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.
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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