1. 1
Investments in Public Infrastructure and
Foreign Direct Investment
by
Kate 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

2. 2
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 framework
2
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

3. 3
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 Ireland
7
Goodspeed, Martinez-Vazquez and Zhang (2006) find that lower taxes, lower corruption and better
infrastructure attract FDI.

4. 4
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 country ,
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, The inverse demand function for country is given
by,
( (1)
where denotes the price of the MNE‟s good in country and is the quantity of the
MNE‟s good in country with
where denotes country ‟s market size. I assume country 2 has a larger market size than
country 1 ( since The fixed cost, , 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 . 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 by , 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

5. 5
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:
(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:
(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 of
domestic firms. For simplicity, I assume for now that there are exogenously given
symmetric domestic monopolist firms in country
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,
(5)
where denotes the price of a good produced by a representative domestic firm and is the
associated quantity.
(6)

6. 6
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:
, (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 is a positive constant.
The weight attached to government expenditure, , 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 the MNE determines optimal outputs for each market by
maximising expression (3) with respect to public infrastructure yielding respectively:
(8a)
(8b)

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For each domestic firm in country 1 optimal output is given by:
(9)
where and are defined as and
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:
(10a)
(10b)
while optimal output for each domestic firm in country 1 when the MNE locates in country 2
is given by:
(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
In the second stage the monopolist MNE selects the country in which to locate. The firm‟s
maximised 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 critical
level of investment at which the MNE is indifferent between locating in country 1 and 2

8. 8
denoted by Formally, at we have Using expressions (12) and (13), the
value of this critical threshold is equal to:
(14)
The MNE values market size and the effectiveness of public infrastructure when deciding
where to locate. Figure 1 depicts 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 country , government determines its optimal investments in
public infrastructure by maximising welfare (see expression ( ) with respect
to .
(15)
The optimal level of public infrastructure given that the MNE locates in country 2, denoted
by , is given by:
(16)
Alternatively, given the MNE locates in country , government ‟s optimal investment in
public infrastructure is obtained by maximising welfare with respect to public
infrastructure. This yields the following first-order condition for welfare maximisation:
(17)

9. 9
The optimal investment level in public infrastructure given that the MNE locates in country
1, denoted by is given by:
(18)
The government invests more in public infrastructure if the MNE locates in its country than
when it is not, i.e., The optimal levels for 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 investing , 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 is willing to invest in order to attract FDI, denoted by , is obtained by letting
the welfare for country when the MNE locates in country equal the welfare for country
when the MNE locates in country , .
If the government is willing to invest more in public infrastructure than the minimum amount
required by the MNE, i.e., if , government 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:
(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, , government is not
willing to invest the amount required to attract FDI, its optimal investment in public
infrastructure is given by,

10. 10
(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 less than the government finds it
relatively cheap to invest in public infrastructure; hence, it invests the optimal unconstrained
level, and attracts the MNE. As 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 increases. For values of between and , the government must
invest the amount of public infrastructure required by the firm, , and will thus attract the
MNE. For values of greater than , the deadweight loss of raising taxes in the economy is
too high to fund investments to attract the MNE; hence, the government invests and
welfare levels continue to fall.
3.2 Relative effectiveness of public infrastructure
Define as the relative effectiveness of investment in public infrastructure with with
held 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 different
values of . For low values of , i.e., , 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 and the welfare level of country is As investments in
public infrastructure become relatively more effective, i.e., , the government
attracts FDI; hence, investment levels immediately increase to the government‟s constrained
optimal level, , the minimum level required by the MNE to do FDI in country Welfare

11. 11
levels 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 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 as the number of domestic firms‟ increases.9
For the government
does not attract FDI and invests The welfare of country is given by As domestic
activity increases to intermediate levels, it is optimal for the government to
attract 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 public
infrastructure increases and the government invests As a result, the welfare level in
country increases to . 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 for different possible
trade costs. When trade costs are prohibitively high, , 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 by . Welfare in country
9
Similar result holds as the size of domestic firms increase

12. 12
is given by As the trade cost fall and approach , the firm exports more to country
and 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 countries
become even more integrated and approach , welfare levels rise. The government does
not need to compensate the MNE with as much public infrastructure, thus 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 lies in between and , the optimal
public infrastructure is and welfare is The welfare level remains the same for values
of in between 0 and as the firm is now located in country , therefore the trade cost does
not affect how much the MNE will produce to serve the host market.
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
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. 13
The demand functions for the products of the MNE and domestic firm in
country 1 are, respectively, given by:
(21)
(22)
The degree of product differentiation is represented by ranging from zero
when products are independent to one when the products are perfect
substitutes.
As increases, the benefit of attracting the MNE falls since the presence
of the MNE results in lower profits for domestic firms. Therefore as
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 domestic firms compete à la Cournot. Assuming the MNE
does not compete with domestic 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

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(23)
Each firm has the same cost function given by:
(24)
where represents the fixed cost of entry into the industry. The zero
profit condition in the domestic industry is
(25)
Assuming free entry, from expression (25), we obtain that the equilibrium
number of domestic firms in the industry is:
(26)
The policy tool investing in public infrastructure induces more competition
among domestic firms. As rises, optimal public infrastructure
investment increases making it more likely the government attracts FDI. As
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 and government ‟s investments in public

15. 15
infrastructure are respectively denoted by and The MNE‟s cost functions if it locates
in country and are respectively given by:
(27)
(28)
The MNE‟s profit function from locating in country and country 2 are respectively given
by,
(29)
(30)
There are domestic firms in country and there are domestic firms in country
4.3.1. Stage 3: Outputs
If the MNE locates in country the MNE determines its optimal output by maximising profit
with 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,

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(34a)
(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 government ‟s best response functions are illustrated in figure 7. 12
, is the minimum investment in public infrastructure government has to offer in order
to attract the MNE, given . If the MNE locates in country government ‟s optimal policy
is to invest , the corresponding value for country will be denoted by . It is in
government ‟s best interest to overbid country only up to the level where is equal
to , that is, the level that country is indifferent between trying and not trying to attract
the 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 invest
more in public infrastructure than government Let be denoted as . In
equilibrium the monopolist locates in country and . Also, let be the
corresponding value of for which country is indifferent between trying and not trying to
attract FDI, where Define . The parameter is an index of the
relative size of the two countries. Assuming country 2 has a larger market size
The government best response functions are given by,
12
Figure 7 illustrates best response functions where n1=n2

17. 17
(35)
(36)
Another case can arise when markets are very different in size. This results in a very low
level for . In this case the asymmetry is so large between the countries, is very low such
that resulting in the smaller country not competing for the investment of the foreign
firm.
5. Conclusion
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.

18. 18
Section 5. Graphs
Figure 1 Location trade off for MNE
MNE locate in country 1
MNE locates in country 2

19. 19
0
Figure 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. 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. 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. 22
(A=1) (b1=1) (τ=0.05) (λ=0.1) (δ=1.02) (B=1) (H=0.22) (b2=0.4
Figure 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. 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 )

24. 24
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