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Competition in Electric Energy Network *

The paper studies the effects of decentralization and competition on the efficiency of markets for electric power. Theoretical conclusions are drawn from a stylized theoretical model which includes the most important topological structure of the market linking spatially separated producers and consumers into a network. Since transmission has a cost, such a link leads to potential price decline but not always increases social welfare measured as the sum of producer and consumer surplus. It is shown that regulation of grid owner remains an important instrument since his profit maximization leads to an increase of transmission costs and generally reduces social surplus. The paper studies when decentralization via privatization of generators can increase efficiency through spatial competition.

Competition in Electric Energy Network∗ Yuri Yegorov† 7 June 2003 Abstract The paper studies the effects of decentralization and competition on the efficiency of markets for electric power. Theoretical conclusions are drawn from a stylized theoretical model which includes the most important topological structure of the market linking spatially separated producers and consumers into a network. Since transmission has a cost, such a link leads to potential price decline but not always increases social welfare measured as the sum of producer and consumer surplus. It is shown that regulation of grid owner remains an important instrument since his profit maximization leads to an increase of transmission costs and generally reduces social surplus. The paper studies when decentralization via privatization of generators can increase efficiency through spatial competition. JEL Classification: L11, L51, L94, N70. KEYWORDS: electric energy, spatial competition, decentralization, efficiency. ∗ The paper was written in CEU, Budapest, in 2001-2002. This version is prepared for presentation at the seminar in IAS, 18 June 2003. I am grateful to Radmilo Pesic, Andrzej Baniak(Central European University, Budapest) and participants of ASPE Conference ”Public Sector Transition” (St.Petersburg, May 2001) for useful comments and discussions. † Author’s address: Institute for Advanced Studies, Stumpergasse 56, A-1060, Vienna, Austria; e-mail: [email protected] 1 1 Introduction There is an evidence of a growing interest of economists to the functioning of markets for electricity which has both theoretical and empirical background. From empirical perspective, such an interest emerges from the processes of privatization and deregulation of electric industry in different countries. While they aim to reduce monopoly power and increase competition, the evidence about welfare increase is mixed and will be discusses subsequently. From a theoretical perspective, such a market differs from those usually considered by economists since it has a special network structure. Electric system is organized like an organism. While the impact of misfunctioning of one element on usual market is small, the same cannot be said about network industries. Electric industry is even less robust to such kinds of element damage than internet or mobile phones, which include a possibility of transmission via a set of parallel channels. Not only damage but a simple congestion in a part of a network poses a negative externality for the whole system. Another problem is non-storability. There also exist more specific technical constraints which require some minimal level of cooperation among the participants of the market, which is not necessarily ensured after decentralization and deregulation. Under some constraints it may not function at all.1 We need to understand under what conditions it can function in the best manner. The present paper has two basic goals. The first is to show that pure traditional economic theories which do not take into account particular network structure of electrical systems may lead to misleading advises related to efficiency improvement. The second is to discuss a real possibility to improve efficiency into electrical system. This possibility is based on creation of an environment of spatial competition across otherwise local monopolists. The structure of the paper is as follows. Section 2 starts with the description of complexity of the problem of pricing electricity, which comes from its network structure, transmission costs, non-storability and necessity to keep some coordination among actions of market participants. This complexity 1 There exists the so called zero-phi problem, which leads to short circuit under some subset of independent strategies of different generators. 2 leads to mixed evidence from electric market reform in different countries, which is presented in Section 3. The main discussion is about comparison of two alternative market structures: vertical integration versus horizontal competition. Section 4 presents the theoretical core of the paper: a game between generators with asymmetric costs and local markets in the environment of transmission cost. In order to derive policy implications, a simpler case of the game, with linear demand and constant marginal cost of production is studied in Section 5. Section 6 contains policy implications and conclusions. 2 2.1 Particular Features of Electricity Market Complexity of a Problem Electricity market like rail, gas, oil, telephone belongs to a network industry. Historically it was developed as a natural monopoly. It still remains one. The problem is that besides increasing-returns-to-scale [1,12] it also contains a physical network. Building multiple set of wires running along the street not only involves high fixed cost, but also poses an externality for street traffic. Stalon [13] argues that ”creating efficient, competitive power markets in an electric industry... requires the existence of some agency with authority to define, impose and enforce for the operation of all control areas... The pursuit of self-interest, unrestrained by suitable institutions, carries no guarantee of anything except for chaos.” Hogan [8] stressed an important role of at least two special features of the electric system that comes from physics and make it different from other markets. The first one is instantaneous balancing: electricity cannot be stored, and market should clear at every infinitezimal moment of time. Any deviation can damage equipment or bring down the whole system. Another property is complex interaction: everything affects everything else. Many hands of the market must work in the environment where changes for one are changes for all. Thus, coordination is crucial. It is simply impossible to fully decentralize decisions: there must be a system operator, and there should be common agreement about the rules. 3 Due to special spatial topology of electric network, it is physically impossible to connect all nodes in a symmetric way. For example, in most cases individual consumer has no chance to choose across two or more alternative suppliers of energy, and thus is facing monopoly power. Hence, there may be a contradiction between satisfying the goals of consumers and firms in this network. Hogan [8] suggested that regulators of market for electricity should ”focus on the public interest” and ”support competition, not competitors”. Summarizing these findings, it is possible to conclude that there are at least three special features of market for electricity which has to be taken into account in models and policy advises: a) special topology of interlinks between producers and consumers via a network structure of a particular grid; b) non-storability of electricity leads to market clearing condition to be fulfilled at every moment of time; c) complex nonlinear interaction of all elements of the system requires a high degree of coordination and cooperation. 2.2 The Role of Scale Economies It is well known that classical welfare theorems do not work for the scale economies. If some markets exhibit increasing returns to scale, a free competition leads to a natural monopoly, while further attempts to decentralize or deregulate it may lead to even less economic efficiency. Andrikopolos and Vlachou [1] found that the publicly owned electric industry in Greece is relatively efficient and exhibit economies of scale. Thus, privatization should be examined with great caution since it might decrease the efficiency. Nelson and Primeaux [12] studied competition on the transmission and distribution costs on a sample of municipally-owned electric utilities in 1961-76. Their results support the existence of scale economies with respect to output, but not in the case when output per capita is hold to be constant. They suggest that competition may be a viable policy option. Since according to [1,12] economies of scale exist in electrical sector, it is possible to add another argument. It is well known that a local monopolist 4 may not survive if market is too small. Beckmann and Thisse [2] consider a monopoly in a spatial environment, which faces customers heterogeneous due to location and a choice of pricing policies. If both transport costs and fixed costs are high, monopoly may not survive in the market. Formally the same result may be applied to different type of heterogeneity. Hence, local monopoly in Siberia may be on the edge of survival and be happy to use price discrimination including barter in order to prevent its own bankruptcy. This example shows that equilibrium and relatively efficient market structures in electricity industry may be far from those described in classical microeconomic literature. 2.3 The Role of Networks The classical concept of microeconomic theory about automatic emergency of efficiency after decentralization of monopoly cannot be directly applied to this model. The reason is in existence of spatial topology of the network and costly energy transmission across nodes. In a classical microeconomic model consumers and producers have costless and symmetric access to market, which is no longer true for electric network. The network components. Electric network can be modeled as a set of generators, connected with consumers via spatial network of transmission lines. Transmission lines, being viewed as technical instrument to link all market participants, play a role of public good, similar to road network. Network structure and possibility to decompose it into elements. At this stage it is useful to reduce complexity of the model by considering a stylized one. Hogan [8] used the following competitive wholesale electricity market structure: several generators (Genco) are using the regional grid (Gridco) which also contains access to local distributors (Disco), which are connected with their set of local customers. The whole regional system is pooled into inter-regional transmission organization (Poolco) which is governed by System Operator2 . 2 This is a technical necessity 5 Network externalities. Due to complex interdependency miscoordinated individual decisions can damage the whole system.3 To avoid network externalities individual freedom should be limited by regulators who care about sustainability and optimal functioning of the whole system. Thus, transmission system should be regulated independently from ownership. Then it is beneficial to have only one owner or public ownership, since decentralization of this part of the network can induce only higher miscoordination without any additional competitiveness. Since this statement contrasts widespread beliefs into efficiency of any decentralized system, it makes sense to provide few arguments in its support. The Arrow-Debreu theory considers markets where all producers and all consumers have costless access to it. In this environment any restriction of competition works towards efficiency decline. Electric network contains some important elements which are not doubled, i.e. there exists elements of network (transmission lines) which are unique paths between some producers and consumers. In an extreme case an owner of an element of this path can be bribed by the third side (it could be terrorist organization) for actions leading to misfunctioning of the whole system. This bribe would simply not work in Arrow-Debreu economy, but it can easily work in network economy. One may suggest that this is unlikely to occur in economy with strong legal system. However, due to existence of incomplete contracts even in such economies, similar actions can be taken by rival firms which could have a strategic interest to block a particular segment of energy flow. Clearly, the strategic power of transmission line owner over other market participants, studied by Joskow and Tirole [9], cannot be eliminated under any ownership structure, but the minimization of the number of owners will lead to minimal power abuse. If ownership belongs to state, than any externalities could be discussed in parliament and there is high probability to work optimal legal framework. Necessity to regulate local distributors and transmission system. Due to technical impossibility to double wires from different companies, going to every small consumer, local distributors keep some monopoly power over consumers they serve. Competition can be introduced only partially, by 3 Here we talk not only about situations when cutting wires by local grid owners can crash the whole system. This is likely to happen in areas controlled by terrorists. But even in developed market economies local actions on a part of a grid may induce congestion in the whole network. 6 giving a possibility to sign a contract with different producers of energy. It usually involves non-negligible fixed cost of switch and the lower bound of consumption capacity, that cuts small users (like individuals) from a competitive market. But even if the previous conditions are eliminated, the price for transmitting somebody’s energy in local network cannot be set by a competitive market, if owner of this local distribution network is not regulated. Hence, the efficiency in this segment of the market can be increased by regulation. The most efficient (although practically unobserved) way to reach efficiency is ownership of local energy distributor by a cooperative of consumers. In this case, the cooperative has an interest to operate at zero profit level, and efficiency in this market segment is achieved. The transmission system should also be publicly regulated in order to provide an equal access to all the ports of it and to create competitive environment. Any mark up in transmission price above transmission cost reduces the competitive environment. Ideally, it should be owned publicly and operate at zero profit level. 3 3.1 Mixed Evidence about Efficiency Increase after Reforms Motivation for Reforms Brief history. Electricity sector did not have universal grid before the First World War, and was owned privately. Between two World Wars the sector received a lot of public investment, and in the middle of the 20th century became a natural monopoly. In most countries it was nationalized or regulated. In 1970ies, after oil price shocks, it was discovered that minimal efficient scale may be smaller. Independent generators emerged, and in many cases vertical integration between generation and transmission took place [5]. Currently we observe a worldwide push to privatize public electric sectors. The arguments in favor of such transition include cost reduction, service improvement, efficiency increase and cash collection for government [11]. The negative trend for electricity prices in 1950-74 has reversed its sign for major OECD countries during 1974-90 [6]. This was a bad sign, showing less efficiency and potential emergence of monopoly power. Due to information asymmetry, direct regulation of electric industry as monopoly not always 7 brings expected results. Reforms, including privatization and creation of competition thus have been viewed as a remedy. On the other hand, Hogan [8] stresses the importance to focus on public interest during reforms. Due to network externalities, market may not produce efficient outcome, and it is necessary to have regulation. Due to indirect translation of privatization and liberalization into efficiency, the evidence from market reforms in electric countries is mixed. A lot depends on the reform structure and particular conditions of a country. At the present time revolution in organization of electricity markets took place in Chile, UK, Spain, Hungary, Canada, Australia and other countries. Some countries are in the middle of the process, others plan to start reforms soon. But some of greatest world producers of electricity (France, USA) are not so fast with reforms.4 USA is in the middle of reforms, with a huge heterogeneity across states. This causes additional problems due to suboptimal energy flows across different states, as local equilibria in states differ not only due to geographical, but also due to legal differences. The degree of horizontal and vertical integration remains high in France and Italy [5]. Electricity prices in different countries. Although different countries are in different stage of restructuring, international comparison of electricity prices (nominated in common currency, USD) can give some information about current state of efficiency. As was shown by Newbery and Green [10, Fig.2-7], in England the cost of generation is about 60 % of the total cost, while transmission, distribution and supply account for relatively small fractions of it. It is clear that the cost of electricity supplied to industry is between generation and total cost. If electricity would be priced at the cost level, as fully competitive markets suggest, the expected ratio of household price to price for industry should be below 2. The data for the analysis (see Table 1) has been taken from [4] for year 1998. France, Germany and Spain have this ratio well above two, which suggests that distribution sec4 According to Hogan [8], only some regions in the USA did reforms. However, California experiences current difficulties (See ”Financial Times” and other newspapers, 1718.01.2001) 8 Table 1: Relative Prices for Electricity, 1998. Source: [4] and author’s calculations. Prices in US cents/KWh Country Price for industry, pin Price for HH, pHH Ratio, pHH /pin France 4.6 12.9 2.76 Germany 6.7 15.9 2.37 Hungary 5.6 7.0 1.25 Italy 9.5 15.9 1.68 Spain 5.9 15.3 2.61 UK 6.3 11.8 1.87 USA 4.0 8.2 2.05 tor in these countries can have some monopoly profits.5 While France did not make any reforms, Spain and Germany moved forward with them, but have not reached significant efficiency increase in distribution. The absolute price level for households in EU in 1998 was between 0.12-0.16 USD/kWh, in comparison to only 0.08 USD/kWh in the USA. 3.2 Evidence about Reforms in Some Countries Below some evidence about efficiency of reforms in different countries is provided. Chile. Chile was one of the first countries to start reforms. Electric sector was mostly privatized by 1990 with little government interference. During less than a decade the sector moved from government to private ownership, including generation, transmission and distribution [5, p.83]. While the process of privatization was generally successful and has motivated experimentation in other countries, later developments have shown some suboptimality. There was electric energy supply crisis of 1998-99. Producers used to dispatch cheaper hydro energy to maximize profits, and the best government could do was to restrict consumption [11]. Chile is not a unique example of a country where consumer interests are neglected. 5 Although there exists tax on household consumption, it is relatively small, 10-20 % and cannot explained all the difference. 9 Spain. Restructuring Spanish electric industry is a hot topic during the last few years. However, there is little evidence about any efficiency increase. Unlike England, Spain does not care about any spatial or temporal structure of the market. Regulators managed to increase the competition across generators, reducing prices for industrial users to 8.8 pts. However, consumers still pay 23 pts/kWh, and there is no evidence that distribution cost is so expensive. ENDESA, a former monopolist, still owns a significant fraction of generating companies and a lion share of distribution companies. Most of inefficiency is likely to arise from asymmetric information of regulator and ENDESA on the cost structure in distribution. Hungary. In Hungary, like in many other post-communist economies the energy intensities of 1 dollar of produced GDP are much higher than in developed economies. Inefficiency is also observed in high transmission and distribution losses (13 % in 1998). Hence, among the objectives of reforms was also an improvement of efficiency in consumption as well as maximizing cash flow from privatization to improve the problem of public finances [10]. Hence, the efficiency as it seen in economic theory (reduction of deadweight loss emerging from insufficient competition) was not a primary target. Distributors sell energy at a uniform price, keeping 8 % as a profit margin. Clearly, the problem of asymmetric information about cost structure still exists. Electricity price for households in Hungary was 15 HUF in 1998 (about 0.07 USD/kWh, about half of EU average). This can be partially explained lower buying capacity of a country with lower GDP. On the other hand, it shows that electricity is still more a non-tradable good, although there exists a potential possibility for international competition on this market. Russia. In the pre-transition period Russia was the second world largest producer of electric energy, and this production was relatively efficient. The industrial structure was a regulated natural monopoly, and due to scale effects the cost of production was below the world level, thus allowing to maintain cheap internal prices and to subsidize production in industries using electric energy. During transition period Russia is still able to keep internal prices at the level of 1-3 US cents per KWh, which is just 10-20 % of typical consumer prices in European Union. These prices allow to cover variable costs, but do not allow to replace fixed cost in a form of depreciated capital. Currently Russian monopoly RAO EES has adopted a reform, which will 10 favor horizontal competition across generators. It is assumed that privatization of generators will lead to investment required to maintain capital and infrastructure. United Kingdom. In England, with previous state ownership of the majority of the companies, privatization became a new mantra. The details of privatization of English electric industry and argumented discussions about its advantages (competitive environment) and disadvantages (lack or coordination) are well described by Newbery and Green [10]. The belief that market forces would drive innovation forward and bring costs down, gave in the end its positive results. Between 1995 and 1998 the prices for household went down by about 10 % [4]. But it took a couple of years of learning on mistakes, before the process finally gave positive results [8]. The problem was that markets did not produce efficiency unless some active coordination of the short-run electricity market is achieved. In the end, the Pool was created with explicit responsibilities for such market coordination. Pool combines the function of market exchange with the management of complex physics of the electricity system [8]. It is useful to mention that England uses electricity prices changing every half-hour to clear bids for demand and supply.6 Another achievement was creation of regional transmission organizations for the prevention of local monopolies. Market clearing prices can and will be different in every location, but regional transmission reduces these differences down to the level of transmission costs. The idea of regional transmission organizations is currently discussed in the USA.7 4 A Game between Generators There exist different possibilities to model electricity market, which capture one or another partricular feature. Since electricity is now traded in auctions, with different prices depending on time during the day, many believe that the temporal componrnt of the market is more important than spatial. Indeed, it is important, since demand has huge daily variation and since electricity is not storable good. But this no-storability also allows to separate time 6 These prices are regularly published in ”Financial Times”. For example, data given on 10.01.2001, show that purchase price was varying from 8.50 to 69.15 pounds/MWh during a day. 7 Hogan in [8] mentions the ”Order 2000” of the Federal Energy Regulatory Commission. 11 and space. In other words, it is possible to consider the market in particulal moment of time, when demand schedule is fixed. The problem is to find the decisions of firms about production at that moment of time. These decisions could be affected by spatial considerations, and this is the core of the proposed model. Once the solution is obtained, it is possible to move to the next period (could be next hour, since contracts are usually set for the shortest time interval of about one hour), when demand schedules and cost structure could be different, solve it again, and so on. There will be no interaction between the actions in different moments of time, again due to non-storability of electricity. That is why spatial aspect of the problem looks like more importasnt.8 4.1 Alternative Structures of Competition Prices generally depend on location and time. Equilibrium spatial pattern in the environment of transport costs was studied by Beckmann and Puu [16]. There is a pronounced dependence of equilibrium price on time in financial markets and markets for commodities. Electricity market trades non-storable good and the efficient market structure should account for temporal price variation (like Pool did in UK). Electricity transmission is also costly. Direct physical losses in transmission line account for about 10 %, depending on country and tension.9 Transmission grid company can also charge price for its services, and even in the case of regulation minimal maintainance cost should be covered. Under monopolistic ownership, accounting for equilibrium price variation in space and time was not taken into account, and price variation could emerge only as discrimination policy. However, under com8 When the electricity is traded on stock exchanges, itntertemporal interaction can emerge. Like in all stock markets, there might be market-driven volatilities, along with emergence of bottlenecks in transmission, due to combinartion of random factors. but it is necessary to understsnd that all this represent the consequence of institutional arrangement of electricity market, rather than being the consequence of its physical and techological properties. Changing the rules of trade or laws would change that, while there exist some physical properties (like loss of electricity during transmission) that cannot be changed. 9 This estimation is taken from an article of T.Nirsha in Russian journal ”Energy saving”, No. 1, 1999, p.25. The average losses for Western Europe and Northern America are 7.4 %, for Russia 10.2 %, other transition economies - from 13.1 % (Lithuania) to 22.7 % (Estonia). While average distance of transmission is the highest in Russia, it also has higher fraction of high voltage lines, with lower losses per km. 12 petition, both factors might and should be taken into account. Decentralization of ownership creates an environment where each generator can have independent policy, but naturally has an asymmetric access to the market. Asymmetry comes both from technologies (hydroelectric energy has much lower variable cost than thermal) and closeness to big markets. Every real market structure depends on topology of transmission grid, locations of generators and clusters of consumers on it. It also depends on property rights (see [9]). To start theoretical analysis, it is necessary to simplify the framework, so that analytical solution can be obtained. The simplest spatial topology includes two locations, with one generator and set of consumers in each of them, and a transmission line [9]. The temporal structure should be also considered. In spatially large countries with several time zones, like USA, Canada or Russia, demand peaks vary across regions, thus allowing for compensating flows. In spatially small countries variation of demand during a day leads to variation in clearing prices. For example, in UK off-peak price could be just 10 % of peak price.10 Sometimes it is possible to separate temporal and spatial effects. Consider market structure in particular time period. Then spatial model described above can be studied. After finding equilibrium prices at each time, it is possible to make integration over time in order to calculate aggregate profits. However, strategic considerations can also be separated (effect of non-storability) and then aggregated. That is why it makes sense to abandon temporal structure and study only spatial structures. The game between two generators will be studied subsequently. A similar framework was considered by Brander and Krugman [15]. However, they concentrated mostly on symmetric case and found the natural result of symmetric intervention into rival markets, which survives relatively low transport cost, but clearly involves inefficient waste of resources on transportation. Electrical physical flows, due to Kirchhoff laws, does not allow for such form of trade if transmission line is unique. Flows clearly may go in opposite directions in different time periods, and this can bring mutual benefit due to time difference in peaks. 10 For example, provisional price for trading on 10.01.2001 in England and Wales was minimal at 5.00 GMT (12.00 pounds/MWt) and maximal at 17.30 GMT (121.92 pounds/MWt). The source: ”Financial Times”, 10.01.2001. 13 4.2 Competition between Generators The idea of creating spatial competition across generators seems to be one of most potentially efficient tool of reforms. This paper presents a model in the spirit of [9], where a simple network with two nodes connected by transmission line was studied. This network design comes also from ideas of Hogan [8]. The idea about node pricing, where every location could have different prices depending on marginal value of transmission and differences in the cost of generation was proposed in [3,7]. The present model studies the possibility to create competition across generators and is related to spatial competition on a network. In a simple framework of two local monopolies the issues of equilibrium and efficiency are formally studied. The main difference of present model from [9] is a shift of accent from congestion effect in transmission line to direct loss during transmission. A simple specification gives the formulae for prices and quantities, and efficiency of network competition can be compared with one emerging in autarky. Networks of more complex structure can also be considered. The model clearly presents a simplification of reality. In real situation, due to non-storability, there exists a necessity to clear market every hour (like it is done in UK now), and the model presented here deals with market in some particular moment of time. Due to high temporal heterogeneity of demand, at peak period all generators may need to work at the upper limit of their capacity. For simplicity, such situation is not considered here. In fact, the presented model is more in the spirit of international trade (IT). Its difference from classical IT literature (which focuses on country’s specialization and flow of at least two types of goods) is in the assumption that good is physically identical but is produced with different technologies in different locations. This framework reminds more industrial organization literature on horizontal competition. Also, transport cost is playing a crucial role here. The estimation for electric energy sector shows that physical losses in transmission account for about 10 % of produced electricity, and thus cannot be neglected. The model studies the competition across generators assuming that transmission network is regulated and charges a fixed fee per transmission of one unit of electric power per one unit of distance. Transmission cost contains 14 several components: direct energy loss in transmission, the cost of maintaining transmission grid (both are approximately proportional to distance) and the cost of expansion. It is also assumed that a direct contract between any producer and consumer can take place.11 Local distributors are also assumed to be regulated and have no monopoly power over local consumers. The competition in every physical node of network defines a unique local price, while transmission costs allow this price to vary across nodes. 4.3 Assumptions of the Model The stylized version of a network formed by Genco, Disco, Gridco, Poolco [8] is considered. In a simple version, it consists of two local markets (with one generator and distributor on each) and a link between them. 1. There are 2 generators of energy located in regions 1,2. They have different cost functions c1 (y1 ), c2 (y2 ), where y1,2 denote outputs.12 2. At the same nodes there are distributors D1,2 , connected to a set of consumers. It is assumed that they are regulated in such a way that their profit is zero.13 3. When local markets are not connected in a global network Poolco, the price in each location 1,2 is determined as monopoly price of local generator. Aggregated local demands are equal to local supplies. Given demand schedules pi = pi (qi ), i = 1, 2, equilibrium prices p∗i are determined from the problem max πi ≡ max[pi (qi )qi − ci (qi )], where qi is a market supply chosen by local generator. 4. Assume that the distance between locations is x, while unit transport cost is t. Thus, transmission costs (including direct losses) per unit of exported energy is T = tx. Poolco allows generators to use its transmission line to deliver energy to the market of a neighbour. 14 As Poolco is regulated, price t is fixed by regulator, so that Poolco does not extract monopolistic 11 As stated in the EU directive 96/92 on internal market for electricity. It is assumed that capacity constraints are never hit, thus we are not dealing with corner solution which corresponds to the situation of Californian crisis of 2001. 13 This is the only way to introduce efficiency in this market segment. 14 This is the only reasonable way to introduce competition in this model 12 15 profits.15 5. Generators play a game with a continuum of strategies. They decide both on quantity produced yi and the quantity delivered to the market of a neighbour ei . We study a Nash equilibrium in such a game. 4.4 General Solution The solution of decentralized optimization problem involves optimization on the set of controlled strategies taking the rival strategy as given. Formally, it is a Nash equilibrium over continuum set of strategies, but now this set is two-dimensional for at least one of the firms. Definition 1 The solution involves equilibrium prices, outputs and trade flows across points (pi , yi , ei , i = 1, 2), satisfying the following conditions: 1) maxyi ,ei πi ; i = 1, 2 2) market clearing condition at each of 2 markets. Formally, market clearing conditions are: q1 (p1 ) = y1 − e1 + e2 ; q2 (p2 ) = y2 + e1 − e2 , (1) (2) where qi - quantities demanded at each market as price function, e1 - trade flow from point 1 to 2 (energy produced at point 1 and sold at point 2), e2 trade flow from point 2 to point 1. It is possible to introduce net flow e ≡ e2 − e1 . Lemma 1 The positivity of both e1 , e2 is not consistent with efficiency. Proof: It is possible to find flow (e, 0) corresponding to each (e1 , e2 ) for e > 0, or (0, −e) for e < 0, which brings the same quantities and prices to the market, but at less costs. 15 It is possible to consider alternative transport costs, of Samuelson iceberg type. Electricity is ”melting” during transmission and heats wires. Effect has purely physical origin and can be technically estimated when parameters (wire diameter, material, frequency) are known. 16 While simultaneous positive flows e1,2 > 0 are formally allowed in noncooperative game framework, they not only reduce efficiency but also can damage the system.16 The paper [15] studies the competition of two symmetric firms and finds a possibility to have multiple equilibria, including both firms trading on rival’s market. But in the case of asymmetry studied here, this case of inefficient equilibrium can be eliminated by the following reasoning. Suppose we have initial situation with monopolies, and then transmission line opens. If both firms learn from small changes in strategies, then such a dynamic process will give rise to more efficient company entering rival’s market but not visa versa. Associated autarky problem. Consider an associated autarky problem, where e1 = e2 = 0. Then qi = yi , y = 1, 2, and equilibrium prices and quantities are found as the solutions of optimization problems of monopoly. Firms take into account these prices when they decide about optimal strategies under possibility of trade flows. Lemma 2 Given that costs and demands depend continuously on prices, profits are continuous functions of yi and ei for i = 1, 2. Proof: obvious. Assume that flow goes from 1 to 2 (e > 0). It happens when p1 < p2 . Then firm 1 can choose among double continuum of strategies y1 , e1 (active position), while firm 2 decides only on y2 (passive position). In this case the Nash equilibrium is defined through the simultaneous solution of the following system of equations: ∂ π1 = 0; ∂y1 ∂ π1 = 0; ∂e1 16 The efficiency loss is obvious: any movement of identical goods in opposite directions involve additional transport cost without changing final allocations. The physical stability of electric network depends on the phase angle between tension and electric current. Under certain conditions, which can easily emerge in a completely unregulated framework, this angle can enter critical region region and cause a short circuit. Thus can be prohibited by system operator Poolco. If two producers generate electric waves in opposite directions, which corresponds to positiveness of both flows e1,2 , they can easily move the whole system into critical region. 17 ∂ π2 = 0. ∂y2 (3) If e < 0, then firm 1 is passive, while firm 2 is active. Then the system contains two equations for the firm 2 and only one for the firm 1. Lemma 3 Assume that profits are quasiconcave functions. Then there exists Nash equilibrium in pure strategies. Proof: The proof immediately follows from Dasgupta-Maskin theorem, which requires even less property than continuity. However, without quasiconcavity Nash equilibrium may not exist. The question of sufficient conditions for quasiconcavity is not addressed here. However, even if equilibrium exists, it might be not unique. Then no policy implications can be derived. That is why special case is studied later. 5 Vertical Integration versus Horizontal Competition 5.1 Solution for a Particular Specification It is useful to consider a simple specification of the model to see what are the properties of the equilibrium. Let the demand be linear: q 1 = a1 − p 1 ; q 2 = a2 − p 2 . (4) Assume also constant marginal cost, allowing for a possibility of a fixed cost:17 c1 (y1 ) = β1 + γ1 y1 ; c2 (y2 ) = β2 + γ2 y2 . 17 (5) This formally introduces economies of scale in generation sector. It does not contradict reality since evidence of IRS is shown in [1,12]. At the same time it does not pose any problem for equilibrium existence, for linear demand at least. 18 Importance of this case. Electric industry normally is operating under scale technology. All type of generators (atomic, hydro and using fossil fuel) have significant fixed cost and thus represent scale economies in production. These costs, β1,2 , depend positively on generator capacity which depends on the size of local market and technology and thus differ across generators. Different variable costs are captured by parameters γ1,2 . Variable cost is the lowest for hydro-energy and the highest for thermal stations working on oil, coal or gas. Thus there is a natural asymmetry across generators which should be taken into account when modeling different schemes of industry structure. While demand can be of any functional form, data are usually not sufficient to estimate more than the slope of demand curve. Since linear demand function is easy for analytical calculations, it was taken in this form. In a particular country (we are talking about competition inside country) distributors deal with aggregated demand, and there is no reason to assume differences in the slope of demand function across regions. On the other hand, technologies and parameters of generators in different locations can be different, and this is captured by difference in parameters βi and γi . We will compare two market structures: vertical integration and horizontal competition. The goal is to see under what conditions one or other brings higher social surplus measured as the sum of producer and consumer surplus. Vertical integration: Autarky solution. In this case π1 = −q12 + (a1 − γ1 )q1 − β1 ; π2 = −q22 + (a2 − γ2 )q2 − β2 . (6) Hence, a1 − γ1 ; 2 a1 + γ1 ; p∗1 = 2 q1∗ = a2 − γ2 ; 2 a2 + γ2 p∗2 = . 2 q2∗ = (7) (8) Fixed costs β1,2 do not enter these formulae, but they influence participation constraint: if πi < 0, firm chooses to stay out of market even being a monopoly. 19 Solution for horizontal competition. Consider the case when p∗1 < p∗2 . The first firm is more efficient, being able to consider an option to sell some of its energy on the second market. Clearly, the second firm has no reason to attempt selling part of its output at market 1. Thus, e1 > 0 while e2 = 0. Consider transport cost, linear in both distance and volume. As we consider the case of only two firms, the distance can be normalized to one, ant transport cost is T per unit of energy. Let y1,2 be the output of firms 1 and 2, while q1,2 denotes the equilibrium consumption of energy on the 1st and the 2nd markets correspondingly. The market clearing condition is q1 = y1 − e1 ; q2 = y2 + e1 , while the profits are: π1 = (y1 − e1 )[a1 − y1 + e1 ] − β1 − γ1 y1 + e1 [a2 − y2 − e1 − T ]; π2 = y2 [a2 − y2 − e1 ] − β2 − γ2 y2 . (9) (10) The Nash conditions leads to a linear system: −2y1 + 2e1 = γ1 − a1 ; 2y1 − 4e1 − y2 = a1 − a2 + T ; −e1 − 2y2 = γ2 − a2 . (11) Since det  = −6 6= 0, it has a solution for all a1 , a2 , γ1 , γ2 , T . The equilibrium is unique and it includes outputs, flow and prices: a2 + γ2 − 2γ1 − 2T ; 3 a1 − γ1 a2 + γ2 − 2γ1 − 2T y1 = + ; 3 2 a2 + γ1 − 2γ2 + T . y2 = 3 e1 = (12) (13) (14) The new equilibrium prices can be calculated from the formulae: p̄1 = a1 − y1 + e1 , p̄2 = a2 − y2 − e1 . (15) Hence, p̄1 = a1 + γ1 = p∗1 ; 2 p̄2 = 20 a2 + γ1 + γ2 + T . 3 (16) 5.2 Comparison of Outputs and Prices under Two Schemes It is useful to compare the direction of price change and total output for two schemes. While it is known from microeconomic literature that competition tends to destroy local monopoly power, undercut prices and increase social welfare, it may be not true when the system has internal losses related to energy transmission. In this model positive transmission costs are taken into account. Besides, both firms have scale technology, for which the usual microeconomic intuition not always works. It makes sense to ask the following questions: ”When some prices will decline?” and ”When the total output would increase?” Conditions for price decline. Note that in competition energy flow can be always from region with lower autarky price, pi = (a1 + γ1 )/2. Thus, for equal market capacity, a1 = a2 , generators with lower fixed cost will tend to export its energy, while for identical generators, the flow will be towards market of higher capacity ai . We agree to denote the exporting area by index 1. After transition from autarky to horizontal competition, the first price does not change, since more efficient firm keeps its local monopoly power on market 1. At the market 2 the price differential equals to ∆p2 ≡ p̄2 − p∗2 = − a2 + γ2 − 2γ1 − 2T . 6 (17) Thus, the second price declines if and only if a2 + γ2 > 2γ1 + 2T . Conditions for the total output increase. Let us calculate the difference, ∆Q, between total output under horizontal competition, y1 + y2 , and under vertical integration, q1∗ + q2∗ : 1 ∆Q ≡ y1 + y2 − q1∗ − q2∗ = [a2 + γ2 − 2γ1 − 2T ]. 6 (18) It is easy to see, that ∆Q > 0, if a2 + γ2 > 2γ1 + 2T . In other words, high market capacity of market 2, a2 , as well as higher marginal cost of local generator, γ2 , work towards superiority of horizontal competition versus vertical integration. At the same time, high transmission cost T can undercut this advantage. There always can exist so high T that no benefits from horizontal competition (in the sense of lower prices and higher output) can be derived. 21 Conditions for shift from autarky to trade. It was implicitly assumed that there are reasons for trade. This is not an obvious question. Our “trade” solution (12-16) was derived under assumption of existing trade. However, if the price differential below transport cost, no trade is preferable option. Let us find the difference between prices given by formula (16), ∆p̄ ≡ p̄2 − p̄1 = 2a2 − 3a1 + 2γ2 − γ1 , 6 (19) and compare it with T . The formulae (16) are valid, iff ∆p̄ ≥ T , or T < T1 ≡ 2(a2 + γ2 ) − 3a1 − γ1 . 4 (20) Thus, we have the following Proposition. Proposition 1 Autarky will be broken, if firm’s advantage in variable cost will be substantial in comparison with transport cost T , given demand parameters a1,2 . It is clear that the price difference between two markets is proportional to T , but does not vanish to zero for T = 0. Consider a sequence of markets characterized by different parameters T , with a tendency of decline.18 For high T , there will still be autarky, with no inter-regional trade. After reaching the threshold T = T1 , trade will start. With the further decline of T , the price difference across regions will decline. 5.3 Case Studies It is important to study some particular cases. Suppose that two markets are identical, while two generators differ only in the variable cost. Assume that γ1 < γ2 . The standard (spaceless) economic theory teaches us that more efficient producer should deliver his output to all the markets, until price equalization. Suppose that there is no explicit accounting of the dependence of energy losses in the electric network for different strategies of priducers. Then we will observe cross-regional trade even if it is not efficient (transport 18 This is consistent with economic development, which goes along with increase of energy consumption, and this requre shift to high voltage lines with less losses per unit of distance (see Appendix). 22 costs are higher than gains). This is what normally happens in present state. The model elaborated in this paper finds such institutional framework that producers will care about this issue in a decentralized way, and the whole system will not incur losses. Proposition 2 If the losses of energy during transmission are not accounted, more efficient firm will always participate in inter-regional trade, even when this is not efficient (total losses are higher than gains). The creation of market rules which account for these “transport costs” will bring the system back to efficeincy. Another interesting case is the competition between different types of generators. Hydrogenerators are characterized by high fixed costs and low variable costs, and they have cost advantage. The variable cost for nuclear generators is below one for coal/petrol/gas power stations.19 It is possible to study the equilibria in decentalized systems given different cost structures of producers and different spatial topology. But as was shown above, for any difference in cost structure there exists so high transport cost, that the system will stay in autarky. Note that for given transmission network, transport costs are monotonously increasing in distance. Hence, Proposition 3 For any given cost asymmetry across generators and given network of high voltage transmission lines, there exists the maximal spatial radius where they can explit this advantage. 5.4 Social Efficiency Issues Consumer and producer surplus. For the case of constant demand slope, equal to one, which is considered here, consumer surplus at market i is given by expression: CSi = (ai − pi )qi /2, where pi is market clearing price under certain market structure, while qi is energy volume sold in this market. Producer surplus, P Si , can be defined simply as profit. In the baseline, autarky case, we have: 1 (21) CSi = (ai − γi )2 , i = 1, 2; 8 1 P Si = (a1 − γi )2 − βi , i = 1, 2. (22) 4 19 The main argument of opponents is explicit accounting for ecological consequences, especially after Chernobil, but even in this case this corresponds more to fixed rather than variable cost of nuclaer power. 23 Transition to horizontal competition does not bring changes at the market 1, while price and quantity in market 2 can move. If ∆p2 > 0, the sum of producer and consumer surplus increases. The gain in social efficiency is connected with the decline in deadweight loss. However, direct physical loss in transmission line has to be taken into account as well. Deadweight loss and physical loss. Deadweight loss, DW L, is usually defined as difference between the sum of producer and consumer surpluses obtained under two different market structures. The recovery of deadweight loss after transition from autarky (vertical integration) to horizontal competition equals to: 1 1 DW L = (p∗2 − p̄2 )2 = (a2 + γ2 − 2γ1 − 2T )2 . 2 2 (23) The transmission cost includes direct physical loss of energy during transmission20 and the cost of operating transmission infrastructure, which also includes its depreciation. Thus, direct physical loss, T̄ , is always lower than transmission cost. We define physical loss as P L ≡ e1 T̄ = (a2 + γ2 − 2γ1 − 2T )T̄ . (24) As we have too many parameters, it makes sense to consider some particular cases. Identical generators operating on markets with different capacity. Consider the case of competition between two physically identical generators using the same technology: β1 = β2 ≡ β, γ1 = γ2 ≡ γ. The asymmetry arises from difference in their local markets. It is assumed that the capacity of the first market is lower: a1 < a2 . Then p∗1 < p∗2 and ∆p2 = −(a2 − γ − T )/6 < 0, for T low enough (since ai < γi to have positive output in autarky equilibrium). In this case firm 1 will have a possibility and interest to enter market 2. In this case, DW L = θ2 /2, P L = θT̄ /3, θ ≡ a2 − γ − 2T. (25) The gain in reduction of deadweight loss is higher than physical loss, if θ > 2 T̄ . Since 0 < T̄ < T , for a2 − γ > 2.67T , transition to competition leads to 3 20 Heating wires depends on voltage, but is proportional to energy flow and distance. 24 an increase in social welfare, while for a2 −γ < 2T it does not do it, since gains in social efficiency are less than physical losses. In the intermediate case, everything depends on the fraction of physical losses in total transmission cost. Identical markets, served by generators with different technology. We have a1 = a2 while γ1 < γ2 . In this case p∗1 < p∗2 , and ∆p2 = −[(a2 − γ2 ) + 2(γ2 − γ1 ) − 2T ]/6. For sufficiently low transmission cost, we have gain in efficiency. The results can be summarized in the following proposition. Proposition 4 1. Ceteris paribus, the firm with lower capacity of local market will tend to export electricity on the market of its neighbour. If markets are with identical aggregate demand function, then a firm with lower variable cost will export its energy on the market of its neighbour. 2. The transition to horizontal competition can bring social gains if transmission costs are lower than some threshold, which depends on parameters of generators and markets. Thus, as an element of reform, it is socially optimal to keep transmission costs at the lowest possible level. Transmission line should operate at zero profit condition, which can be reached under public ownership or regulation. 5.5 The Case of Many Markets The simple model shows that pooling markets is efficient. The market power of less efficient generator (one that has higher autarky price) is reduced through competition with more efficient generator. If we have a network of N generators, with different autarky price levels, pooling markets will keep monopoly power only for the most efficient generator. But it also under constant threat of more efficient entrant in his market. 6 Policy Implications The history of electric industry in USA shows that the structure of natural monopoly in electric industry was efficient at a particular stage of development. The fact of price decline between 1940 and 1970 is a typical scale 25 effect. When other industries were less developed in the sense of energysaving technologies, cheap electricity was a crucial condition for their successful performance in the market. After ”green taxes” electricity consumers learned how to use energy more efficiently. At the present time they can afford paying for it more than equilibrium market price. This created a gap between the acceptable selling price at which electric industry can operate without losses and the buying price at which consumers can afford to pay for electricity. The richer the country, the higher the gap. But it is also natural to see the dynamics of the development, when this gap is growing over time along with technological development in every country. In rich countries surplus occurs, and problems are in its sharing across producer and consumers. There are two ways to understand efficiency. The first is typical for economists and assumes no deadweight loss, which always occurs in unregulated monopoly. The model of the present paper proposes a tool how to create spatial competition across generators. But non less important part of the problem is to take out surplus from distributor, who is a natural local monopolist. The paper studies theoretically the problem of competition between generators when particular market structure is created. While 1 kWh of electricity is physically identical good, its price depends on location and time. The paper focuses on spatial component of competition. It is clear that the grid owner should be regulated since his profit maximization would lead to inefficiently high T , which can destroy any gains from competition. An example of linear demand and cost functions is studied under assumption of asymmetry across markets and firms, which often takes place in reality. It is shown that firms with less variable costs (hydroelectric energy, atomic energy) will tend to export their output to other markets. In the spatial competition of two firms using fossil fuel (gas, oil, coal) for energy production, the firm with smaller capacity of local market will tend to export its electricity to markets of its neighbours. 26 7 Conclusions 1. The complexity of network structure and its pure physical properties do not allow to create a perfectly competitive market at all levels. While natural monopoly in electric sector perfectly solves important coordination problems, there is clear loss of economic efficiency. The efficiency is always lost at the level of distributor, which always has a local monopoly power, even after separation from generator. Here regulation is important. 2. The problems of efficiency gains after decentralization of electric energy network are studied. It is shown that while at some segments it is impossible to introduce full competition into market for electricity, significant efficiency gain can be reached through arrangement of Poolco, the possibility for each generator to trade its energy at different regions via transmission. The first model studies a simple network with 2 nodes. It is shown that unique Nash equilibrium exists under reasonable assumptions about demand and cost structure. 3. Pooling spatially separate markets results in efficiency gains as less efficient generators loose their local monopoly power. However, transmission costs should be low enough. It is possible to predict the direction of energy flows on the basis of cost and demand structure. Literature 1. Andrikoupolos A., Vlachou A. (1993) The Structure and Efficiency of the Publicly Owned Electric Power Industry in Greece. - Journal of Energy and Development, v.19, iss.1, pp.57-79. 2. Beckmann M., Thisse J.-F. (1986) The Location of Production Activities. - In: Handbook of Regional and Urban Economics. Vol. 1. Ed. P.Nijkamp. 3. Caramanis M., Bohn R., Schweppe F. (1986) The Cost of Wheeling and Optimal Wheeling Rates. - IEEE Transactions on Power Systems, v.1, pp.63-73. 4. Electricity Information. IEA Statistics. (2000) - OECD/IEA, 700 p. 27 5. Electricity Market Reform. An IEA Handbook. (1999) OECD, 106 p. 6. Gilbert R., Kahn E., Newbery D. (1996) Introduction: International Comparisons of Electricity Regulation. - In: Gilbert R., Kahn E., Ed. International Comparisons of Electricity Regulation. - Cambr. Univ. Press. 7. Hogan W. (1992) Contract Networks for Electric Power Transmission. - Journal of Regulatory Economics, v.4, pp.211-242. 8. Hogan W. (2000) Making Markets in Power. - Cantor Lecture Series 2000: Energy and Society, London, 21 Feb. 2000. 9. Joskow P., Tirole J. (2000) Transmission Rights and Market Power on Electric Power Networks. - RAND Journal of Economics, v.31, No.3, pp.450-487. 10. Newbery D., Green R. (1996) Regulation, Public Ownership and Privatization of the English Electric Industry. - In: Gilbert R., Kahn E., Ed. International Comparisons of Electricity Regulation. - Cambr. Univ. Press. 11. Maldonado P., Friedmann R., Jannuzzi G. (2000) Energy Efficiency in Public or Privatized Power Systems: Contrasts of the Brazilian, Chilean and Mexican Experiences. - Proceedings of the 2000 ACEEE Summer Study on Energy Efficiency in Buildings. Vol.5, pp. 187-198. 12. Nelson R., Primeaux W. (1988) The Effects of Competition and Distribution Costs in the Municipal Electric Industry. - Land Economics, v.64, iss.4, pp.338-346. 13. Stalon C. (1997) Electric Industry Governance: Reconciling Competitive Power Markets and the Physics of Complex Transmission Interconnections. - Resource and Energy Economics, v.19, iss.1-2, pp.47-83. 14. Pesic R., Urge-Vorzatz D. (2000) Lessons from the Restructuring of the Hungarian Electricity Industry. - Proceedings of the 2000 ACEEE Summer Study. v.5, pp.253-264. 28 15. Brander J.A., Krugman P.R. (1983) A Reciprocal Dumping Model of International Trade. - Journal of International Economics, v.15, p.313-321. 16. Beckmann M., Puu T. (1991) Spatial Economics: Density, Potential and Flow. - North-Holland. Appendix: Basics from Physics In order to understand the importance of arguments for explicit accounting of energy loss during transmission, some basic knowledge from physics is required. Its level is chosen to be minimal. Electric circuits are governed by laws of Omm and Kirkhof. Let I denotes current, U - voltage, and R - resistence. Then, in the case of fixed current, I = U/R (Omm law). The resistence R for electric wire depends on its material and temperature, but mostly important, on cross-section S and length L. In general, R = ρL/S, where ρ is specific resistance. For example, at the temperature 20 degrees of Centigrade, ρ = 0.028 Om ∗ mm2 /m for aluminium and ρ = 0.0175 for copper. Long distance electric lines are usually done from aluminium; here its lower specific weight is also taken into account. The dependence of resistance from temperature cannot be controlled, and its influence does not bring significant changes in economic variables. The length L also cannot be chosen; if the geographical distance between two points is 200 km, there is no way to connect them with electric line of lower length. The cross-section of electric wires is an important parameter. Usually higher S are chosen for high voltage electric lines, which are used for electricity transmission on longer distances. A simple economic justification is provided below. In reality electric current is not constant, but has low frequency, f = ω/(2π) (f = 50 Hz, by European standard). Such circuits are analysed using complex numbers. Besides active resistance R, imaginary (reactive) resistances, RL = ωL and RC = 1/(ωC) have to be accounted for. If they are connected sequentially, there is an angle φ between the waves of current, I, and voltage, U . In this case, I = I0 Sin(ωt − φ), U = U0 Sin(ωt), 29 (26) U0 I0 = q , R2 + (ωL − 1/(ωC))2 ωL − φ = arctg( R 1 ωC ). (27) (28) Losses in electric lines. Consider an electric line of length n, where each unit of length has resistance R, which is used to deliver electricty to consumer, who has active resistance R0 . By the law of Joyle-Lenz, the electric power is transformed into heat, and the coefficient of losses η is given by the formula η= nR nR ≈ , nR + R0 R0 (29) if the losses in electric wires are relatively small. This formula shows that the losses for heating wires are approximately proportional to distance. Optimal cross-section S. Consider a problem of optimal cross-section (or diameter) of electric wires. The higher S, the higher is the cost of constructing transmission line. On the other hand, high S will diminish losses of energy in such lines. We have optimization problem of the total cost minimization: min(T C), T C = aS + b/S, q (30) which has the unique minimum: S ∗ = b/a. The higher the power flows, the more important is to save electricity (b becomes higher), and the higher should be S ∗ . 30