ï»¿ WPS6494
Policy Research Working Paper 6494
Powering Up Developing Countries
through Integration?
Emmanuelle Auriol
Sara Biancini
The World Bank
Development Economics Vice Presidency
Partnerships, Capacity Building Unit
June 2013
Policy Research Working Paper 6494
Abstract
Power market integration is analyzed in a two-country the importing country benefits from lower prices. In
model with nationally regulated firms and costly public this case, market integration also improves incentives
funds. If the generation costs between the two countries to invest compared to autarky. The investment levels
are too similar, negative business stealing outweighs remain inefficient, however, especially for transportation
efficiency gains so that the subsequent integration facilities. Free riding reduces incentives to invest in
welfare decreases in both regions. Integration is welfare these public-good components of the network, whereas
enhancing when the cost difference between two regions business stealing tends to decrease the capacity to finance
is large enough. The benefits from export profits increase new investment.
the total welfare in the exporting country, whereas
This paper is a product of the Partnerships, Capacity Building Unit, Development Economics Vice Presidency. It is part
of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy
discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org.
The authors may be contacted at emmanuelle.auriol@tse-fr.eu and sara.biancini@unicaen.fr.
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Produced by the Research Support Team
Powering Up Developing Countries through Integration?
Emmanuelle Auriol and Sara Bianciniâˆ—
JEL Classification: L43, L51, F12, F15, R53.
Keywords: regulation, competition, market integration, investment, electricity.
Sector board: Energy and Mining (EM)
âˆ—
Emmanuelle Auriol is a professor at Toulouse School of Economics and a researcher at TSE, ARQADE and
IDEI; her email adress is emmanuelle.auriol@tse-fr.eu. Sara Biancini (corresponding author) is a professor at
UCBN Caen Basse-Normandie and a researcher at Normandie UniversitÂ´ e and CREM UMR CNRS 6211; her email
address is sara.biancini@unicaen.fr. The authors are grateful for the ï¬?nancial support of the French Development
Agency (AFD). Part of this paper was completed while Sara Biancini was a research fellow at the European
University Institute. For their help and comments, we thank the seminar audiences at the University of Cergy-
Pontoise, the University of Milan, the French Development Agency (AFD), the 2008 EUDN conference, and the
JEI 2009 in Vigo. We are also extremely grateful for the comments and suggestions of Claude Crampes, Rafael
Moner, Aymeric Blanc, Alexis Bonnel, and Yannick Perez on early versions of this paper. Finally, this paper
has greatly beneï¬?ted from the insightful comments, criticisms, and suggestions of three anonymous referees. We
thank them for their input.
1
The worldâ€™s electricity demand is projected to double by the year 2030 (International Elec-
tricity Agency 2006). Financing the volume of investment required to meet this demand increase
is a challenge for developing countries.1 With scarce public resources, little assistance from the
private sector, and limited aid,2 these countries attempt to address their investment needs by
creating regional power markets. Integrated power pools should allow for the better use of
existing resources and infrastructures between the countries involved and for the realization of
projects that would otherwise be oversized for an isolated country. In most cases, this integra-
tion is likely to occur in the absence of legitimate supranational regulation. This paper studies
the costs and beneï¬?ts of this partial economic integration. This paper shows that coordination
problems between independent regulators prevent them from eï¬ƒciently using the stock of exist-
ing infrastructure, and they distort countriesâ€™ incentives to invest in new generation and, more
importantly, in interconnection facilities. These countriesâ€™ competition for market share limits
the beneï¬?t of integration. Because of these losses, the diï¬€erence in these countriesâ€™ generation
costs must be large for a regional power pool to successfully emerge.
Consistent with the theory, cost complementarities in generation are the main engine of
integration in electricity markets. For instance, in South America, several generation and inter-
connection projects have been launched to exploit eï¬ƒciency gains between countries that do not
have suï¬ƒcient energy resources, such as Brazil or Chile, and countries that have a large supply
potential in terms of hydropower, heavy oil, and gas, such as Paraguay, Venezuela, Bolivia,
1
The total cumulative investment in power generation, transmission, and distribution that is necessary to
meet this increase in demand is estimated by the International Electricity Agency 2006to reach $11.3 trillion.
This amount covers investments in OECD countries and in rapidly growing developing countries, such as India
and China, as well as the investments necessary to relieve the acute power penury experienced by some of the
worldâ€™s poorest nations, especially in Sub-Saharan Africa (International Electricity Agency 2006). Indeed, in
2000, only 40% of the population of low-income countries had access to electricity, and this percentage dropped
to 10% for the poorest quintile (Estache and Wren-Lewis 2009).
2
The share of infrastructure assistance in the energy and communications sectors has dramatically declined
in recent years (Estache and Iimi 2008). At the same time, as Estache and Wren-Lewis 2009 note, â€?For many
countries, particularly those with the lowest income, private-sector participation has been disappointingâ€?. As
rich countries emerge from the global ï¬?nancial crisis with high debt, it is unlikely that development assistance
will increase signiï¬?cantly in the near future, and there is a risk that aid to large infrastructure projects could be
reduced.
2
and Peru. Similarly, the Greater Mekong Subregion countries, such as Thailand and Vietnam,
want to integrate with countries with a large supply potential in terms of hydropower and gas
resources, such as Laos and Myanmar. To exploit the potential gains from cross-border trade
and to increase their system eï¬ƒciency, African countries, sustained by the World Bank, have
created several regional power pools: the South African power pool (SAPP), the West African
power pool (WAPP), the Central African Power Pool (CAPP), and the East African Power
Pool (EAPP), along with interconnection initiatives in North Africa with ties to the Middle
East. The pools, which were created to overcome the Sub-Saharaâ€™s acute shortage problems,
are designed to foster the emergence of major projects, such as large hydroelectric-generation
facilities. These projects are unlikely to be achieved otherwise because they are oversized for
the local demand. For instance, the hydro potential of the Democratic Republic of Congo alone
is estimated to be suï¬ƒcient to provide three times as much power as is currently consumed in
Africa. Large hydroelectric projects, such as the Grand Inga in the region of the Congo River
and the projects for the Senegal River basin, could beneï¬?t all countries in the region.3 The
challenging question, however, is how to ï¬?nance these projects.
Electricity is a non-storable good that requires large speciï¬?c investments, such as transporta-
tion and interconnection facilities, before it can be transferred to other markets. For instance,
it is estimated that some 26 GW of interconnectors, at a cost of $500 million per year, are
lacking for the creation of a regional power-trading market in SSA (Rosnes and Vennemo 2008).
This investment requirement is a major diï¬€erence between electricity and the trade of standard
commodities. In the absence of a binding commitment mechanism, ï¬?rms and governments are
unwilling to sink huge investments with the sole purpose of selling electricity to a neighboring
country in the future. Once these speciï¬?c investments are realized, the investing country would
incur a classic hold-up problem. The trade partner could always renegotiate the price, but the
3
For West Africa, Sparrow et al. 2002 estimate the potential cost reduction associated with market integration
at between 5 and 20% (based on the expansion of the thermal and hydroelectric capacities).
3
investor has no ability to sell the energy elsewhere. This commercial risk is particularly acute in
developing countries.4 In this context, the creation of a power pool, with a free trade agreement
and a sound mechanism for dispute resolution, mitigates commercial, political, and regulatory
risks because it strengthens the coordination between countries and limits political interference.
This structure has been chosen to promote investment in neighboring developing countries that
are endowed with unequal energy resources.5
This paper studies the impact of the creation of a regional power pool (i.e., an integrated
electricity market with a free trade agreement) on energy production and on incentives to
invest in generation and transmission infrastructures in a two-country model. Because the
integration is imperfect (i.e., it is neither political nor ï¬?scal), governments focus on their own
national welfare. Governments are biased in favor of their national (public) ï¬?rms because the
governments are the residual claimant for their proï¬?ts and losses. Theoretically, the relevant
analytical framework is asymmetric regulation (i.e., each ï¬?rm is nationally regulated) with costly
public funds. This framework was introduced by Caillaud 1990 and Biglaiser and Ma 1995 to
study the liberalization of regulated industries.6 Because market integration is a process of
reciprocal market opening, the present paper extends these authorsâ€™ analysis, which focuses on
the eï¬€ects of unregulated competition in a closed economy, to a case in which the unregulated
entrant is the incumbent of the foreign market. Considering both countries simultaneously
permits the black box of sectorial integration in non-competitive industries to be opened. This
4
For instance, in 2009, the electricity ministry of Iraq announced that it could not pay the $2.4 billion bill
to G.E.; hence, power production would stop (Attwood 2009). In Madagascar, the Enelec ï¬?rm decreased its
provision of electricity to the public distributor company Jirama, leading to a power shortage due to billions in
unpaid bills (Navalona 2012). In Zimbabwe, the utility Zesa Holdings failed to pay for electricity imports due to
US $ 537 million in unpaid electricity bills (The Herald 2011).
5
For instance, in December 2003, the members of the Economic Community of West African States (ECOWAS)
signed the ECOWAS Energy Protocol, which calls for the elimination of cross-border barriers to trade in energy.
The project, known as the West African Power Pool (WAPP), began with Nigeria, Benin, Togo, Ghana, CË† ote
dâ€™Ivoire, Burkina Faso, and Niger because these countries were already interconnected.
6
Caillaud 1990 studies a regulated market in which a dominant incumbent is exposed to competition from an
unregulated, competitive fringe that is pricing at marginal cost. Biglaiser and Ma 1995 extend the analysis to a
case in which a dominant regulated ï¬?rm is exposed to competition from a single strategic competitor. Allowing
for horizontal and vertical diï¬€erentiation, these authors ï¬?nd that competition helps to extract the information
rent of the regulated ï¬?rm, but allocative ineï¬ƒciency arises in equilibrium.
4
analysis will help us to predict cases in which this integration is likely to be successful and those
in which it is doomed to fail.
We show that the integration of power markets is welfare enhancing for both countries when
the cost diï¬€erence between the two regions is suï¬ƒciently large. For the low-cost region, the
beneï¬?ts from increased export proï¬?t (due to the possibility of also serving foreign demand)
increase the total welfare in the exporting country. For the high-cost region, the domestic
market beneï¬?ts from the reduction in price caused by importation, which enhances consumer
surplus.7 In contrast, sectorial integration is not likely to occur if the cost diï¬€erence between
the two countries is small. Indeed, unregulated competition tends to undermine the tax base
(see Armstrong and Sappington 2005). Without a signiï¬?cant technological gap, competition
for market share is ï¬?erce between the two countries, and thus, the negative business stealing
outweighs the gain from trade. In contrast to the literature on trade subsidization policies (see
Brander 1997), welfare may decrease in both regions following integration. All countries may
lose, even in the absence of sizeable transportation costs and/or non-convexities.8
This paper next studies the impact of regional integration on countriesâ€™ incentives to invest in
new infrastructure. The paper distinguishes a cost-reducing investment (e.g., a new generation
facility) from an investment in interconnection infrastructure (e.g., high voltage links). Com-
pared to autarky, market integration improves incentives to invest in generation. First, when
one country is much more eï¬ƒcient than another, a case in which integration is particularly
appealing, the level of sustainable investment increases with regional integration. Integration
remains suboptimal because the country endowed with the low-cost technology does not fully
7
Even if the eï¬ƒciency gains from integration are large enough so that both countries win from integration,
opposition might persist internally because when production is reallocated toward more eï¬ƒcient providers, trade
liberalization creates winners and losers internally.
8
This ï¬?nding diï¬€ers strikingly from the results in the trade literature. Starting with Brander and Spencer
1983, a portion of this literature has focused on the strategic eï¬€ect of trade subsidization policies. These policies
have a rent-shifting eï¬€ect that creates a prisonerâ€™s dilemma, so ï¬?rms beneï¬?t from jointly reducing the subsidies.
However, even if the beneï¬?t from trade is lower, it is always positive. Similarly, in models ` a la Brander and
Krugman 1983, welfare loss cannot occur with trade unless transportation costs are very high or there are
non-convexities (see Markusen 1981).
5
internalize the foreign countryâ€™s consumer surplus (i.e., it only internalizes sales), but it in-
creases compared to autarky. Moreover, incentives to invest in obsolete technology decrease,
whereas incentives to invest in eï¬ƒcient technology increase. Second, when the two countriesâ€™
technologies are similar, the ï¬?rms must ï¬?ght for their market share and may thus overinvest
in generation compared to the optimal solution. In practice, this risk of over-investment is nil.
First, the countries will resist the creation of a power pool if their cost diï¬€erence is not large
enough. Second, developing countries suï¬€er from massive underinvestment in generation. By
stimulating investment, market integration can alleviate this problem.
In contrast, there is a major risk of underinvestment in infrastructures that constitute a
public good, such as interconnection or transportation facilities. Free-riding behavior reduces
incentives to invest, and business stealing reduces the capacity to ï¬?nance new investment, es-
pecially in the importing country. The problem is sometimes so severe that global investment
decreases compared to autarky. In other words, when the ï¬?rmsâ€™ generation costs are too close,
the maximal level of investment in public-good facilities is not only suboptimal but is also
smaller than in autarky. In practice, this risk is limited because the ineï¬ƒcient country will
resist integration when the generation costs are too close. However, even if the gap between the
costs is large enough that integration beneï¬?ts both countries, the investment level in the pub-
lic good components of the network will remain suboptimal. This structural underinvestment
problem has important policy implications. Several programs supported by the World Bank in
Bangladesh, Pakistan, and Sri Lanka have failed because they failed to address the interconnec-
tion problem. The World Bank supported lending to generators through the Energy Fund in the
spirit of Public Private Partnerships. An investment in generation was made, and the produc-
tion of kilowatts rose. However, due to poor transmission and distribution infrastructures, the
plants were kept well below eï¬ƒcient production levels. On the one hand, power consumption
stagnated because power was largely stuck at the production sites. On the other hand, public
6
subsidies to the industry increased because take-or-pay Power Purchase Agreements had been
used to commit to generation investment (see Manibog and Wegner 2003). Ultimately, both
consumers and taxpayers were worse oï¬€.
Section I of the paper presents the model and the benchmark of a closed economy. Sec-
tion II studies sectoral integration, and Section III focuses on countriesâ€™ incentives to invest
in generation and transportation infrastructure. Finally, Section IV oï¬€ers some concluding
remarks.
I. A MODEL OF SECTORIAL INTEGRATION WITH INDEPENDENTLY REGULATED
FIRMS
We consider two symmetrical countries, identiï¬?ed by i = 1, 2. The inverse demand in each
country is provided by 9
pi = d âˆ’ Qi , (1)
where Qi is the home demand in country i = 1, 2. The demand symmetry assumption is made
to ease the exposition. Appendix G shows that our primary results are robust to asymmetric
demands (i.e., diï¬€erent d1 = d2 ). Before market integration, there is a monopoly in each
country. In a closed economy, Qi corresponds to qi , the quantity produced by the national
monopoly, also identiï¬?ed by i âˆˆ {1, 2}. When the markets are integrated, Qi can be produced
by both ï¬?rms 1 and 2 (i.e., Qi = qii + qji , i = j , where qij , is the quantity sold by ï¬?rm i in
country j ). The total demand in the integrated market is given by
Q
p=dâˆ’ (2)
2
9
For the use of linear demand models in international oligopoly contexts, see Neary 2003, who also discusses
the interpretation of these models and their extension to a general equilibrium framework.
7
where Q = Q1 + Q2 is the total demand in the integrated market, which can be satisï¬?ed by
ï¬?rm 1 or 2 (i.e., Q = q1 + q2 ).
On the production side, ï¬?rm i = 1, 2 incurs a ï¬?xed cost that measures the economies of
scale in the industry. The ï¬?xed cost is sunk, so it does not play a role in the optimal production
choices.10 We thus avoid introducing new notation for this sunk cost.
The ï¬?rm also incurs a variable cost function provided by
2
qi
c(Î¸i , qi ) = Î¸i qi + Î³ . (3)
2
The variable cost function includes both a linear term Î¸i âˆˆ [Î¸, Î¸], which represents the
production cost, and an additional quadratic term, weighted by Î³ , which represents a trans-
portation cost. The cost function (3) can be generated from a horizontal diï¬€erentiation model
`
a la Hotelling with a linear transportation cost in which Firm 1 is located at the left extremity
and Firm 2 is at the right extremity of the unit interval. The linear market is ï¬?rst separated in
two contiguous segments (the â€?national marketsâ€?). Market integration corresponds to the uni-
ï¬?cation of the two segments. The common market is then represented by the full Hotelling line.
To serve consumers, ï¬?rms, which sell the good at a uniform price, must cover the transportation
cost. This Hotelling model generates the cost function in (3), allowing the interpretation of Î³
as a transportation cost (see Auriol 1998).11
The model assumes that the cost is increasing with the distance between the producer
and the consumer. This assumption is legitimate in the electricity example because of the
Joule eï¬€ect and the associated transport charges and losses. Moreover, in the interconnected
network, the transportation cost Î³ is the same for both domestic and international consumers.
This assumption is also consistent with the physical characteristics of electric networks. This
10
Because the cost is already sunk at the time that the countries choose whether to integrate and their pro-
duction levels, it does not play a role in their decision.
11
In other words, assume that the consumers are uniformly distributed over [0, 1]. To deliver one unit to a
consumer located at q âˆˆ [0, 1], the transportation cost is Î³q for ï¬?rm 1 and Î³ (1 âˆ’ q ) for ï¬?rm 2. The variable
q
production cost of ï¬?rm i with market share equal to qi can then be written as c(Î¸i , qi ) = 0 i (Î¸i + Î³ q )dq , or
2
qi
equivalently c(Î¸i , qi ) = Î¸i qi + Î³ 2
(i = 1, 2).
8
physical unity, which comes from the fact that electricity cannot be routed, is what diï¬€erentiates
electric systems from other systems of distribution of goods and services.12
In summary, Î¸i âˆˆ [Î¸, Î¸] can be interpreted as a generation cost that is constant after some
ï¬?xed investment has been performed, whereas Î³ is a measure of transportation costs (i.e.,
transport charges and losses). In the following, we assume that Î³ and Î¸i are common knowledge.
Any distortions occurring at equilibrium can thus be ascribed to a coordination failure between
the national regulators. However, our results are robust to the assumption of asymmetric
information on these parameters.13 To rule out the corner solution, we make the following
assumption:
A0 d > Î¸.
Assumption A0 ensures that in equilibrium, the quantities are strictly positive. The proï¬?t
of ï¬?rm i = 1, 2 is
2
qi
Î i = P (Q)qi âˆ’ Î¸i qi âˆ’ Î³ âˆ’ ti (4)
2
where ti is the tax that the ï¬?rm pays to the government (it is a subsidy if it is negative). The
participation constraint of the regulated ï¬?rm is
Î i â‰¥ 0 (5)
The regulator of country i has jurisdiction over the national monopoly i. She regulates
the quantities and the investments of the ï¬?rm and is allowed to transfer funds to and from
the ï¬?rm, and she taxes operating proï¬?ts when they are positive and subsidizes losses. This
12
For more details on the speciï¬?cities of electric markets, see Joskow and Schmalensee 1985.
13
Because Î³ is a common value, the regulator can implement some yardstick competition to freely learn its
value in the case of asymmetric information. In contrast, if the regulator does not observe the independent cost
parameter Î¸i , some rent must be abandoned to the producer to extract this information. The cost parameter is
replaced by the virtual cost (i.e., the production cost plus the information rent, Î¸i +Î› F (Î¸i )
f (Î¸i )
, where f and F are the
density and repartition functions of Î¸i ). Introducing asymmetric information does not change our primary results
except for the inï¬‚ated cost parameter (computations available upon request). In the event that a supranational
regulator is created, the impact of asymmetric information will depend on the supranational regulatorâ€™s ability
to gather information on the ï¬?rms as compared to the national regulators.
9
process is consistent with public ownership. In the case of electricity, public and mixed ï¬?rms
are key players in most developing countries: in 2004, 60% of the less developed countries had
no signiï¬?cant private participation in electricity (Estache, Perelman, and Trujillo 2005).14
In contrast, rent extraction does not apply to foreign ï¬?rms because they do not report
their proï¬?ts locally. The regulator does not seize the rent of foreign ï¬?rm and does not have to
subsidize the losses. Moreover, the regulator of country i does not control the production or
the investment of ï¬?rm j (i.e., asymmetric regulation).
Each utilitarian regulator in country i maximizes the home welfare, Wi = S (Qi ) âˆ’ P (Q) Qi +
Qi Q2
Î i + (1 + Î»)ti , where S (Qi ) = 0 pi (Q)dQ = dQi âˆ’ 2
i
is the gross consumer surplus, Î i is the
proï¬?t of the national ï¬?rm, and (1+ Î»)ti is the opportunity cost of public transfers. Because Wi is
decreasing in Î i when Î» â‰¥ 0, leaving rents to the monopoly is socially costly. The participation
constraint of the national ï¬?rm (5) always binds: Î i = 0.15 The utilitarian welfare function in
country i = 1, 2 is
2
qi
Wi = S (Qi ) âˆ’ P (Q) Qi + (1 + Î»)P (Q)qi âˆ’ (1 + Î»)(Î¸i qi + Î³ ) (6)
2
The regulator of country i is not indiï¬€erent between producing power locally (i.e., qi ) and
importing it (i.e., Qi âˆ’ qi ). She is biased in favor of local production. This national preference,
which is consistent with countriesâ€™ objective of energy independence, reï¬‚ects the fact that the
regulator is the residual claimant for the ï¬?rm proï¬?t and loss. The bias increases with Î» â‰¥ 0,
which can be interpreted as the shadow price of the government budget constraint (i.e., the
Lagrange multiplier of this constraint).16 Any additional investment in public utilities implies a
14
This lack of private participation also exists in many advanced economies. For instance, 87.3% of ElectricitÂ´
e
de France (EDF), which is one of the largest exporters of electricity in the world, is owned by the French
government. In 2007, the ï¬?rm paid over EUR 2.4 billion in dividends to the government.
15
Here, regulation is eï¬€ective (there is no problem from reducing the monopoly power in the closed economy).
We thus abstract from a possible alternative motivation for integration as a way to reduce the market power of
the incumbent.
16
The government pursues multiple objectives, such as producing public goods, regulating noncompetitive in-
dustries, and controlling externalities, under a single budget constraint. The opportunity cost of public funds
indicates how much social welfare can be improved when the budget constraint is relaxed marginally; it includes
the forgone beneï¬?ts of alternative investment choices and spending. In advanced economies, Î» is usually esti-
10
reduction in the production of essential public goods or in any other commodities that generate
positive externalities, such as health care. Additional investment may also imply an increase in
taxes or public debt. All of these actions have a social cost that must be compared with the
social beneï¬?t of the additional investment. Conversely, when the transfer is positive (i.e., taxes
on proï¬?ts), it helps to reduce distortionary taxation or to ï¬?nance investment. The assumption
of costly public funds is a way to capture the general equilibrium eï¬€ects of sectoral intervention.
To avoid introducing bias into the integration decision, we assume that both countries have the
same cost of public funds, Î».
In the following, we express the results in terms of Î›, which increases with Î» âˆˆ [0, +âˆž):
Î»
Î›= âˆˆ [0, 1]. (7)
1+Î»
We ï¬?rst brieï¬‚y describe the case of a closed economy, marked C . Each regulator maximizes
the expected national welfare (6) subject to the autarky production condition Qi = qi . The
optimal autarky quantity is
C d âˆ’ Î¸i
qi = . (8)
1+Î³+Î›
C) =
When Î› = 0, public funds are costless, and the price is equal to the marginal cost P (qi
C . When Î› > 0, the price is raised above the marginal cost with a rule that is inversely
Î¸i + Î³qi
C)
P (qi
C ) = Î¸ + Î³ qC + Î›
proportional to the elasticity of demand (Ramsey pricing): P (qi i i Îµ . The
optimal pricing rule diverges from marginal cost pricing in proportion to the opportunity cost
of public fund Î› because the revenue of the regulated ï¬?rm allows the level of other transfers in
the economy (and thus distortive taxation) to be decreased.
The closed economy case corresponds to a pure autarky model in which the electricity is
mated at approximately 0.3 (Snow and Warren 1996). In developing countries, low income levels and diï¬ƒculty
implementing eï¬€ective taxation imply higher values for Î». The World Bank 1998 suggests an opportunity cost
of 0.9 as a benchmark, but it may be much higher in heavily indebted countries.
11
distributed and produced internally. Alternatively, we could consider other forms for the import
and export of energy without the formation of a power pool or the existence of a free trade
agreement. In this case, countries could negotiate to import a certain quantity of electricity from
abroad (at a given price) and then sell it internally at the regulated price. This strategy diï¬€ers
from the integrated case studied below because the regulator would be able to control the total
quantity sold in the internal market. For the national regulator, this case of negotiated import
(or equivalently regulated import quotas) boils down to a problem of production allocation
over two plants with diï¬€erent cost functions (one plant would be the national producer and the
other the import possibility). This case would lead to a diï¬€erent (lower) aggregate cost function.
Nevertheless, the regulator would still choose the total quantity sold in the market. Given the
demand and the new cost function, she would determine a Ramsey price that is similar to that
described above. This solution, which does not diï¬€er qualitatively from autarky, would allow a
superior foreign technology to be exploited without incurring the coordination problems related
to business stealing.
In practice, import agreements of this type remain small in size and do not constitute
a valid solution to the capacity shortage faced by most developing countries because these
agreements do not stimulate investment. The complexity and ï¬?nancial commitments demanded
by international electricity trade projects require a level of coordination among the parties that
cannot be achieved by a simple ex-post purchase agreement. The creation of a power pool
encourages investment in the energy sector by providing international arbitration for dispute
resolution, the repatriation of proï¬?ts, protection against the expropriation of assets, and other
terms that are considered attractive by potential investors. The next section studies the impact
of the creation of an integrated power pool on energy production.
II. COMMON POWER POOL
12
When barriers to trade in the power market are removed, ï¬?rms can serve consumers in both
countries so that there is a single price. The demand functions are symmetric, which implies that
1 O
the level of consumption is the same in the two countries: Qi = 2 Q , i = 1, 2. In contrast, the
generation cost functions are diï¬€erent, which implies a diï¬€erent level of production in the two
countries. We ï¬?rst consider the solution that would be chosen by a global welfare-maximizing
social planner. This theoretical benchmark describes a process of integration in which the two
countries are fully integrated politically and ï¬?scally. We then consider sectorial integration
with two independent regulators. Finally, we perform a welfare analysis and determine the
distributive impact of integration.
Full Integration
The supranational utilitarian social planner has no national preferences. He maximizes
W = W1 + W2 , the sum of welfare functions deï¬?ned in (6),
2
q1 q2
W = S (Q1 ) + S (Q2 ) + Î»P (Q)Q âˆ’ (1 + Î»)(Î¸1 q1 + Î³ + Î¸2 q2 + Î³ 2 ) (9)
2 2
with respect to quantities (Q1 , Q2 , q1 , q2 ), under the constraint that consumption Q = Q1 + Q2
equals production q = q1 + q2 . This problem can be solved sequentially. First, the optimal
consumption sharing rule between the two countries (Q1 , Q2 ) is computed for any level of
production q . This calculation maximizes S (Q1 ) + S (Q2 ) under the constraint that Q1 + Q2 =
Q2
q1 + q2 . Because S (Qi ) = dQi âˆ’ 2 , we easily deduce that the optimal consumption allocations
i
Q1 +Q2
are Q1 = Q2 = 2 . Hence, the supranational utilitarian objective function (9) becomes
2
q1 q2
W = 2S ( q1 + q2
2 ) + Î»P (q1 + q2 )(q1 + q2 ) âˆ’ (1 + Î»)(Î¸1 q1 + Î³ + Î¸2 q2 + Î³ 2 ) (10)
2 2
Let Î¸min = min{Î¸1 , Î¸2 } and âˆ† = Î¸2 âˆ’ Î¸1 , which can be positive or negative. Second, (10) is
optimized with respect to the quantities q1 and q2 .
13
Proposition 1 The socially optimal quantity is
ï£±
2 âˆ— 2Î³ (dâˆ’Î¸min )
ï£´
ï£² 1+Î›+2Î³ (d âˆ’ Î¸min ) by monopoly if |âˆ†| > âˆ† = 1+2Î³ +Î›
Qâˆ— = (11)
ï£´
ï£³ 2 Î¸1 +Î¸2 âˆ— Qâˆ— Î¸j âˆ’Î¸i
1+Î›+Î³ (d âˆ’ 2 ) by duopoly i = 1, 2 with qi = 2 + 2Î³ otherwise.
Proof. See Appendix A.
When the cost diï¬€erence between the two ï¬?rms is large (i.e., when |âˆ†| > âˆ†âˆ— ), the less
eï¬ƒcient producer is shut down, and the most eï¬ƒcient ï¬?rm is in a monopoly position. This
result implies that when there is no transportation cost (i.e., Î³ = 0), the ï¬?rst best contract
always prescribes the shut down of the less eï¬ƒcient ï¬?rm. However the â€?shut downâ€? result is
upset with the introduction of a transportation cost. When Î³ is positive, both ï¬?rms produce
whenever |âˆ†| â‰¤ âˆ†âˆ— . The most eï¬ƒcient ï¬?rm (i.e., the ï¬?rm with the cost parameter Î¸min ) has
a larger market share than its competitor (see (11)). However, the market share diï¬€erences
decrease with Î³ .
In practice, sectorial integration generally excludes ï¬?scal and political institutions, which
remain decentralized at the country level.17 Sovereign governments and regulators do not share
proï¬?ts and tariï¬€ revenues among themselves. Taxpayers enjoy taxation by regulation insofar
as the rents come from their national ï¬?rms. The next section studies the distortions induced
by the non-cooperative equilibrium between two governments.18
Sectorial Integration with Asymmetric Regulation
In the case of sectoral integration, marked O, national regulators simultaneously ï¬?x the
17
The fusion of regulatory bodies and ï¬?scal systems is rarely achieved. The German reuniï¬?cation, with the
East and West German economic systems uniï¬?ed under the same government, is an exception. Consistent with
the theory, many ï¬?rms have been shut down in East Germany. The reallocation of production toward more
eï¬ƒcient units has been sustained by transfers from West Germany.
18
If governments could bargain eï¬ƒciently among themselves, the optimal solution to Proposition 1 could be
achieved. The problem is that the Coase solution requires zero transaction costs to hold. In the context of two
developing countries, bargaining over enormous investments is not a realistic assumption. Because developing
countries are plagued with weak property rights and rule of law, signiï¬?cant corruption, and ineï¬ƒcient justice
systems, transaction costs are higher in developing countries than in advanced economies. In practice, we do not
observe eï¬ƒcient bargaining in either type of country, but the ineï¬ƒciencies are worse in developing countries.
14
O , maximizing national welfare (6). The reaction
quantity produced by the national ï¬?rm, qi
functions of the regulators determine the non-cooperative equilibrium.
Proposition 2 The quantity produced at the non-cooperative equilibrium of the sectorial inte-
gration game is
ï£± 2(1+2Î³ )(dâˆ’Î¸min )
ï£´ 4 O
ï£² 3+4Î³ +Î› (d âˆ’ Î¸min ) by monopoly if |âˆ†| â‰¥ âˆ† = 3+4Î³ +Î›
QO = (12)
ï£´
ï£³ 4 Î¸1 +Î¸2 O QO Î¸j âˆ’Î¸i
2+2Î³ +Î› (d âˆ’ 2 ) by duopoly i = 1, 2 with qi = 2 + 1+2Î³ otherwise
Proof. See Appendix B.
Comparing equations (12) and (11), the equilibrium solution implies that the closure of the
less eï¬ƒcient ï¬?rm occurs less often than in the socially optimal solution. That is, âˆ†O â‰¥ âˆ†âˆ—
under assumption A0.
Comparing the common market with the closed economy case, it is straightforward to check
C + q C deï¬?ned in equation (8).
that QO deï¬?ned in equation (12) is always larger than QC = q1 2
The fact that the total quantity increases under market integration does not necessarily imply
a welfare improvement. Indeed, when |âˆ†| â‰¤ âˆ†âˆ— , we have that QC = Qâˆ— deï¬?ned in equation
(11). We deduce that excessive production occurs in the common market. To be more speciï¬?c,
comparing QO and Qâˆ— yields
(2Î³ +Î›)(dâˆ’Î¸min )
QO â‰¥ Qâˆ— â‡” |âˆ†| â‰¤ âˆ†O/âˆ— = 1+2Î³ +Î› . (13)
When |âˆ†| is smaller than âˆ†O/âˆ— , the regulators ï¬?ght to maintain their market shares by
boosting domestic production. Aggregate quantities are then larger in the common market
than at the optimum. In a closed economy, the regulator with the less eï¬ƒcient technology
chooses a small quantity to enjoy a high Ramsey margin. However, in the open economy, the
Ramsey margin is eroded by competition, and producing such a small quantity is no longer
optimal; it only reduces the market share of the domestic ï¬?rm. In his attempt to mitigate
the business stealing eï¬€ect, the regulator increases the quantity of the domestic ï¬?rm so that
15
QO > Qâˆ— .19 Symmetrically, when |âˆ†| is larger than âˆ†O/âˆ— , the regulator of the most eï¬ƒcient
country controls a large market share (the ï¬?rm even becomes a monopolist in the common
market when |âˆ†| > âˆ†O ). The problem is that the regulator does not internalize the welfare of
foreign consumers. She chooses a suboptimal production level QO < Qâˆ— .
The Political Economy of Sectorial Integration
Even if one country has lower generation costs than the other, competition for the rents of
the sector yields ineï¬ƒciencies that might prevent sectorial integration. Both countries must win
from the creation of a common power pool for the integration to occur. Replacing the optimal
quantities in the welfare function, we show the following result.
Proposition 3 For any Î› that is strictly positive, market integration increases welfare in both
countries if and only if the diï¬€erence in the marginal costs |âˆ†| is large enough.
Proof. See Appendix C.
Figure 1 illustrates Proposition 3. The ï¬?gure contrasts the welfare gains of country 1 for
Î› > 0 with the welfare gains of country 1 for Î› = 0. When Î› = 0, taxation by regulation is not
an issue, and an increase in |âˆ†| increases the welfare gains identically in the low- and high-cost
countries. The less eï¬ƒcient country enjoys a lower price, whereas the more eï¬ƒcient country
enjoys higher proï¬?ts. Business stealing creates no loss because it is compensated by an increase
in the consumer surplus in the country with a smaller market share. However, the equilibrium
quantities (12) do not correspond with the optimal levels (11) because not all gains from trade
are exploited. The results are modiï¬?ed when Î› > 0. When Î› > 0, the intercept corresponding
19
Substituting QO from equation (12) into market share equation qiO
and comparing it with equation (8) yields
O C Î›(dâˆ’Î¸i )(1+Î³ )
qi > qi â‡” Î¸j âˆ’ Î¸i â‰¥ âˆ’ (1+Î³ +Î›)2 j = i i = 1, 2. A regulator might choose to expand the national quantity
with respect to the quantity produced in a closed economy even if the competitor is slightly more eï¬ƒcient. The
reason for this choice is that competition decreases the net proï¬?ts of the national ï¬?rm without generating a
drastic increase in the consumersâ€™ surplus.
16
to âˆ† = 0, is negative, which means that if Î¸1 = Î¸2 , both countries lose from integration. To
ï¬?ght business stealing, both countries increase their quantities. The price is decreased below
the optimal monopoly Ramsey level, and taxation by regulation decreases (or, alternatively,
subsidies increase). However, competition does not increase eï¬ƒciency because the ï¬?rms have
the same cost. The net welfare impact is negative for both countries. For âˆ† = 0, the welfare
gains of the two countries are asymmetric. For the most eï¬ƒcient country, the gains are strictly
increasing. For the less eï¬ƒcient country, they are U-shaped. For a large enough |âˆ†|, the welfare
gains are positive in both countries.
O âˆ’ W C.
Figure 1: Welfare Gains from Integration, W1 1
The country with the less eï¬ƒcient technology generally has lower gains from integration
Ë† â‰¥ âˆ†). The level of gains depends on the adverse eï¬€ect of business stealing on the budget
(âˆ†
constraint of the less eï¬ƒcient ï¬?rm, which will in general receive a higher transfer (or pay lower
taxes) in the common market. It is clear that for a âˆ† belonging to the interval [âˆ’âˆ†, âˆ†], the
creation of a power pool managed by two independent regulators is ineï¬ƒcient. Each countryâ€™s
welfare is decreased by integration. The region as a whole is better oï¬€ with the co-existence of
two separate markets. This result is not related to the assumption of limited competition (i.e.,
17
duopoly). Increasing the number of unregulated competitors, including a foreign ï¬?rm reporting
its proï¬?t in a third country, would only worsen the negative business stealing. Similarly, a
laissez-faire policy would not suppress the welfare losses related to business stealing.20
Ë† the most eï¬ƒcient country wins, and the less eï¬ƒcient country
For values of |âˆ†| âˆˆ [âˆ†, âˆ†],
loses. If one region loses and the other wins, there will be resistance to integration. In contrast,
Ë† despite
Ë† and larger than âˆ†
welfare increases in both countries for values of âˆ† smaller than âˆ’âˆ†
the uncoordinated policies. In other words, the theory predicts that integration will be easier
to achieve when the cost diï¬€erence between the two countries is large.
In addition to the global welfare impact, the creation of an integrated market with a common
price P (QO ) has redistributive eï¬€ects. To see this point, let us focus on |âˆ†| â‰¤ âˆ†O . Market
integration induces a price reduction in country i = 1, 2 if and only if the cost diï¬€erence is not
Î›(dâˆ’Î¸i ) 21
too large, that is, if Î¸j âˆ’ Î¸i â‰¤ 1+Î³ +Î› . Consumers from the relatively eï¬ƒcient region are thus
worse oï¬€ after integration, which may be a source of social discontent and opposition toward
sectorial integration. The interests of the national ï¬?rm/taxpayers conï¬‚ict with the interests of
the domestic consumers.22 If the government is unable to seize a ï¬?rmâ€™s rents, both domestic
taxpayers and consumers are worse oï¬€ (shareholders are the only winners).
Î›(dâˆ’Î¸min )
In contrast, if the ï¬?rms are not drastically diï¬€erent (i.e., if |âˆ†| â‰¤ 1+Î³ +Î› ), prices decrease
in both countries because of the business stealing eï¬€ect. Benevolent regulators are willing to
increase their transfers to the national ï¬?rm to sustain low prices so that taxation by regulation
decreases, harming taxpayers and the total welfare. The negative ï¬?scal eï¬€ect is a major concern
20
The trade and competition literature shows that when ï¬?rms are identical, the welfare losses can be reduced
by jointly banning the subsidies and committing to a laissez-faire policy (Brander and Spencer 1983; Collie 2000).
When ï¬?rms are identical, we obtain similar results for some values of Î› (as in Collie 2000). However, this result
is not robust to the assumption of heterogeneous ï¬?rms.
21
Substituting QO from equation (12) in the inverse demand function yields the equilibrium price P (QO ) =
Î¸ +Î¸
d( Î› +Î³ )+ 1 2 2
2
1+Î³ + Î›
if |âˆ†| â‰¤ âˆ†O (Î¸min ). c
Comparing this price with the price in the closed economy, P (qi ) = Î¸i + (Î› +
2
dâˆ’Î¸i
Î³ ) 1+ Î³ +Î›
yields the result.
22
In the international trade literature, a similar conï¬‚ict of interest arises between domestic producers and
consumers (see Feenstra, 2008).
18
in developing countries, where tariï¬€s play an important role in raising funds (see Laï¬€ont, 2005,
and Auriol and Picard, 2006). When public funds are scarce and other sources of taxation are
distortionary or limited, market integration, which has a negative impact on taxpayers and on
industriesâ€™ ability to ï¬?nance new investments, induces welfare losses.
Our welfare analysis is conducted under several simplifying assumptions that should be
discussed. First, we focus on asymmetry in costs. However, countries may diï¬€er in other di-
mensions. In particular, they may have diï¬€erent market sizes (i.e., d1 = d2 ). We explore this
possibility in Appendix G. Because of the quadratic transportation costs, a smaller country
has a smaller marginal cost in a closed economy. Market integration generates additional ef-
ï¬?ciency gains by reallocating production toward the producers that initially had the smaller
internal demand. We show in the appendix that the smallest country always wins more from
integration than the largest one. This result is consistent with the ï¬?nding in the international
trade literature that smaller economies tend to gain more from trade in oligopolistic markets
than large economies (see Markusen, 1981). Appendix G also shows that our primary result is
robust: sectoral integration is welfare degrading if countries are too similar (i.e., in cost and in
demand).
Second, one could decide that the ineï¬ƒciency result yielded by sectoral integration is related
to the limited set of tax instruments used by the regulator. We concentrate on the proï¬?t taxation
of regulated ï¬?rms, and we do not study the possibility of introducing additional taxes (e.g., a
general tax on consumers such as a VAT or a tax on transport or distribution). In a closed
economy, this focus does not incur a loss of generality because there is no need for additional
taxes when it is possible to ï¬?x both the price and the tax on total industry proï¬?ts. In the
integrated market, this irrelevant result does not hold because the national regulator is unable
to tax the importing ï¬?rmâ€™s proï¬?t or to control its oï¬€er. Competition for market share erodes the
national ï¬?rmâ€™s proï¬?t and thus the possibility of taxation. Assuming that new instruments are
19
introduced, if the regulator is allowed to use diï¬€erent tax rates on foreign and domestic ï¬?rms,
she will be able to inï¬‚uence the volume of import. The regulator uses the tax structure to
reduce the market share of the foreign ï¬?rm whenever it does not bring enough eï¬ƒciency gains
(i.e., by reducing the market share of the competitor in such a way that it does not â€?stealâ€?
demand with respect to autarky). However, this type of asymmetric treatment is incompatible
with the creation of an integrated electricity market aimed at promoting investment. Investors
must ensure that they will be able to sell their production in the foreign market without facing
the ex-post threat of abusive taxation or other hold-up problems. In this case, the regulator
is obliged to apply the same tax rate to local and foreign ï¬?rms. Adding taxes to the volume
of transactions could be used to generate income on the activities of the foreign ï¬?rm and to
inï¬‚uence its scale of production. In addition to greatly complicating the model resolution, this
form of taxation cannot restore eï¬ƒciency. The heart of the problem is not the nature of the tax
instrument used to collect revenue and inï¬‚uence production but rather that each ï¬?rmâ€™s proï¬?ts
(and the consumer surplus) are accounted for locally.23 This sub-optimal equilibrium creates an
asymmetry (i.e., a national preference) between the valuation of local and foreign production,
which is at the heart of the ineï¬ƒciency result.
III. INVESTMENT
Proponents of regional power pools claim that by fostering the emergence of a larger market,
the pools will stimulate investment. However, it is not clear that the model of integration often
favored by international aid agencies provides an adequate framework for investment incentives.
Unless the cost diï¬€erence between two regions is suï¬ƒciently large, market integration with
asymmetric regulation may decrease total welfare and thus may undermine the global capacity
23
To see this point more clearly, we focus on the case in which Î› = 0, so ï¬?scal issues are irrelevant for the
regulators. Substituting Î› = 0 in (13), one can easily check that the ineï¬ƒciency in production levels remains.
The equilibrium is always sub-optimal, and it is worse when Î› > 0.
20
to ï¬?nance new investment. Our analysis focuses on two types of investment. The ï¬?rst type
reduces the production cost of the investing ï¬?rm (e.g., generation facilities). This investment is
referred to as â€?production cost reducingâ€? or â€?Î¸-reducingâ€? investment. This type only beneï¬?ts
the investing producer and makes the producer more aggressive in the common market. We
assume that this investment is only possible in one country (by convention, country 1) because
of the availability of a speciï¬?c input or technology. Consider a dam: hydropower potentials
(and natural resources such as oil or gas) are unevenly distributed across countries. Country 1
can reduce its production cost from Î¸1 to Î´ Î¸1 (Î´ < 1) by investing a ï¬?xed amount IÎ¸ .
The second type of investment decreases the transportation cost Î³ . We refer to this type
of investment as â€?transportation cost reducingâ€? or â€?Î³ -reducingâ€? investment. In the integrated
market, the competitor of the investing ï¬?rm also beneï¬?ts from the investment. One can think
of an investment in transmission, interconnection, or interoperability facilities. We assume that
both countries can reduce the collective transportation cost from Î³ to sÎ³ with s âˆˆ (0, 1) by
investing a ï¬?xed amount IÎ³ > 0.
For both types of investment, we focus on interior solutions. The cost diï¬€erence is assumed
to be small enough that the production of the two ï¬?rms is positive in the common market. The
following assumption ensures that there is no closure in the ï¬?rst best case.24
2sÎ³ (dâˆ’min{Î´Î¸1 ,Î¸2 })
A1 |Î¸2 âˆ’ Î´Î¸1 | â‰¤ 1+2sÎ³ +Î› .
Investment in Generation
We begin by considering the solution induced by the global welfare maximizer in the case
âˆ—IÎ¸
of a Î¸-reducing investment by ï¬?rm 1. The optimal quantities, denoted qi (i = 1, 2), are
provided by equations (11), where Î¸1 is replaced by Î´Î¸1 (Î´ < 1). Substituting the quantities
24
Assumption A1, which is the condition in equation (11) with âˆ†âˆ— evaluated at Î´Î¸1 instead of Î¸1 and sÎ³
instead of Î³ , ensures that both ï¬?rms produce in all possible cases. As illustrated by the analysis in Section 2, this
assumption is not crucial, but it greatly simpliï¬?es the exposition. Our results are preserved when the shut-down
cases are considered (computations are available on request).
21
âˆ—IÎ¸
qi (i = 1, 2) into the welfare function deï¬?nes equation (10), and the gross utilitarian welfare is
âˆ—IÎ¸ âˆ—IÎ¸
W âˆ—IÎ¸ = W (q1 , q2 ). The welfare gain of the investment W âˆ—IÎ¸ âˆ’ W âˆ— must be compared with
the social cost of the investment (1 + Î»)IÎ¸ . The social cost of investment IÎ¸ is weighted by the
opportunity cost of public funds because devoting resources to investment decreases the ï¬?rmâ€™s
operating proï¬?t and the governmentâ€™s revenue by IÎ¸ , which has an opportunity cost of 1 + Î».
The global welfare maximizer regulator invests if and only if W âˆ—IÎ¸ âˆ’ W âˆ— â‰¥ (1 + Î»)IÎ¸ . Let us
âˆ— as the maximal level of investment that satisï¬?es this inequality:
denote IÎ¸
âˆ— 1
IÎ¸ = [W âˆ—IÎ¸ âˆ’ W âˆ— ]. (14)
1+Î»
OIÎ¸
The non-cooperative equilibrium quantities in the case of sectoral integration, qi , and the
CIÎ¸
quantities in the case of a closed economy, qi , are derived using a similar method from the
equations (12) and (8), respectively, where Î¸1 is replaced by Î´Î¸1 . Substituting the quantities
kIÎ¸
qi (i = 1, 2 and k = O, C ) in the welfare function of the country 1 deï¬?ned in equation (6), the
kIÎ¸ k â‰¥ (1 + Î»)I . We deduce the maximal
regulator of country 1 invests if and only if W1 âˆ’ W1 Î¸
level of investment that country 1 is willing to commit in the common market and in the closed
economy:
k 1 kIÎ¸ k
IÎ¸ = [W1 âˆ’ W1 ] k = O, C. (15)
1+Î»
The next proposition compares the diï¬€erent investment levels (i.e., when k = âˆ—, O, C ) as a
function of the initial cost diï¬€erence âˆ† = Î¸2 âˆ’ Î¸1 .
âˆ— and I k (k = O, C ) be deï¬?ned in
Proposition 4 Let Î› > 0, Î´ âˆˆ (0, 1) and âˆ† = Î¸2 âˆ’ Î¸1 . Let IÎ¸ Î¸
Ë†b < âˆ†
Ë†a < âˆ†
(14) and (15), respectively. There are three thresholds âˆ† Ë† c , such that
Ë† a.
O > IC â‡” 0 > âˆ† > âˆ†
â€¢ IÎ¸ Î¸
Ë† b.
âˆ— > IC â‡” 0 > âˆ† > âˆ†
â€¢ IÎ¸ Î¸
Ë† c.
âˆ— > IO â‡” âˆ† > âˆ†
â€¢ IÎ¸ Î¸
22
Proof. See Appendix D.
Figure 2 illustrates the results of Proposition 4. The ï¬?gure is drawn for a ï¬?xed value of Î´Î¸1 .
C represents the autarky equilibrium
The static comparative parameter is âˆ†. The ï¬‚at line IÎ¸
level of investment for country 1. This level is independent of the eï¬ƒciency of ï¬?rm 2 (i.e., it
is independent of âˆ†, hence the ï¬‚at shape) because in the absence of trade, what happens in
O
country 2 does not inï¬‚uence the investment choice of the regulator in country 1. The line IÎ¸
âˆ— represents the optimal level.
represents the equilibrium investment in the open market, and IÎ¸
Both increase with âˆ†: the gains from trade and the incentives to invest are larger when the gap
in generation costs is large.
Figure 2: Î¸1 -Reducing Investment.
23
One relevant policy question is whether economic integration can improve the autarky
outcome. When Î› = 0, business stealing has no adverse impact on national welfare, so
Ë†a = âˆ†
Ë†b = âˆ†
Ë†c = (1âˆ’Î´ )Î¸1
âˆ† 2 . In this case, market integration unambiguously reduces (without
eliminating) the gap between the optimal and the equilibrium levels of investment. However,
Ë† c shift to the left and to the right, respectively, whereas âˆ†
Ë† a and âˆ†
when Î› > 0, the thresholds âˆ† Ë†b
is not aï¬€ected (see Appendix D).25 Theoretically, there are cases in which integration worsens
the gap between the equilibrium investment level and the optimum.
To be more speciï¬?c, Proposition 4 implies that market integration improves the situation
with respect to autarky when the initial cost diï¬€erence between the two regions is large. First,
Ë† c , country 1 chooses a level of investment in autarky that is ineï¬ƒciently low. The
when âˆ† > âˆ†
O
region is endowed with abundant resources (e.g., hydroelectric potential), but the investment IÎ¸
is oversized for the domestic demand. Integration helps to increase the level of investment that
country 1 is willing to sustain by enlarging its market size through access to foreign demand. In
this case, the creation of a power pool moves the equilibrium investment closer to the optimal
Ë† c , the open market
âˆ— . However, it does not restore the ï¬?rst best level. When âˆ† > âˆ†
level IÎ¸
O is lower than the optimal level I âˆ— because the investing country
equilibrium of investment IÎ¸ Î¸
does not fully internalize the increase in the foreign consumer surplus (it only internalizes sales).
Ë† a , country 1 is very ineï¬ƒcient.26 In autarky, the only way to increase the
Second, when âˆ† < âˆ†
level of consumption (and, thus, total welfare) is through a cost-reducing investment. Yet, in
the open economy, this investment is a waste because the market can be served by the superi-
orforeign technology. The creation of a power pool improves the situation by reducing the level
of investment in obsolete technology. However, the power pool does not restore eï¬ƒciency. The
25 O âˆ— C
When Î› increases, all thresholds IÎ¸ , IÎ¸ IÎ¸ shift downward because the social cost of investment increases.
O
However, IÎ¸ has less of a decrease because investment becomes important to reduce the business stealing eï¬€ect
in the common market. As a result, the region of over-investment increases.
26
Indeed, we ï¬?nd that âˆ† Ë†a < âˆ† Ë† b < 0, and in the closed economy, investment is higher than the optimal value
Ë† b.
for the integrated market (i.e., it is ineï¬ƒciently high) as soon as âˆ† < âˆ†
24
possibility of reducing the cost gap and expanding market share by serving foreign consumers
O is higher than I âˆ— ).
makes a higher than optimal level of investment attractive (i.e., IÎ¸ Î¸
Ë† b , the level of investment is ineï¬ƒciently high under both a closed and an
Ë†a < âˆ† < âˆ†
For âˆ†
open economy.27 However, the over-investment problem is more severe in the open economy
because of the business stealing problem. A production cost-reducing investment increases the
relative eï¬ƒciency of the national ï¬?rm. The ï¬?rm invests to strengthen its position in the common
market and to reduce its competitive gap; it does not internalize the cost that it imposes on
country 2, and it overinvests. In this case, market integration worsens incentives to invest
Ë† b ],
Ë† a, âˆ†
with respect to autarky. However, the values of âˆ† corresponding to this situation, [âˆ†
Ë† , âˆ†] within which the country with the less eï¬ƒcient
are generally included in the interval [âˆ’âˆ†
technology would not accept integration in the ï¬?rst place.28 . Therefore, unless the creation of a
power pool is forced on the countries, it is very unlikely that this over-investment problem will
arise in equilibrium. In practice, developing countries face a chronic underinvestment problem.
Market integration should thus improve their incentive to invest in generation facilities. As
argued by the proponents of market integration, it should allow more projects to be ï¬?nanced.
Transportation Cost Reducing Investment
In this section, we study the case in which the collective transportation cost can be reduced
from Î³ to sÎ³ with s âˆˆ (0, 1) by an investment of IÎ³ > 0. We ï¬?rst consider the level of investment
âˆ—IÎ³
induced by the global welfare maximizer. Let qi be the quantity produced by ï¬?rm i = 1, 2 in
the case of investment. The optimal quantities are obtained by substituting sÎ³ into equation
(11). The gross utilitarian welfare in the case of investment is the welfare function deï¬?ned by
âˆ—I âˆ—I
equation (10) evaluated at the actualized quantities: W âˆ—IÎ³ = W (q1 Î³ , q2 Î³ ). The global welfare
27
There is an over-investment problem in the open market if âˆ† â‰¤ âˆ† Ë† c and in the closed economy if âˆ† â‰¤ âˆ† Ë† b.
28
We have tested many values for the parameters by simulations. The intervals âˆ† Ë† b always fell in [âˆ’âˆ†
Ë† a, âˆ† Ë† , 0].
For instance, for d = 2, Î› = 0.15, Î¸1 = 1/2, Î´ = 9/10, and s = 9/10, we have that âˆ’âˆ† Ë† = âˆ’0.5, âˆ† = 0.01,
âˆ†Ë† a = âˆ’0.23, âˆ† Ë† c = 0.02. Finally, the admissible values for âˆ† under Assumption A1 are in the
Ë† b = âˆ’0.08 and âˆ†
interval [âˆ’1.0, 0.57]
25
âˆ— be the maximal level
maximizer chooses to invest if and only if W âˆ—IÎ³ âˆ’ W âˆ— â‰¥ (1 + Î»)IÎ³ . Let IÎ³
of investment that satisï¬?es this inequality:
âˆ— 1
IÎ³ = [W âˆ—IÎ³ âˆ’ W âˆ— ]. (16)
1+Î»
The non-cooperative equilibrium investment level of market integration is obtained using
OIÎ³
a similar method. The quantity produced by ï¬?rm i after investment qi is obtained by sub-
OIÎ³
stituting sÎ³ into equation (12). Let Wi be the i = 1, 2 welfare function (6) of country i
OIÎ³ OIÎ³
evaluated at (q1 , q2 ). The maximum level of investment that country i is willing to make
in the common market is
O 1 OI
IÎ³i = max 0, [W Î³ âˆ’ WiO ] . (17)
1+Î» i
Intuitively, reducing transportation costs increases the business stealing eï¬€ect. Although
this increase in business stealing has an adverse eï¬€ect on both countries, the negative impact
is larger for the high cost ï¬?rm. One can therefore check equation (12) to see that the market
share of the less eï¬ƒcient country decreases after the investment. For this reason, the welfare
eï¬€ect generated by the transportation cost reducing investment in the less eï¬ƒcient country may
O can be equal to zero. In particular, this occurs for large values of Î› (see
be negative, so IÎ³i
Appendix E for details). In contrast, the investment always increases the gross welfare of the
most eï¬ƒcient country. The maximal level of investment for the more eï¬ƒcient ï¬?rm is always
positive and higher than the maximal level of investment for the less eï¬ƒcient ï¬?rm. Because
the Î³ -reducing investment is a public good, in the common market, the level of investment that
each country is willing to ï¬?nance depends on the investment choice by the other country. The
next lemma focuses on equilibria in pure strategy.29
29
There is also a mixed strategy equilibrium in which ï¬?rm i, i = j invests with probability Ï€i =
OIÎ³ O
Wj âˆ’(1+Î»)IÎ³ âˆ’Wj
OIÎ³ O
. This equilibrium is ineï¬ƒcient because, with positive probability, either both ï¬?rms invest
Wj âˆ’Wj
or, alternatively, neither invests. Moreover, this equilibrium is not very realistic. An investment in transporta-
tion infrastructure requires a good deal of coordination between the two regions and is observed by all.
26
O
Lemma 1 Let I Î³ be the maximal level of investment for the more eï¬ƒcient ï¬?rm and I O
Î³ be the
maximal level of investment for the less eï¬ƒcient ï¬?rm, as deï¬?ned in (17).
O
â€¢ If IÎ³ > I Î³ , there is no investment.
O
â€¢ If I O
Î³ < IÎ³ , â‰¤ I Î³ , the more eï¬ƒcient ï¬?rm is the only one to invest.
â€¢ If IÎ³ â‰¤ I O
Î³ , there are two Nash equilibria in pure strategy in which one of the ï¬?rm invests
and the other does not.
Proof. See Appendix E.
Because of the public good nature of the investment, only one of the two ï¬?rms invests,
whereas the other free rides on the investment. The decision of the most eï¬ƒcient ï¬?rm generally
determines the maximal level of investment attainable in the common market.30 We are now
ready to compare the equilibrium level with the optimum.
Proposition 5 In the integrated market, the investment level in Î³ -reducing technology is always
suboptimal:
O O
IÎ³ â‰¤ IÎ³ + IO âˆ—
Î³ â‰¤ IÎ³ âˆ€âˆ†, Î› â‰¥ 0. (18)
Proof. See Appendix E.
In our speciï¬?cation, a Î³ -reducing investment has a public good nature. This investment
equally reduces the transportation costs in both investing and non-investing countries. It is
O
thus intuitive that investment level I Î³ is sub-optimal. The investing country does not take into
account the impact of the investment on the foreign country. However, the underinvestment
30
Lemma 1 implies that the most eï¬ƒcient ï¬?rm is willing to sustain relatively high levels of investment, and
both ï¬?rms are able to sustain lower levels. Because of the public good nature of the investment, the identity of
the investing ï¬?rm in this case is not important (and, in practice, might be determined by local circumstances).
Our model only predicts that one of the ï¬?rms will always want to invest for the deï¬?ned thresholds. For projects
above the maximal threshold, there will be no investment.
27
problem goes deeper than the standard free riding in public good problem. Even if each country
is willing to contribute to the point at which the cost of investment outweighs the welfare gains
generated by investment (i.e., without free riding on the investment made by the other country),
O
the total investment level I Î³ + I O
Î³ would still be sub-optimal. To analyze the origin of this
ineï¬ƒciency, it is useful to study the countriesâ€™ incentives to invest in a closed economy.
CIÎ³
Let qi be the quantity produced by ï¬?rm i in the case of an investment in a closed economy.
CIÎ³ CIÎ³
qi is obtained by substituting sÎ³ into equation (8). Let Wi be the welfare function of
CIÎ³
country i = 1, 2 (6), evaluated at qi . The investment is optimal in country i if and only if
CIÎ³
Wi âˆ’ WiC â‰¥ (1 + Î»)IÎ³ so that
C 1 CI
IÎ³i = [W Î³ âˆ’ WiC ]. (19)
1+Î» i
Comparing (19) with (17) yields the next proposition.
C be the maximal amount that the most eï¬ƒcient country is willing to
Proposition 6 Let IÎ³
O be the maximal amount
invest to reduce transportation costs in the closed economy, and let IÎ³
Ëœ > 0 such that IÎ³
that it is willing to invest in the common market. There exists a âˆ† O > I C if
Î³
Ëœ.
and only if |âˆ†| > âˆ†
Proof. See Appendix F.
The maximal level of investment sustainable in the open economy is lower than it is in the
case of autarky if âˆ† is relatively small. Investment reduces the costs of the competitor and
makes the competitor more aggressive in the common market. The business stealing eï¬€ect,
while reducing the investing countryâ€™s total welfare, also reduces its capacity to ï¬?nance new
investment. Market integration may thus generate an insuï¬ƒcient level of Î³ -reducing investment
for two reasons. The ï¬?rst reason is that investment has a public good nature. The investing
country does not internalize the beneï¬?ts of foreign stakeholders. The second reason is that
28
investment decreases the competitorâ€™s costs, worsening the business stealing eï¬€ect.31 Figure 3
illustrates the results of Propositions 5 and 6.
Figure 3: Î³ -Reducing Investment.
Ëœ the maximal level
Under market integration, when âˆ† is relatively small (i.e., (|âˆ†| â‰¤ âˆ†),
of investment is not only sub-optimal but is also smaller than under a closed economy. When
the two regionsâ€™ costs are not drastically diï¬€erent, business stealing is ï¬?erce. Business stealing
reduces the capacity to ï¬?nance new investment, worsening the gap between the optimal invest-
ment and the equilibrium level. However, this poor outcome is unlikely to occur if the less
Ëœ is higher than âˆ†,
eï¬ƒcient country can resist integration. Indeed, simulations suggest that âˆ†
the threshold above which the most eï¬ƒcient country would win from market integration, but
Ë† the equivalent threshold for the less eï¬ƒcient country (see Figure 1).32
below âˆ†,
31 O C O C
In contrast, for Î› = 0, IÎ³ > IÎ³ âˆ€âˆ† â‰¥ 0 and IÎ³ âˆ’ IÎ³ is an increasing function of âˆ†. When public funds
are free, business stealing is no longer a problem, so market integration always increases the level of sustainable
investment compared to a closed economy.
32
We have tested many values for the parameters by simulation, and the threshold âˆ† Ëœ was always larger than
29
Ëœ it is willing
In contrast, when one country has a signiï¬?cant cost advantage (i.e., |âˆ†| > âˆ†),
to invest more in the common market than under a closed economy because the investment in-
creases its market share and proï¬?ts. Integration can then help to increase investment, although
not to the ï¬?rst best level. With a public good type of investment, there is always underinvest-
ment. This result is in sharp contrast with the results from investment in generation, in which
sectorial integration might lead to a level of investment that is ineï¬ƒciently high.33
IV. Conclusion
The integration of market economies is generally presented by its proponents as a powerful
tool to stimulate investment in infrastructure industries. Intuitively, some investments that are
oversized for a country should be proï¬?table in an enlarged market. However, market integration
in non-competitive industries has complex implications for welfare and investment.
When the cost diï¬€erence between the two countries is large enough, market integration
tends to increase the level of sustainable investment in generation. The investment level remains
suboptimal because the countries endowed with cheap power (e.g., hydropower) do not fully
internalize the surplus of the consumers in the foreign countries. These countreis internalize
only the sales. Symmetrically, when the investing country is less eï¬ƒcient than its competitor,
it chooses an ineï¬ƒciently high level of investment to close its productivity gap and win market
share. With generation facilities, there is underinvestment in eï¬ƒcient technologies and over-
investment in ineï¬ƒcient ones compared to the optimum. This result is in contrast with the
systematic underinvestment problem that arises for interconnection and transportation facilities
Ë† For instance, for d = 2, Î› = 0.15, Î¸1 = 1/2, Î´ = 9/10 and s = 9/10, we have âˆ’âˆ†
âˆ†. Ë† = âˆ’0.5, âˆ† = 0.01 and
âˆ†Ëœ = 0.02, whereas the admissible values under Assumption A1 are in the interval [âˆ’1.0, 0.57].
33
When the initial level of cost diï¬€erence between the two regions is not large enough, the business stealing
eï¬€ect tilts the investment incentives in the wrong direction. For instance, if âˆ† Ëœ , âˆ’âˆ†
Ë† b < Î¸1 âˆ’ Î¸2 < min{âˆ† Ë† b } with
âˆ†Ëœ deï¬?ned as Proposition 6, then under market integration, country 2 underinvests in Î³ -reducing technology,
whereas country 1 over-invests in Î¸-reducing technology. The latter investment reduces the gap between the
two regionsâ€™ production costs, which further reduces the incentives of country 2 to invest in transportation and
interconnection facilities. By virtue of Proposition 3, welfare decreases in both regions.
30
and with other public-good components of the industry, such as reserve margins. Free riding
reduces incentives to invest, whereas business stealing reduces the capacity to ï¬?nance new
investment, especially in the importing country.
These nuanced results are important for policy purposes. The countries involved in the
creation of a power pool at an early stage should establish a supra-national body to address
the ï¬?nancing and management of interconnection links and other transmission infrastructures.
A good example of a supra-national authority that has been created to address interconnection
problems is the Electric Interconnection Project of Central America (SIEPAC). The six countries
involved in the project (i.e., Guatemala, Nicaragua, El Salvador, Honduras, Panama, and Costa
Rica) have established a common regulatory body, the Regional Commission of Electricity
Interconnection (CRIE). The investment programs have been ï¬?nanced through loans obtained
from several European banks together with the contributions of the member countries. The
CRIE is now in charge of setting the access tariï¬€s needed to repay the loans that ï¬?nanced
the investment. Based on the CRIE experience, the West African power pool (WAPP) is
egulation RÂ´
also working on the creation of a regional regulatory body, â€?Organe de RÂ´ egionaleâ€?
(ORR). International organizations and aid agencies can play an important role in fostering the
creation of these types of regional regulation authorities.
In addition to coordinating sustainable levels of investment in public good infrastructures,
a central authority could help to move the non-cooperative equilibrium closer to the globally
optimal solution. This objective is more ambitious and challenging than the former. Indeed,
to mimic perfect integration, these agencies should be able to redistribute (i.e., share) the
gains from trade and thus to transfer funds between countries. However, most countries have
a policy of energy independence. Governments do not want to rely on their neighbors for
their electricity supply and are thus very reluctant to abandon their national ï¬?rm. Opening
up this supranational regulatory authority to international involvement could have important
31
policy implications in this context. An international authority would be able to limit hold-up
problems and to enforce contracts. An international authority would also ï¬?nd it easier to tax
energy trade to subsidize public good investment and possibly limit business stealing.
APPENDIX
A. Proof of Proposition 1
The supra-national regulator i maximizes welfare (10) with respect to qi , i âˆˆ {1, 2}. The
ï¬?rst-order condition provides
qi + qj
(1 + Î»)(d âˆ’ qi (1 + Î³ ) âˆ’ qj âˆ’ Î¸i ) + = 0. (20)
2
First, consider the interior solution. Solving the system characterized in (20) for i = 1, 2 and
Î»
allowing Î› = 1+Î» , we obtain
âˆ— d âˆ’ Î¸1 +
2
Î¸2
Î¸j âˆ’ Î¸i
qi = + . (21)
1+Î›+Î³ 2Î³
In this case, the total quantity Q is provided by
d âˆ’ Î¸1 + Î¸2
Qâˆ— = q1 + q2 = 2 2
.
1+Î›+Î³
2Î³ (dâˆ’Î¸j )
We now consider the shut-down case qi = 0. This case arises when Î¸i âˆ’ Î¸j â‰¥ 1+2Î³ +Î› . In this
case, only the most eï¬ƒcient ï¬?rm j is allowed to produce, and the total quantity is provided by
âˆ— (d âˆ’ Î¸j )
qj = Qâˆ— = 2 .
1 + 2Î³ + Î›
If Î¸i < Î¸j , a symmetric condition describes the shut down case for ï¬?rm j , i = j , i.e., Î¸j âˆ’ Î¸i â‰¥
2Î³ (dâˆ’Î¸i )
1+2Î³ +Î› . Allowing Î¸min = min{Î¸1 , Î¸2 } and |âˆ†| = |Î¸2 âˆ’ Î¸1 | = |Î¸1 âˆ’ Î¸2 |, Equation (11) resumes
the results. Substituting into the inverse demand function (2), we then obtain the expression
for the price.
32
B. Proof of Proposition 2
Maximizing the welfare function (6), we obtain the ï¬?rst-order condition:
1
(1 + Î»)(d âˆ’ Î¸i ) âˆ’ [qj (1 + 2Î») + qi (3 + 4Î» + 4Î³ (1 + Î»))] = 0. (22)
4
Î»
Rearranging terms and allowing Î› = 1+Î» , we obtain the reaction function of regulator i to the
quantity induced by regulator j (i = j ), namely qi (qj )
4(d âˆ’ Î¸i ) âˆ’ qj (1 + Î›)
qi (qj ) = . (23)
3 + Î› + 4.Î³
The equilibrium is given by the intersection of the two best response functions characterized in
(23) (taking into account that quantities must be non-negative). If the intersection is reached
when both quantities are positive, we have
O d âˆ’ Î¸1 +
2
Î¸2
Î¸j âˆ’ Î¸i
qi =4 + . (24)
2(1 + Î³ ) + Î› 1 + 2Î³
In this case, the total quantity Q is provided by
d âˆ’ Î¸1 + Î¸2
O
QO = q1 O
+ q2 =4 2
.
2(1 + Î³ ). + Î›
However, we must also consider the shut-down case qi = 0. This situation arises when qj â‰¥ 4 d âˆ’Î¸i
1+Î›
2(1+2Î³ )(dâˆ’Î¸i )
or, equivalently, Î¸i âˆ’ Î¸j â‰¥ 3+4Î³ +Î› < 0. The shut-down case is thus written, for Î¸i > Î¸j ,
d âˆ’ Î¸j
QO = qj (qi = 0) = 4 .
3 + 4Î³ + Î›
If Î¸i < Î¸j , a symmetric condition describes the shut-down case for ï¬?rm j , i = j . Letting
Î¸min = min{Î¸1 , Î¸2 } and |âˆ†| = |Î¸2 âˆ’ Î¸1 | = |Î¸1 âˆ’ Î¸2 |, the expression for the optimal quantity
is thus reassumed in (12). Substituting into the inverse demand function (2), we obtain the
expression for the price given in (12).
33
Figure 4: Total Quantities Qâˆ— , QO and QC as a function of |âˆ†|.
Figure 4 illustrates the quantities result, representing, for a given Î¸min , the quantity levels
Qâˆ— , QO and QC in the function of |âˆ†| âˆˆ [0, d]. The ï¬‚at sections correspond to the shut down
of the less eï¬ƒcient producer.
Finally, comparing the shut-down threshold in the optimal case with the shut-down threshold
of the less eï¬ƒcient ï¬?rm in the integrated market with independent regulators yields âˆ†O > âˆ†âˆ— .
Figure 5 illustrates this result. The solid lines represent the equilibrium shut-down threshold
of the less eï¬ƒcient ï¬?rm in the integrated market with independent regulators. The dotted lines
represent the optimal threshold. The ï¬?gure is plotted for d = 1, Î› = 0.3, Î³ = 0.5, Î¸i âˆˆ [0, 1]
2Î³ (dâˆ’Î¸min )
and Î¸min = 0. The same shape is obtained for any support, such as Î¸ âˆ’ Î¸ > 1+2Î³ +Î› .
C. Proof of Proposition 3
Consider country 1 (the same holds for country 2, inverting Î¸1 and Î¸2 and replacing âˆ† with âˆ’âˆ†
in all expressions). Making a replacement for the participation constraint of the national ï¬?rm,
the welfare in country 1 in the case of closed economy is written as
C
q1
C
W1 C
= S (q1 C C
) + Î»P (q1 )q1 âˆ’ (1 + Î»)(Î¸1 + Î³ )q C (25)
2 1
34
Figure 5: Shut Down Threshold of the Less-Eï¬ƒcient Firm. Dotted line: optimal threshold;
Solid line: non-cooperative equilibrium.
and, in the case of an open economy,
O
q1
O
W1 = S (QO O O O O
1 ) âˆ’ P (Q )Q1 + Î»P (Q )q1 âˆ’ (1 + Î»)(Î¸1 + Î³ )q O . (26)
2 1
Substituting for the value of the quantities (8) and (12) in (25) and (26), respectively, we
O âˆ’ W C.
compute the welfare gains from integration W1 1
O C
W1 âˆ’ W1 = âˆ†2 Î“1 (Î³, Î›) + âˆ†(d âˆ’ Î¸1 )Î“2 (Î³, Î›) + (d âˆ’ Î¸1 )2 Î“3 (Î³, Î›),
where
ï£±
ï£´
ï£´
ï£²
2
(3+4Î³ +Î›)2
, if âˆ† < âˆ’ 2(1+2Î³ )(dâˆ’Î¸2 )
3+4Î³ +Î› ;
(1+Î³ (1âˆ’Î›))(3+4Î³ +Î›)
Î“1 (Î³, Î›) = 2(1+2Î³ )2 (1âˆ’Î›)(2(1+Î³ )+Î›)2
, if âˆ’ 2(1+2Î³ )(dâˆ’Î¸2 )
3+4Î³ +Î› â‰¤âˆ†â‰¤ 2(1+2Î³ )(dâˆ’Î¸1 )
3+4Î³ +Î› ;
ï£´
ï£´
ï£³ 0, if âˆ† > 2(1+2Î³ )(dâˆ’Î¸1 )
.
3+4Î³ +Î›
ï£±
ï£´
ï£² âˆ’ (3+4Î³ +Î›)2 ,
ï£´
8
if âˆ† < âˆ’ 2(1+2Î³ )(dâˆ’Î¸2 )
3+4Î³ +Î› ;
Î›(3+4Î³ +Î›)
Î“2 (Î³, Î›) = (1+2Î³ )(1+Î›)(2(1+Î³ )+Î›)2
, if âˆ’ 2(1+2 Î³ )(dâˆ’Î¸2 )
3+4Î³ +Î› â‰¤ âˆ† â‰¤ 2(1+2 Î³ )(dâˆ’Î¸1 )
3+4Î³ +Î› ;
ï£´
ï£´
ï£³ 0, 2(1+2Î³ )(dâˆ’Î¸1 )
if âˆ† > 3+4Î³ +Î› .
ï£±
ï£´ 15+16Î³ 2 +4Î³ (5+3Î›)+Î›(6+5Î›) 2(1+2Î³ )(dâˆ’Î¸2 )
ï£² 2(1âˆ’Î›)(1+Î³ +Î›)(3+4Î³ +Î›)2 , if âˆ† < âˆ’ 3+4Î³ +Î› ;
ï£´
Î›2
Î“3 (Î³, Î›) = âˆ’ 2(1âˆ’Î›)(1+Î³ +Î›)(2(1+ Î³ )+Î›)2
, if âˆ’ 2(1+2 Î³ )(dâˆ’Î¸2 )
3+4Î³ +Î› â‰¤ âˆ† â‰¤ 2(1+2 Î³ )(dâˆ’Î¸1 )
3+4Î³ +Î› ;
ï£´
ï£´
ï£³ 1+3Î›
, if âˆ† > 2(1+2Î³ )(dâˆ’Î¸1 )
.
2(1âˆ’Î›)(1+Î³ +Î›)(3+4Î³ +Î›) 3+4Î³ +Î›
35
O âˆ’ W C is a U-shaped function of âˆ†. For Î› = 0, W O âˆ’ W C is always non-negative, with
W1 1 1 1
O âˆ’ W C = 0. For Î› > 0, the minimum is attained in âˆ† =
the minimum âˆ† = 0, where W1 1
2
âˆ’ Î›(1+2Î³ )(dâˆ’Î¸1 )
1+Î³ (1+Î›)
O âˆ’ WC = âˆ’
< 0. In this case, in âˆ† = 0, W1 1
Î›
2(1âˆ’Î›)(1+Î³ +Î›)(2(1+Î³ )+Î›)2
< 0. The U
shape and the condition |âˆ†| â‰¤ d ensure the behavior described in Proposition 3.
D. Proof of Proposition 4
We begin computing the maximal level of investment for country 1 at the non-cooperative
equilibrium. The welfare in the absence of investment is deï¬?ned in (26), and with investment,
it is
OIÎ¸
OIÎ¸ q1
W1 = S (QOI
1 ) âˆ’ P (Q
Î¸ OIÎ¸
)QOI
1
Î¸ OIÎ¸
+ Î»P (QOIÎ¸ )q1 âˆ’ (1 + Î»)(Î´Î¸1 + Î³ OIÎ¸
)q1 âˆ’ (1 + Î»)IÎ¸ .
2
Replacing for the relevant quantities in Equation (15) and rearranging terms, we obtain
(1+Î´ )Î¸1 âˆ† (1âˆ’Î´ )Î¸1
(1 âˆ’ Î´ )Î¸1 d âˆ’ 2 + (1 + Î›) 2Î³ + 4Î³
âˆ—
IÎ¸ =
1+Î³+Î›
(1+Î´ )Î¸1
(1 âˆ’ Î´ )Î¸1 d âˆ’ 2
C
IÎ¸ =
1+Î³+Î›
(1+Î´ )Î¸1 âˆ† (1âˆ’Î´ )Î¸1
(1 âˆ’ Î´ )Î¸1 dâˆ’ 2 (4 + 8Î³ 2 + (3 + Î›)(Î› + 4Î³ )) + 1+2Î³ + 2(1+2Î³ ) (1 + Î›)(3 + 4Î³ + Î›)
O
IÎ¸ = .
(1 + 2Î³ )(2(1 + Î³ ) + Î›)2
âˆ— > I C if and only if
Then, IÎ¸ Î¸
Ë† a = âˆ’ (1 âˆ’ Î´ )Î¸1 âˆ’ d âˆ’ (1 + Î´ )Î¸1 Î“i
âˆ†>âˆ† 1 (Î³, Î›),
2 2
where
2Î›Î³ (1 + 2Î³ )(3 + 4Î³ 2 + Î›(3 + Î› + Î³ (7 + 3Î›))
Î“i
1 (Î³, Î›) =
(1 + Î›)(8Î³ 4 + (2 + Î»)2 + 2Î³ (3 + Î›)2 + Î³ 3 (26 + 6Î›) + 2Î³ 2 (16 + Î›(7 + Î›)))
âˆ— > I O if and only if
IÎ¸ Î¸
Ë† b = âˆ’ (1 âˆ’ Î´ )Î¸1
âˆ†>âˆ†
2
36
O > I O if and only if
IÎ¸ Î¸
Ë† c = âˆ’ (1 âˆ’ Î´ )Î¸1 + d âˆ’ (1 + Î´ )Î¸1 Î“i
âˆ†>âˆ† 2 (Î³, Î›)
2 2
where
Î›(1 + 2Î³ )(3 + 4Î³ 2 + Î›(3 + Î› + Î³ (7 + 3Î›)))
Î“i
2 (Î³, Î›) =
(1 + Î›)(1 + Î³ )(1 + Î³ + Î›)(3 + 4Î³ + Î›)
Ë†a = âˆ†
It is easy to see that if Î› = 0, âˆ† Ë† c = âˆ’ (1âˆ’Î´)Î¸1 < 0. Moreover, for all Î› > 0,
Ë†b = âˆ†
2
Ë†b < âˆ†
Ë†a < âˆ†
âˆ† Ë† a decreases in Î›, while âˆ†
Ë† c . Finally, âˆ† Ë† c is
Ë† c increases. For a large enough Î›, âˆ†
always positive.
E. Proof of Lemma 1 and Proposition 5
We begin computing the maximal level of investment for country 1 at the non-cooperative
equilibrium. We have
OI
OI OI OIÎ³ OI OIÎ³ OI q Î³ OI
W1 Î³ = S (Q1 Î³ ) âˆ’ P (Q )Q1 Î³ + Î»P (Q )q1 Î³ âˆ’ (1 + Î»)(Î¸1 + sÎ³ 1 )q1 Î³ âˆ’ (1 + Î»)IÎ³ .
2
Substituting the relevant quantities into this welfare function and into (26) and replacing them
into Equation (17), we obtain
O 2 ii ii 2 ii
IÎ³ 1 = âˆ† Î“1 (Î³, Î›) + (d âˆ’ Î¸1 )âˆ†Î“2 (Î³, Î›) + (d âˆ’ Î¸1 ) Î“3 (Î³, Î›),
where
(1 + sÎ³ (1 âˆ’ Î›))(3 + 4sÎ³ + Î›) (1 + Î³ (1 âˆ’ Î›))(3 + 4Î³ + Î›)
Î“ii
1 (Î³, Î›) = âˆ’
(1 + 2sÎ³ )2 (2(1 + sÎ³ ) + Î›)2 (1 + 2Î³ )2 (2(1 + Î³ ) + Î›)2
Î›(3 + 4sÎ³ + Î›) Î›(3 + 4Î³ + Î›)
Î“ii
2 (Î³, Î›) = 2
âˆ’
(1 + 2sÎ³ )(2(1 + sÎ³ ) + Î›) (1 + 2Î³ )(2(1 + Î³ ) + Î›)2
2(1 âˆ’ s)Î³ (4(1 + Î³ )(1 + sÎ³ ) âˆ’ Î›)2
Î“ii
3 (Î³, Î›) =
(1 + 2sÎ³ )2 (2(1 + sÎ³ ) + Î›)2
Î“ii ii O
1 (Î³, Î›) and Î“2 (Î³, Î›) are positive âˆ€s âˆˆ (0, 1), Î› âˆˆ [0, 1). IÎ³i is an upward-sloping parabola with
(dâˆ’Î¸i )Î“ii
2 (Î³,Î›)
its axis of symmetry in âˆ† = âˆ’ 2Î“ii ( Î³, Î›)
< 0, implying the following result:
1
37
O > I O if and only if Î¸ < Î¸ .
Result 1 IÎ³ 1 Î³2 1 2
O
By deï¬?nition, this implies that I Î³ > I O
Î³ . This result is useful to prove Lemma 1.
Proof of Lemma 1
Because investment reduces the costs of both ï¬?rms, if one ï¬?rm invests, the best response
of the other is to not invest. However, if one ï¬?rm does not invest, the best response of the
O . From Result 1, we know that I O O
other ï¬?rm is to invest whenever IÎ³ < IÎ³i Î³ > I Î³ . Then, for
O
IO O
Î³ < IÎ³ < I Î³ , the less eï¬ƒcient ï¬?rm never invests, and the more eï¬ƒcient ï¬?rm does. For IÎ³ < I Î³ ,
a ï¬?rm invests if and only if the other ï¬?rm does not.
O âˆ— and the
Before comparing the maximum level of investment I Î³ with the optimal level IÎ³
âˆ—
closed economy I Î³ , we prove that a Î³ -investment can reduce the welfare of the less eï¬ƒcient
O
âˆ‚IÎ³ O
country. We have âˆ‚âˆ†
1
= 2âˆ†Î“ii ii
1 (Î³, Î›) + (d âˆ’ Î¸1 )Î“2 (Î³, Î›). Then, I Î³ is strictly positive and
I
increasing in |âˆ†|, while I O O Î³
Î³ is U shaped. The sign of I Î³ is thus ambiguous. Let W1 âˆ’ W1 be
the impact of Î³ -reducing investment country 1 when âˆ† < 0 (i.e., Î¸2 < Î¸1 ). By the deï¬?nition of
IO
Î³ , we can write
I IO
Î³
W1 Î³ âˆ’ W1 = .
1âˆ’Î›
Then, the welfare gains of country 1 are positive if and only if I O O
Î³ is positive. If âˆ† = 0, I Î³ is
positive and decreasing in |âˆ†|. We must prove that I O
Î³ might be negative for some âˆ† < 0. In
I
sÎ³ )(dâˆ’Î¸2 )
âˆ† = âˆ’ 2(1+21+Î› (the minimal admissible value under A1), W1 Î³ âˆ’ W1 is negative if and only
âˆš
9+8sÎ³ +4Î³ (10+7sÎ³ +Î³ (3+Î³ (1+s))(5+Î³ (1+s)))âˆ’(1+2Î³ (2+Î³ (1+s)))
if Î› > Î› = 1+2Î³ . Then, Î› > Î› is a suï¬ƒcient
(although non-necessary) condition to achieve gains in the less eï¬ƒcient country that are smaller
than zero for some âˆ† < 0.
Proof of Proposition 5
âˆ—IÎ³ âˆ—I
âˆ— + q âˆ— and Qâˆ—IÎ³ = q
Let Qâˆ— = q1 2 1 + q2 Î³ . The maximal investment at the global optimum is
38
deï¬?ned by (16). Global welfare in the case of non-investment and investment are, respectively,
âˆ—
q1 âˆ—
q2
W âˆ— = S (Qâˆ— ) + Î»P (Qâˆ— )Qâˆ— âˆ’ (1 + Î»)(Î¸1 + Î³ âˆ—
2 )q1 âˆ’ (1 + Î»)(Î¸2 + Î³ âˆ—
2 )q2
âˆ—I âˆ—I
q1 Î³ q2 Î³ âˆ—IÎ³
W âˆ—IÎ³ = S (Qâˆ—IÎ³ ) + Î»P (Qâˆ—IÎ³ )Qâˆ—IÎ³ âˆ’ (1 + Î»)(Î¸1 + sÎ³ 2
âˆ—
)q1 âˆ’ (1 + Î»)(Î¸2 + sÎ³ 2 )q2 âˆ’ (1 + Î»)IÎ³
Replacing for the relevant quantities and rearranging terms, we obtain
âˆ—
IÎ³ = âˆ†2 Î“iii iii 2 iii
1 (Î³, Î›) + (d âˆ’ Î¸min )|âˆ†|Î“2 (Î³, Î›) + (d âˆ’ Î¸min ) Î“3 (Î³, Î›),
where
1âˆ’s 1 Î³2
Î“iii
1 (Î³, Î›) = +
4Î³ s (1 + sÎ³ + Î›)(1 + Î³ + Î›)
(1 âˆ’ s)Î³
Î“iii
2 (Î³, Î›) = âˆ’
(1 + Î³ + Î›)(1 + sÎ³ + Î›)
(1 âˆ’ s)Î³
Î“iii
3 (Î³, Î›) =
(1 + Î³ + Î›)(1 + sÎ³ + Î›)
âˆ— is symmetric with respect to the origin (âˆ† = 0) because at the global optimum, production
IÎ³
is always reallocated in favor of the most eï¬ƒcient ï¬?rm. Moreover, for both âˆ† > 0 and âˆ† < 0,
production is U-shaped in âˆ† (Î“iii
1 (Î³, Î›) > 0, âˆ€s âˆˆ (0, 1), Î› âˆˆ [0, 1), Î³ â‰¥ 0).
âˆ— and I O .
We now compare the thresholds IÎ³ Î³
âˆ— O
IÎ³ âˆ’ IÎ³ = âˆ†2 Î“iv iv 2 iv
1 (Î³, Î›) + (d âˆ’ Î¸i )âˆ†Î“2 (Î³, Î›) âˆ’ (d âˆ’ Î¸i ) Î“3 (Î³, Î›)
1 1 2(1 + sÎ³ (1 âˆ’ Î›))(3 + 4sÎ³ + Î›)
Î“iv
1 (Î³, Î›) = + âˆ’
sÎ³ 1 + sÎ³ + Î› (2(1 + sÎ³ ))(2(1 + sÎ³ ) + Î›)2
1 1 2(1 + Î³ (1 âˆ’ Î›))(3 + 4Î³ + Î›)
âˆ’ âˆ’ +
Î³ 1+Î³+Î› (2(1 + Î³ ))(2(1 + Î³ ) + Î›)2
1 1 4(1 + sÎ³ )2 + Î›
Î“iv
2 ( Î³, Î›) = âˆ’ âˆ’ +
1 + 2sÎ³ 1 + sÎ³ + Î› (1 + 2sÎ³ )((2(1 + sÎ³ ) + Î›)2 )
1 1 4(1 + Î³ )2 + Î›
+ + âˆ’
1 + 2Î³ 1 + Î³ + Î› (1 + 2Î³ )((2(1 + Î³ ) + Î›)2 )
1 2(1 + sÎ³ ) 1 2(1 + Î³ )
Î“iv
3 (Î³, Î›) = âˆ’ 2
âˆ’ +
1 + sÎ³ + Î› (2(1 + sÎ³ ) + Î›) 1 + Î³ + Î› (2(1 + Î³ ) + Î›)2
Î“iv âˆ— O
1 (Î³, Î›) is positive for all s âˆˆ (0, 1), Î› âˆˆ [0, 1), Î³ > 0. Then, IÎ³ âˆ’ IÎ³ is a U-shaped function of
âˆ— âˆ’ I O decreases with Î›. An increase in Î› shifts the U
âˆ†. Moreover, one can easily show that IÎ³ Î³
39
âˆ— âˆ’ I O to always be positive is to have
curve downwards. Therefore, a suï¬ƒcient condition for IÎ³ Î³
âˆ— âˆ’ I O is a convex function of âˆ†, the minimum is
a positive minimum when Î› = 1. Because IÎ³ Î³
âˆ— âˆ’I O )
âˆ‚ (IÎ³ Î³
obtained from the ï¬?rst-order condition âˆ‚âˆ† = 0. In Î› = 1, this minimum is equal to
[(1 âˆ’ s)2 (57 + 292(1 + s)Î³ + 252(1 + s(3 + 2s))Î³ 2 + 48(1 + s)(7 + s(12 + 7s))Î³ 3 + 16(5 + s(33 +
s(43 + s(33 + 5s))))Î³ 4 + 28s(1 + s)(1 + s(1 + s))Î³ 5 + 64s2 (1 + s2 )Î³ 6 )]/[s(2 + Î³ )(2 + sÎ³ )(1 +
2sÎ³ )2 (3 + 2sÎ³ )2 (3 + 4Î³ (2 + Î³ ))] > 0 âˆ€ s âˆˆ (0, 1).
âˆ— âˆ’ I O is always positive.
Then, IÎ³ Î³
O
âˆ— âˆ’ I âˆ’ I O is also positive. If I O = 0, then I + I O = I O O
We now show that IÎ³ Î³ Î³ Î³ Î³ Î³ Î³ and the
result has been proved above. If I O
Î³ > 0, we have
O
IÎ³ + IO 2 v v 2 v
Î³ = âˆ† Î“1 (Î³, Î›) + (d âˆ’ Î¸i )âˆ†Î“2 (Î³, Î›) + (d âˆ’ Î¸i ) Î“3 (Î³, Î›),
where
(1 âˆ’ s)Î³ (3 + 4(Î³ + sÎ³ (1 + Î³ )) 1+Î³ 1 + sÎ³
Î“v
1 (Î³, Î›) = 2 2
âˆ’ 2
+
(1 + 2Î³ ) (1 + 2sÎ³ ) (2(1 + Î³ ) + Î›) (2(1 + sÎ³ ) + Î›)2
2
4(1 âˆ’ s)Î³ (4(1 + Î³ )(1 + sÎ³ ) âˆ’ Î› )
Î“v
2 (Î³, Î›) = âˆ’
(2(1 + Î³ ) + Î›)2 (2(1 + sÎ³ ) + Î›)2
4(1 âˆ’ s)Î³ (4(1 + Î³ )(1 + sÎ³ ) âˆ’ Î›2 )
Î“v
3 ( Î³, Î›) = .
(2(1 + Î³ ) + Î›)2 (2(1 + sÎ³ ) + Î›)2
Then,
âˆ— O
IÎ³ âˆ’ IÎ³ âˆ’ IO 2 vi vi 2 vi
Î³ = âˆ† Î“1 (Î³, Î›) + (d âˆ’ Î¸i )âˆ†Î“2 (Î³, Î›) âˆ’ (d âˆ’ Î¸i ) Î“3 (Î³, Î›),
where
1+Î³ 1 + sÎ³ 1 1
Î“vi
1 (Î³, Î›) = 2
âˆ’ 2
âˆ’ +
(2(1 + Î³ ) + Î›) (2(1 + sÎ³ ) + Î›) 4(1 + Î³ + Î›) 4(1 + sÎ³ + Î›)
1 1
âˆ’ +
4Î³ (1 + 2Î³ )2 4sÎ³ (1 + 2sÎ³ )2
1 1 4(1 + Î³ ) 4(1 + sÎ³ )
Î“vi
2 (Î³, Î›) = âˆ’ + 2
âˆ’
(1 + Î³ + Î›) (1 + sÎ³ + Î›) (2(1 + Î³ ) + Î›) (2(1 + sÎ³ ) + Î›)2
(1 âˆ’ s)Î³ Î›2 4(1 + s(1 + s))Î³ 2 + 4(1 + s)Î³ (3 + 2Î›) + (2 + Î›)(6 + 5Î›)
Î“vi
3 (Î³, Î›) =
(1 + Î³ + Î›)(1 + sÎ³ + Î›)(2(1 + Î³ ) + Î›)2 (2(1 + sÎ³ ) + Î›)2
40
Î“vi âˆ— J
1 (Î³, Î›) is positive for s âˆˆ (0, 1), Î› âˆˆ [0, 1), Î³ â‰¥ 0, then IÎ³ âˆ’ IÎ³ is a convex U-shaped function
âˆ— âˆ’ I J is decreasing with Î›. Then the
of âˆ†. Moreover, one can verify that the diï¬€erence IÎ³ Î³
diï¬€erence is minimal in Î› = 0, where
âˆ— O Î³ (1 + 2Î³ )2 âˆ’ sÎ³ (1 + 2sÎ³ )2
IÎ³ âˆ’ IÎ³ âˆ’ IO
Î³ = > 0, âˆ€ s âˆˆ (0, 1)
4Î³ (1 + 2Î³ )2 (1 + 2sÎ³ )2
O
âˆ— âˆ’ I âˆ’ I O is always positive.
Then, IÎ³ Î³ Î³
F. Proof of Proposition 6
In the case of a closed economy, welfare with no investment is given by (25). If IÎ³ is invested,
the welfare function becomes
C
qi
CIÎ³ CIÎ³ CIÎ³ CIÎ³ CI
Wi = S (qi ) + Î»P (qi )qi âˆ’ (1 + Î»)(Î¸i + sÎ³ )q Î³ âˆ’ (1 + Î»)IÎ³ .
2 i
Substituting the equilibrium quantities into this expression and using equation (19), the maximal
amount that regulator i is willing to invest in a closed economy is
C (1 âˆ’ s)Î³ (d âˆ’ Î¸i )2
IÎ³i = .
2(1 + Î³ + Î›)(1 + sÎ³ + Î›)
C is smaller than I âˆ— . Because I âˆ— is a convex function of âˆ†, whereas
We ï¬?rst check that IÎ³ Î³ Î³
C is constant, I O âˆ’ I C is also convex in âˆ†.
IÎ³ O âˆ’ I C is zero at âˆ† =
The derivative ofIÎ³
Î³ Î³ Î³
2sÎ³ 2 (dâˆ’Î¸i )
2sÎ³ 2 +(1+s)Î³ (1+Î›)+(1+Î›2 )
, where it reaches the minimum value:
(1 + s)Î³ (d âˆ’ Î¸i )2 (1 + Î›)(1 + Î³ (1 + s) + Î›)
> 0.
2(1 + Î³ + Î›)(1 + sÎ³ + Î›)(2sÎ³ + (1 + s)Î³ (1 + Î›)(1 + Î³ )2 )
O âˆ’ I C is always positive.
Then, IÎ³ Î³
O and I C . Because I O is increasing and convex and I C is constant,
We now compare IÎ³ Î³ Î³ Î³
O âˆ’ I C is also increasing and convex in âˆ†. In particular, if Î› = 0,
IÎ³ Î³
O C (1 âˆ’ s)Î³ (11 + 4Î³ (3(2 + Î³ ) + s(3 + 4Î³ )(2 + Î³ (1 + s)))) 2
IÎ³ âˆ’ IÎ³ = âˆ† â‰¥ 0 âˆ€s âˆˆ (0, 1).
8(1 + Î³ )(1 + sÎ³ )(1 + 2Î³ )2 (1 + 2sÎ³ )2
O âˆ’ I C is increasing with |âˆ†|.
Then, for Î› = 0, the minimum is attained in âˆ† = 0, and IÎ³ Î³
However, if Î› > 0 and âˆ† = 0,
41
O C 1 1 1 4(1 + sÎ³ ) 4(1 + Î³ )
IÎ³ âˆ’IÎ³ = âˆ’ (1âˆ’s)Î³ (dâˆ’Î¸i )2 âˆ’ + âˆ’ .
2 (1 + sÎ³ + Î›) (1 + Î³ + Î›) (2(1 + sÎ³ ) + Î›) (2(1 + Î³ ) + Î›)
O,
This result is negative for all s âˆˆ (0, 1), Î› âˆˆ [0, 1), Î³ â‰¥ 0. From the increasing shape of IÎ³
Ëœ IO > IC.
Ëœ > 0 such that for all âˆ† > âˆ†,
there exists a âˆ† Î³ Î³
G. Asymmetric Demand
In the main text, we have assumed that countries only diï¬€er in their available technology. We
now check the robustness of our results to the case in which demands are asymmetric. Let
pi = di âˆ’ Qi , (27)
where i denotes the country, i = 1, 2. To make meaningful comparisons, we keep the total size
of the market constant in this extension compared to our base case, i.e.,
d1 + d2
d=
2
. Moreover, to ensure interior solutions, we make the following assumption:
(A0bis) min{d1 , d2 } > Î¸.
Under autarky, the results are the same as in the base case, with d replaced by di , i = 1, 2. In
Q
the integrated market, total demand is as in equation (2): p = d âˆ’ 2 with Q = q1 + q2 .
Full integration
In the case of full integration, we ï¬?rst determine the optimal consumption sharing rule, max-
Q2
imizing S1 (Q1 ) + S2 (Q2 ) under the constraint that Q1 + Q2 = Q. Because Si (Qi ) = di Qi âˆ’ 2 ,
i
Q1 +Q2 di âˆ’dj
we deduce that Qi = 2 + 2 . Computing the total consumer surplus S1 (Q1 ) + S2 (Q2 ),
(d1 âˆ’d2 )2 d1 +d2 1
we now obtain S1 (Q1 ) + S2 (Q2 ) = 4 + 2 (Q1 + Q2 ) âˆ’ 4 (Q1 + Q2 )2 . Substituting this
expression into the total welfare function (9), the maximization problem of the supranational
(d1 âˆ’d2 )2
regulator is the same as in the base case plus a constant term 4 . Then, the optimal
42
quantities are the same as in (11).
Replacing these optimal quantities in the welfare functions (9) and replacing the autarky quan-
tities from equation (8) evaluated at di in the welfare function (6), we compute the welfare
âˆ— âˆ’ W C and compare them with those obtained in the base case of
gains from integration Wasy asy
symmetric demand.
âˆ— C (d2 âˆ’ d1 ) (d2 âˆ’ d1 ) 2Î³ (1 âˆ’ Î›) âˆ’ 2Î›2 + 1 + 2âˆ†
Wasy âˆ’ Wasy = Wâˆ— âˆ’ WC + â‰¥0 (28)
4(1 âˆ’ Î›)(Î³ + Î› + 1)
The additional term in the welfare gains can be positive or negative. The term is positive
when d2 âˆ’ d1 is positive and âˆ† = Î¸2 âˆ’ Î¸1 is relatively large and when d2 âˆ’ d1 is negative and âˆ† is
relatively small. Demand asymmetry plays a similar role to cost asymmetry. To see this point,
consider the limit case in which âˆ† = 0 (i.e., generation costs are identical). This case implies that
1+Î› 2Î³ (1âˆ’Î›)âˆ’2Î›2 +1
W âˆ— âˆ’W C = 4Î³ (1âˆ’Î›)(1+Î³ +Î›) âˆ†
2 âˆ— âˆ’W C =
= 0 and that Wasy asy
2
4(1âˆ’Î›)(1+Î³ +Î›) (d2 âˆ’ d1 ) . Due to the
quadratic shape of the transportation cost function, the smaller country has a lower marginal
cost. THerefore, when the smaller country is also the most eï¬ƒcient one, integration allows
the regulator to expand the smaller countryâ€™s market share to exploit the low generation and
transportation costs. Reallocating production toward the producer with the smaller national
market increases productive eï¬ƒciency and the total welfare gains from trade.
Sectorial integration with asymmetric regulation
Q2 Q di âˆ’dj
Consumer surplus is written Si (Qi ) = di Qi âˆ’ 2
i
and Qi = 2 + 2 , where Q = Q1 + Q2 =
q1 + q2 and i, j = 1, 2 i = j . Substituting this expression into (6) yields the national welfare
function. The regulator of country i chooses qi to maximize this function given the quantity qj
chosen by the regulator of country j. At the non-cooperative equilibrium, we have
O d âˆ’ Î¸1 +
2
Î¸2
Î¸j âˆ’ Î¸i (1 âˆ’ Î›)(di âˆ’ dj )
qi =4 + + . (29)
2(1 + Î³ ) + Î› 1 + 2Î³ 2 + 4Î³
43
The last term, which cancels out when d1 = d2 , is an additional term due to the asymmetry
of demand. Replacing these quantities in the social welfare function (6), we can compute the
welfare gains. As in Appendix C, we focus without loss of generality on country 1. The results
O
for country 2 are symmetrical. The welfare gain of country 1, W1 C
,asy âˆ’ W1,asy , is equal to the
gain obtained in the symmetric case plus an additional term Î¶ (d2 âˆ’ d1 , âˆ†, Î›, Î³, Î¸1 ):
O C O C
W1 ,asy âˆ’ W1,asy = W1 âˆ’ W1 + Î¶ (d2 âˆ’ d1 , âˆ†, Î›, Î³, Î¸1 )
where
1
Î¶ (d2 âˆ’ d1 , âˆ†, Î›, Î³, Î¸1 ) = (d2 âˆ’ d1 )âˆ†Ï†1 (Î³, Î›) + (d2 âˆ’ d1 )2 Ï†2 (Î³, Î›) + (d2 âˆ’ d1 )(d1 âˆ’ Î¸1 )Ï†3 (Î³, Î›)
8
and
4Î³ (3 + 4Î³ + Î›)
Ï†1 (Î³, Î›) = â‰¥0
(1 + 2Î³ )2 (2 + 2Î³ + Î›)
8Î³ 4 (1 âˆ’ Î›) + 2Î³ 3 ((4 âˆ’ 7Î›)Î› + 7) + Î³ 2 (6 + Î›(19 + (2 âˆ’ 7Î›)Î›) + 6) + Î›Î³ (3 âˆ’ Î›)(2 + Î›(4 + Î›)) + Î›2 (2 + Î›)
Ï†2 (Î³, Î›) = â‰¥0
(1 + 2Î³ )2 (1 âˆ’ Î›)(1 + Î³ + Î›)(2 + 2Î³ + Î›)
4Î› 4Î³ 2 + Î³ (3 + 5Î›) + Î›(2 + Î›)
Ï†3 (Î³, Î›) = â‰¥0
(1 + 2Î³ )(1 âˆ’ Î›)(1 + Î³ + Î›)(2 + 2Î³ + Î›)
The additional eï¬€ect Î¶ is decomposed into three terms. The ï¬?rst term, which is identical
for both countries, has the sign of (d2 âˆ’ d1 )âˆ†: it is positive whenever (d2 âˆ’ d1 ) and âˆ† = Î¸2 âˆ’ Î¸1
have the same sign. These variables have the same sign when country 1 is small and possesses
the most eï¬ƒcient technology or when it is large and endowed with the less eï¬ƒcient technology.
The second term is always positive and increases with the absolute value of (d2 âˆ’ d1 ). This term
is also identical for both countries. This term captures the eï¬ƒciency gains related to production
reallocation in the presence of a positive quadratic transportation cost.
Finally, because (di âˆ’ Î¸i ) is always positive by assumption A0, the third term has the sign of
(dj âˆ’ di ) for country i, meaning that it is positive for the smallest country and negative for the
largest one.
Because the ï¬?rst and second terms are identical for both countries whereas the third term
is positive for the small country and negative for the large country, we deduce that, everything
else being equal, the smaller country always wins more from integration than the larger one.
44
The net eï¬€ect of Î¶ depends on the opportunity cost of public funds. When Î› is relatively
small, the ï¬?rst term in Î¶ is the largest. Compared to the base case, the welfare gains increase
when the smallest country is also the most eï¬ƒcient. In contrast, the two eï¬€ects (i.e., generation
and transportation costs) contradict each other when the large country is the most eï¬ƒcient, so
the welfare gains are lower than in the base case. Now, for large values of Î›, the third term
in Î¶ tends to be the largest, unless Î³ is also very large. Thus, for a suï¬ƒciently large Î›, the
additional welfare gains obtained with asymmetric demand tend to be positive for the smaller
country and negative for the larger one.
We next want to check that our resultâ€“that market integration is welfare degrading when
countries are too similar and that ï¬?scal issues are importantâ€“is robust to asymmetric demand.
Let âˆ† = 0. The welfare gains are written as
O C 2 1
W1 ,asy âˆ’ W1,asy = Î“1 (Î›, Î³ )(d âˆ’ Î¸1 ) + (d2 âˆ’ d1 )2 Ï†2 (Î³, Î›) + (d2 âˆ’ d1 )(d1 âˆ’ Î¸1 )Ï†3 (Î³, Î›)
8
1 Î›2
where Î“1 (Î›, Î³ ) = âˆ’ 4 (1âˆ’Î›)(1+Î³ +Î›)(2+2Î³ +Î›)2
< 0. For d2 = d1 , the term Î“1 (Î›, Î³ )(d âˆ’ Î¸1 )2 corre-
sponds to the welfare gains in the base model (see Appendix C when âˆ† = 0). If Î› > 0, then
the welfare gains are always negative for d1 = d2 and âˆ† = 0. By continuity, this net welfare loss
result holds true for strictly positive values of |d2 âˆ’ d1 |, as illustrated in ï¬?gures 6 and 7. These
ï¬?gures show that both countries lose from integration if they are too similar (i.e., the engine of
integration is cost complementarities).
The welfare gain is a convex function of d2 âˆ’ d1 when âˆ† = 0. The function is increasing
for d2 âˆ’ d1 â‰¥ 0 (i.e., for the smaller country) and, depending on the value of Î³ , is U-shaped or
decreasing for d2 âˆ’ d1 â‰¤ 0 (i.e., for the larger country). The U-shaped result is similar to the
result illustrated in ï¬?gure 1 because when Î³ is large, d2 âˆ’ d1 plays the same role as âˆ†. When
transportation costs are very large, both countries gain from integration (one through export
45
O
Figure 6: The Welfare Gains W1 C
,asy âˆ’ W1,asy , âˆ† = 0, Î› = 1/3, Î³ = 10.
O
Figure 7: The Welfare Gains W1 C
,asy âˆ’ W1,asy , âˆ† = 0, Î› = 1/3, Î³ = 1.
proï¬?ts, the other through a reduction in the price).
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