metadata: authors: 0: author: Auriol,Emmanuelle
1: author: Biancini, Sara
count: World
docna: 0: docna: Powering up developing countries through
            integration ?
docty: Policy Research Working Paper
subtopic: Macro-Fiscal Policy,Taxation & Subsidies,Economic Adjustment and Lending,Public Sector Economics,Energy Policies & Economics,International Trade and Trade Rules,Energy Demand,Energy and Environment,Energy and Mining,Public Finance Decentralization and
            Poverty Reduction,Transport Services
teratopic: Transport,Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: Power market integration is analyzed in
            a two-country model with nationally regulated firms and
            costly public funds. If the generation costs between the two
            countries are too similar, negative business stealing
            outweighs efficiency gains so that the subsequent
            integration welfare decreases in both regions. Integration
            is welfare enhancing when the cost difference between two
            regions is large enough. The benefits from export profits
            increase the total welfare in the exporting country, whereas
            the importing country benefits from lower prices. In this
            case, market integration also improves incentives to invest
            compared to autarky. The investment levels remain
            inefficient, however, especially for transportation
            facilities. Free riding reduces incentives to invest in
            these public-good components of the network, whereas
            business stealing tends to decrease the capacity to finance
            new investment.
repnme: repnme: Powering up developing countries through
            integration ?
display_title: Powering up developing countries
            through integration
listing_relative_url: /research/2013/06/17888008/powering-up-developing-countries-through-integration
topicv3: Energy and Extractives m1326595 507,Transport m1326661 135,Trade m1326924 698,Power and Electricity Sector m1327094 515,Taxation m1327615 1121
publishtoextweb_dt: 2013-06-01T00:00:00Z
historic_topic: Transport,Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 51
author_keys: 0: author_key: 901922
model_extractions: 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 model with nationally regulated firms and costly public funds. If the generation costs between the two countries are too similar, negative business stealing outweighs efficiency gains so that the subsequent integration welfare decreases in both regions. Integration is welfare enhancing when the cost difference between two regions is large enough. The benefits from export profits increase the total welfare in the exporting country, whereas the importing country benefits from lower prices. In this case, market integration also improves incentives to invest compared to autarky. The investment levels remain inefficient, however, especially for transportation facilities. Free riding reduces incentives to invest in these public-good components of the network, whereas business stealing tends to decrease the capacity to finance new investment.

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.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Powering Up Developing Countries through Integration?

Emmanuelle Auriol and Sara Biancini<sup>_∗_</sup> JEL Classification: L43, L51, F12, F15, R53. Keywords: regulation, competition, market integration, investment, electricity. Sector board: Energy and Mining (EM)

> _∗_ 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 Universit ́e and CREM UMR CNRS 6211; her email address is sara.biancini@unicaen.fr. The authors are grateful for the financial 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 CergyPontoise, 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 benefited from the insightful comments, criticisms, and suggestions of three anonymous referees. We thank them for their input.

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The world’s electricity demand is projected to double by the year 2030 (International Electricity Agency 2006). Financing the volume of investment required to meet this demand increase is a challenge for developing countries.<sup>1</sup> With scarce public resources, little assistance from the private sector, and limited aid,<sup>2</sup> 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 integration is likely to occur in the absence of legitimate supranational regulation. This paper studies the costs and benefits of this partial economic integration. This paper shows that coordination problems between independent regulators prevent them from efficiently using the stock of existing infrastructure, and they distort countries’ incentives to invest in new generation and, more importantly, in interconnection facilities. These countries’ competition for market share limits the benefit of integration. Because of these losses, the difference in these countries’ 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 interconnection projects have been launched to exploit efficiency gains between countries that do not have sufficient 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,

> 1The 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 world’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).

> 2The 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, ”For many countries, particularly those with the lowest income, private-sector participation has been disappointing”. As rich countries emerge from the global financial crisis with high debt, it is unlikely that development assistance will increase significantly in the near future, and there is a risk that aid to large infrastructure projects could be reduced.

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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 efficiency, 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-Sahara’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 sufficient 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 benefit all countries in the region.<sup>3</sup> The challenging question, however, is how to finance these projects.

Electricity is a non-storable good that requires large specific investments, such as transportation 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 difference between electricity and the trade of standard commodities. In the absence of a binding commitment mechanism, firms and governments are unwilling to sink huge investments with the sole purpose of selling electricity to a neighboring country in the future. Once these specific investments are realized, the investing country would incur a classic hold-up problem. The trade partner could always renegotiate the price, but the

> 3For 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).

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investor has no ability to sell the energy elsewhere. This commercial risk is particularly acute in developing countries.<sup>4</sup> 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.<sup>5</sup> 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 fiscal), governments focus on their own national welfare. Governments are biased in favor of their national (public) firms because the governments are the residual claimant for their profits and losses. Theoretically, the relevant analytical framework is asymmetric regulation (i.e., each firm 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.<sup>6</sup> Because market integration is a process of reciprocal market opening, the present paper extends these authors’ analysis, which focuses on the effects 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

> 4For 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 firm 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).

> 5For 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, Cˆote d’Ivoire, Burkina Faso, and Niger because these countries were already interconnected.

> 6Caillaud 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 firm is exposed to competition from a single strategic competitor. Allowing for horizontal and vertical differentiation, these authors find that competition helps to extract the information rent of the regulated firm, but allocative inefficiency arises in equilibrium.

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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 difference between the two regions is sufficiently large. For the low-cost region, the benefits from increased export profit (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 benefits from the reduction in price caused by importation, which enhances consumer surplus.<sup>7</sup> In contrast, sectorial integration is not likely to occur if the cost difference between the two countries is small. Indeed, unregulated competition tends to undermine the tax base (see Armstrong and Sappington 2005). Without a significant technological gap, competition for market share is fierce 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.<sup>8</sup> This paper next studies the impact of regional integration on countries’ 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). Compared to autarky, market integration improves incentives to invest in generation. First, when one country is much more efficient 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

> 7Even if the efficiency gains from integration are large enough so that both countries win from integration, opposition might persist internally because when production is reallocated toward more efficient providers, trade liberalization creates winners and losers internally.

> 8This finding differs strikingly from the results in the trade literature. Starting with Brander and Spencer 1983, a portion of this literature has focused on the strategic effect of trade subsidization policies. These policies have a rent-shifting effect that creates a prisoner’s dilemma, so firms benefit from jointly reducing the subsidies. However, even if the benefit 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).

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internalize the foreign country’s consumer surplus (i.e., it only internalizes sales), but it increases compared to autarky. Moreover, incentives to invest in obsolete technology decrease, whereas incentives to invest in efficient technology increase. Second, when the two countries’ technologies are similar, the firms must fight 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 difference is not large enough. Second, developing countries suffer 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 finance new investment, especially in the importing country. The problem is sometimes so severe that global investment decreases compared to autarky. In other words, when the firms’ 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 inefficient country will resist integration when the generation costs are too close. However, even if the gap between the costs is large enough that integration benefits both countries, the investment level in the public 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 interconnection 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 production of kilowatts rose. However, due to poor transmission and distribution infrastructures, the plants were kept well below efficient 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 off.

Section I of the paper presents the model and the benchmark of a closed economy. Section II studies sectoral integration, and Section III focuses on countries’ incentives to invest in generation and transportation infrastructure. Finally, Section IV offers some concluding remarks.

# _I. A MODEL OF SECTORIAL INTEGRATION WITH INDEPENDENTLY REGULATED_

# _FIRMS_

We consider two symmetrical countries, identified by _i_ = 1 _,_ 2. The inverse demand in each country is provided by<sup>9</sup> 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., different _d_ 1 = _d_ 2). 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 identified by _i ∈{_ 1 _,_ 2 _}_ . When the markets are integrated, _Qi_ can be produced by both firms 1 and 2 (i.e., _Qi_ = _qii_ + _qji, i_ = _j_ , where _qij_ , is the quantity sold by firm _i_ in country _j_ ). The total demand in the integrated market is given by

> 9For 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.

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where _Q_ = _Q_ 1 + _Q_ 2 is the total demand in the integrated market, which can be satisfied by firm 1 or 2 (i.e., _Q_ = _q_ 1 + _q_ 2).

On the production side, firm _i_ = 1 _,_ 2 incurs a fixed cost that measures the economies of scale in the industry. The fixed cost is sunk, so it does not play a role in the optimal production choices.<sup>10</sup> We thus avoid introducing new notation for this sunk cost.

The firm also incurs a variable cost function provided by The variable cost function includes both a linear term _θi ∈_ <u>[</u> _<u>θ,</u> θ_ ], which represents the production cost, and an additional quadratic term, weighted by _γ_ , which represents a transportation cost. The cost function (3) can be generated from a horizontal differentiation 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 first separated in two contiguous segments (the ”national markets”). Market integration corresponds to the unification of the two segments. The common market is then represented by the full Hotelling line. To serve consumers, firms, 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 _γ_ as a transportation cost (see Auriol 1998).<sup>11</sup> 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 effect and the associated transport charges and losses. Moreover, in the interconnected network, the transportation cost _γ_ is the same for both domestic and international consumers.

This assumption is also consistent with the physical characteristics of electric networks. This

> 10Because the cost is already sunk at the time that the countries choose whether to integrate and their production levels, it does not play a role in their decision.

> 11In other words, assume that the consumers are uniformly distributed over [0 _,_ 1]. To deliver one unit to a consumer located at _q ∈_ [0 _,_ 1], the transportation cost is _γq_ for firm 1 and _γ_ (1 _− q_ ) for firm 2. The variable production cost of firm _i_ with market share equal to _qi_ can then be written as _c_ ( _θi, qi_ ) = �0 _qi_<sup>(</sup><sup>_θi_+</sup><sup>_γ q_)d</sup><sup>_q_,or</sup> equivalently _c_ ( _θi, qi_ ) = _θiqi_ + _γ_ _<u>q</u>_ 2 _<u>i</u>_<sup>2(</sup><sup>_i_= 1</sup><sup>_,_2).</sup>

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physical unity, which comes from the fact that electricity cannot be routed, is what differentiates electric systems from other systems of distribution of goods and services.<sup>12</sup> In summary, _θi ∈_ <u>[</u> _<u>θ,</u> θ_ ] can be interpreted as a generation cost that is constant after some fixed investment has been performed, whereas _γ_ is a measure of transportation costs (i.e., transport charges and losses). In the following, we assume that _γ_ and _θi_ 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.<sup>13</sup> To rule out the corner solution, we make the following assumption:

# **A0**

Assumption A0 ensures that in equilibrium, the quantities are strictly positive. The profit of firm _i_ = 1 _,_ 2 is where _ti_ is the tax that the firm pays to the government (it is a subsidy if it is negative). The participation constraint of the regulated firm is The regulator of country _i_ has jurisdiction over the national monopoly _i_ . She regulates the quantities and the investments of the firm and is allowed to transfer funds to and from the firm, and she taxes operating profits when they are positive and subsidizes losses. This

> 12For more details on the specificities of electric markets, see Joskow and Schmalensee 1985.

> 13Because _γ_ 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 _θi_ , 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, _θi_ +Λ<sup>_F_</sup> _f_ (<sup><u>(</u></sup> _θ_<sup>_θ_</sup> _i_<sup>_<u>i</u>_</sup> )<sup><u>)</u>, where</sup><sup>_f_and</sup><sup>_F_are the</sup> density and repartition functions of _θi_ ). Introducing asymmetric information does not change our primary results except for the inflated 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 regulator’s ability to gather information on the firms as compared to the national regulators.

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process is consistent with public ownership. In the case of electricity, public and mixed firms are key players in most developing countries: in 2004, 60% of the less developed countries had no significant private participation in electricity (Estache, Perelman, and Trujillo 2005).<sup>14</sup> In contrast, rent extraction does not apply to foreign firms because they do not report their profits locally. The regulator does not seize the rent of foreign firm and does not have to subsidize the losses. Moreover, the regulator of country _i_ does not control the production or the investment of firm _j_ (i.e., asymmetric regulation).

Each utilitarian regulator in country _i_ maximizes the home welfare, _Wi_ = _S_ ( _Qi_ ) _−P_ ( _Q_ ) _Qi_ + Π _i_ + (1 + _λ_ ) _ti_ , where _S_ ( _Qi_ ) = �0 _Qi pi_ ( _Q_ )d _Q_ = _dQi −_<sup>_<u>Q</u>_</sup> 2 _<u>i</u>_<sup>2isthegrossconsumersurplus,Π</sup><sup>_i_isthe</sup> profit of the national firm, and (1+ _λ_ ) _ti_ is the opportunity cost of public transfers. Because _Wi_ is decreasing in Π _i_ when _λ ≥_ 0, leaving rents to the monopoly is socially costly. The participation constraint of the national firm (5) always binds: Π _i_ = 0.<sup>15</sup> The utilitarian welfare function in country _i_ = 1 _,_ 2 is The regulator of country _i_ is not indifferent between producing power locally (i.e., _qi_ ) and importing it (i.e., _Qi − qi_ ). She is biased in favor of local production. This national preference, which is consistent with countries’ objective of energy independence, reflects the fact that the regulator is the residual claimant for the firm profit and loss. The bias increases with _λ ≥_ 0, which can be interpreted as the shadow price of the government budget constraint (i.e., the Lagrange multiplier of this constraint).<sup>16</sup> Any additional investment in public utilities implies a

> 14This lack of private participation also exists in many advanced economies. For instance, 87.3% of Electricit ́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 firm paid over EUR 2.4 billion in dividends to the government.

> 15Here, regulation is effective (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.

> 16The government pursues multiple objectives, such as producing public goods, regulating noncompetitive industries, 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 benefits of alternative investment choices and spending. In advanced economies, _λ_ is usually esti-

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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 benefit of the additional investment. Conversely, when the transfer is positive (i.e., taxes on profits), it helps to reduce distortionary taxation or to finance investment. The assumption of costly public funds is a way to capture the general equilibrium effects of sectoral intervention. To avoid introducing bias into the integration decision, we assume that both countries have the same cost of public funds, _λ_ .

In the following, we express the results in terms of Λ, which increases with _λ ∈_ [0 _,_ + _∞_ ): We first briefly 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 When Λ = 0, public funds are costless, and the price is equal to the marginal cost _P_ ( _qi_<sup>_C_) =</sup> _θi_ + _γqi_<sup>_C_.WhenΛ</sup><sup>_>_0,thepriceisraisedabovethemarginalcostwitharulethatisinversely</sup> _<u>i</u>_<sup><u>)</u></sup> proportional to the elasticity of demand (Ramsey pricing): _P_ ( _qi_<sup>_C_)=</sup><sup>_θi_+</sup><sup>_γ q_</sup> _i_<sup>_C_+ Λ</sup><sup>_P_</sup><sup><u>(</u></sup> _ε_<sup>_<u>qC</u>_</sup> . The optimal pricing rule diverges from marginal cost pricing in proportion to the opportunity cost of public fund Λ because the revenue of the regulated firm 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 difficulty implementing effective taxation imply higher values for _λ_ . The World Bank 1998 suggests an opportunity cost of 0.9 as a benchmark, but it may be much higher in heavily indebted countries.

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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 differs 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 different cost functions (one plant would be the national producer and the other the import possibility). This case would lead to a different (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 differ 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 financial 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 profits, 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_

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When barriers to trade in the power market are removed, firms can serve consumers in both countries so that there is a single price. The demand functions are symmetric, which implies that the level of consumption is the same in the two countries: _Qi_ = 2<sup><u>1</u></sup><sup>_QO_,</sup><sup>_i_= 1</sup><sup>_,_2.Incontrast,the</sup> generation cost functions are different, which implies a different level of production in the two countries. We first 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 fiscally. 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_ = _W_ 1 + _W_ 2, the sum of welfare functions defined in (6), with respect to quantities ( _Q_ 1 _, Q_ 2 _, q_ 1 _, q_ 2), under the constraint that consumption _Q_ = _Q_ 1 + _Q_ 2 equals production _q_ = _q_ 1 + _q_ 2. This problem can be solved sequentially. First, the optimal consumption sharing rule between the two countries ( _Q_ 1 _, Q_ 2) is computed for any level of production _q_ . This calculation maximizes _S_ ( _Q_ 1) + _S_ ( _Q_ 2) under the constraint that _Q_ 1 + _Q_ 2 = _q_ 1 + _q_ 2. Because _S_ ( _Qi_ ) = _dQi −_<sup>_<u>Q</u>_</sup> 2 _<u>i</u>_<sup>2,weeasilydeducethattheoptimalconsumptionallocations</sup> are _Q_ 1 = _Q_ 2 =<sup>_<u>Q</u>_</sup><sup><u>1+</u></sup> 2<sup>_<u>Q</u>_</sup><sup><u>2</u></sup> . Hence, the supranational utilitarian objective function (9) becomes Let _θ_ min = min _{θ_ 1 _, θ_ 2 _}_ and ∆= _θ_ 2 _− θ_ 1, which can be positive or negative. Second, (10) is optimized with respect to the quantities _q_ 1 and _q_ 2.

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**Proposition 1** _The socially optimal quantity is_

**Proof.** See Appendix A.

When the cost difference between the two firms is large (i.e., when _|_ ∆ _| >_ ∆<sup>_∗_</sup> ), the less efficient producer is shut down, and the most efficient firm is in a monopoly position. This result implies that when there is no transportation cost (i.e., _γ_ = 0), the first best contract always prescribes the shut down of the less efficient firm. However the ”shut down” result is upset with the introduction of a transportation cost. When _γ_ is positive, both firms produce whenever _|_ ∆ _| ≤_ ∆<sup>_∗_</sup> . The most efficient firm (i.e., the firm with the cost parameter _θ_ min) has a larger market share than its competitor (see (11)). However, the market share differences decrease with _γ_ .

In practice, sectorial integration generally excludes fiscal and political institutions, which remain decentralized at the country level.<sup>17</sup> Sovereign governments and regulators do not share profits and tariff revenues among themselves. Taxpayers enjoy taxation by regulation insofar as the rents come from their national firms. The next section studies the distortions induced by the non-cooperative equilibrium between two governments.<sup>18</sup>

# _Sectorial Integration with Asymmetric Regulation_

In the case of sectoral integration, marked _O_ , national regulators simultaneously fix the

> 17The fusion of regulatory bodies and fiscal systems is rarely achieved. The German reunification, with the East and West German economic systems unified under the same government, is an exception. Consistent with the theory, many firms have been shut down in East Germany. The reallocation of production toward more efficient units has been sustained by transfers from West Germany.

> 18If governments could bargain efficiently 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, significant corruption, and inefficient justice systems, transaction costs are higher in developing countries than in advanced economies. In practice, we do not observe efficient bargaining in either type of country, but the inefficiencies are worse in developing countries.

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quantity produced by the national firm, _qi_<sup>_O_,maximizingnationalwelfare(6).Thereaction</sup> functions of the regulators determine the non-cooperative equilibrium.

**Proposition 2** _The quantity produced at the non-cooperative equilibrium of the sectorial integration game is_

**Proof.** See Appendix B.

Comparing equations (12) and (11), the equilibrium solution implies that the closure of the less efficient firm occurs _less often_ than in the socially optimal solution. That is, ∆<sup>_O_</sup> _≥_ ∆<sup>_∗_</sup> under assumption A0.

Comparing the common market with the closed economy case, it is straightforward to check that _Q_<sup>_O_</sup> defined in equation (12) is always larger than _Q_<sup>_C_</sup> = _q_ 1<sup>_C_+</sup><sup>_q_</sup> 2<sup>_C_definedinequation(8).</sup> The fact that the total quantity increases under market integration does not necessarily imply a welfare improvement. Indeed, when _|_ ∆ _| ≤_ ∆<sup>_∗_</sup> , we have that _Q_<sup>_C_</sup> = _Q_<sup>_∗_</sup> defined in equation (11). We deduce that excessive production occurs in the common market. To be more specific, comparing _Q_<sup>_O_</sup> and _Q_<sup>_∗_</sup> yields

When _|_ ∆ _|_ is smaller than ∆<sup>_O/∗_</sup> , the regulators fight 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 efficient 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 firm. In his attempt to mitigate the business stealing effect, the regulator increases the quantity of the domestic firm so that

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_Q_<sup>_O_</sup> _> Q_<sup>_∗_</sup> .<sup>19</sup> Symmetrically, when _|_ ∆ _|_ is larger than ∆<sup>_O/∗_</sup> , the regulator of the most efficient country controls a large market share (the firm even becomes a monopolist in the common market when _|_ ∆ _| >_ ∆<sup>_O_</sup> ). The problem is that the regulator does not internalize the welfare of foreign consumers. She chooses a suboptimal production level _Q_<sup>_O_</sup> _< Q_<sup>_∗_</sup> .

# _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 inefficiencies 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_ Λ _that is strictly positive, market integration increases welfare in both countries if and only if the difference in the marginal costs |_ ∆ _| is large enough._

**Proof.** See Appendix C.

Figure 1 illustrates Proposition 3. The figure contrasts the welfare gains of country 1 for Λ _>_ 0 with the welfare gains of country 1 for Λ = 0. When Λ = 0, taxation by regulation is not an issue, and an increase in _|_ ∆ _|_ increases the welfare gains identically in the low- and high-cost countries. The less efficient country enjoys a lower price, whereas the more efficient country enjoys higher profits. 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 modified when Λ _>_ 0. When Λ _>_ 0, the intercept corresponding

> 19Substituting _QO_ from equation (12) into market share equation _qiO_<sup>and comparing it with equation (8) yields</sup> _qi_<sup>_O_</sup> _> qi_<sup>_C⇔θj−θi≥−_Λ(</sup> (1+<sup>_d−θ_</sup> _γ_<sup>_<u>i</u>_</sup> +Λ)<sup><u>)(1+2</u></sup><sup>_<u>γ</u>_</sup><sup><u>)</u></sup> _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 efficient. The reason for this choice is that competition decreases the net profits of the national firm without generating a drastic increase in the consumers’ surplus.

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duopoly). Increasing the number of unregulated competitors, including a foreign firm reporting its profit 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.<sup>20</sup> For values of _|_ ∆ _| ∈_ [∆ _,_ ∆],<sup>ˆ</sup> the most efficient country wins, and the less efficient country loses. If one region loses and the other wins, there will be resistance to integration. In contrast, welfare increases in both countries for values of ∆smaller than _−_ ∆and<sup>ˆ</sup> larger than ∆despite<sup>ˆ</sup> the uncoordinated policies. In other words, the theory predicts that integration will be easier to achieve when the cost difference between the two countries is large.

In addition to the global welfare impact, the creation of an integrated market with a common price _P_ ( _Q_<sup>_O_</sup> ) has redistributive effects. To see this point, let us focus on _|_ ∆ _| ≤_ ∆<sup>_O_</sup> . Market integration induces a price reduction in country _i_ = 1 _,_ 2 if and only if the cost difference is not too large, that is, if _θj − θi ≤_<sup>Λ</sup> 1+<sup><u>(</u></sup><sup>_d_</sup> _γ_<sup>_−_</sup> +Λ<sup>_θi_</sup><sup><u>)</u>.21Consumersfromtherelativelyefficientregionarethus</sup> worse off after integration, which may be a source of social discontent and opposition toward sectorial integration. The interests of the national firm/taxpayers conflict with the interests of the domestic consumers.<sup>22</sup> If the government is unable to seize a firm’s rents, both domestic taxpayers and consumers are worse off (shareholders are the only winners).

In contrast, if the firms are not drastically different (i.e., if _|_ ∆ _| ≤_<sup>Λ(</sup> 1+<sup>_d−_</sup> _γ_<sup>_θ_</sup> +Λ<sup><u>min)</u>),pricesdecrease</sup> in _both_ countries because of the business stealing effect. Benevolent regulators are willing to increase their transfers to the national firm to sustain low prices so that taxation by regulation

decreases, harming taxpayers and the total welfare. The negative fiscal effect is a major concern

> 20The trade and competition literature shows that when firms 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 firms are identical, we obtain similar results for some values of Λ (as in Collie 2000). However, this result is not robust to the assumption of heterogeneous firms.

> 21Substituting _QO_ from equation (12) in the inverse demand function yields the equilibrium price _P_ ( _QO_ ) = _d_ (<sup><u>Λ</u></sup> <u>2</u><sup>+</sup> 1+<sup>_γ_</sup> _γ_<sup>)+</sup> +<sup>_θ_</sup><sup><u>Λ</u></sup> 2<sup><u>1+</u></sup> <u>2</u><sup>_θ_</sup><sup><u>2</u></sup> if _|_ ∆ _| ≤_ ∆<sup>_O_</sup> ( _θ_ min). Comparing this price with the price in the closed economy, _P_ ( _qi_<sup>_c_) =</sup><sup>_θi_+ (Λ +</sup> _γ_ ) 1+ _d−γθ_ +Λ _<u>i</u>_<sup>yieldstheresult.</sup>

> 22In the international trade literature, a similar conflict of interest arises between domestic producers and consumers (see Feenstra, 2008).

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in developing countries, where tariffs play an important role in raising funds (see Laffont, 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 industries’ ability to finance 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 differ in other dimensions. In particular, they may have different market sizes (i.e., _d_ 1 = _d_ 2). 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 efficiency 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 finding 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 inefficiency result yielded by sectoral integration is related to the limited set of tax instruments used by the regulator. We concentrate on the profit taxation of regulated firms, 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 fix both the price and the tax on total industry profits. In the integrated market, this irrelevant result does not hold because the national regulator is unable to tax the importing firm’s profit or to control its offer. Competition for market share erodes the national firm’s profit and thus the possibility of taxation. Assuming that new instruments are 19
introduced, if the regulator is allowed to use different tax rates on foreign and domestic firms, she will be able to influence the volume of import. The regulator uses the tax structure to reduce the market share of the foreign firm whenever it does not bring enough efficiency gains (i.e., by reducing the market share of the competitor in such a way that it does not ”steal” 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 firms. Adding taxes to the volume of transactions could be used to generate income on the activities of the foreign firm and to influence its scale of production. In addition to greatly complicating the model resolution, this form of taxation cannot restore efficiency. The heart of the problem is not the nature of the tax instrument used to collect revenue and influence production but rather that each firm’s profits (and the consumer surplus) are accounted for locally.<sup>23</sup> 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 inefficiency 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 difference between two regions is sufficiently large, market integration with asymmetric regulation may decrease total welfare and thus may undermine the global capacity

> 23To see this point more clearly, we focus on the case in which Λ = 0, so fiscal issues are irrelevant for the regulators. Substituting Λ = 0 in (13), one can easily check that the inefficiency in production levels remains. The equilibrium is always sub-optimal, and it is worse when Λ _>_ 0.

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to finance new investment. Our analysis focuses on two types of investment. The first type reduces the production cost of the investing firm (e.g., generation facilities). This investment is referred to as ”production cost reducing” or ” _θ_ -reducing” investment. This type only benefits 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 specific 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 _θ_ 1 to _δ θ_ 1 ( _δ <_ 1) by investing a fixed amount _Iθ_ .

The second type of investment decreases the transportation cost _γ_ . We refer to this type of investment as ”transportation cost reducing” or ” _γ_ -reducing” investment. In the integrated market, the competitor of the investing firm also benefits 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 _γ_ to _sγ_ with _s ∈_ (0 _,_ 1) by investing a fixed amount _Iγ >_ 0.

For both types of investment, we focus on interior solutions. The cost difference is assumed to be small enough that the production of the two firms is positive in the common market. The following assumption ensures that there is no closure in the first best case.<sup>24</sup>

# _Investment in Generation_

We begin by considering the solution induced by the global welfare maximizer in the case of a _θ_ -reducing investment by firm 1. The optimal quantities, denoted _qi_<sup>_∗Iθ_</sup> ( _i_ = 1 _,_ 2), are provided by equations (11), where _θ_ 1 is replaced by _δθ_ 1 ( _δ <_ 1). Substituting the quantities 24Assumption A1, which is the condition in equation (11) with ∆ _∗_ evaluated at _δθ_ 1 instead of _θ_ 1 and _sγ_ instead of _γ_ , ensures that both firms produce in all possible cases. As illustrated by the analysis in Section 2, this assumption is not crucial, but it greatly simplifies the exposition. Our results are preserved when the shut-down cases are considered (computations are available on request).

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_qi_<sup>_∗Iθ_</sup> ( _i_ = 1 _,_ 2) into the welfare function defines equation (10), and the gross utilitarian welfare is _W_<sup>_∗Iθ_</sup> = _W_ ( _q_ 1<sup>_∗Iθ_</sup> _, q_ 2<sup>_∗Iθ_</sup> ). The welfare gain of the investment _W_<sup>_∗Iθ_</sup> _− W_<sup>_∗_</sup> must be compared with the social cost of the investment (1 + _λ_ ) _Iθ_ . The social cost of investment _Iθ_ is weighted by the opportunity cost of public funds because devoting resources to investment decreases the firm’s operating profit and the government’s revenue by _Iθ_ , which has an opportunity cost of 1 + _λ_ . The global welfare maximizer regulator invests if and only if _W_<sup>_∗Iθ_</sup> _− W_<sup>_∗_</sup> _≥_ (1 + _λ_ ) _Iθ_ . Let us denote _Iθ_<sup>_∗_asthemaximallevelofinvestmentthatsatisfiesthisinequality:</sup> The non-cooperative equilibrium quantities in the case of sectoral integration, _qi_<sup>_OIθ_</sup> , and the quantities in the case of a closed economy, _qi_<sup>_CIθ_</sup> , are derived using a similar method from the equations (12) and (8), respectively, where _θ_ 1 is replaced by _δθ_ 1. Substituting the quantities _qi_<sup>_kIθ_</sup> ( _i_ = 1 _,_ 2 and _k_ = _O, C_ ) in the welfare function of the country 1 defined in equation (6), the regulator of country 1 invests if and only if _W_ 1<sup>_kIθ_</sup> _− W_ 1<sup>_k≥_(1 +</sup><sup>_λ_)</sup><sup>_Iθ_.Wededucethemaximal</sup> level of investment that country 1 is willing to commit in the common market and in the closed economy: The next proposition compares the different investment levels (i.e., when _k_ = _∗, O, C_ ) as a function of the initial cost difference ∆= _θ_ 2 _− θ_ 1.

**Proposition 4** _Let_ Λ _>_ 0 _, δ ∈_ (0 _,_ 1) _and_ ∆= _θ_ 2 _− θ_ 1 _. Let Iθ_<sup>_∗andI_</sup> _θ_<sup>_k_(</sup><sup>_k_=</sup><sup>_O, C_)</sup><sup>_bedefinedin_</sup> _(14) and (15), respectively. There are three thresholds_ ∆<sup>ˆ</sup> _a <_ ∆<sup>ˆ</sup> _b <_ ∆<sup>ˆ</sup> _c, such that_

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|
One relevant policy question is whether economic integration can improve the autarky outcome. When Λ = 0, business stealing has no adverse impact on national welfare, so ˆ∆ _a_ = ˆ∆ _b_ = ˆ∆ _c_ =<sup><u>(1</u></sup><sup>_−_</sup> 2<sup>_δ_</sup><sup><u>)</u></sup><sup>_θ_1</sup> . In this case, market integration unambiguously reduces (without eliminating) the gap between the optimal and the equilibrium levels of investment. However, when Λ _>_ 0, the thresholds ∆<sup>ˆ</sup> _a_ and ∆<sup>ˆ</sup> _c_ shift to the left and to the right, respectively, whereas ∆<sup>ˆ</sup> _b_ is not affected (see Appendix D).<sup>25</sup> Theoretically, there are cases in which integration worsens the gap between the equilibrium investment level and the optimum.

To be more specific, Proposition 4 implies that market integration improves the situation with respect to autarky when the initial cost difference between the two regions is large. First, when ∆ _>_ ∆<sup>ˆ</sup> _c_ , country 1 chooses a level of investment in autarky that is inefficiently low. The region is endowed with abundant resources (e.g., hydroelectric potential), but the investment _Iθ_<sup>_O_</sup> 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 level _I_<sup>_∗_However,itdoesnotrestorethefirstbestlevel.When∆</sup><sup>_>_ˆ∆</sup><sup>_c_,theopenmarket</sup> _θ_<sup>.</sup> equilibrium of investment _Iθ_<sup>_O_islowerthantheoptimallevel</sup><sup>_I_</sup> _θ_<sup>_∗_becausetheinvestingcountry</sup> does not fully internalize the increase in the foreign consumer surplus (it only internalizes sales). Second, when ∆ _<_ ∆<sup>ˆ</sup> _a_ , country 1 is very inefficient.<sup>26</sup> In autarky, the only way to increase the 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 superiorforeign 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 efficiency. The

> 25When Λ increases, all thresholds _IθO_<sup>,</sup><sup>_I_</sup> _θ_<sup>_∗I_</sup> _θ_<sup>_C_shiftdownwardbecausethesocialcostofinvestmentincreases.</sup> However, _Iθ_<sup>_O_haslessofadecreasebecauseinvestmentbecomesimportanttoreducethebusinessstealingeffect</sup> in the common market. As a result, the region of over-investment increases.

> 26Indeed, we find that ˆ∆ _a <_ ˆ∆ _b <_ 0, and in the closed economy, investment is higher than the optimal value for the integrated market (i.e., it is inefficiently high) as soon as ∆ _<_ ∆<sup>ˆ</sup> _b_ .

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possibility of reducing the cost gap and expanding market share by serving foreign consumers makes a higher than optimal level of investment attractive (i.e., _Iθ_<sup>_O_ishigherthan</sup><sup>_I_</sup> _θ_<sup>_∗_).</sup> For ∆<sup>ˆ</sup> _a <_ ∆ _<_ ∆<sup>ˆ</sup> _b_ , the level of investment is inefficiently high under both a closed and an open economy.<sup>27</sup> 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 efficiency of the national firm. The firm 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 with respect to autarky. However, the values of ∆corresponding to this situation, [∆<sup>ˆ</sup> _a,_ ∆<sup>ˆ</sup> _b_ ], are generally included in the interval [ _−_ ∆<sup>ˆ</sup> _,_ ∆] within which the country with the less efficient technology would not accept integration in the first place.<sup>28</sup> . 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 financed.

# _Transportation Cost Reducing Investment_

In this section, we study the case in which the collective transportation cost can be reduced from _γ_ to _sγ_ with _s ∈_ (0 _,_ 1) by an investment of _Iγ >_ 0. We first consider the level of investment induced by the global welfare maximizer. Let _qi_<sup>_∗Iγ_</sup> be the quantity produced by firm _i_ = 1 _,_ 2 in the case of investment. The optimal quantities are obtained by substituting _sγ_ into equation (11). The gross utilitarian welfare in the case of investment is the welfare function defined by equation (10) evaluated at the actualized quantities: _W_<sup>_∗Iγ_</sup> = _W_ ( _q_ 1<sup>_∗Iγ_</sup> _, q_ 2<sup>_∗Iγ_</sup> ). The global welfare

> 27There is an over-investment problem in the open market if ∆ _≤_ ˆ∆ _c_ and in the closed economy if ∆ _≤_ ˆ∆ _b_ .

> 28We have tested many values for the parameters by simulations. The intervals ˆ∆ _a,_ ˆ∆ _b_ always fell in [ _−_ ˆ∆ _,_ 0]. For instance, for _d_ = 2, Λ = 0 _._ 15, _θ_ 1 = 1 _/_ 2, _δ_ = 9 _/_ 10, and _s_ = 9 _/_ 10, we have that _−_ ∆=<sup>ˆ</sup> _−_ 0 _._ 5, ∆= 0 _._ 01, ˆ∆ _a_ = _−_ 0 _._ 23, ˆ∆ _b_ = _−_ 0 _._ 08 and ˆ∆ _c_ = 0 _._ 02. Finally, the admissible values for ∆under Assumption A1 are in the interval [ _−_ 1 _._ 0 _,_ 0 _._ 57]

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maximizer chooses to invest if and only if _W_<sup>_∗Iγ_</sup> _− W_<sup>_∗_</sup> _≥_ (1 + _λ_ ) _Iγ_ . Let _Iγ_<sup>_∗_bethemaximallevel</sup> of investment that satisfies this inequality: The non-cooperative equilibrium investment level of market integration is obtained using a similar method. The quantity produced by firm _i_ after investment _qi_<sup>_OIγ_</sup> is obtained by substituting _sγ_ into equation (12). Let _Wi_<sup>_OIγ_</sup> be the _i_ = 1 _,_ 2 welfare function (6) of country _i_ evaluated at ( _q_ 1<sup>_OIγ_</sup> _, q_ 2<sup>_OIγ_</sup> ). The maximum level of investment that country _i_ is willing to make in the common market is Intuitively, reducing transportation costs increases the business stealing effect. Although this increase in business stealing has an adverse effect on both countries, the negative impact is larger for the high cost firm. One can therefore check equation (12) to see that the market share of the less efficient country decreases after the investment. For this reason, the welfare effect generated by the transportation cost reducing investment in the less efficient country may be negative, so _Iγi_<sup>_O_canbeequaltozero.Inparticular,thisoccursforlargevaluesofΛ(see</sup> Appendix E for details). In contrast, the investment always increases the gross welfare of the most efficient country. The maximal level of investment for the more efficient firm is always positive and higher than the maximal level of investment for the less efficient firm. Because the _γ_ -reducing investment is a public good, in the common market, the level of investment that each country is willing to finance depends on the investment choice by the other country. The next lemma focuses on equilibria in pure strategy.<sup>29</sup>

> 29There is also a mixed strategy equilibrium in which firm _i_ , _i_ = _j_ invests with probability _πi_ = _WjOIγW−OIγ_ (1+ _−λW_ ) _Iγ_<sup>_O_</sup> _−Wj_<sup>_O_</sup> . This equilibrium is inefficient because, with positive probability, either both firms invest _j j_ or, alternatively, neither invests. Moreover, this equilibrium is not very realistic. An investment in transportation infrastructure requires a good deal of coordination between the two regions and is observed by all.

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**Lemma 1** _Let I Oγ_<sup>_bethemaximallevelofinvestmentforthemoreefficientfirmand_</sup><sup>_<u>I</u>_</sup> _O_ _~~γ~~_<sup>_bethe_</sup> _maximal level of investment for the less efficient firm, as defined in (17)._

- _O O_

- _• If_ _<u>I</u>_ _~~γ~~_<sup>_< Iγ, ≤_</sup> _I γ_<sup>_,themoreefficientfirmistheonlyonetoinvest._</sup>

- _O_

- _• If Iγ ≤_ _<u>I</u> γ_<sup>_,therearetwoNashequilibriainpurestrategyinwhichoneofthefirminvests_</sup> _and the other does not._

# **Proof.** See Appendix E.

Because of the public good nature of the investment, only one of the two firms invests, whereas the other free rides on the investment. The decision of the most efficient firm generally determines the maximal level of investment attainable in the common market.<sup>30</sup> We are now ready to compare the equilibrium level with the optimum.

**Proposition 5** _In the integrated market, the investment level in γ-reducing technology is always suboptimal:_

**Proof.** See Appendix E.

In our specification, a _γ_ -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 γ_<sup>is sub-optimal.The investing country does not take into</sup> account the impact of the investment on the foreign country. However, the underinvestment

> 30Lemma 1 implies that the most efficient firm is willing to sustain relatively high levels of investment, and both firms are able to sustain lower levels. Because of the public good nature of the investment, the identity of the investing firm in this case is not important (and, in practice, might be determined by local circumstances). Our model only predicts that one of the firms will always want to invest for the defined thresholds. For projects above the maximal threshold, there will be no investment.

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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), the total investment level _I Oγ_<sup>+</sup><sup>_<u>I</u>_</sup> _Oγ_<sup>wouldstillbesub-optimal.Toanalyzetheoriginofthis</sup> inefficiency, it is useful to study the countries’ incentives to invest in a closed economy.

Let _qi_<sup>_CIγ_</sup> be the quantity produced by firm _i_ in the case of an investment in a closed economy. _qi_<sup>_CIγ_</sup> is obtained by substituting _sγ_ into equation (8). Let _Wi_<sup>_CIγ_</sup> be the welfare function of country _i_ = 1 _,_ 2 (6), evaluated at _qi_<sup>_CIγ_</sup> . The investment is optimal in country _i_ if and only if _Wi_<sup>_CIγ_</sup> _− Wi_<sup>_C_</sup> _≥_ (1 + _λ_ ) _Iγ_ so that Comparing (19) with (17) yields the next proposition.

**Proposition 6** _Let Iγ_<sup>_C_</sup> _be the maximal amount that the most efficient country is willing to invest to reduce transportation costs in the closed economy, and let Iγ_<sup>_Obethemaximalamount_</sup> _that it is willing to invest in the common market. There exists a_ ∆<sup> ̃</sup> _>_ 0 _such that Iγ_<sup>_O>I_</sup> _γ_<sup>_Cif_</sup> _and only if |_ ∆ _| >_ ∆<sup> ̃</sup> _._

**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 ∆is relatively small. Investment reduces the costs of the competitor and makes the competitor more aggressive in the common market. The business stealing effect, while reducing the investing country’s total welfare, also reduces its capacity to finance new investment. Market integration may thus generate an insufficient level of _γ_ -reducing investment for two reasons. The first reason is that investment has a public good nature. The investing country does not internalize the benefits of foreign stakeholders. The second reason is that 28
In contrast, when one country has a significant cost advantage (i.e., _|_ ∆ _| >_ ∆),<sup> ̃</sup> it is willing to invest more in the common market than under a closed economy because the investment increases its market share and profits. Integration can then help to increase investment, although not to the first best level. With a public good type of investment, there is always underinvestment. 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 inefficiently high.<sup>33</sup>

# _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 profitable in an enlarged market. However, market integration in non-competitive industries has complex implications for welfare and investment.

When the cost difference 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 efficient than its competitor, it chooses an inefficiently high level of investment to close its productivity gap and win market share. With generation facilities, there is underinvestment in efficient technologies and overinvestment in inefficient ones compared to the optimum. This result is in contrast with the systematic underinvestment problem that arises for interconnection and transportation facilities

> ˆ∆. For instance, for _d_ = 2, Λ = 0 _._ 15, _θ_ 1 = 1 _/_ 2, _δ_ = 9 _/_ 10 and _s_ = 9 _/_ 10, we have _−_ ˆ∆= _−_ 0 _._ 5, ∆= 0 _._ 01 and  ̃∆= 0 _._ 02, whereas the admissible values under Assumption A1 are in the interval [ _−_ 1 _._ 0 _,_ 0 _._ 57].

> 33When the initial level of cost difference between the two regions is not large enough, the business stealing effect tilts the investment incentives in the wrong direction. For instance, if ∆<sup>ˆ</sup> _b < θ_ 1 _− θ_ 2 _<_ min _{_ ∆<sup> ̃</sup> _, −_ ∆<sup>ˆ</sup> _b}_ with  ̃∆defined as Proposition 6, then under market integration, country 2 underinvests in _γ_ -reducing technology, whereas country 1 over-invests in _θ_ -reducing technology. The latter investment reduces the gap between the two regions’ 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.

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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 finance 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 financing 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 financed 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 tariffs needed to repay the loans that financed the investment. Based on the CRIE experience, the West African power pool (WAPP) is also working on the creation of a regional regulatory body, ”Organe de R ́egulation R ́egionale” (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 firm. Opening up this supranational regulatory authority to international involvement could have important 31