference locus, the firm decides to invest in country 2. To

the right of the locus the firm invests in country 1.

2.3 Stage 1: Optimal Public Infrastructure

Given that the MNE locates in country2, government 1 determines its optimal investments in

public infrastructure by maximising welfare W (Q12 , q1

2)(see expression (6¿) with respect toX .

dWdX

=∂ W∂ X

+ ∂ W∂ Q1

2

d Q12

dX+n1

∂W∂ q1

2

d q12

dX=0

(15)

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The optimal level of public infrastructure given that the MNE locates in country 2, denoted

by XO, is given by:

XO= 3 λnH

4 βδγ−3 λ2 n

(16)

Alternatively, given the MNE locates in country1, government1’s optimal investment in

public infrastructure is obtained by maximising welfare W (Q11 , q1

1) with respect to public

infrastructure. This yields the following first-order condition for welfare maximisation:

dWdX

=∂ W∂ X

+ ∂ W∂ Q1

1

d Q11

dX+n1

∂W∂ q1

1

d q11

dX=0

(17)

The optimal investment level in public infrastructure given that the MNE locates in country

1, denoted by X ¿ is given by:

X ¿=βAλ+3 b1 λnH

4 β b1 δγ−β λ2−3 b1 λ2 n

(18)

The government invests more in public infrastructure if the MNE locates in its country than

when it is not, i.e.,X ¿>XO . The optimal levels for X derived so far treated the decision of the

MNE as given. However as the policy active government moves prior to the MNE makes its

location choice, it can compel the MNE to locate in its country by investingX=X , if it wishes

to do so. However, the government is not willing to invest an infinite amount of funds on

public infrastructure. It has a threshold of investment in public infrastructure, above which, it

is no longer worthwhile trying to attract FDI. The maximum level of investment government

1is willing to invest in order to attract FDI, denoted by X , is obtained by letting the welfare

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for country 1when the MNE locates in country 1 equal the welfare for country 1when the

MNE locates in country2, W ¿=W o.

If the government is willing to invest more in public infrastructure than the minimum amount

required by the MNE, i.e., if X ≥ X , government1 has influenced the MNE in investing in its

country, and has thus actively attracted FDI. In that case, the optimal investment in public

infrastructure is given by:

X=max [( X¿) , ( X )] (19)

On the other hand, if the minimum amount of public infrastructure required by the MNE is

greater than the maximum the government is willing to invest, X< X , government1 is not

willing to invest the amount required to attract FDI, its optimal investment in public

infrastructure is given by,

X=( Xo) (20)

3. Determinants of optimal public infrastructure investment and welfare

3.1 Social cost of public funds

Figures 2a and 2b depict optimal investment in public infrastructure and welfare levels as the

social cost of public funds change. For values of δ less than δL the government finds it

relatively cheap to invest in public infrastructure; hence, it invests the optimal unconstrained

level, X ¿ and attracts the MNE. As δ rises, it becomes costlier to raise taxes elsewhere in the

economy to fund investments in public infrastructure; for this reason optimal investments and

welfare levels fall as δ increases. For values of δ between δL andδH , the government must

invest the amount of public infrastructure required by the firm, X , and will thus attract the

MNE. For values of δ greater than δH , the deadweight loss of raising taxes in the economy is

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too high to fund investments to attract the MNE; hence, the government invests X oand

welfare levels continue to fall.

3.2 Relative effectiveness of public infrastructure

Define η as the relative effectiveness of investment in public infrastructure withη ≡λ2

γ with γ

held constant and allowing λ to change for different values of η . Figures 3(a) and 3(b)

respectively depict optimal investment levels and welfare levels for country 1for different

values ofη. For low values of η, i.e., η ¿ηL, it is relatively costly for the government to invest

in public infrastructure, therefore, the government does not try to attract FDI; the optimal

investment level is XOand the welfare level of country 1 is W O . As investments in public

infrastructure become relatively more effective, i.e., ηL<η<ηH, the government attracts FDI;

hence, investment levels immediately increase to the government’s constrained optimal level,

X , the minimum level required by the MNE to do FDI in country 1. Welfare levels for

country 1 continue to increase as η increases. For even higher values of η, η>¿ ηH , the

government invests its unconstrained optimal level of public infrastructure given by, X ¿ and

obtains a welfare level ofW ¿. Summarising, as public infrastructure is relatively more

effective, the government invests more in public infrastructure, the government has a higher

willingness to attract FDI and, as a result, the government is more likely to obtain FDI.

3.3 Number of domestic firms

Figures 4(a) and 4(b) illustrate the optimal investment in public infrastructure and welfare

levels for country 1 as the number of domestic firms’ increases.9 For n<¿ nLthe government

does not attract FDI and invests XO . The welfare of country 1 is given by W O . As domestic

activity increases to intermediate levels, nL<n<nH , it is optimal for the government to attract

9 Similar result holds as the size of domestic firms increase

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FDI, therefore increasing investment levels to its constrained optimal given byX , welfare

levels continue to rise. As n increases beyond this value, the optimal level of public

infrastructure increases and the government invests X ¿ . As a result, the welfare level in

country 1 increases toW ¿. As there is more domestic activity, the government invests more in

public infrastructure, has a higher willingness to attract FDI and is more likely to obtain FDI.

3.4 Trade liberalisation

Figure 5(a) illustrates the non-monotonic relationship between trade liberalisation and

optimal investment. Figure 5(b) shows the welfare level for country 1 for different possible

trade costs. When trade costs are prohibitively high, τ>τ H, the firm requires high levels of

public infrastructure to be compensated for the high trade costs. The government does not

attract FDI; optimal investment in public infrastructure is given byXO. Welfare in country 1 is

given by W O . As the trade cost fall and approachτ H, the firm exports more to country 1 and

thereby increasing country 1’s welfare.

When trade costs lie between τ Handτ L, it is optimal for the government to attract FDI.

Hence, the government invests X , the amount required by the firm. As the two countries

become even more integrated and τapproachτ L, welfare levels rise. The government does not

need to compensate the MNE with as much public infrastructure, thus X is falling. The

government moves closer in investing its optimal unconstrained level of investment, thus

increasing welfare.

As we move even closer to zero trade costs where τ lies in between τ Land0, the optimal

public infrastructure is X ¿and welfare is W ¿ . The welfare level remains the same for values

of τ in between 0 and τ Las the firm is now located in country1, therefore the trade cost does

not affect how much the MNE will produce to serve the host market.

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4. Extensions

The key message remains relevant even when the basic model is extended in a number of

ways. 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 firms

Let us now suppose the MNE and domestic firm are in competition in country 1.10 I model

product differentiation using Shubik-Levitan demand functions.11

The demand functions for the products of the MNE and domestic firm in country 1 are,

respectively, given by:

PM 1=a−b1qM 1

1+θ−

b1θ qD1

1+θ (21)

PD1=α−b1 qD1

1+θ−

b1θ qM1

1+θ (22)

The degree of product differentiation is represented by θ ranging from zero when products

are independent to one when the products are perfect substitutes.

As θ increases, the benefit of attracting the MNE falls since the presence of the MNE results

in lower profits for domestic firms. Therefore as θ increases the government is less willing to

invest in public infrastructure to try attract the MNE and the MNE is more likely to locate in

the larger market.

4.2. Endogenous number of domestic firms

So far, I have assumed that the number of domestic firms in the model is exogenous. Assume

n domestic firms compete à la Cournot. Assuming the MNE does not compete with domestic

10 It is assumed the domestic firm does not export and the MNE serves both markets.11 The alternative method using Bowley linear demand functions has the property that that the size of the market increases as product differentiation increases. Shubik-Levitan demand functions do not have this market size effect as the degree of product differentiation increases.

13

firms. When domestic firms are faced with fixed costs of entry into the industry, the number

of domestic competitors is endogenously determined within the model, imagining that firms

enter in the market until their profits are zero. The demand for domestic firms is given by

p=α−β(q1+q2…+qn) (23)

Each firm has the same cost function given by:

c (q )=(c−λX ) q+φ (24)

where φ represents the fixed cost of entry into the industry. The zero profit condition in the

domestic industry is

π=( p−c+λX ) q−φ=0 (25)

Assuming free entry, from expression (25), we obtain that the equilibrium number of

domestic firms in the industry is:

n¿=α−c+λX

√βφ−1

(26)

The policy tool investing in public infrastructure induces more competition among domestic

firms. As n¿rises, optimal public infrastructure investment increases making it more likely

the government attracts FDI. As φ increases, less domestic firms exist resulting in the

government investing less in public infrastructure.

4.3 Two policy active governments

One could assume that the government of country 2 is policy active too. Assume both

governments simultaneously invest in public infrastructure and the MNE and domestic firms

are not in competition. Government 1 and government2’s investments in public

infrastructure are respectively denoted by X1 and X2 . The MNE’s cost functions if it locates

in country 1 and 2 are respectively given by:

14

c1=c−λ X1 (27)

c2=c−λ X2 (28)

The MNE’s profit function from locating in country 1 and country 2 are respectively given

by,

П 1=( P1−c+ λ X1 ) Q11+ ( P2−c+λ X1−τ ) Q2

1−F (29)

П 2=( P1−c+ λ X2−τ ) Q12+ ( P2−c+λ X2 )Q2

2−F (30)

There are n1 domestic firms in country 1 and there are n2 domestic firms in country 2.

4.3.1. Stage 3: Outputs

If the MNE locates in country 2 , the MNE determines its optimal output by maximising

profit with respect to output, yielding the following:

Q12=

A+λ X2−τ

2b1

(31a)

Q22=

A+λ X2

2 b2

(31b)

The domestic firm’s optimal output is given by,

q12=

H + λ X1

2 β

(32a)

q22=

H + λ X2

2 β

(32b)

If the MNE locates in country 1 , the MNE’s optimal output is given by,

15

Q11=

A+λ X1

2 b1

(33a)

Q21=

A+λ X1−τ

2b2

(33b)

The domestic firm’s optimal output is given by,

q11=

H + λ X1

2 β

(34a)

q21=

H + λ X2

2 β

(34b)

4.3.2. Stage 2: Location decision

The location decision of the monopolist will be influenced by the difference between the

profits in the two locations. This depends on relative country sizes, the trade cost and

differences in investment levels in public infrastructure between them.

4.3.3. Stage 1: Optimal Public Infrastructure

Government 1 and government2’s best response functions are illustrated in figure 7. 12

X i( X j), is the minimum investment in public infrastructure government i has to offer in order

to attract the MNE, givenX j. If the MNE locates in country i , government i’s optimal policy

is to invest X i¿, the corresponding value for country j will be denoted by

~X j. It is in

governmenti’s best interest to overbid country j ,only up to the level where W i¿is equal toW i

o,

that is, the level that country i is indifferent between trying and not trying to attract the MNE.

Let X j' be the corresponding critical value ofX j. For higher values ofX j, governmenti‘s best

12 Figure 7 illustrates best response functions where n1=n2

16

response is to offerX io. If X j>X j

' then government j is willing to invest more in public

infrastructure than government i . Let X j' +ε be denoted asX NE. In equilibrium the

monopolist locates in country jandX j=X NE. Also, let X i' be the corresponding value of X i for

which country j is indifferent between trying and not trying to attract FDI, where W j¿=W j

o .

Define ρ ≡S2

S1

≥ 1. The parameter ρ is an index of the relative size of the two countries.

Assuming country 2 has a larger market size ( S2>S1 ) . The government best response

functions are given by,

X1 ( X2 )={X 1

¿ if X 2<~X2

{X2+τ ( ρ−1 )λ ( ρ+1 )

+ε if ~X2<X 2< X2'

{X1o if X2>X 2

' (35)

X2 ( X1 )={X 2¿ if X1<

~X1

{X1−τ ( ρ−1 )λ ( ρ+1 )

+ε if ~X 1< X1< X1'

{X2o if X1>X1

' (36)

Another case can arise when markets are very different in size. This results in a very low

level forX1. In this case the asymmetry is so large between the countries, X1is very low such

that X2' < X2

¿ , resulting in the smaller country not competing for the investment of the foreign

firm.

5. Conclusion

17

In this paper I have developed a theoretical model to examine how optimal investments in

public infrastructure may influence a MNE’s location decision. I have discussed the

determinants of optimal public infrastructure and welfare. A non monotonic relationship

exists between trade liberalisation and optimal investment. For high trade costs the

government does not attract FDI. However there exists a threshold value for the trade cost

below which the government attracts FDI. An important relationship exists between the

number of domestic firms and optimal public infrastructure. As there are more domestic

firms in the country, the government invests more in public infrastructure, the government

has a higher willingness to attract FDI and the government is more likely to obtain FDI.

Section 5. Graphs

Figure 1 Location trade off for MNE

18

X τλ

MNE locate in country 1(П 1>П 2)

П 1=П 2

MNE locates in country 2 (П 1<П 2)

0 1

S1

S2

Figure 2a) Social cost of funds and optimal public infrastructure

19

Figure 2b) Social cost of funds and welfare analysis

Figure 3a) Relative effectiveness of public infrastructure and optimal investment

20

Figure 3b) Relative effectiveness of public infrastructure and welfare analysis

Figure 4a) Number of domestic firms and optimal public infrastructure

21

Figure 4b) Number of domestic firms and welfare analysis

Figure 5a) Trade liberalisation and optimal public infrastructure

22

Figure 5b) Trade liberalisation and welfare analysis

Figure 7. Equilibrium when governments compete in public infrastructure investment

23

(Asymmetric countriesS2>S1)

X2 τ ( ρ−1 )λ ( ρ+1 )

X2

X2'

X2¿

X2o

~X2

X1

X1o X1

¿

~X1 X1 X1

'

24

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