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. 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∗ 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 �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 bene�ted from the insightful comments, criticisms, and suggestions of three anonymous referees. We thank them for their input. 1 The world’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 bene�ts of this partial economic integration. This paper shows that coordination problems between independent regulators prevent them from efficiently using the stock of exist- ing 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 bene�t 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 inter- connection 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, 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 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). 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, �For many countries, particularly those with the lowest income, private-sector participation has been disappointing�. As rich countries emerge from the global �nancial crisis with high debt, it is unlikely that development assistance will increase signi�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 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 bene�t all countries in the region.3 The challenging question, however, is how to �nance these projects. Electricity is a non-storable good that requires large speci�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 difference between electricity and the trade of standard commodities. In the absence of a binding commitment mechanism, �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 speci�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 �scal), governments focus on their own national welfare. Governments are biased in favor of their national (public) �rms because the governments are the residual claimant for their pro�ts and losses. Theoretically, the relevant analytical framework is asymmetric regulation (i.e., each �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 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 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 �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, Cˆ ote d’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 �rm is exposed to competition from a single strategic competitor. Allowing for horizontal and vertical differentiation, these authors �nd that competition helps to extract the information rent of the regulated �rm, but allocative inefficiency 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 difference between the two regions is sufficiently large. For the low-cost region, the bene�ts from increased export pro�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 bene�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 difference between the two countries is small. Indeed, unregulated competition tends to undermine the tax base (see Armstrong and Sappington 2005). Without a signi�cant technological gap, competition for market share is �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 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). Com- pared 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 7 Even 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. 8 This �nding 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 �rms bene�t from jointly reducing the subsidies. However, even if the bene�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 country’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 efficient technology increase. Second, when the two countries’ technologies are similar, the �rms must �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 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 �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 �rms’ 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 bene�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 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. Sec- tion 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, identi�ed by i = 1, 2. The inverse demand in each country is provided by 9 pi = d − 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., different 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 identi�ed by i ∈ {1, 2}. When the markets are integrated, Qi can be produced by both �rms 1 and 2 (i.e., Qi = qii + qji , i = j , where qij , is the quantity sold by �rm i in country j ). The total demand in the integrated market is given by Q p=d− (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 satis�ed by �rm 1 or 2 (i.e., Q = q1 + q2 ). On the production side, �rm i = 1, 2 incurs a �xed cost that measures the economies of scale in the industry. The �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 �rm also incurs a variable cost function provided by 2 qi c(θi , qi ) = θi qi + γ . (3) 2 The variable cost function includes both a linear term θi ∈ [θ, θ], which represents the production cost, and an additional quadratic term, weighted by γ , which represents a trans- portation 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 �rst separated in two contiguous segments (the �national markets�). Market integration corresponds to the uni- �cation of the two segments. The common market is then represented by the full Hotelling line. To serve consumers, �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 γ 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 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 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 ∈ [0, 1], the transportation cost is γq for �rm 1 and γ (1 − q ) for �rm 2. The variable q production cost of �rm i with market share equal to qi can then be written as c(θi , qi ) = 0 i (θi + γ q )dq , or 2 qi equivalently c(θi , qi ) = θi qi + γ 2 (i = 1, 2). 8 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.12 In summary, θi ∈ [θ, θ] can be interpreted as a generation cost that is constant after some �xed 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.13 To rule out the corner solution, we make the following assumption: A0 d > θ. Assumption A0 ensures that in equilibrium, the quantities are strictly positive. The pro�t of �rm i = 1, 2 is 2 qi Πi = P (Q)qi − θi qi − γ − ti (4) 2 where ti is the tax that the �rm pays to the government (it is a subsidy if it is negative). The participation constraint of the regulated �rm is Πi ≥ 0 (5) The regulator of country i has jurisdiction over the national monopoly i. She regulates the quantities and the investments of the �rm and is allowed to transfer funds to and from the �rm, and she taxes operating pro�ts when they are positive and subsidizes losses. This 12 For more details on the speci�cities of electric markets, see Joskow and Schmalensee 1985. 13 Because 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 F (θi ) f (θi ) , where f and F are the 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 �rms as compared to the national regulators. 9 process is consistent with public ownership. In the case of electricity, public and mixed �rms are key players in most developing countries: in 2004, 60% of the less developed countries had no signi�cant private participation in electricity (Estache, Perelman, and Trujillo 2005).14 In contrast, rent extraction does not apply to foreign �rms because they do not report their pro�ts locally. The regulator does not seize the rent of foreign �rm and does not have to subsidize the losses. Moreover, the regulator of country i does not control the production or the investment of �rm j (i.e., asymmetric regulation). Each utilitarian regulator in country i maximizes the home welfare, Wi = S (Qi ) − P (Q) Qi + Qi Q2 Πi + (1 + λ)ti , where S (Qi ) = 0 pi (Q)dQ = dQi − 2 i is the gross consumer surplus, Πi is the pro�t of the national �rm, and (1+ λ)ti is the opportunity cost of public transfers. Because Wi is decreasing in Πi when λ ≥ 0, leaving rents to the monopoly is socially costly. The participation constraint of the national �rm (5) always binds: Πi = 0.15 The utilitarian welfare function in country i = 1, 2 is 2 qi Wi = S (Qi ) − P (Q) Qi + (1 + λ)P (Q)qi − (1 + λ)(θi qi + γ ) (6) 2 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 �rm pro�t 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).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 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 �rm paid over EUR 2.4 billion in dividends to the government. 15 Here, 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. 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 bene�ts of alternative investment choices and spending. In advanced economies, λ 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 bene�t of the additional investment. Conversely, when the transfer is positive (i.e., taxes on pro�ts), it helps to reduce distortionary taxation or to �nance 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, +∞): λ Λ= ∈ [0, 1]. (7) 1+λ We �rst 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 C d − θi qi = . (8) 1+γ+Λ C) = When Λ = 0, public funds are costless, and the price is equal to the marginal cost P (qi C . When Λ > 0, the price is raised above the marginal cost with a rule that is inversely θi + γqi C) P (qi C ) = θ + γ qC + Λ proportional to the elasticity of demand (Ramsey pricing): P (qi i i ε . 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 �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 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. 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 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 �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 pro�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, �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 different, which implies a different level of production in the two countries. We �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 �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 de�ned in (6), 2 q1 q2 W = S (Q1 ) + S (Q2 ) + λP (Q)Q − (1 + λ)(θ1 q1 + γ + θ2 q2 + γ 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 − 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 ) + λP (q1 + q2 )(q1 + q2 ) − (1 + λ)(θ1 q1 + γ + θ2 q2 + γ 2 ) (10) 2 2 Let θmin = min{θ1 , θ2 } and ∆ = θ2 − θ1 , 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  2 ∗ 2γ (d−θmin )   1+Λ+2γ (d − θmin ) by monopoly if |∆| > ∆ = 1+2γ +Λ Q∗ = (11)   2 θ1 +θ2 ∗ Q∗ θj −θi 1+Λ+γ (d − 2 ) by duopoly i = 1, 2 with qi = 2 + 2γ otherwise. Proof. See Appendix A. When the cost difference between the two �rms is large (i.e., when |∆| > ∆∗ ), the less efficient producer is shut down, and the most efficient �rm is in a monopoly position. This result implies that when there is no transportation cost (i.e., γ = 0), the �rst best contract always prescribes the shut down of the less efficient �rm. However the �shut down� result is upset with the introduction of a transportation cost. When γ is positive, both �rms produce whenever |∆| ≤ ∆∗ . The most efficient �rm (i.e., the �rm with the cost parameter θmin ) has a larger market share than its competitor (see (11)). However, the market share differences decrease with γ . In practice, sectorial integration generally excludes �scal and political institutions, which remain decentralized at the country level.17 Sovereign governments and regulators do not share pro�ts and tariff revenues among themselves. Taxpayers enjoy taxation by regulation insofar as the rents come from their national �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 �x the 17 The fusion of regulatory bodies and �scal systems is rarely achieved. The German reuni�cation, with the East and West German economic systems uni�ed under the same government, is an exception. Consistent with the theory, many �rms have been shut down in East Germany. The reallocation of production toward more efficient units has been sustained by transfers from West Germany. 18 If 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, signi�cant 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. 14 O , maximizing national welfare (6). The reaction quantity produced by the national �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  2(1+2γ )(d−θmin )  4 O  3+4γ +Λ (d − θmin ) by monopoly if |∆| ≥ ∆ = 3+4γ +Λ QO = (12)   4 θ1 +θ2 O QO θj −θi 2+2γ +Λ (d − 2 ) by duopoly i = 1, 2 with qi = 2 + 1+2γ otherwise Proof. See Appendix B. Comparing equations (12) and (11), the equilibrium solution implies that the closure of the less efficient �rm occurs less often than in the socially optimal solution. That is, ∆O ≥ ∆∗ under assumption A0. Comparing the common market with the closed economy case, it is straightforward to check C + q C de�ned in equation (8). that QO de�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 |∆| ≤ ∆∗ , we have that QC = Q∗ de�ned in equation (11). We deduce that excessive production occurs in the common market. To be more speci�c, comparing QO and Q∗ yields (2γ +Λ)(d−θmin ) QO ≥ Q∗ ⇔ |∆| ≤ ∆O/∗ = 1+2γ +Λ . (13) When |∆| is smaller than ∆O/∗ , the regulators �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 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 �rm. In his attempt to mitigate the business stealing effect, the regulator increases the quantity of the domestic �rm so that 15 QO > Q∗ .19 Symmetrically, when |∆| is larger than ∆O/∗ , the regulator of the most efficient country controls a large market share (the �rm even becomes a monopolist in the common market when |∆| > ∆O ). The problem is that the regulator does not internalize the welfare of foreign consumers. She chooses a suboptimal production level QO < Q∗ . 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 �gure 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 pro�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 modi�ed when Λ > 0. When Λ > 0, the intercept corresponding 19 Substituting QO from equation (12) into market share equation qiO and comparing it with equation (8) yields O C Λ(d−θi )(1+γ ) qi > qi ⇔ θj − θi ≥ − (1+γ +Λ)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 efficient. The reason for this choice is that competition decreases the net pro�ts of the national �rm without generating a drastic increase in the consumers’ surplus. 16 to ∆ = 0, is negative, which means that if θ1 = θ2 , both countries lose from integration. To �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 efficiency because the �rms have the same cost. The net welfare impact is negative for both countries. For ∆ = 0, the welfare gains of the two countries are asymmetric. For the most efficient country, the gains are strictly increasing. For the less efficient country, they are U-shaped. For a large enough |∆|, the welfare gains are positive in both countries. O − W C. Figure 1: Welfare Gains from Integration, W1 1 The country with the less efficient technology generally has lower gains from integration ˆ ≥ ∆). The level of gains depends on the adverse effect of business stealing on the budget (∆ constraint of the less efficient �rm, which will in general receive a higher transfer (or pay lower taxes) in the common market. It is clear that for a ∆ belonging to the interval [−∆, ∆], the creation of a power pool managed by two independent regulators is inefficient. Each country’s welfare is decreased by integration. The region as a whole is better off 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 �rm reporting its pro�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 ˆ the most efficient country wins, and the less efficient country For values of |∆| ∈ [∆, ∆], loses. If one region loses and the other wins, there will be resistance to integration. In contrast, ˆ despite ˆ and larger than ∆ welfare increases in both countries for values of ∆ smaller than −∆ 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 (QO ) has redistributive effects. To see this point, let us focus on |∆| ≤ ∆O . Market integration induces a price reduction in country i = 1, 2 if and only if the cost difference is not Λ(d−θi ) 21 too large, that is, if θj − θi ≤ 1+γ +Λ . Consumers from the relatively efficient region are thus worse off after integration, which may be a source of social discontent and opposition toward sectorial integration. The interests of the national �rm/taxpayers conflict with the interests of the domestic consumers.22 If the government is unable to seize a �rm’s rents, both domestic taxpayers and consumers are worse off (shareholders are the only winners). Λ(d−θmin ) In contrast, if the �rms are not drastically different (i.e., if |∆| ≤ 1+γ +Λ ), prices decrease in both countries because of the business stealing effect. Benevolent regulators are willing to increase their transfers to the national �rm to sustain low prices so that taxation by regulation decreases, harming taxpayers and the total welfare. The negative �scal effect is a major concern 20 The trade and competition literature shows that when �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 �rms 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 �rms. 21 Substituting QO from equation (12) in the inverse demand function yields the equilibrium price P (QO ) = θ +θ d( Λ +γ )+ 1 2 2 2 1+γ + Λ if |∆| ≤ ∆O (θmin ). c Comparing this price with the price in the closed economy, P (qi ) = θi + (Λ + 2 d−θi γ ) 1+ γ +Λ yields the result. 22 In the international trade literature, a similar conflict of interest arises between domestic producers and consumers (see Feenstra, 2008). 18 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 �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 differ in other di- mensions. In particular, they may have different 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- �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 �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 inefficiency result yielded by sectoral integration is related to the limited set of tax instruments used by the regulator. We concentrate on the pro�t taxation of regulated �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 �x both the price and the tax on total industry pro�ts. In the integrated market, this irrelevant result does not hold because the national regulator is unable to tax the importing �rm’s pro�t or to control its offer. Competition for market share erodes the national �rm’s pro�t 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 �rms, she will be able to influence the volume of import. The regulator uses the tax structure to reduce the market share of the foreign �rm 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 �rms. Adding taxes to the volume of transactions could be used to generate income on the activities of the foreign �rm 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 �rm’s pro�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 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 23 To see this point more clearly, we focus on the case in which Λ = 0, so �scal 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. 20 to �nance new investment. Our analysis focuses on two types of investment. The �rst type reduces the production cost of the investing �rm (e.g., generation facilities). This investment is referred to as �production cost reducing� or �θ-reducing� investment. This type only bene�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 speci�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 θ1 to δ θ1 (δ < 1) by investing a �xed 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 �rm also bene�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 γ to sγ with s ∈ (0, 1) by investing a �xed 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 �rms is positive in the common market. The following assumption ensures that there is no closure in the �rst best case.24 2sγ (d−min{δθ1 ,θ2 }) A1 |θ2 − δθ1 | ≤ 1+2sγ +Λ . Investment in Generation We begin by considering the solution induced by the global welfare maximizer in the case ∗Iθ of a θ-reducing investment by �rm 1. The optimal quantities, denoted qi (i = 1, 2), are provided by equations (11), where θ1 is replaced by δθ1 (δ < 1). Substituting the quantities 24 Assumption A1, which is the condition in equation (11) with ∆∗ evaluated at δθ1 instead of θ1 and sγ instead of γ , ensures that both �rms produce in all possible cases. As illustrated by the analysis in Section 2, this assumption is not crucial, but it greatly simpli�es the exposition. Our results are preserved when the shut-down cases are considered (computations are available on request). 21 ∗Iθ qi (i = 1, 2) into the welfare function de�nes equation (10), and the gross utilitarian welfare is ∗Iθ ∗Iθ W ∗Iθ = W (q1 , q2 ). The welfare gain of the investment W ∗Iθ − W ∗ 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 �rm’s operating pro�t 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 ∗Iθ − W ∗ ≥ (1 + λ)Iθ . Let us ∗ as the maximal level of investment that satis�es this inequality: denote Iθ ∗ 1 Iθ = [W ∗Iθ − W ∗ ]. (14) 1+λ OIθ The non-cooperative equilibrium quantities in the case of sectoral integration, qi , and the CIθ quantities in the case of a closed economy, qi , are derived using a similar method from the equations (12) and (8), respectively, where θ1 is replaced by δθ1 . Substituting the quantities kIθ qi (i = 1, 2 and k = O, C ) in the welfare function of the country 1 de�ned in equation (6), the kIθ k ≥ (1 + λ)I . We deduce the maximal regulator of country 1 invests if and only if W1 − W1 θ level of investment that country 1 is willing to commit in the common market and in the closed economy: k 1 kIθ k Iθ = [W1 − W1 ] k = O, C. (15) 1+λ The next proposition compares the different investment levels (i.e., when k = ∗, O, C ) as a function of the initial cost difference ∆ = θ2 − θ1 . ∗ and I k (k = O, C ) be de�ned in Proposition 4 Let Λ > 0, δ ∈ (0, 1) and ∆ = θ2 − θ1 . Let Iθ θ ˆb < ∆ ˆa < ∆ (14) and (15), respectively. There are three thresholds ∆ ˆ c , such that ˆ a. O > IC ⇔ 0 > ∆ > ∆ • Iθ θ ˆ b. ∗ > IC ⇔ 0 > ∆ > ∆ • Iθ θ ˆ c. ∗ > IO ⇔ ∆ > ∆ • Iθ θ 22 Proof. See Appendix D. Figure 2 illustrates the results of Proposition 4. The �gure is drawn for a �xed value of δθ1 . C represents the autarky equilibrium The static comparative parameter is ∆. The flat line Iθ level of investment for country 1. This level is independent of the efficiency of �rm 2 (i.e., it is independent of ∆, hence the flat shape) because in the absence of trade, what happens in O country 2 does not influence the investment choice of the regulator in country 1. The line Iθ ∗ represents the optimal level. represents the equilibrium investment in the open market, and Iθ Both increase with ∆: the gains from trade and the incentives to invest are larger when the gap in generation costs is large. Figure 2: θ1 -Reducing Investment. 23 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 ˆa = ∆ ˆb = ∆ ˆc = (1−δ )θ1 ∆ 2 . In this case, market integration unambiguously reduces (without eliminating) the gap between the optimal and the equilibrium levels of investment. However, ˆ c shift to the left and to the right, respectively, whereas ∆ ˆ a and ∆ when Λ > 0, the thresholds ∆ ˆb is not affected (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 speci�c, 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, ˆ c , country 1 chooses a level of investment in autarky that is inefficiently low. The when ∆ > ∆ O region is endowed with abundant resources (e.g., hydroelectric potential), but the investment Iθ 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 ˆ c , the open market ∗ . However, it does not restore the �rst best level. When ∆ > ∆ level Iθ O is lower than the optimal level I ∗ because the investing country equilibrium of investment Iθ θ does not fully internalize the increase in the foreign consumer surplus (it only internalizes sales). ˆ a , country 1 is very inefficient.26 In autarky, the only way to increase the Second, when ∆ < ∆ 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 efficiency. The 25 O ∗ C When Λ increases, all thresholds Iθ , Iθ Iθ shift downward because the social cost of investment increases. O However, Iθ has less of a decrease because investment becomes important to reduce the business stealing effect in the common market. As a result, the region of over-investment increases. 26 Indeed, we �nd that ∆ ˆa < ∆ ˆ b < 0, and in the closed economy, investment is higher than the optimal value ˆ b. for the integrated market (i.e., it is inefficiently high) as soon as ∆ < ∆ 24 possibility of reducing the cost gap and expanding market share by serving foreign consumers O is higher than I ∗ ). makes a higher than optimal level of investment attractive (i.e., Iθ θ ˆ b , the level of investment is inefficiently high under both a closed and an ˆa < ∆ < ∆ For ∆ 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 efficiency of the national �rm. The �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 ˆ b ], ˆ a, ∆ with respect to autarky. However, the values of ∆ corresponding to this situation, [∆ ˆ , ∆] within which the country with the less efficient are generally included in the interval [−∆ technology would not accept integration in the �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 �nanced. 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 �rst consider the level of investment ∗Iγ induced by the global welfare maximizer. Let qi be the quantity produced by �rm 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 de�ned by ∗I ∗I equation (10) evaluated at the actualized quantities: W ∗Iγ = W (q1 γ , q2 γ ). The global welfare 27 There is an over-investment problem in the open market if ∆ ≤ ∆ ˆ c and in the closed economy if ∆ ≤ ∆ ˆ b. 28 We have tested many values for the parameters by simulations. The intervals ∆ ˆ b always fell in [−∆ ˆ a, ∆ ˆ , 0]. For instance, for d = 2, Λ = 0.15, θ1 = 1/2, δ = 9/10, and s = 9/10, we have that −∆ ˆ = −0.5, ∆ = 0.01, ∆ˆ a = −0.23, ∆ ˆ c = 0.02. Finally, the admissible values for ∆ under Assumption A1 are in the ˆ b = −0.08 and ∆ interval [−1.0, 0.57] 25 ∗ be the maximal level maximizer chooses to invest if and only if W ∗Iγ − W ∗ ≥ (1 + λ)Iγ . Let Iγ of investment that satis�es this inequality: ∗ 1 Iγ = [W ∗Iγ − W ∗ ]. (16) 1+λ The non-cooperative equilibrium investment level of market integration is obtained using OIγ a similar method. The quantity produced by �rm i after investment qi is obtained by sub- OIγ stituting sγ into equation (12). Let Wi be the i = 1, 2 welfare function (6) of country i OIγ OIγ evaluated at (q1 , q2 ). The maximum level of investment that country i is willing to make in the common market is O 1 OI Iγi = max 0, [W γ − WiO ] . (17) 1+λ i 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 �rm. 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 O can be equal to zero. In particular, this occurs for large values of Λ (see be negative, so Iγi 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 �rm is always positive and higher than the maximal level of investment for the less efficient �rm. Because the γ -reducing investment is a public good, in the common market, the level of investment that each country is willing to �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 �rm i, i = j invests with probability πi = OIγ O Wj −(1+λ)Iγ −Wj OIγ O . This equilibrium is inefficient because, with positive probability, either both �rms invest Wj −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 γ be the maximal level of investment for the more efficient �rm and I O γ be the maximal level of investment for the less efficient �rm, as de�ned in (17). O • If Iγ > I γ , there is no investment. O • If I O γ < Iγ , ≤ I γ , the more efficient �rm is the only one to invest. • If Iγ ≤ I O γ , there are two Nash equilibria in pure strategy in which one of the �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 �rms invests, whereas the other free rides on the investment. The decision of the most efficient �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 γ -reducing technology is always suboptimal: O O Iγ ≤ Iγ + IO ∗ γ ≤ Iγ ∀∆, Λ ≥ 0. (18) Proof. See Appendix E. In our speci�cation, 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 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 efficient �rm is willing to sustain relatively high levels of investment, and both �rms are able to sustain lower levels. Because of the public good nature of the investment, the identity of the investing �rm in this case is not important (and, in practice, might be determined by local circumstances). Our model only predicts that one of the �rms will always want to invest for the de�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 γ + I O γ would still be sub-optimal. To analyze the origin of this inefficiency, it is useful to study the countries’ incentives to invest in a closed economy. CIγ Let qi be the quantity produced by �rm i in the case of an investment in a closed economy. CIγ CIγ qi is obtained by substituting sγ into equation (8). Let Wi be the welfare function of CIγ country i = 1, 2 (6), evaluated at qi . The investment is optimal in country i if and only if CIγ Wi − WiC ≥ (1 + λ)Iγ so that C 1 CI Iγi = [W γ − WiC ]. (19) 1+λ i Comparing (19) with (17) yields the next proposition. C be the maximal amount that the most efficient country is willing to Proposition 6 Let Iγ O be the maximal amount invest to reduce transportation costs in the closed economy, and let Iγ ˜ > 0 such that Iγ that it is willing to invest in the common market. There exists a ∆ O > I C if γ ˜. and only if |∆| > ∆ 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 �nance new investment. Market integration may thus generate an insufficient level of γ -reducing investment for two reasons. The �rst reason is that investment has a public good nature. The investing country does not internalize the bene�ts of foreign stakeholders. The second reason is that 28 investment decreases the competitor’s costs, worsening the business stealing effect.31 Figure 3 illustrates the results of Propositions 5 and 6. Figure 3: γ -Reducing Investment. ˜ the maximal level Under market integration, when ∆ is relatively small (i.e., (|∆| ≤ ∆), of investment is not only sub-optimal but is also smaller than under a closed economy. When the two regions’ costs are not drastically different, business stealing is �erce. Business stealing reduces the capacity to �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 ˜ is higher than ∆, efficient country can resist integration. Indeed, simulations suggest that ∆ the threshold above which the most efficient country would win from market integration, but ˆ the equivalent threshold for the less efficient country (see Figure 1).32 below ∆, 31 O C O C In contrast, for Λ = 0, Iγ > Iγ ∀∆ ≥ 0 and Iγ − Iγ is an increasing function of ∆. 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 ∆ ˜ was always larger than 29 ˜ it is willing In contrast, when one country has a signi�cant cost advantage (i.e., |∆| > ∆), to invest more in the common market than under a closed economy because the investment in- creases its market share and pro�ts. Integration can then help to increase investment, although not to the �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 inefficiently 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 pro�table 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 over- investment 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, θ1 = 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]. 33 When 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 ∆ ˜ , −∆ ˆ b < θ1 − θ2 < min{∆ ˆ b } with ∆˜ de�ned 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. 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 �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 �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 �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 tariffs needed to repay the loans that �nanced the investment. Based on the CRIE experience, the West African power pool (WAPP) is egulation R´ also working on the creation of a regional regulatory body, �Organe de 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 �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 �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 ∈ {1, 2}. The �rst-order condition provides qi + qj (1 + λ)(d − qi (1 + γ ) − qj − θi ) + = 0. (20) 2 First, consider the interior solution. Solving the system characterized in (20) for i = 1, 2 and λ allowing Λ = 1+λ , we obtain ∗ d − θ1 + 2 θ2 θj − θi qi = + . (21) 1+Λ+γ 2γ In this case, the total quantity Q is provided by d − θ1 + θ2 Q∗ = q1 + q2 = 2 2 . 1+Λ+γ 2γ (d−θj ) We now consider the shut-down case qi = 0. This case arises when θi − θj ≥ 1+2γ +Λ . In this case, only the most efficient �rm j is allowed to produce, and the total quantity is provided by ∗ (d − θj ) qj = Q∗ = 2 . 1 + 2γ + Λ If θi < θj , a symmetric condition describes the shut down case for �rm j , i = j , i.e., θj − θi ≥ 2γ (d−θi ) 1+2γ +Λ . Allowing θmin = min{θ1 , θ2 } and |∆| = |θ2 − θ1 | = |θ1 − θ2 |, 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 �rst-order condition: 1 (1 + λ)(d − θi ) − [qj (1 + 2λ) + qi (3 + 4λ + 4γ (1 + λ))] = 0. (22) 4 λ Rearranging terms and allowing Λ = 1+λ , we obtain the reaction function of regulator i to the quantity induced by regulator j (i = j ), namely qi (qj ) 4(d − θi ) − qj (1 + Λ) qi (qj ) = . (23) 3 + Λ + 4.γ 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 − θ1 + 2 θ2 θj − θi qi =4 + . (24) 2(1 + γ ) + Λ 1 + 2γ In this case, the total quantity Q is provided by d − θ1 + θ2 O QO = q1 O + q2 =4 2 . 2(1 + γ ). + Λ However, we must also consider the shut-down case qi = 0. This situation arises when qj ≥ 4 d −θi 1+Λ 2(1+2γ )(d−θi ) or, equivalently, θi − θj ≥ 3+4γ +Λ < 0. The shut-down case is thus written, for θi > θj , d − θj QO = qj (qi = 0) = 4 . 3 + 4γ + Λ If θi < θj , a symmetric condition describes the shut-down case for �rm j , i = j . Letting θmin = min{θ1 , θ2 } and |∆| = |θ2 − θ1 | = |θ1 − θ2 |, 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 Q∗ , QO and QC as a function of |∆|. Figure 4 illustrates the quantities result, representing, for a given θmin , the quantity levels Q∗ , QO and QC in the function of |∆| ∈ [0, d]. The flat sections correspond to the shut down of the less efficient producer. Finally, comparing the shut-down threshold in the optimal case with the shut-down threshold of the less efficient �rm in the integrated market with independent regulators yields ∆O > ∆∗ . Figure 5 illustrates this result. The solid lines represent the equilibrium shut-down threshold of the less efficient �rm in the integrated market with independent regulators. The dotted lines represent the optimal threshold. The �gure is plotted for d = 1, Λ = 0.3, γ = 0.5, θi ∈ [0, 1] 2γ (d−θmin ) and θmin = 0. The same shape is obtained for any support, such as θ − θ > 1+2γ +Λ . C. Proof of Proposition 3 Consider country 1 (the same holds for country 2, inverting θ1 and θ2 and replacing ∆ with −∆ in all expressions). Making a replacement for the participation constraint of the national �rm, the welfare in country 1 in the case of closed economy is written as C q1 C W1 C = S (q1 C C ) + λP (q1 )q1 − (1 + λ)(θ1 + γ )q C (25) 2 1 34 Figure 5: Shut Down Threshold of the Less-Efficient 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 ) − P (Q )Q1 + λP (Q )q1 − (1 + λ)(θ1 + γ )q O . (26) 2 1 Substituting for the value of the quantities (8) and (12) in (25) and (26), respectively, we O − W C. compute the welfare gains from integration W1 1 O C W1 − W1 = ∆2 Γ1 (γ, Λ) + ∆(d − θ1 )Γ2 (γ, Λ) + (d − θ1 )2 Γ3 (γ, Λ), where     2 (3+4γ +Λ)2 , if ∆ < − 2(1+2γ )(d−θ2 ) 3+4γ +Λ ; (1+γ (1−Λ))(3+4γ +Λ) Γ1 (γ, Λ) = 2(1+2γ )2 (1−Λ)(2(1+γ )+Λ)2 , if − 2(1+2γ )(d−θ2 ) 3+4γ +Λ ≤∆≤ 2(1+2γ )(d−θ1 ) 3+4γ +Λ ;    0, if ∆ > 2(1+2γ )(d−θ1 ) . 3+4γ +Λ    − (3+4γ +Λ)2 ,  8 if ∆ < − 2(1+2γ )(d−θ2 ) 3+4γ +Λ ; Λ(3+4γ +Λ) Γ2 (γ, Λ) = (1+2γ )(1+Λ)(2(1+γ )+Λ)2 , if − 2(1+2 γ )(d−θ2 ) 3+4γ +Λ ≤ ∆ ≤ 2(1+2 γ )(d−θ1 ) 3+4γ +Λ ;    0, 2(1+2γ )(d−θ1 ) if ∆ > 3+4γ +Λ .   15+16γ 2 +4γ (5+3Λ)+Λ(6+5Λ) 2(1+2γ )(d−θ2 )  2(1−Λ)(1+γ +Λ)(3+4γ +Λ)2 , if ∆ < − 3+4γ +Λ ;  Λ2 Γ3 (γ, Λ) = − 2(1−Λ)(1+γ +Λ)(2(1+ γ )+Λ)2 , if − 2(1+2 γ )(d−θ2 ) 3+4γ +Λ ≤ ∆ ≤ 2(1+2 γ )(d−θ1 ) 3+4γ +Λ ;    1+3Λ , if ∆ > 2(1+2γ )(d−θ1 ) . 2(1−Λ)(1+γ +Λ)(3+4γ +Λ) 3+4γ +Λ 35 O − W C is a U-shaped function of ∆. For Λ = 0, W O − W C is always non-negative, with W1 1 1 1 O − W C = 0. For Λ > 0, the minimum is attained in ∆ = the minimum ∆ = 0, where W1 1 2 − Λ(1+2γ )(d−θ1 ) 1+γ (1+Λ) O − WC = − < 0. In this case, in ∆ = 0, W1 1 Λ 2(1−Λ)(1+γ +Λ)(2(1+γ )+Λ)2 < 0. The U shape and the condition |∆| ≤ 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 de�ned in (26), and with investment, it is OIθ OIθ q1 W1 = S (QOI 1 ) − P (Q θ OIθ )QOI 1 θ OIθ + λP (QOIθ )q1 − (1 + λ)(δθ1 + γ OIθ )q1 − (1 + λ)Iθ . 2 Replacing for the relevant quantities in Equation (15) and rearranging terms, we obtain (1+δ )θ1 ∆ (1−δ )θ1 (1 − δ )θ1 d − 2 + (1 + Λ) 2γ + 4γ ∗ Iθ = 1+γ+Λ (1+δ )θ1 (1 − δ )θ1 d − 2 C Iθ = 1+γ+Λ (1+δ )θ1 ∆ (1−δ )θ1 (1 − δ )θ1 d− 2 (4 + 8γ 2 + (3 + Λ)(Λ + 4γ )) + 1+2γ + 2(1+2γ ) (1 + Λ)(3 + 4γ + Λ) O Iθ = . (1 + 2γ )(2(1 + γ ) + Λ)2 ∗ > I C if and only if Then, Iθ θ ˆ a = − (1 − δ )θ1 − d − (1 + δ )θ1 Γi ∆>∆ 1 (γ, Λ), 2 2 where 2Λγ (1 + 2γ )(3 + 4γ 2 + Λ(3 + Λ + γ (7 + 3Λ)) Γi 1 (γ, Λ) = (1 + Λ)(8γ 4 + (2 + λ)2 + 2γ (3 + Λ)2 + γ 3 (26 + 6Λ) + 2γ 2 (16 + Λ(7 + Λ))) ∗ > I O if and only if Iθ θ ˆ b = − (1 − δ )θ1 ∆>∆ 2 36 O > I O if and only if Iθ θ ˆ c = − (1 − δ )θ1 + d − (1 + δ )θ1 Γi ∆>∆ 2 (γ, Λ) 2 2 where Λ(1 + 2γ )(3 + 4γ 2 + Λ(3 + Λ + γ (7 + 3Λ))) Γi 2 (γ, Λ) = (1 + Λ)(1 + γ )(1 + γ + Λ)(3 + 4γ + Λ) ˆa = ∆ It is easy to see that if Λ = 0, ∆ ˆ c = − (1−δ)θ1 < 0. Moreover, for all Λ > 0, ˆb = ∆ 2 ˆb < ∆ ˆa < ∆ ∆ ˆ a decreases in Λ, while ∆ ˆ c . Finally, ∆ ˆ c is ˆ c increases. For a large enough Λ, ∆ 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 OIγ OI OIγ OI q γ OI W1 γ = S (Q1 γ ) − P (Q )Q1 γ + λP (Q )q1 γ − (1 + λ)(θ1 + sγ 1 )q1 γ − (1 + λ)Iγ . 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 Iγ 1 = ∆ Γ1 (γ, Λ) + (d − θ1 )∆Γ2 (γ, Λ) + (d − θ1 ) Γ3 (γ, Λ), where (1 + sγ (1 − Λ))(3 + 4sγ + Λ) (1 + γ (1 − Λ))(3 + 4γ + Λ) Γii 1 (γ, Λ) = − (1 + 2sγ )2 (2(1 + sγ ) + Λ)2 (1 + 2γ )2 (2(1 + γ ) + Λ)2 Λ(3 + 4sγ + Λ) Λ(3 + 4γ + Λ) Γii 2 (γ, Λ) = 2 − (1 + 2sγ )(2(1 + sγ ) + Λ) (1 + 2γ )(2(1 + γ ) + Λ)2 2(1 − s)γ (4(1 + γ )(1 + sγ ) − Λ)2 Γii 3 (γ, Λ) = (1 + 2sγ )2 (2(1 + sγ ) + Λ)2 Γii ii O 1 (γ, Λ) and Γ2 (γ, Λ) are positive ∀s ∈ (0, 1), Λ ∈ [0, 1). Iγi is an upward-sloping parabola with (d−θi )Γii 2 (γ,Λ) its axis of symmetry in ∆ = − 2Γii ( γ, Λ) < 0, implying the following result: 1 37 O > I O if and only if θ < θ . Result 1 Iγ 1 γ2 1 2 O By de�nition, this implies that I γ > I O γ . This result is useful to prove Lemma 1. Proof of Lemma 1 Because investment reduces the costs of both �rms, if one �rm invests, the best response of the other is to not invest. However, if one �rm does not invest, the best response of the O . From Result 1, we know that I O O other �rm is to invest whenever Iγ < Iγi γ > I γ . Then, for O IO O γ < Iγ < I γ , the less efficient �rm never invests, and the more efficient �rm does. For Iγ < I γ , a �rm invests if and only if the other �rm does not. O ∗ and the Before comparing the maximum level of investment I γ with the optimal level Iγ ∗ closed economy I γ , we prove that a γ -investment can reduce the welfare of the less efficient O ∂Iγ O country. We have ∂∆ 1 = 2∆Γii ii 1 (γ, Λ) + (d − θ1 )Γ2 (γ, Λ). Then, I γ is strictly positive and I increasing in |∆|, while I O O γ γ is U shaped. The sign of I γ is thus ambiguous. Let W1 − W1 be the impact of γ -reducing investment country 1 when ∆ < 0 (i.e., θ2 < θ1 ). By the de�nition of IO γ , we can write I IO γ W1 γ − W1 = . 1−Λ Then, the welfare gains of country 1 are positive if and only if I O O γ is positive. If ∆ = 0, I γ is positive and decreasing in |∆|. We must prove that I O γ might be negative for some ∆ < 0. In I sγ )(d−θ2 ) ∆ = − 2(1+21+Λ (the minimal admissible value under A1), W1 γ − W1 is negative if and only √ 9+8sγ +4γ (10+7sγ +γ (3+γ (1+s))(5+γ (1+s)))−(1+2γ (2+γ (1+s))) if Λ > Λ = 1+2γ . Then, Λ > Λ is a sufficient (although non-necessary) condition to achieve gains in the less efficient country that are smaller than zero for some ∆ < 0. Proof of Proposition 5 ∗Iγ ∗I ∗ + q ∗ and Q∗Iγ = q Let Q∗ = q1 2 1 + q2 γ . The maximal investment at the global optimum is 38 de�ned by (16). Global welfare in the case of non-investment and investment are, respectively, ∗ q1 ∗ q2 W ∗ = S (Q∗ ) + λP (Q∗ )Q∗ − (1 + λ)(θ1 + γ ∗ 2 )q1 − (1 + λ)(θ2 + γ ∗ 2 )q2 ∗I ∗I q1 γ q2 γ ∗Iγ W ∗Iγ = S (Q∗Iγ ) + λP (Q∗Iγ )Q∗Iγ − (1 + λ)(θ1 + sγ 2 ∗ )q1 − (1 + λ)(θ2 + sγ 2 )q2 − (1 + λ)Iγ Replacing for the relevant quantities and rearranging terms, we obtain ∗ Iγ = ∆2 Γiii iii 2 iii 1 (γ, Λ) + (d − θmin )|∆|Γ2 (γ, Λ) + (d − θmin ) Γ3 (γ, Λ), where 1−s 1 γ2 Γiii 1 (γ, Λ) = + 4γ s (1 + sγ + Λ)(1 + γ + Λ) (1 − s)γ Γiii 2 (γ, Λ) = − (1 + γ + Λ)(1 + sγ + Λ) (1 − s)γ Γiii 3 (γ, Λ) = (1 + γ + Λ)(1 + sγ + Λ) ∗ is symmetric with respect to the origin (∆ = 0) because at the global optimum, production Iγ is always reallocated in favor of the most efficient �rm. Moreover, for both ∆ > 0 and ∆ < 0, production is U-shaped in ∆ (Γiii 1 (γ, Λ) > 0, ∀s ∈ (0, 1), Λ ∈ [0, 1), γ ≥ 0). ∗ and I O . We now compare the thresholds Iγ γ ∗ O Iγ − Iγ = ∆2 Γiv iv 2 iv 1 (γ, Λ) + (d − θi )∆Γ2 (γ, Λ) − (d − θi ) Γ3 (γ, Λ) 1 1 2(1 + sγ (1 − Λ))(3 + 4sγ + Λ) Γiv 1 (γ, Λ) = + − sγ 1 + sγ + Λ (2(1 + sγ ))(2(1 + sγ ) + Λ)2 1 1 2(1 + γ (1 − Λ))(3 + 4γ + Λ) − − + γ 1+γ+Λ (2(1 + γ ))(2(1 + γ ) + Λ)2 1 1 4(1 + sγ )2 + Λ Γiv 2 ( γ, Λ) = − − + 1 + 2sγ 1 + sγ + Λ (1 + 2sγ )((2(1 + sγ ) + Λ)2 ) 1 1 4(1 + γ )2 + Λ + + − 1 + 2γ 1 + γ + Λ (1 + 2γ )((2(1 + γ ) + Λ)2 ) 1 2(1 + sγ ) 1 2(1 + γ ) Γiv 3 (γ, Λ) = − 2 − + 1 + sγ + Λ (2(1 + sγ ) + Λ) 1 + γ + Λ (2(1 + γ ) + Λ)2 Γiv ∗ O 1 (γ, Λ) is positive for all s ∈ (0, 1), Λ ∈ [0, 1), γ > 0. Then, Iγ − Iγ is a U-shaped function of ∗ − I O decreases with Λ. An increase in Λ shifts the U ∆. Moreover, one can easily show that Iγ γ 39 ∗ − I O to always be positive is to have curve downwards. Therefore, a sufficient condition for Iγ γ ∗ − I O is a convex function of ∆, the minimum is a positive minimum when Λ = 1. Because Iγ γ ∗ −I O ) ∂ (Iγ γ obtained from the �rst-order condition ∂∆ = 0. In Λ = 1, this minimum is equal to [(1 − s)2 (57 + 292(1 + s)γ + 252(1 + s(3 + 2s))γ 2 + 48(1 + s)(7 + s(12 + 7s))γ 3 + 16(5 + s(33 + s(43 + s(33 + 5s))))γ 4 + 28s(1 + s)(1 + s(1 + s))γ 5 + 64s2 (1 + s2 )γ 6 )]/[s(2 + γ )(2 + sγ )(1 + 2sγ )2 (3 + 2sγ )2 (3 + 4γ (2 + γ ))] > 0 ∀ s ∈ (0, 1). ∗ − I O is always positive. Then, Iγ γ O ∗ − I − I O is also positive. If I O = 0, then I + I O = I O O We now show that Iγ γ γ γ γ γ γ and the result has been proved above. If I O γ > 0, we have O Iγ + IO 2 v v 2 v γ = ∆ Γ1 (γ, Λ) + (d − θi )∆Γ2 (γ, Λ) + (d − θi ) Γ3 (γ, Λ), where (1 − s)γ (3 + 4(γ + sγ (1 + γ )) 1+γ 1 + sγ Γv 1 (γ, Λ) = 2 2 − 2 + (1 + 2γ ) (1 + 2sγ ) (2(1 + γ ) + Λ) (2(1 + sγ ) + Λ)2 2 4(1 − s)γ (4(1 + γ )(1 + sγ ) − Λ ) Γv 2 (γ, Λ) = − (2(1 + γ ) + Λ)2 (2(1 + sγ ) + Λ)2 4(1 − s)γ (4(1 + γ )(1 + sγ ) − Λ2 ) Γv 3 ( γ, Λ) = . (2(1 + γ ) + Λ)2 (2(1 + sγ ) + Λ)2 Then, ∗ O Iγ − Iγ − IO 2 vi vi 2 vi γ = ∆ Γ1 (γ, Λ) + (d − θi )∆Γ2 (γ, Λ) − (d − θi ) Γ3 (γ, Λ), where 1+γ 1 + sγ 1 1 Γvi 1 (γ, Λ) = 2 − 2 − + (2(1 + γ ) + Λ) (2(1 + sγ ) + Λ) 4(1 + γ + Λ) 4(1 + sγ + Λ) 1 1 − + 4γ (1 + 2γ )2 4sγ (1 + 2sγ )2 1 1 4(1 + γ ) 4(1 + sγ ) Γvi 2 (γ, Λ) = − + 2 − (1 + γ + Λ) (1 + sγ + Λ) (2(1 + γ ) + Λ) (2(1 + sγ ) + Λ)2 (1 − s)γ Λ2 4(1 + s(1 + s))γ 2 + 4(1 + s)γ (3 + 2Λ) + (2 + Λ)(6 + 5Λ) Γvi 3 (γ, Λ) = (1 + γ + Λ)(1 + sγ + Λ)(2(1 + γ ) + Λ)2 (2(1 + sγ ) + Λ)2 40 Γvi ∗ J 1 (γ, Λ) is positive for s ∈ (0, 1), Λ ∈ [0, 1), γ ≥ 0, then Iγ − Iγ is a convex U-shaped function ∗ − I J is decreasing with Λ. Then the of ∆. Moreover, one can verify that the difference Iγ γ difference is minimal in Λ = 0, where ∗ O γ (1 + 2γ )2 − sγ (1 + 2sγ )2 Iγ − Iγ − IO γ = > 0, ∀ s ∈ (0, 1) 4γ (1 + 2γ )2 (1 + 2sγ )2 O ∗ − I − I O is always positive. Then, Iγ γ γ F. Proof of Proposition 6 In the case of a closed economy, welfare with no investment is given by (25). If Iγ is invested, the welfare function becomes C qi CIγ CIγ CIγ CIγ CI Wi = S (qi ) + λP (qi )qi − (1 + λ)(θi + sγ )q γ − (1 + λ)Iγ . 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 − s)γ (d − θi )2 Iγi = . 2(1 + γ + Λ)(1 + sγ + Λ) C is smaller than I ∗ . Because I ∗ is a convex function of ∆, whereas We �rst check that Iγ γ γ C is constant, I O − I C is also convex in ∆. Iγ O − I C is zero at ∆ = The derivative ofIγ γ γ γ 2sγ 2 (d−θi ) 2sγ 2 +(1+s)γ (1+Λ)+(1+Λ2 ) , where it reaches the minimum value: (1 + s)γ (d − θi )2 (1 + Λ)(1 + γ (1 + s) + Λ) > 0. 2(1 + γ + Λ)(1 + sγ + Λ)(2sγ + (1 + s)γ (1 + Λ)(1 + γ )2 ) O − I C is always positive. Then, Iγ γ O and I C . Because I O is increasing and convex and I C is constant, We now compare Iγ γ γ γ O − I C is also increasing and convex in ∆. In particular, if Λ = 0, Iγ γ O C (1 − s)γ (11 + 4γ (3(2 + γ ) + s(3 + 4γ )(2 + γ (1 + s)))) 2 Iγ − Iγ = ∆ ≥ 0 ∀s ∈ (0, 1). 8(1 + γ )(1 + sγ )(1 + 2γ )2 (1 + 2sγ )2 O − I C is increasing with |∆|. Then, for Λ = 0, the minimum is attained in ∆ = 0, and Iγ γ However, if Λ > 0 and ∆ = 0, 41 O C 1 1 1 4(1 + sγ ) 4(1 + γ ) Iγ −Iγ = − (1−s)γ (d−θi )2 − + − . 2 (1 + sγ + Λ) (1 + γ + Λ) (2(1 + sγ ) + Λ) (2(1 + γ ) + Λ) O, This result is negative for all s ∈ (0, 1), Λ ∈ [0, 1), γ ≥ 0. From the increasing shape of Iγ ˜ IO > IC. ˜ > 0 such that for all ∆ > ∆, there exists a ∆ γ γ G. Asymmetric Demand In the main text, we have assumed that countries only differ in their available technology. We now check the robustness of our results to the case in which demands are asymmetric. Let pi = di − 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 } > θ. 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 − 2 with Q = q1 + q2 . Full integration In the case of full integration, we �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 − 2 , i Q1 +Q2 di −dj we deduce that Qi = 2 + 2 . Computing the total consumer surplus S1 (Q1 ) + S2 (Q2 ), (d1 −d2 )2 d1 +d2 1 we now obtain S1 (Q1 ) + S2 (Q2 ) = 4 + 2 (Q1 + Q2 ) − 4 (Q1 + Q2 )2 . Substituting this expression into the total welfare function (9), the maximization problem of the supranational (d1 −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 ∗ − W C and compare them with those obtained in the base case of gains from integration Wasy asy symmetric demand. ∗ C (d2 − d1 ) (d2 − d1 ) 2γ (1 − Λ) − 2Λ2 + 1 + 2∆ Wasy − Wasy = W∗ − WC + ≥0 (28) 4(1 − Λ)(γ + Λ + 1) The additional term in the welfare gains can be positive or negative. The term is positive when d2 − d1 is positive and ∆ = θ2 − θ1 is relatively large and when d2 − d1 is negative and ∆ is relatively small. Demand asymmetry plays a similar role to cost asymmetry. To see this point, consider the limit case in which ∆ = 0 (i.e., generation costs are identical). This case implies that 1+Λ 2γ (1−Λ)−2Λ2 +1 W ∗ −W C = 4γ (1−Λ)(1+γ +Λ) ∆ 2 ∗ −W C = = 0 and that Wasy asy 2 4(1−Λ)(1+γ +Λ) (d2 − 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 efficient one, integration allows the regulator to expand the smaller country’s market share to exploit the low generation and transportation costs. Reallocating production toward the producer with the smaller national market increases productive efficiency and the total welfare gains from trade. Sectorial integration with asymmetric regulation Q2 Q di −dj Consumer surplus is written Si (Qi ) = di Qi − 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 − θ1 + 2 θ2 θj − θi (1 − Λ)(di − dj ) qi =4 + + . (29) 2(1 + γ ) + Λ 1 + 2γ 2 + 4γ 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 − W1,asy , is equal to the gain obtained in the symmetric case plus an additional term ζ (d2 − d1 , ∆, Λ, γ, θ1 ): O C O C W1 ,asy − W1,asy = W1 − W1 + ζ (d2 − d1 , ∆, Λ, γ, θ1 ) where 1 ζ (d2 − d1 , ∆, Λ, γ, θ1 ) = (d2 − d1 )∆φ1 (γ, Λ) + (d2 − d1 )2 φ2 (γ, Λ) + (d2 − d1 )(d1 − θ1 )φ3 (γ, Λ) 8 and 4γ (3 + 4γ + Λ) φ1 (γ, Λ) = ≥0 (1 + 2γ )2 (2 + 2γ + Λ) 8γ 4 (1 − Λ) + 2γ 3 ((4 − 7Λ)Λ + 7) + γ 2 (6 + Λ(19 + (2 − 7Λ)Λ) + 6) + Λγ (3 − Λ)(2 + Λ(4 + Λ)) + Λ2 (2 + Λ) φ2 (γ, Λ) = ≥0 (1 + 2γ )2 (1 − Λ)(1 + γ + Λ)(2 + 2γ + Λ) 4Λ 4γ 2 + γ (3 + 5Λ) + Λ(2 + Λ) φ3 (γ, Λ) = ≥0 (1 + 2γ )(1 − Λ)(1 + γ + Λ)(2 + 2γ + Λ) The additional effect ζ is decomposed into three terms. The �rst term, which is identical for both countries, has the sign of (d2 − d1 )∆: it is positive whenever (d2 − d1 ) and ∆ = θ2 − θ1 have the same sign. These variables have the same sign when country 1 is small and possesses the most efficient technology or when it is large and endowed with the less efficient technology. The second term is always positive and increases with the absolute value of (d2 − d1 ). This term is also identical for both countries. This term captures the efficiency gains related to production reallocation in the presence of a positive quadratic transportation cost. Finally, because (di − θi ) is always positive by assumption A0, the third term has the sign of (dj − di ) for country i, meaning that it is positive for the smallest country and negative for the largest one. Because the �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 effect of ζ depends on the opportunity cost of public funds. When Λ is relatively small, the �rst term in ζ is the largest. Compared to the base case, the welfare gains increase when the smallest country is also the most efficient. In contrast, the two effects (i.e., generation and transportation costs) contradict each other when the large country is the most efficient, so the welfare gains are lower than in the base case. Now, for large values of Λ, the third term in ζ tends to be the largest, unless γ is also very large. Thus, for a sufficiently large Λ, 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 result–that market integration is welfare degrading when countries are too similar and that �scal issues are important–is robust to asymmetric demand. Let ∆ = 0. The welfare gains are written as O C 2 1 W1 ,asy − W1,asy = Γ1 (Λ, γ )(d − θ1 ) + (d2 − d1 )2 φ2 (γ, Λ) + (d2 − d1 )(d1 − θ1 )φ3 (γ, Λ) 8 1 Λ2 where Γ1 (Λ, γ ) = − 4 (1−Λ)(1+γ +Λ)(2+2γ +Λ)2 < 0. For d2 = d1 , the term Γ1 (Λ, γ )(d − θ1 )2 corre- sponds to the welfare gains in the base model (see Appendix C when ∆ = 0). If Λ > 0, then the welfare gains are always negative for d1 = d2 and ∆ = 0. By continuity, this net welfare loss result holds true for strictly positive values of |d2 − d1 |, as illustrated in �gures 6 and 7. These �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 − d1 when ∆ = 0. 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