1
Diagnosing Market Power in Chile’s Electricity Industry1
M.Soledad Arellano2,3
Abstract
Chile’s electricity market is modeled as a Cournot duopoly with a competitive fringe. Due to the
importance of hydro-storage resources (62% of total generation in 2000) particular care was given to the
hydro scheduling issue. The model was estimated over a 1-month planning horizon using real cost and load
data for April 2000. I found that if an unregulated spot market were implemented in Chile’s electricity
industry, large generators, especially the largest (Endesa) would have the incentive and ability to exercise
market power unilaterally. Endesa would exercise market power by keeping its thermal portfolio outside of
the market and by allocating its hydro production in order to take advantage of differences in price
elasticity of demand. In particular, it would allocate too little supply to high demand periods and too much
to low demand periods (relative to the competitive equilibrium). Endesa has so much market power,
especially when demand is high, that the second largest producer (Gener)’s optimal strategy is to produce at
capacity. It only has the incentive to exercise market power by constraining its production when demand is
low. The source of Endesa’s market power is its hydro capacity. Indeed, when hydro flows are reduced, so
is its market power. Under these conditions, Gener has the incentive and ability to constrain its production
in order to hold prices above competitive levels. Still, prices are lower than when Endesa had all of its
hydro capacity. Endesa’s incentive to exercise market power by shifting hydro production from one month
to another depends on how large are the inter-month differences in price elasticity. As expected, final
equilibrium is also very sensitive to the value of the price elasticity of demand.
JEL classification: D43, L11, L13, L94
Keywords: electric utilities, market power, scheduling of hydro reservoirs
1
This is the first chapter of my Ph.D Thesis submitted to the Department of Economics at MIT.
2
Department of Industrial Engineering at the University of Chile (DII). Postal address: República 701,
Santiago – Chile. Email: sarellano@dii.uchile.cl
3
I am grateful to Paul Joskow, Frank Fisher, Alex Galetovic, and Fernando Ordoñez for their comments
and suggestions. I also benefited from comments made by participants at the IO lunches and the IO
Seminar held at MIT and from Seminars held at the Instituto de Economía, Universidad Católica de Chile
and Centro de Economía Aplicada, Universidad de Chile. Financial support from the MIT Center for
Energy and Environmental Policy Research (CEEPR) is gratefully acknowledged.
2
I. Introduction
Chile was the first country that reformed and restructured its power industry. The power
sector reform, implemented in the early 80’s, was an element of a more general economic
reform that introduced competition rules to different industries. Basically, the
government tried to limit its market interventions only to those industries where the
private sector was not able to make appropriate investment, production and/or
consumption decisions. In particular, the regulatory authority decided that, since the
generation segment of the electricity industry was not a natural monopoly, the
appropriate approach was to promote competition among generators. Entry into the
generation business was opened up to competitors and generators were encouraged to
enter into supply contracts with large industrial customers and distribution companies.
The reforms also created a spot market, but the prices in the spot market were determined
based on the marginal costs of generators in the system and the associated least cost
dispatch. That is, generators effectively were required to bid their available capacity and
associated audited marginal costs into the spot market. The marginal cost of the last
generator required to balance supply and demand, taking into account transmission
constraints and losses, then determined a simulated spot market clearing price at each
node on the system. The prices for supplies made under long-term contracts to
distribution companies were based on 4-year projections of these nodal prices as
determined by the regulator. Thus, generation prices were not “deregulated” in the usual
sense of the term, except for the very largest industrial customers who chose to enter into
contracts directly with generators4
. Rather, the system defined a “simulated” perfectly
competitive set of spot and forward contract prices. The latter, have been constrained
indirectly by a requirement that they be no higher than 110% and no lower than 90% of
the prices charged to large industrial customers who negotiate prices directly with
generators. The transmission and distribution segments continued to be regulated based
on traditional cost-of-service regulatory principles because of their natural monopoly
features. This economic policy was implemented in conjunction with a huge privatization
effort, where most of the electricity companies were re-organized and then sold to the
private sector.5
Two decades have passed since the restructuring of the industry took place. It is fair to
say that in general terms, the reforms have had a positive effect: installed capacity
increased and both efficiency and quality of service and quality of supply indices have
exhibited a positive trend. However, in the past years there have been some warning signs
that call for new changes; private companies for instance, have been reluctant to increase
their installed capacity in spite of the signs of future shortages. Currently, both Chilean
regulatory authorities and private companies are analyzing the question of moving to a
system in which spot prices for electric energy would be truly deregulated by creating a
uniform market clearing price “power exchange” through which generators would be free
to bid whatever prices they choose with competition between generators determining the
4
Distribution companies were not allowed to purchase energy from the simulated spot market. Instead,
they were required to sign long term contracts with generators. The contract price was the regulated price.
5
For more information on the privatization process, see Luders and Hachette (1991).
3
bids and market clearing prices.6
One major concern that has been raised regarding this
deregulation proposal is that the incumbent generators would be in a position to exercise
market power, leading to prices far above competitive levels. In particular the high
degree of concentration in the generation segment has raised concerns regarding the
desirability of implementing a system like this one.
The electricity industry has been subject in the past years to restructuring and reforms in
different countries (UK, many states in the US, Argentina, Colombia, Australia, New
Zealand and so on). There is not a unique approach to follow as different countries have
implemented different reforms with different results. However, some lessons have been
learned from them. First of all, it is clear that in order to get the benefits of a competitive
wholesale electricity market, reforms must be designed and implemented correctly. It is
important to look at the industry as a whole and do not treat its different segments
(generation, transmission, system operation, distribution and retailing) independently as
they continually interact, and the effectiveness (and success) of one segment’s regulation
certainly depends on the other segments’. This interaction partially explains some of the
problems experienced by California: utilities had to buy electricity at a volatile (and at
sometimes very high) spot price, sell to retail consumers at a fixed price, and were not
able to hedge against the risk that spot market prices could rise above the fixed retail
price at which the power purchased in the spot market had to be resold at retail. In
addition, the market design must realize that the electricity industry is prone to the
exercise of market power, as electricity cannot be stored, producers interact very
frequently, capacity constraints may be binding when demand is high and thus even a
small supplier may be able profitably and unilaterally increase the market price by
withholding supplies from the market. The importance of an adequate number of
generating companies that compete in the wholesale market has also been emphasized.
For instance, the experience in the UK, although successful in many aspects, has shed
light of the problems that high concentration may yield to, especially with respect to the
exercise of market power7
.
In this paper I analyze whether the high concentration in the generation sector will result
in anti-competitive behavior if all electricity supplies were traded in an hourly
unregulated spot market.8
Following Borenstein and Bushnell (1999) and Bushnell
(1998) I model Chile’s electricity market as a Cournot duopoly with a competitive fringe.
Particular care is given to the modeling of hydro resources, which are not only important
because of its large share in total installed capacity and in total generation (61% and 62%
respectively in 2000), but because of its impact on the incentives firms face when
competing. As it will be analyzed in the paper, having hydro resources as a source of
electric generation, means that firms do not take static production decisions at each
6
There is no consensus regarding how the price paid by distribution companies for the supply of their
franchise’s small consumers would be regulated. Different alternatives have been proposed. Among them:
to allow distribution companies to freely negotiate the price with generators and to use the regulated price
(as it is currently calculated) as a price cap.
7
For more details on the lessons learned from the UK and US experience, see Joskow (2002).
8
See Borenstein et al (2000) for an analysis of why concentration indices are not a sufficient indicator of
market power.
4
moment in time, but that firms have to take account that more water used today, means
less water is available for tomorrow: the model becomes dynamic rather than static.
Quantitative simulation results obtained from this model depend on assumptions that,
unfortunately, cannot be supported (or rejected) by strong empirical evidence, as the
latter simply doesn’t exist in many cases. For instance, prices, the production level,
markups, and many other variables are a function of price-elasticity of demand, a variable
for which there is no precise estimation. Even if there were, it is likely that after the
power exchange and other reforms are implemented, demand for electricity (and price
elasticity) will change. Accordingly the main contribution of this paper is given by the
qualitative results. I do not expect the reader to remember exactly how high prices or
markups would be. Instead, I expect him/her to remember what conditions are more
favorable to the exercise of market power, who is really able to exercise it and how. In
addition, this model will be a useful tool to evaluate the impact of different policies that
could be implemented in this industry to mitigate market power.
I found that if an unregulated spot market were implemented in Chile prices could rise far
above competitive levels as suppliers, in particular Endesa, the largest supplier, would
exercise unilateral market power. The large thermal portfolio owned by Gener, the
second largest generator, is not enough for the exercise of market power, as the relevant
plants are mostly base load plants. Indeed, Endesa has so much market power and can
move prices up so much, that Gener’s optimal strategy is to produce at full capacity,
profiting from the high prices set by Endesa. Even though Endesa keeps most of its
thermal plants outside of the market, the real source of its market power is its large hydro
capacity. In particular, it schedules its hydro production in order to exploit differences in
price elasticity, allocating too little supply to high demand periods and too much to low
demand periods, relative to the competitive equilibrium. This hydro scheduling strategy
may be observed no matter what planning horizon is assumed in the model (a month, a
year); the only “requirement” is that there is enough “inter-period” differences in demand
elasticity. The smaller the fluctuation, the closer is the hydro scheduling strategy to the
traditional competitive supply-demand or value-maximizing optimization analysis’
conclusions (i.e. water is stored when it is relatively abundant and released when it is
relatively scarce). The importance of hydro resources for Endesa is such that when hydro
flows are reduced (as it occurs if the hydrological year is “dry”), Endesa loses its market
power. Under these circumstances, Gener has incentives to act strategically to increase
prices, but the resulting prices are still lower than when Endesa had all of its capacity.
Not surprisingly, alternative assumptions about the elasticity of demand for electricity
turned out to be very important, as the more elastic is demand, the less market power can
be exercised.
The paper is organized as follows: in Chapter II, I review the main findings of the
literature that are related to this topic. In Chapter III, I briefly describe the Chilean power
industry. In the fourth Chapter I analyze the model that will be used to diagnose market
power. Data used to estimate the model is described in Chapter V while results are
5
reported in Chapter VI. Two extensions to the main model are analyzed and estimated in
Chapter VII. The final chapter concludes and gives directions for further research.
II. Empirical literature Review
This paper is related to two areas of research: the modeling of electricity markets in order
to (ex-ante) simulate strategic behavior after the industry has been deregulated and to the
analysis of the strategic use of hydro resources to exercise market power.
Three types of model have been used to simulate the strategic behavior of electricity
firms. In the supply function equilibrium (SFE) approach, used by Green and Newbery
(1992) and Halseth (1998) based on the work by Klemperer and Meyer (1989), the
producers bid a supply function that relates quantity supplied to the market price. In the
general case, the duopoly supply lies between the competitive and Cournot equilibrium;
the range of feasible equilibria is reduced when uncertainty is added to the model.
Green and Newbery (1992) modeled the England and Wales electricity market using the
Supply Function Equilibrium (SFE) framework developed by Klemperer and Meyer
(1989) as applied to an empirical characterization of supply and demand, designed to
match the attributes of the electricity system in England and Wales (making alternative
assumptions about the elasticity of demand)9
. They first present simulated values for
prices, output and welfare for the duopoly case. They found that generators were able to
drive prices far above competitive levels, depending on the assumed elasticity of demand,
while creating a significant deadweight loss and producing supra-competitive profits for
the generators..10
They then examined the impact of restructuring the industry so that
there were five equal-sized firms. In this case, the equilibrium price was significantly
lower and close to competitive levels. In order to take account of the effect of potential
entry, they examined the effects of entry in the duopoly case under alternative
assumptions about the price responses of the incumbents to the entry of generators who
acted as price takers. If the incumbents adopted a strategy of not responding to entry by
lowering prices, substantial entry was attracted by the excess profits in the system.
Eventually entry eroded the incumbents’ profits completely, yielding an equilibrium with
inefficient expenditures on new generating capacity and high prices. The welfare losses
in these cases were very large.
Halseth (1998) used the SFE approach to analyze the potential for market power in the
Nordic market. In his model, the supply function is restricted to be linear, with a constant
markup over marginal cost. This markup is independent of the particular technology used
by the producer but it varies between the different time periods. Asymmetry in
production technologies is incorporated through the marginal cost function (each
production level is associated to a specific marginal technology (hydro, nuclear or
thermal). Due to the importance of hydro production in the Nordic market (it accounts for
9
Von der Fehr and Harbord (1993) and Halseth (1998) criticize on theoretical grounds the Green and
Newbery (1992) use of the SFE approach.
10
Wolfram (1999) found that prices in the British market had been much lower than what Green and
Newbery (1992) predicted.
6
50% of annual production), the hydro scheduling issue is explicitly modeled. In
particular, annual hydro production is restricted to be less than the annual inflow and the
water inflow that is stored between periods has to be within the reservoir capacity. He
found that the potential for market power was less than expected due to the fringe’s
excess capacity. Only two of the six largest producers had incentives to reduce
production.11
Remaining producers did not have incentive to do so. In particular, he
found that hydro producers were not interested in reducing its market supply. He argued
that since all of its income came from hydro production (with a very low marginal cost),
the price increase had to be very large in order to induce it not to use its generating
capacity to the full.12
It should be noted that all the results of this model are reported in
annual terms. In particular, he found that hydro generating capacity was used to the full
in the year. However, nothing is said regarding how it is allocated throughout the year.
This is an important omission because it may be the case that hydro producers do not
exercise market power by using less than its hydro capacity but through a strategy that
distinguishes between periods of high demand from periods of low demand.
Auction theory has also been used to analyze strategic behavior in the electricity market.
Von der Fehr and Harbord (1993) model the UK electricity spot market as a first price,
sealed-bid, multiple unit private-value auction with a random number of units. In their
model, generators simultaneously bid supply schedules (reflecting different prices for
each individual plant), then demand is realized and the market price is given by the offer
price of the marginal plant. They argue that producers face two opposing forces when
bidding: by bidding a high price, the producer gets higher revenue but a lower probability
of being dispatched. Equilibrium has different properties depending on the demand level.
In particular, when demand is low, producers bid a price equal to the marginal cost of the
least efficient generator and equilibrium is unique. When demand is high, there are
multiple equilibria and the price is equal to the highest admissible price.13
They remark
that some of these equilibria may result in inefficient dispatching: the high cost generator
will be dispatched with its total capacity if it submitted the lowest bid, while the low cost
generator will be dispatched for only a fraction of it. Finally they argue that their model is
supported by the bidding behavior observed in the UK electricity industry from May
1990 to April 1991. In particular, they report that while bids were close to generation cost
at the beginning of the period, they diverged thereafter, Even though contracts were in
place in the first part of the analyzed period, they argue that contracting practice is not a
plausible explanation to the observed bidding behavior because contracts started to expire
after the change of pattern took place. The coincidence of the first period with the low
demand season (warm weather) and the second with the high demand season (cold
weather) makes their model a more appropriate explanation. It should be noticed however
that they analyzed a very short period. In order to be really able to separate the contract
11
This two producers are Vattenfall and IVO. The portfolio of the first one is split between hydro (42%),
nuclear (48%) and conventional thermal plants (10%). IVO is mostly a thermal producer.
12
Johnsen et al (1999) concluded from this result that market power cannot be exercised in a market
dominated by hydroelectric producers, to what they add, unless transmission constraint binds.
13
Multiplicity of equilibria is given by the fact that both producers want to be the “low bidder” because the
received price is the same but the producer is ranked first, and thus output is greater.
7
effect from the high/low demand effect, and in this way to get more conclusive support to
their theory, the following seasons should be analyzed.14
Finally a third approach that has been used in the literature is to model the electricity
industry as a Cournot oligopoly where producers are assumed to bid fix quantities.
Andersson and Bergman (1995) simulated market behavior of the Swedish electricity
industry after deregulation took place. They assumed a constant elasticity demand
function (with an elasticity of demand equal to 0.3 in the main case), constant marginal
costs for hydro and nuclear power plants and a non-linear marginal cost function for
conventional thermal units. They found that prices would increase and production would
be constrained. In particular, they found that the Cournot price equilibrium was 36%
higher than the current (base) case and 62% than the Bertrand equilibrium. Markups were
not analyzed. They also analyzed the impact of alternative market structures like splitting
the largest company in 2 firms of the same size and a merge between the six smallest
companies. In both cases equilibrium price was reduced below the base case. Finally they
analyzed the impact of increased price responsiveness solving the model for a higher
elasticity value (0.6). Since hydro production is modeled on an average basis, nothing is
said regarding how resources are allocated within the year (for instance there is no
differentiation between peak and off peak periods). In addition, nothing is said regarding
how the portfolio of resources is used and how it compares to the base and Bertrand
equilibrium cases. This is an important omission given the importance of hydro
resources in the Swedish electricity market.
Borenstein and Bushnell (1999) and Bushnell (1998) modeled the California power
industry as a Cournot triopoly with a competitive fringe.15
Cournot producers face a
residual demand where must run generation, the fringe’s supply and hydro generation in
the case of Borenstein and Bushnell (1999) are subtracted from total demand. Marginal
cost functions were estimated using cost data at the plant level. A big difference between
those articles is given by the treatment of hydro resources: Bushnell (1998) assumes that
Cournot producers use them strategically while Borenstein and Bushnell (1999) assume
that they are allocated competitively.16
In other words, in Bushnell (1998)’s model, hydro
producers are “allowed” to store water inflows from one period and use them in another
one in order to manipulate prices. As a result, in his model the different periods are not
independent and thus the maximization has to be solved simultaneously over the entire
planning horizon, as opposed to Borenstein and Bushnell (1999)’s model where each
period can be treated independently. Borenstein and Bushnell (1999) use a constant
elasticity demand and estimate the model for a range of demand elasticity values (-0.1,
-0.4 and -1.0) and six different demand levels. They found that the potential for market
power was greater when demand was high and the fringe’s capacity was exhausted,
making it impossible for the small producers to increase production. In lower demand
hours, Cournot producers had less incentive to withhold production because the fringe
had excess capacity. In addition they found that the more elastic was demand, the less
14
Wolfram (1998) analyzes the bidding behavior in the UK and tests the theoretical predictions of the multi
unit auction theory.
15
Their market definitions are slightly different.
16
In particular, hydro production is allocated over the period using a peak shaving technique.
8
was the incentive to exercise market power. Finally they analyzed the hydro scheduling
issue by allocating hydro production across periods so as to equalize marginal revenue.
They found that even though the resulting hydro allocation was very different from the
one implied by the peak shaving approach, prices did not change much because as hydro
production was moved out from one period, the resulting price increase induces the other
large producers and the fringe to increase production. This result is different from
Bushnell (1998)’s findings.
Overall, the literature seems to agree on the following conclusions: more market power
can be exercised when the fringe’s capacity is exhausted (which usually occurs when
demand is high) because this makes the residual demand curve faced by the firms with
market power less elastic. The exercise of market power results in high prices, reduced
output and in an inefficient allocation (production costs are not minimized). Results are
very sensitive to the elasticity of demand as well as the elasticity of fringe supply. In
order to say something regarding the role of hydro resources in the exercise of market
power, a formal study of the hydro scheduling issue is needed.
The analysis of the hydro scheduling issue is always done following a similar approach:
producers maximize their inter-temporal profits subject to certain constraints such as
hydro generation being within a range determined by min and max flow constraints and
by the availability of water. Then, an assumption is made regarding what sort of strategy
producers may choose. Scott and Read (1996), Scott (1998) and Bushnell (1998) used a
quantity strategy and the industry was modeled as a Cournot oligopoly. The main
difference between their approaches is given by the method they chose to solve the
optimization problem. While Scott and Read used a dual dynamic programming
methodology (DDP), Bushnell solved the model by searching for the dual variables that
satisfied the equilibrium conditions of the model. In particular, Scott and Read used DDP
to optimize reservoir management for the New Zealand electricity market over a medium
term planning horizon (1 year). They estimate a “water value surface” (WVS) that relates
the optimal storage level at each period to the marginal value of water (MVW). The latter
is interpreted as the marginal cost of generating at the hydro stations. The schedule of the
system is determined by running each period a Cournot model in which the hydro plant is
treated as a thermal plant using the WVS to determine the marginal cost of water (i.e.
MVW), given the period and the storage level at that period. 17
The Scott and Read
approach is rich in details as hydro allocation for the whole planning horizon is derived
as a function of the MVW. However it is computationally intensive, especially when
there is more than one producer who owns hydro-storage plants. It is also data demanding
as information on water inflows is required on a very frequent basis. Bushnell modeled
the Western US electricity market, where the three largest producers had hydro-storage
17
The water value surface consists on a set of curves, one for each period, which relates the storage level at
a certain period to the marginal value of water. It is derived recursively. The storage level at the beginning
of a certain period is calculated by adding to the end of period storage level a demand curve for release of
water (DCR), which is a function of MVW, and subtracting the (expected) water inflows of the period. This
is done recursively starting from the end of the planning horizon, resulting on a water value surface. The
demand curve for release of water is calculated by running a one stage Cournot model for a representative
range of MWVs holding all other inputs constant. The DCR is given by plotting hydro generation versus
MWV.
9
plants. He adopted a dual method to solve the model, treating the marginal value of water
multiplier and the shadow prices on the flow constraints as the decision variables. He
derived an analytic solution by searching for values of the dual variables that satisfy the
equilibrium conditions at every stage of the multi-period problem. In order to solve his
model, he simplified it by assuming that demand and the marginal cost functions were
linear18
. The planning horizon was assumed to be one month and the model was
estimated for March, June and September. Bushnell (1998) found that firms could profit
from shifting production from peak to off peak hours, i.e. from hours when the fringe was
capacity constrained to when it was not. In particular, he estimated that hydro production
was reduced by 10% (relative to perfect competition) during the peak hours, resulting in
more than 100% price increase. Based on the estimated marginal water values for
different months, he found that against what it was expected producers did not shift
production from months of high demand to months of low demand. He argued “since the
market is relatively competitive at least some of the time in each month, strategic firms
do not need to reallocate across months in order to find hours in which extra output will
have little impact on prices” (p.30)
III. Chile’s Electricity industry
Electricity supply in Chile is provided through four non-interconnected electric systems:
Interconnected System of Norte Grande (SING) in the north, Central Interconnected
System (SIC) in the center and Aysen and Magallanes in the south of the country. Total
installed capacity in 2000 amounted to 9713 MW. The SIC is largest system in the
country in terms of installed capacity and it concentrates more than 90% of the country’s
population. Due to differences in resource availability, each system generates energy
from different sources. While the north relies almost completely in thermal sources, the
rest of the country also generates energy from hydroelectric sources and recently from
natural gas. The most important source of energy in Chile is hydrological resources. They
are concentrated in the central and southern part of the country, which explains why the
SIC relies heavily on hydro generation. Fuel resources are not abundant: natural gas and a
large fraction of the oil used are imported and Chilean coal is not of good quality. In what
follows, all the analysis and estimations will refer to the SIC, the biggest electric system.
Gross generation in 2000 amounted to 29.577 GWh, 37% of which was hydro-reservoir
generation, 38% thermal generation and 26% hydro-Run-of-River (ROR) generation.
Maximum demand in the year 2000 amounted to 4576 MW (April). The generating
sector is highly concentrated: 93% of total installed capacity and 90% of total generation
are in hands of three economic groups (Endesa, Gener and Colbun) Endesa being the
largest of them. (See Table 1). The Hirschmann-Herfindahl index is 3716. In order to
simplify the reading of the paper, I will refer to these companies as “Firm 1” (Endesa),
“Firm 2” (Gener), and “Firm 3”(Colbun). These three firms differ in terms of size, their
generating plants portfolio and the associated marginal cost functions (See Figure 1).
18
The slope of the demand function was assumed to be constant across periods and set at a level such that
the elasticity of demand at the peak forecasted quantity was -0.1.
10
While Endesa relies mostly on hydro sources, Gener owns the majority of the thermal
plants of the system.
Firm 3 has the lowest marginal cost plant, but is also the smallest firm in terms of
capacity. Firms 1 and 2 both own low and high marginal cost plants, being this feature
more accentuated in the case of Firm 1.19
Generating companies are allowed to sell to three different customers: large consumers,
distribution companies and other generating companies20
. Transfers of energy between
generators take place in a simulated “uniform price” spot market. The “market” clearing
price, called the Short Run Marginal Cost (SRMC), is given by the marginal cost of the
last generator required to balance supply and demand, taking into account transmission
constraints and losses. It is calculated by an independent entity, called the “Load and
Economic Dispatch Center” (CDEC), according to marginal cost information reported by
the generators themselves. Neither distribution companies nor large consumers have
access to the simulated spot market. Large consumers are entitled to enter into contracts
directly with generators and to freely negotiate the price for electricity. Distribution
companies are required to enter into long-term contracts with the generators, at a
regulated price, in order to purchase electricity for the supply of their regulated
consumers. This regulated price is set every 6 months by the regulatory agency called the
National Energy Commission (CNE). A particular feature of the Chilean pricing system
is that the nodal price is required to lie within a band of +/- 10% of the non-regulated
price; this means that every time the regulated price is set, the regulator has to get
information on the free price and make sure that that constraint is satisfied.
The CDEC is in charge of the dispatch, of the operation of the system, the estimation of
the SRMC, of guaranteeing open access to transmission lines and of other administrative
tasks. For a detailed analysis of the Chilean regulation, see Arellano (2001a, 2001b)
IV. Theoretical Model
I will estimate an ex-ante model much in the spirit of Green and Newbery (1992),
Borenstein and Bushnell (1999) and Bushnell (1998) using real demand and cost data for
the year 2000. Following Borenstein and Bushnell (1999) and Bushnell (1998) the
industry is modeled as a Cournot duopoly (Firms 1 and 2) with a competitive fringe21
.
The model that is analyzed in this Chapter will be referred to as the “base model”.
The portfolio of generation sources is very important; in fact, it defines the way market
power can be exercised. The whole idea behind the exercise of market power is to reduce
19
In addition, there is an important degree of vertical integration in the SIC. In particular, Enersis, the
owner of Endesa, is also the owner of two large distribution companies, Chilectra and Rio Maipo whose
customers amount to 43% of the SIC.
20
Large consumers are those whose maximum demand > 2 MW. They amount to 50% of total
consumption. 70% of them are really free to choose whom to contract with.
21
I also estimated the model assuming that the third largest firm (Colbun, “Firm 3”) had market power but
it turned out that it always ended up behaving as a price taker. In other words, it wasn’t big enough to be
able to use its resources strategically.
11
output in order to increase market price. However, the decisions that producers can make
are different depending on whether they are in a purely thermal / purely hydro or in a
mixed electric system. In a purely thermal system, the only decision that can be taken is
when to switch on or off a plant and how much to produce at every moment in time; in
this context, market power is exercised by reducing output when rival generators are
capacity constrained, which usually corresponds to periods of high demand. A system
with hydro-reservoirs, on the other hand, allows producers to store water during some
periods and release it in some others; in other words, they are able to “store” power and
release it to the market at their convenience. Therefore, hydro producers are entitled to
decide not only when to switch on or off their plants and how much to produce, but also
to decide when they want to use their hydro resources over a certain period of time. This
(dynamic) scheduling decision is not available to thermal producers22
. In a purely hydro
system producers exercise market power by exploiting differences in demand elasticities
in different hours. In particular, they shift production from periods where demand
elasticity is high to periods when it is low.23
Only water from hydro reservoirs can be used strategically. Since water from run of the
river (ROR) sources can’t be stored, it can’t be used by producers to manipulate the price.
ROR plants will be treated in the model as “must-run” (MR) units except for those ROR
plants that are associated to a reservoir system upstream, which will be included as part
of the reservoir complex. In the Chilean system, Firm 1 and the Fringe own hydroreservoir
plants. Their hydro capacity amounts to 78% and 22% of total hydro-reservoir
capacity respectively. Firm 2 is a purely thermal plant, concentrating the largest fraction
of thermal resources in the SIC (46%). See Table 1 for more detailed information. In
order to simplify the model as much as possible, I will assume that Firm 1 and the fringe
only have one reservoir complex. They will be made up by the aggregate of individual
reservoirs.
The model will determine hydro scheduling by Firm 1. However, since the Fringe also
owns a medium size reservoir, it will be necessary to allocate its hydro production in a
certain manner. In particular, I will use the Peak Shaving approach. The basic idea is the
following: when there are no flow constraints, producers schedule hydro generation so as
to equalize the marginal profit that they earn from one more unit of production over the
whole period in which the hydro plant is being used. If the market were perfectly
competitive, prices would be equalized. If there were market power, then generators
would equalize marginal revenues over time. As long as demand level is a good indicator
of the firm’s marginal revenue, a peak shaving strategy would consist in allocating hydro
production to the periods of higher demand.24
In addition, producers also have to take
account of minimum flow constraints, given by technical requirements and irrigation
needs, and maximum flow constraints, given by capacity. As a result, hydro production
by the fringe was distributed across periods allocating as much as possible (given
22
Notice that even in a perfectly competitive market producers are able to hydro schedule. The difference is
that when the market is competitive, difference between on peak and off-peak hours is reduced as opposed
to when producers exercise market power in which case difference is enlarged.
23
See Johnsen et al (1999), Bushnell (1998) and Halseth (1998).
24
This is true when using either a linear or a constant price-elasticity demand.
12
min/max flow constraints) to every period in order to eliminate or reduce demand
peaks25
.
Cournot producers face a residual demand given by:
DR
(Pt) = D(Pt) – S f
(Pt) – qMR
t - qPS
h t
where D(P) is market demand, DR
(P) is residual demand, S f
(P) is the Fringe’s thermal
supply function , qMR
is must-run units’ generation and qPS
h is the Fringe’s hydro
production from reservoirs distributed across periods according to a Peak shaving
strategy.
Each firm’s maximization problem is given by:
Firm 1’s Optimization problem
Max ∑t { Pt (q t)*(q1ht + q1Tht) – CT1 (q1Th t) } (1)
s.t.
(2) q1Th MIN ≤ q1Th t ≤ q1Th MAX ∀ t (thermal production min/max constraints)
(3) q1h MIN ≤ q1h t ≤ q1h MAX ∀ t (hydro production min/max constraints)
(4) ∑t q1h t ≤ q1h tot (hydro resources availability)
Firm 2’s optimization problem
Max ∑t {P t (qt) * (q2Tht) – CT2 (q2Tht ) } (5)
s.t.
(6) q2Th MIN ≤ q2 Th t ≤ q2Th MAX ∀ t (thermal production min/max constraints)
where:
P t (qt) = is the inverse function of the residual demand in period t
Qt = is total production by firms 1 and 2 in period t, (Qt = q1t + q2t ),
qit = qiTh t + qih t is total production by Firm i in period t,
qiTh t = total energy produced by Firm i out of thermal plants, period t
q1h t= total energy produced by Firm 1 out of hydro-storage plants, period t
CTi(qiTh t) = Total Cost function, thermal plants, firm i
qiTh MIN = Minimum thermal production, Firm i, period t
25
For more detail on the peak shaving approach see Borenstein and Bushnell (1999).
13
qiTh MAX = Maximum thermal production, Firm i, period t
q1h MIN = Minimum hydro production, Firm 1, period t
q1h MAX = Maximum hydro production, Firm 1, period t
q1h tot = available hydro production for the whole period
t =time period within the planning horizon. The planning horizon of the
model will be assumed to be a month and will be divided in 6 sub-periods
(t=1,2,..6) of equal length.
Firm 1’s Lagrangean is given by:
L= ∑t { Pt (q t)*(q1ht + q1Tht) – CT1 (q1Tht) - λ 1t*( q1Tht - q1Th MAX ) - α 1t *( q1Th MIN - q1Tht)
- γ1t (q1ht - q1h MAX) - δ1t ( q1hMIN - q1h t) } - σ1 (∑t q1h t - q1h tot) (7)
Firm 2’s optimization problem is simpler because it only owns thermal plants. Its
Lagrangean is given by
L = ∑t {Pt (qt)*(q2Tht) – CT2 (q2Tht ) - λ2t*( q2Tht – q2Th MAX ) - α2 t*( q1Th MIN - q2Tht )} (8)
Where λit, α it , γ1t , δ1t and σ1 are the Lagrange multipliers for maximum thermal
capacity, minimum thermal capacity, maximum hydro capacity, minimum hydro capacity
and available hydro flows constraint respectively. They all must be positive. It is
important to keep in mind that σ1 is the only multiplier that is constant over time; it
indicates the marginal value of water, i.e. the additional profit Firm 1 would get if an
additional unit of water became available.
FOC for Firms 1 and 2 are26
:
∂ L = Pt (q t) + q1t * ∂ Pt (q t) - ∂ CT1 (q1Tht) - λ1t + α 1t = 0 (9)
∂ q1Tht ∂q t ∂ q1t
∂ L = Pt (q t) + q1t * ∂ Pt (q t) - γ1t + δ1t - σ 1= 0 (10)
∂ q1ht ∂ qt
∂ L = Pt (q t) + q2Tht * ∂ Pt (q t) - ∂ CT2 (q2Tht) - λ 2t + α 2t = 0 (11)
∂ q2Tht ∂q2 t ∂ q2Tht
These conditions can be reformulated as follows:
26
Slackness conditions are not reported.
14
(9’) MR1t = c1 + λ1t - α 1t
(10’) MR1t = σ 1 + γ1t - δ1t = Ω1t
(11’) MR2t = c2 + λ2t - α 2t
where MRi is Firm i’s marginal revenue and ci is Firm i’s thermal production marginal
cost.
Each firm schedules its production in order to equalize marginal revenue to thermal
marginal cost each period (adjusted for shadow prices), as expected (constraints 9’ and
11’). In addition, Firm 1 allocates water across time so as to equalize the marginal cost of
water (Ω1t) with the cost of producing an additional unit of power from the marginal
thermal plant (constraints 9’ and 10’)27
. This means that an extra unit of water will be
generated until its cost is equal to the cost of the most expensive thermal plant in use. The
intuition of this is the following: an additional unit of water would replace production
from the least efficient thermal plant that is in use and profits would increase by the cost
of production that has been saved. If minimum and maximum hydro production
constraints were not binding, then marginal cost and marginal revenue would be constant
as the marginal value of water (σ) is constant over time. Firm 1 would allocate hydro
storage resources in order to equalize marginal cost across periods. Firm 1 peak shaves
marginal revenues rather than prices.
If thermal and/or hydro min/max capacity constraints are binding, these conclusions still
hold but applied to a broader definition of marginal cost / marginal value of water that
includes the shadow price of increasing/decreasing installed capacity.
The Fringe solves exactly the same optimization problem solved by Firm 1; the only
difference is that ∂ Pt (q t) / ∂q Ft = 0 as it does not have any market power, and thus behaves
as a price taker. As a consequence, the fringe uses its plants (thermal and hydro) until the
marginal cost (thermal or hydro plants) is equal to the market price:
(12) P = cF + λFt - α Ft
(13) P = σ F + γFt - δFt = Ω Ft
Some final remarks regarding the model that will be used to analyze the exercise of
market power are in order. First of all, and as the reader has probably noticed, this is a
completely deterministic model. In particular, hydrological resources, marginal costs and
load levels are assumed to be known in advance by the agents. Certainty with respect to
thermal marginal cost functions and demand fluctuations should not be a real concern, as
the former are well known in the electricity industry and the shape of the load curve has
been relatively stable in the past years. Certainty with respect to hydrological inflows is
clearly a more arbitrary assumption. In the context of my model, this should not be too
27
Notice that Firm 1 allocates its plants (thermal and hydro) efficiently given the total level of production
(which is inefficient as the firm produces until marginal cost = marginal revenue < price).
15
problematic either because I assumed that producers maximize over a short time horizon
(one month). The longer the planning horizon, the more uncertain are the hydro inflows,
and the more important it is to incorporate uncertainty into the model. Secondly, the
model lacks of dynamic competition elements. This omission is clearly important for this
particular industry. In the context of a power exchange system, the producers interact on
a very frequent basis providing optimal conditions to engage in (tacit) collusive practices.
For instance, producers can easily learn their competitors’ strategies, monitor their
behavior and credibly threat in case of deviating from the “collusive” strategy. In this
sense, the results of the model should be seen as a lower bound of market power. On the
other hand, the model does not incorporate the effect of high prices on potential entry or
in consumption patterns; accordingly market power might be overestimated. Finally,
transmission constraints and contracts were not taken into account yet. 28
V. Model estimation
Supply side
Each firm’s marginal cost function was calculated aggregating their thermal plants’
marginal cost functions. I assumed that each plant had a constant marginal cost up to its
expected capacity level.29
The constant marginal cost at the plant level (and at the plant
“mouth”) was calculated as the monthly average of the weekly marginal cost reported by
the CDEC. This reported value does not incorporate transmission losses. Since market
behavior will be modeled as if all transactions took place at the same geographic node, it
is necessary to incorporate the fact that the MC of delivering energy at one node of the
system is different from the MC of “producing” energy because a fraction of the energy
that is generated in the plant is lost while it is being transmitted to the consumption node.
In other words, the marginal cost of a KW produced by a plant located in node A and
consumed at node B is “production MCA
” + “transmission charge”. In order to
incorporate this, I calculated for each plant a “system-equivalent marginal cost” as
Production MC x Penalty factor (calculated by the CNE).
Each plant’s capacity was adjusted for transmission losses, auto-consumption and
average availability30
. Unfortunately it was not possible to get separate data for scheduled
and non-scheduled (non-expected) maintenance periods31
. Related papers do not adjust
for transmission losses that occur within the market but only for those that take place
when energy is imported. I think this assumption is not appropriate for the Chilean case.
The distance from North to South in the SIC is approximately 2300 kms. (about 1430
miles) and so transmission losses are likely to be important. In order to take them into
account I adjusted capacity by the transmission loss factor. In other words, if maximum
28
These issues are analyzed in two companion papers. See Arellano (2002a and 2002b).
29
Start-up costs were not taken into account.
30
As it was discussed in Borenstein et al (2000) the use of average availability may underestimate true
expected capacity.
31
Availability figures are high for international standards. This may be due to the way they are calculated:
a plant is considered to be available if it doesn’t go down when it is dispatched. However plants that are not
dispatched but are available are also considered being available. The issue here is that there is no certainty
that those apparently available, non-dispatched plants would be effectively available if dispatched. In
addition, availability data seems to include maintenance periods, which is a strategic variable.
16
capacity is q, then the maximum delivered capacity is q*(1-LF) where LF is the loss
factor. Finally since demand will be calculated as the sales of the system, autoconsumption
must also be subtracted from total production. I used the last 5 years
average for both the transmission loss and auto-consumption factors (4.6% and 2%
respectively).
Resulting marginal cost functions are plotted in Figure 2. Notice that both Firms own low
and high marginal cost plants, being this feature more accentuated in the case of Firm 1.
Demand
As it was said before, Cournot producers face a residual demand given by:
DR
(Pt) = D(Pt) – S f
(Pt) – qMR
t - qPS
ht
Where D(P) is market demand, DR
(P) is residual market demand, S f
(P) is the fringe
supply’s function (adjusted by transmission losses), qMR
is must-run units’ generation and
qPS
h is the hydro production from reservoirs owned by the fringe that is distributed across
periods according to a Peak shaving strategy.
a) Market demand: I constructed a step function representation of April-2000’s load
curve with 6 discrete load levels (t=1 for the highest load level)32
. The load level of each
step was set equal to the average of the loads covered by those hours in the full load
profile33
. See Figure 3. Each load level has an associated price given by the regulated
price, which is the price paid by final consumers. This price-quantity point will be
referred to as the “anchor point” for each period (Figure 4). Given that there is only one
price-quantity observation for each period, it is not possible to directly estimate the
market demand function; all that can be done is to assume a functional form and
parameterize it using each period’s anchor point and an assumption for the priceelasticity
of demand for electricity.
Demand is assumed to be linear D(pt) = At – BPt.34
As a consequence, price elasticity
increases as the level of production is reduced and the elasticity of demand at the price
where the market clears is always higher when there is market power.
The empirical literature has emphasized the importance of price elasticity of demand in
the results. In my model, demand elasticity will also turn out to be very important, as
Cournot equilibrium will be closer to the competitive equilibrium the more elastic is
demand. In addition hydro scheduling will be determined in part by demand elasticity.
Estimates of the price elasticity of demand for electricity vary widely in the literature. As
Dahl (1993) pointed out, the estimation of price elasticity is sensitive to the type of model
used, to the estimation technique and to the data set used. In addition, studies differ on
32
I chose April because historically it has been the month where the maximum demand of the year takes
place.
33
The observed load per hour was increased by 13% to take account of spinning reserves.
34
A linear functional form is consistent with the peak shaving criteria that will be used later to allocate
hydro generation: periods of high demand are also periods of high marginal revenue.
17
their definition of short run and long run price elasticity35
. In lagged adjustment models
short run is defined as the 1-year response to a permanent increase in prices. GarciaCerruti
(2000) using panel aggregate data for selected California counties (1983-1997)
estimated that short run price elasticity went from –0.132 to –0.172, while the range for
the long run was from –0.17 to –0.19. In the particular case of Chile, Galetovic et al
(2001) used a partial adjustment model to estimate the demand for electricity by
commercial and residential users. Their estimates of short run (long run) price elasticity
were –0.33 (-0.41) and -0.19 (-0.21) for residential and commercial users respectively.36
Short run estimates of price elasticity are lower when the period in which the
consumption pattern may be adjusted is shorter. Wolak and Patrick (2001) looked for
changes in electricity consumption due to half hourly price changes in the England and
Wales market. They focused on 5 large and medium sized industrial and commercial
customers. Not surprisingly, they got much lower estimates of price elasticity. In the
water supply industry, which was the most price responsive industry analyzed, price
elasticity estimates went from nearly zero (at peak) to -0.27. The steel tube industry was
the least price responsive industry, with price elasticity estimates going from nearly zero
to –0.007 (there is no indication of the demand level at which the upper estimate was
observed). Finally, Dahl (1992) found no clear evidence that the developing world’s
energy demand were less price elastic than for the industrial world.
Because of the large variation in the price-elasticity estimates, I follow the traditional
approach of estimating and reporting the results of the model for different values of
elasticity. In particular, the market demand will be estimated for 5 different assumptions
of price elasticity of demand E = {-0.1, -1/3, -1/2, -2/3, -1.0}, measured at the anchor
point at peak hours. In the main text of the paper I only report results for –1/3 and –2/3.37
These values may appear to be high compared to some of the estimates reported.
However and under the assumption that consumers are sensitive to price changes at least
until a certain degree, it is not reasonable to assume that consumers will not react to the
exercise of market power. In particular, we should expect them to learn, after a while,
that the price is higher in certain periods than in others and to adjust their consumption
behavior accordingly.38
This change should mitigate the potential for market power. It is
very difficult to explicitly incorporate this demand side reaction to market power into the
model. An indirect way of doing it is to assume that the market is more price responsive
than short run estimates of price elasticity indicate. Results for the E=-2/3 assumption are
35
Nesbakken (1999) suggested that since there is a lot of individual variation in energy used, estimates
based on micro data were more reliable.
36
As I mentioned before, the regulated price in Chile is fixed for a period of 6 months. During that period,
it changes mostly according to he evolution of inflation. This means that the authors did not have much
price variation over time. However, since the price that was used to estimate price elasticity was the final
price, and since that price includes transmission and distribution charges that vary across consumers
according to different parameters, they did have cross-section price variation.
37
For comparison purposes, I report price elasticity values (“E”) assumed by other authors. A constant
elasticity of demand was assumed by Borenstein and Bushnell (1999), estimating the model for E=-0.1, -
0.4 and -1.0 and by Andersson and Bergman (1995) who used E=-0.3. A linear demand was assumed by
Wolfram (1999) with E=-0.17 at the mean price and quantity and by Bushnell (1998) who assumed E=-0.1
at peak forecasted price/quantity point.
38
See Wolak and Patrick (2001) and Herriges et al (1993) for estimations of elasticity of substitution within
the day.
18
reported as a way to illustrate the effect of increasing price-sensitivity of demand. The
results for the case of E = -0.1, E=-1/2 and E=-1.0 are reported in the Appendix.
The price elasticity assumption was incorporated in the model through the slope
parameter B, which was calculated such that the elasticity at the peak demand level was
equal to “E”. This implies that I will work with parallel demands (“same slope”). The
intercept was calculated so as to fit anchor quantity and anchor price at each demand
level (given the calculated slope B).39
See Table 2 for demand parameters used assuming
E = -1/3.
By assuming that market demand is linear and the slope is constant across load levels, I
am implicitly assuming that market demand at peak hours is less elastic than demand at
off peak hours (at a constant price). 40
Neither the linear demand assumption nor the
anchor point chosen had any influence on the results. The main conclusions (even order
of magnitudes) were the same when running the simulation assuming that the slope was
not constant41
.
a) Fringe’s supply: In order to minimize the number of steps that the residual demand
faced by Cournot producers have, I decided to use a linear approximation of the
Fringe’s supply function. This linear function is given by the following expression
(see Figure 5):
(14) MC F
= 3.66 for 0≤ QF
≤ 54.9 MW
=-114.60441+2.156038QF
for 54.9 ≤ QF
≤ 58.5 MW
= 11.51217 for 58.5 ≤ QF
≤ 399.9 MW
=-333.526 + 0.8628848QF
for 399.9 ≤ QF
≤ 433.7 MW
b) Must run quantity: The plants that have to be dispatched all the time (no matter the
price) and thus cannot be used strategically by their owners were designated as “must
run” plants. This includes two small co-generator thermal plants that produce
electricity and steam and all the hydro-ROR plants that are not associated to any
reservoir system. qMR
was calculated as April 2000’s average generation per hour in
the case of thermal plants, and in the case of hydro-ROR plants, as the average
39
A similar approach was used by Bushnell (1998).
40
Empirical evidence supports the assumption of price elasticity being a function of the output level as the
linear functional form implies. However, evidence is not conclusive regarding whether demand at peak
hours is more or less elastic than at off peak hours. Aigner et al (1994) estimated that demand for electricity
in the winter was more elastic during peak periods while in the spring/autumn season it was the off peak
demand the one that was more price responsive.
41
In the “different slope approach”, the slope parameter B was such that the elasticity at every anchor point
was equal to “E”. Results are reported in Appendix #1. I decided to report in the main text the results for
the same slope approach because when using the different slope approach, residual demands intersect on a
certain (and relevant) price range making it more difficult to interpret results. Results are almost the same
under both approaches.
19
generation in a normal hydro year calculated according to the Energy Matrix provided
by the CDEC. 42
c) Hydro-reservoir generation by the Fringe (qPS
h). In order to allocate the hydrostorage
generation by the Fringe, I calculated, for each plant, the average generation
per month (in this case April) in a normal hydrological year based on the Energy
Matrix estimated by the CDEC. This monthly hydro generation was assumed to be
total hydro production available for the period. It was allocated over the month
according to the peak shaving strategy described before. Minimum and maximum
flow constraints were also taken into account. qPS
h used to estimate the model is the
average hydro generation per hour allocated to each sub-period according to this
approach.
Since the Fringe owns relatively small hydro-storage plants, the amount of hydro
production that can be allocated through a peak shaving approach is also small. Peaks
are only slightly reduced and the shape of the “shaved load” curve remains mostly the
same. (See Figure 6).
d) Residual demand: See Table 3 for a summary of what was subtracted from market
demand (April 2000) to get the residual demand faced by the Cournot producers. The
shape and position of residual demands faced by Cournot producers is explained by a
combination of three elements: the anchor point, the fringe’s supply for thermal
production and the load curve shape that results after allocating fringe’s hydro
production through a peak shaving strategy and. (See Figure 7).
Hydro data
Minimum hydro production per hour is given by technical requirements and by irrigation
contracts. Maximum hydro production per hour is determined by technical requirements.
Total April’s available hydro production is 1118.1 GWh according to the Energy Matrix
provided by the CDEC (See Table 4)43
. Fringe’s hydro production was allocated
according to the Peak shaving strategy, as was explained before. Hydro scheduling by
Firm 1 will be a result of the model.
VI. Results
Competitive equilibrium
As a benchmark case, I calculated the competitive equilibrium. System’s hydro-storage
production (from the fringe and Firm 1) was allocated according to the peak shaving
strategy. The competitive equilibrium was calculated as the quantity - price point where
42
Since must run plants’ production was subtracted from total demand, must run plants were also removed
from the set of available units (in other words, they are not included in the aggregated marginal cost
function).
43
Unfortunately, the CDEC does not have and estimation for the Laja system (the largest in the country).
Because of that I used the observed average generation of that hydro system in April of a normal year.
20
demand (net of hydro production) and the aggregate marginal cost function intersect.
Resulting competitive equilibrium is reported in Tables 5 and 6.
Observe that the equilibrium is exactly the same for the first four periods (t=1 to 4) and
almost the same for the fifth one. This is a consequence of net demand being the same in
those periods, or, in other words, of hydro production being so large that its allocation
across the month completely flattens demand in those periods, eliminating (reducing) the
peaks44
. See Figure 8.
Cournot equilibrium
The Cournot-fringe was solved with GAMS/CONOPT using an iterative process. I
started assuming that each firm produced at the average level observed in April 2000, and
then solved for the Cournot equilibrium for Firm 2. Given the resulting production
schedule, I solved for Firm 1 and used the resulting Cournot equilibrium as an input for
Firm 2’s maximization problem. I continued this iteration process until the model
converged to a solution for each of the firms45
. Results are reported in Tables 7 and 8.
Total quantity is smaller than in the competitive model and prices are considerably
higher, especially when demand is high (see figures 9 and 10). Notice that as demand
falls, the Cournot equilibrium (price and production) converges monotonically to the
competitive equilibrium. The exception is given by the last period when demand is at its
lowest level which may be explained by Firm 2 increasingly constraining production as
demand falls. The more elastic is demand, the larger is total production and the closer is
hydro scheduling to the competitive equilibrium
When demand is at high and medium levels Firm 1 is the one that really enjoys market
power. Indeed, Firm 1 has so much market power and is able to drive prices up by so
much that Fim 2’s optimal strategy is to produce at capacity. Firm 2 exercises market
power only in the last 2 periods, when demand is low. (See Figure 12) 46
.
44
A similar result holds for the “different slope approach”. The difference is that since the slope is
different, net demand functions are not exactly the same in the first four periods but they are very close.
45
Uniqueness of equilibrium was not investigated theoretically but empirically. In particular, the
simulation was solved for 400 randomly chosen starting points. The model always converged to the same
aggregated equilibrium: prices, each firm's total production, marginal cost, marginal value of water and
profits. The only exception is given by the Firm 1's production strategy. Even though it is true that the
equilibrium for Firm 1's total production is unique, this is not true for its production strategy, i.e. the
decision of how much is produced from its thermal and hydro-storage plants. Multiplicity of equilibrium is
explained by Firm 1 being able to allocate hydro production over time and by marginal cost being constant
over relevant intervals of output. Indeed, observe that the FOCs are in terms of MR and MC and that the
MR is a function of total sales and independent of what plants were used. This problem only affects Firm 1
as it is the only one who is able to allocate hydro production over time and that is able to combine thermal
and hydro plants to produce a certain output level. I want to remark that in spite of this multiplicity of
equilibrium, all the qualitative conclusions hold and magnitudes are very similar. Values reported in the
tables for q1h and q1th are averages calculated over 400 diferent estimations of the model.
46
Strictly speaking, Firm 2 is not producing at capacity as it still has some thermal plants that are not being
run. However, the big difference observed between the marginal cost of Firm 2’s next available plant and
the marginal plant at that demand level (almost $30) prevents Firm 2 from increasing production. By
contrast, Firm 1 has a large capacity at a relatively low marginal cost. See Figure 2
21
Firm 1 chooses to satisfy demand mainly through hydro production. In particular, it uses
all the hydro production that is available but allocates it differently than in the
competitive model. Firm 1 allocates relatively less water to high demand periods and
relatively more water to the low demand periods (See Figure 12) 47
. This hydro allocation
enlarges the difference between peak and off-peak periods, as opposed to what is
observed under competition. This effect is smaller the more elastic is demand. 48
. Firm
1’s hydro scheduling strategy is consistent with what has been found in the literature. In
their study of the Norwegian electricity market, Johnsen et al (1999) argued that “market
power can not be exercised in markets dominated by hydroelectric producers unless there
are transmission constraints”. The hydro producer exploits differences in demand
elasticity, reducing production when the constraint is binding (and demand is less elastic).
Notice that whether or not transmission constraints bind has an impact on the elasticity of
the residual demand faced by the Cournot producers as imports/exports of energy take
place (or not). My model results show that transmission constraints are not a necessary
condition for the exercise of market power by hydro producers. Capacity constraints
(supply constraints) will have the same effect. In other words if a hydro producer
competes with a thermal producer, the first one may choose to restrict production when
the thermal producer is capacity constrained, and to increase production the rest of the
time. In this way, one could say that Firm 1 faced a less elastic demand when Firm 2 is
capacity constrained. As a consequence, the shifting of hydro production is also the result
of Firm 1 exploiting differences in price elasticity.
Firm 1’s large hydro capacity is the source of its market power. Accordingly, Firm 1
explicitly schedules its hydro production in order to exploit differences in price elasticity
and exercises as much market power as it can. However Firm 1 also exercises market
power in a less observable way, namely the use (or more strictly speaking the “no use”)
of its thermal capacity. Indeed Firm 1 uses, on average, only 15% of its thermal capacity.
If Firm 1’s thermal portfolio were in a third generator’s portfolio, Firm 1 would be more
constrained in the exercise of its market power49
. On the other side, Firm 2’s large
thermal capacity was not enough to enable it to exercise market power. Behind this result
is the fact that a large fraction of its capacity are baseload plants, which are usually not
marginal and thus do not set the market price.
Firm 1’s markups are decreasing as the demand it faces falls and they go from 66% to
76%, with a weighted average of 72% when demand elasticity is –1/3 . The more elastic
is demand, the smaller are the Lerner Indices, as expected. Firm 2’s markups do not
47
This finding is consistent with Bushnell (1998)’s findings.
48
It cannot be argued that the demand assumptions are driving the results. Even though I am implicitly
imposing that peak demand is less elastic than off-peak demand (at a constant price) I am not imposing in
any way how the water should be allocated across periods. This is just a result of the model.
49
Arellano (2002a) estimates the market equilibrium assuming that Firm 1’s thermal portfolio is divested.
In particular, she analyzes the impact of selling Firm 1’s thermal portfolio to two different set of agents: i) a
unique producer and ii) many small producers with no market power.
22
exhibit the same monotone pattern. In particular, the Lerner index is larger during the
middle hours (Table 9). 50
The Cournot equilibrium is not only inefficient because production falls short the
competitive equilibrium production level but also because costs of production are not
minimized. In particular, the fringe is running plants that are less efficient (higher
marginal cost) than the ones that are being withheld by Firm 1 and hydro production is
used to increase the difference between peak and off peak periods.51
A final question regarding the exercise of market power in this industry is who are the
winners and the losers. In order to analyze this issue, I calculated each firm’s producer
surplus, the consumer surplus and welfare (as the sum of producer and consumer
surplus). Results are reported in Table 10.
All of the producers are better off when market power can be exercised. As expected the
less elastic is demand, the better off producers are and the worse off consumers are as
more market power can be exercised. Observe that even though it is Firm 1 the one who
is really able to constrain production and drive prices up, the real winner, in relative
terms, is Firm 2. The reason behind this result is clear: since Firm 2 is capacity
constrained when demand is high, its production level is very close to the competitive
level but the price is considerable higher.52
Finally notice that the increase in the producer
surplus almost compensates the consumer surplus’ reduction, keeping welfare loss at a
relatively low level.
VII. Extensions to the model
In order to evaluate how sensitive these results are to the assumptions used, I re-estimate
the model under two different conditions. First, I analyze the effect of a smaller amount
of water inflows being available to allocate over the planning horizon. This exercise is
motivated by the role hydro resources play in Firm 1’s market power. Secondly, it is
more realistic to think that Firm 1 may prefer to schedule its hydro production over a
longer planning horizon, saving a fraction of the hydropower available in a particular
month to be used in a later period. Therefore, the effect of producers maximizing over an
entire year rather than a month will be studied.
Cournot equilibrium with reduced hydro inflows.
The model was estimated assuming that the hydrology was “dry” rather than normal. In
particular, I assumed that hydro flows were 60% of the flows registered in a “normal”
50
The Lerner index shows market power that is exercised. Since Firm 2 is “capacity constrained”, it is
probably not exercising market power. Consequently, Firm 2’s Lerner index doesn’t have an economic
meaning during those periods.
51
The possibility of inefficient dispatching was pointed out by Von der Fehr and Harbord (1993),
Borenstein et al (2000) and Wolfram (1998).
52
Firm 1’s profits are considerably larger than Firm 2’s and so in absolute terms, the winner is Firm 1.
23
year53
. Since all hydro flows are assumed to be smaller, the fringe is also smaller and
residual demand is relatively less elastic than in the base model. Data used to calculate
residual demand are reported in Table 11 while Cournot and competitive equilibrium for
the E=-1/3 case is in Tables 12 and 13. The results for the E=-0.1, E=-1/2, E=-2/3 and
E=-1.0 are reported in Appendix #1.
Hydro flows are just enough to satisfy the minimum hydro production constraint; as a
consequence, Firm 1 and the Fringe have little hydro scheduling to do. In particular, the
fringe is not able to schedule its plants differently than running them at minimum
capacity. Therefore the shape of the load curve is completely preserved and peaks are not
eliminated, just reduced by a very small amount.
Since hydro resources are not abundant as before, thermal capacity is more intensely
used, driving prices considerably up - no matter whether the market is competitive or not.
The marginal value of water is also considerably higher as less efficient thermal plants
must be dispatched in order to meet demand.
Results reported in Table 13 show that even under these extreme circumstances
significant unilateral market power could be exercised. However, while Firm 1’s market
power has been diminished, Firm 2 has the incentive and the ability to act strategically by
withholding supplies from the market to keep them from falling further. Prices are lower
than when Firm 1’s hydro capacity was larger but at the same time, they are still above
the competitive equilibrium. Unlike what happened before, prices are increasingly
different the lower is demand. How can this be explained? Observe that Firm 1 is
capacity constrained when demand is at its maximum level. Therefore, Firm 1 constrains
more its thermal production (relative to the competitive equilibrium) the lower is
demand. In addition, and contrarily to what was found before, relatively more water is
allocated to periods of high demand and relatively less to periods of low demand54
. Firm
1 behaves like a price taker when demand is high and exercises some market power when
demand is low. On the other hand, Firm 2 constrains more its (thermal) production when
demand is high.
Firm 2 is still the producer who is benefited the most by the exercise of market power,
but similarly to what happens to the remaining producers, its net benefit is smaller than
when hydro flows are “normal”. (See Table 14). Observe that in relative terms,
consumers’ loss is smaller (relative to the competitive equilibrium) when hydro flows are
reduced as less market power is exercised. Since this more than compensates the smaller
increase in the producer surplus, welfare loss is also smaller.55
The finding that the
53
Actual values for the 1998/99 year (the driest in the past 40 years) are 55%, 78% and 60% for hydro
reservoirs, ROR and total hydro flows.
54
The shadow price of the minimum hydro production constraint is, for the first time, different than zero.
In particular, Firm 1is willing to pay to reduce the lower bound limit when demand is at medium and low
levels. Indeed it is willing to pay more the lower is the level of demand. This result is consistent with a
producer who is able to exercise market power only when demand is at medium-low levels.
55
Welfare loss from the exercise of market power being smaller when hydro flows are reduced (as opposed
to normal) does not mean that in absolute terms society is also better off. Indeed society is better off when
hydro flows are normal than dry, even is market power is exercised.
24
welfare loss from the exercise of market power is smaller when hydro flows are reduced
(as opposed to normal) does not mean that in absolute terms society is also better off.
Indeed society is better off when hydro flows are normal than dry, even if market power
is exercised.
Hydro scheduling over a longer time horizon
The model that was used to analyze the exercise of market power in Chile’s electricity
industry assumed that the hydro producer was able to allocate its hydro production over a
1 month planning horizon. Indeed, the optimization problem solved by Firm 1 in that
model, assumed that the water left in the reservoir at the end of the period had no value;
accordingly, the incentive to use less water than what is available is reduced. In real life,
however, producers usually maximize over a longer time horizon, and thus it is
reasonable to expect them to save a fraction of their hydro flows available in a particular
month to be used in a later period. An interesting question is whether Firm 1 would
follow the same hydro scheduling strategy that was found optimal in the 1-month model
if the planning horizon was longer. In particular, would Firm 1 exploit inter-month
differences in demand elasticity by moving water around? If so, then water should be
stored in those months in which demand is less elastic and released when demand is more
elastic. According to Table 15, this means that hydro production should be shifted from
October, November and December to March, January and the winter months (June-
August).56
There are at least two different approaches to investigate Firm 1’s hydro scheduling
strategy over the year: analysis of the marginal value of water (MVW) and a direct
estimation of the model assuming that the planning horizon is longer. Since the data set
required to estimate a comprehensive 1-year version of the model is not available, and
therefore many arbitrary assumptions would be needed, I will concentrate on the MVW
analysis. A very simple version of a 1-year model is analyzed and estimated in Appendix
#2.
The basic idea behind the MVW analysis is the following: given that generators allocate
their hydro production in order to equalize the marginal revenue across periods (subject
to capacity and/or production constraints) and that in equilibrium marginal revenue is
equal to the MVW, it is possible to use the latter to determine the hydro scheduling
strategy (when is water stored/ when it is released) that the producer would follow over
the year. In particular, if min/max flow constraints and min/max reservoir capacity
constraints are not binding, the MVW analysis would conclude that water inflows are
stored in months in which water is cheap (low MVW) and released in months in which
water is more expensive (high MVW). In other words, hydro production would be shifted
from low MR months to high MR months. If the hydro scheduling strategy that I found
that was optimal in the 1-month model is also followed by producers over the year, I
56
Market demand was parameterized as before, and thus it was assumed that price elasticity was –1/3 at the
peak anchor point. Residual demand is not constant throughout the year because must run production and
the fringe’s production fluctuates over the different months.
25
should find that: water is cheap (low MVW) in October, November and December and
more costly in March, January and the winter months (June-August) 57
.
In order to check for this hypothesis, I run the model and calculated the MVW for each
month of the year (Table 16). Observe that the MVW fluctuates over the year. Water is
more valuable in the first months of the year and less valuable in October, June, July and
November. Accordingly, if Firm 1 could reallocate hydro flows throughout the year, it
would store a fraction of them in the second half of the year and would use them in the
first half of the next year.58
The MVW is positively correlated to the inter-month
differences in demand elasticity suggesting that the hydro scheduling strategy is
consistent with the conclusions of the 1-month model, as hydro production would be
shifted from low demand elasticity months (low MVW) to high demand elasticity months
(High MVW). MVW is also positively correlated to the intra-month variation of demand
elasticity (fluctuations of demand elasticity within each month). According to this
evidence, the hydro producer would choose to “flood” the market not only when average
residual demand is relatively more elastic (and hence the market more competitive) but
also when the difference between min/max demand and price elasticity across periods is
larger, reinforcing the first effect.
Even though the hydro producer has incentive to exploit inter-month differences in
demand elasticity, and intra-month demand fluctuations, the incentive is not strong
enough to completely explain the hydro scheduling strategy over a longer planning
horizon. Indeed, the correlation coefficient between average elasticity of demand and the
MVW and between intra-month demand fluctuation and the MVW are relatively small
(0.24 and 0.26 respectively). Unlike that, the correlation between MVW and the ratio
inflows/net demand is very strong (correlation coefficient = -0.93) suggesting that
producers store hydro flows and release them across months according to how scarce
these flows are relative to demand. This relationship being stronger implies that the value
of water and its allocation over the year is mainly explained by a traditional supplydemand
analysis (i.e. store water when it is relatively abundant) than by a market power
argument (i.e. store water when demand is less elastic).
Why is it that Firm 1 would not schedule its hydro plants in order to exploit inter-month
differences in demand elasticity? There are, at least, two possible explanations. First,
producers may not need to allocate water from less elastic months to more elastic months
in order to exercise market power if they are already able to exercise it within a month. In
the 1-month version of the model, I found that Firm 1 exercised market power by
constraining its hydro production in periods of high demand, as its rivals were capacity
constrained and by using the “stored” water when the market was more competitive (low
demand). If there is enough intra-month demand variability, it is more likely that there
will be periods in which the producer will be able to release the stored water without a
57
Winter in the Southern hemisphere goes from June 21st
to September 21st
. January, February and
September coincide with vacation periods. In addition, the first two months are in the middle of the
summer. AC use is not spread in Chile.
58
This simple analysis does not take into account any technical constraint regarding maximum and
minimum capacity of reservoirs.
26
big impact on the market price. The Cournot equilibrium converging each month to the
competitive equilibrium as the demand level falls, indicates that the market is competitive
a fraction of the time, providing qualitative support to this argument59
. In order to check
for this hypothesis more formally, I estimated a calibrated version of the model assuming
that there were only inter-month differences in demand elasticity but no intra-month
demand fluctuation. If it is true that intra-month fluctuations are the reason why Firm 1
does not exploit differences in demand elasticity across months, then the correlation
coefficient should be higher. Results are reported in Table 17, column (2). As expected,
the correlation coefficient between the elasticity of demand and the MVW is higher but
only marginally. At the same time, the relationship between the value of water and its
availability (measured by the ratio inflows/net demand) is still very strong. These results
suggest that the intra-month demand fluctuation is only a second order explanation to the
hydro scheduling strategy followed over the year.
Alternatively, Firm 1 may not have incentive to exercise market power by shifting water
from one month to another because inter-month differences in price elasticity are not big
enough. Remember that the 1-month model, and associated marginal value of water was
estimated assuming that the price elasticity of market demand for electricity was –1/3 at
the peak anchor point (see Chapter V). Even though elasticity of residual demand
fluctuates both intra and inter-month as the size of the fringe and must run production
varies, it may be possible that this fluctuation is not sufficiently large. In order to check
for this hypothesis, I estimated the model assuming that the elasticity of market demand
was different over the year (but constant within each month).60
As a result of larger
differences in price elasticity (almost ten times), the correlation between the marginal
value of water and the average elasticity of demand also increased; the correlation
coefficient amounted to 0.88 (Table 17, column (3)). In other words, the larger are the
differences in inter-month price elasticity of demand, the greater the incentive to exercise
market power by shifting water from one month to another and the smaller the
relationship between the availability of water relative to demand and the value of water.
The larger the inter-month difference, the closer is the hydro scheduling strategy to the
market power explanation and further from the traditional supply/demand analysis. 61
Summing up, producers exercise market power by exploiting differences in price
elasticity, allocating too little supply to periods in which demand is relatively less elastic,
and relatively too much to periods with more elastic demand. This hydro scheduling
strategy may be observed no matter what the planning horizon of the model is; the only
“requirement” is that there is enough “inter-period” demand variability. The smaller the
fluctuation, the closer is the hydro scheduling strategy to the traditional supply-demand
analysis’ conclusions (i.e. more water to periods in which water is relatively scarce).
59
The correlation coefficient between the price ratio Cournot/Competitive equilibrium and the MVW is –
0.72.
60
It could take one of the following values: -0.1, -0.33, -0.5, -0.67, -1.0. These were randomly allocated to
each month.
61
In order to completely discard that this effect is explained by greater demand fluctuation within each
month, I re-calibrated the model, assuming the same inter-month difference in price elasticity but no intramonth
fluctuation (Table 17, column (4)). The correlation coefficient between the marginal value of water
and the average elasticity is almost unchanged.
27
VIII. Conclusions
Currently Chilean authorities are evaluating the desirability of moving one step forward
in the de-regulation process; in particular they are analyzing whether to stop regulating
the nodal price. Concerns have been raised due to the high concentrations indices that the
industry exhibits. In this paper I analyzed the question of whether these high
concentration indices would translate into prices significantly higher than the
competitive level as a result of suppliers exercising market power.
A model with 2 Cournot producers (Firms 1 and 2) and a competitive fringe was built.
Both producers own thermal plants but only one of them (Firm 1) also owns hydrostorage
plants. These plants turned out to be very important because they allowed the
producer to store water (and power) and to allocate it over a certain planning horizon at
its convenience. This alternative was not available to Firm 2.
I found that if an unregulated spot market were implemented in Chile’s electricity
industry, generators would have the incentive and ability to exercise market power,
raising prices significantly above competitive levels. In particular, Firm 1 would keep its
thermal plants outside of the market and would allocate its hydro resources in order to
take advantage of differences in price elasticity of demand; this means allocating too little
supply to high demand periods and too much to low demand periods (relative to the
competitive equilibrium). As a consequence, differences between peak and off peak
periods would be enlarged rather than reduced (as it would be if the market were
competitive). On the other side, Firm 2 would not be able to use its large thermal
portfolio to exercise market power most of the time. In fact, when demand is high, Firm 1
has so much market power and can drive prices up by so much that Firm 2’s best strategy
is to produce at capacity. Firm 2 is able to constrain its production only when demand is
low. Results slightly change when hydro flows are reduced, as it is Firm 2 the one who
really enjoys and exercises market power.
Conditions for the exercise of market power are more favorable the more inelastic is
demand, an expected result. However, since in this case a generator is able to “shift
power” from one period to another, there is an additional element that must be looked at
when diagnosing market power: the inter-period differences in price elasticity. In
particular, the larger the difference of price elasticity of demand across periods, the
greater the incentive Firm 1 has to exercise market power by shifting hydro production
from one period to another. This result applies no matter the length of the planning
horizon assumed in the model. These conclusions call for more accurate estimations of
elasticity of demand for electricity.
There are some elements of the model that should be kept in mind when analyzing its
results. First of all, results in general, and the magnitude of distortions in particular,
depend on the demand elasticity. The approach taken in this paper was to estimate the
model assuming different parameters for the demand elasticity. Because of the
importance of this parameter in the final result, more rigorous research in this topic is
28
required for the Chilean case. Secondly, the model has no dynamic elements although a
power exchange system is clearly a perfect scenario for repeated competition. It is
reasonable to think that this omission results in my model underestimating market power.
In light of these results, Chilean authorities should be aware of the risks entailed in deregulating
prices. A careful analysis of complementary measures that could be
implemented to mitigate market power is recommended. The model used in this paper
would certainly be a useful tool in that task, as it will allow estimating the impact of
alternative policies and doing comparative analysis. Chapter 2 examines policies (a) that
mitigate market power by breaking up the largest generating company through divestiture
of generating capacity and (b) that impose fixed price forward supply contracts on
varying amounts of the capacity owned by firms with market power.
29
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32
Tables
Table 1: Installed capacity in the SIC (December 2000), MW
Economic
Group
Thermal Hydro-
ROR
Hydro-
reservoir
Hydro Total %
thermal
% hydro % total
Endesa (Firm 1) 939 238 2454 2693 3632 25.9% 74.1% 55%
Gener (Firm 2) 1212 245 0 245 1457 83.2% 16.8% 22%
Colbun (Firm 3) 370 0 697 697 1067 34.7% 65.3% 16%
Other 102 403 0 403 504 20.1% 79.9% 8%
Total 2622 886 3151 4037 6660 39.0% 61.0% 100%
Source: CDEC-SIC
Table 2: Demand Estimation, April 2000, Elasticity = -1/3
Demand
level
# hours Anchor
quantity MW
Anchor price
US$/MW
A B Elasticity at
anchor point
1 120 4749.7 31.1 6332.9 50.9 0.333
2 120 4329.6 31.1 5912.8 50.9 0.366
3 120 4091.1 31.1 5674.3 50.9 0.387
4 120 3643.3 31.1 5226.5 50.9 0.435
5 120 3270.8 31.1 4854.0 50.9 0.484
6 120 2988.5 31.1 4571.7 50.9 0.530
Table 3: Data to calculate residual demand (MW), Base Model
Demand level Hydro peak
shaving
Thermal must run
generation
Hydro ROR Must run
generation
Total
1 274.6 14.2 380.3 669.1
2 183.8 14.2 380.3 578.2
3 183.8 14.2 380.3 578.2
4 183.8 14.2 380.3 578.2
5 183.8 14.2 380.3 578.2
6 183.8 14.2 380.3 578.2
Table 4: Hydro Data used to estimate the Base Model
Firm qh
min (MW) qh
max (MW) q~h
(GWh month)
Firm 1 743.7 2436.1 974.9
Fringe 183.8 489.2 143.2
Table 5: Base Model, Competitive results (E= -1/3)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe Qtot Price
1 673.1 944.4 1617.5 2133.1 0.0 2133.1 3750.6 420.5 4839.0 29.4
2 673.1 944.4 1617.5 1802.6 0.0 1802.6 3420.1 420.5 4418.9 29.4
3 673.1 944.4 1617.5 1564.1 0.0 1564.1 3181.6 420.5 4180.4 29.4
4 673.1 944.4 1617.5 1116.3 0.0 1116.3 2733.8 420.5 3732.6 29.4
5 673.1 944.4 1617.5 764.7 0.0 764.7 2382.2 420.1 3380.5 28.9
6 566.2 944.4 1510.6 743.7 0.0 743.7 2254.4 416.6 3249.3 26.0
33
Table 6: Base Model, Competitive results (E= -2/3)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe Qtot Price
1 673.1 944.4 1617.5 2133.1 0.0 2133.1 3750.6 421.5 4840.0 30.2
2 673.1 944.4 1617.5 1802.6 0.0 1802.6 3420.1 421.5 4419.9 30.2
3 673.1 944.4 1617.5 1564.1 0.0 1564.1 3181.6 421.5 4181.4 30.2
4 673.1 944.4 1617.5 1116.3 0.0 1116.3 2733.8 421.5 3733.6 30.2
5 673.1 944.4 1617.5 764.7 0.0 764.7 2382.2 421.3 3381.7 30.0
6 673.1 944.4 1617.5 743.7 0.0 743.7 2361.2 418.4 3357.8 27.5
Table 7: Base Model, Cournot Equilibrium (E=-1/3)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe Qtot Price
1 133.7 944.4 1078.1 1743.0 0.0 1743.0 2821.3 441.2 3931.3 47.2
2 140.1 944.4 1084.5 1572.0 0.0 1572.0 2656.5 437.5 3672.3 44.0
3 120.3 944.4 1064.7 1472.6 0.0 1472.6 2537.3 434.9 3550.4 41.7
4 122.0 944.4 1066.4 1247.0 0.0 1247.0 2313.4 429.9 3321.5 37.4
5 127.0 867.7 994.7 1094.1 0.0 1094.1 2088.7 426.6 3093.6 34.6
6 131.9 773.6 905.4 995.1 0.0 995.1 1900.6 424.5 2903.3 32.8
# denotes Multiple equilibrium. Values reported are averages over 400 different simulations
Table 8: Base Model, Cournot Equilibrium (E=-2/3)
t qth1# qth2 QRth qh1# qh2 QRh QR Qthfringe Qtot Price
1 377.7 944.4 1322.1 1768.1 0.0 1768.1 3090.2 429.0 4188.3 36.6
2 376.0 944.4 1320.4 1605.2 0.0 1605.2 2925.6 427.1 3930.9 35.0
3 378.3 944.4 1322.7 1483.6 0.0 1483.6 2806.3 425.8 3810.3 33.9
4 375.8 944.4 1320.2 1262.2 0.0 1262.2 2582.4 423.2 3583.9 31.7
5 379.6 944.4 1324.0 1072.2 0.0 1072.2 2396.2 421.1 3395.6 29.9
6 378.2 944.4 1322.5 932.5 0.0 932.5 2255.0 419.6 3252.8 28.5
# denotes Multiple equilibrium. Values reported are averages over 400 different simulations.
Table 9: Lerner Indices, Base Model
E = -1/3 E= -2/3
T Firm 1 Firm 2 Firm 1 Firm 2
1 76% 38% 57% 25%
2 75% 41% 55% 26%
3 73% 43% 53% 27%
4 70% 48% 50% 29%
5 68% 48% 47% 31%
6 66% 45% 45% 32%
Table 10: Welfare Analysis
Index (Perfect Competition = 100)
Elasticity Firm 1’s
Producer
surplus
Firm 2’s
Producer
surplus
Fringe’s
Producer
surplus
Producer
surplus
Consumer
surplus
Welfare
E = -0.1 242.7 586.0 352.6 319.1 64.0 94.6
E= -1/3 124.0 178.9 145.8 138.3 73.3 95.9
E= -1/2 112.4 131.8 118.5 117.0 82.7 98.1
E= -2/3 107.3 120.6 111.7 110.6 84.9 98.4
E= -1.0 104.0 109.8 105.7 105.4 88.4 99.1
34
Table 11: Data to calculate residual demand (MW).
Model with reduced hydro flows
Demand level Hydro peak
shaving
Thermal must run
generation
Hydro ROR Must run
generation
Total
1 119.3 14.2 228.2 361.7
2 119.3 14.2 228.2 361.7
3 119.3 14.2 228.2 361.7
4 119.3 14.2 228.2 361.7
5 119.3 14.2 228.2 361.7
6 119.3 14.2 228.2 361.7
Table 12: Competitive results with reduced hydro flows (E= -1/3)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe Qtot Price
1 779.2 992.9 1772.1 833.4 0.0 833.4 2605.5 572.6 3420.4 57.6
2 673.1 992.9 1666.0 808.2 0.0 808.2 2474.2 566.0 3282.6 51.9
3 673.1 992.9 1666.0 808.2 0.0 808.2 2474.2 560.6 3277.2 47.2
4 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 551.5 3219.6 39.4
5 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 543.3 3211.3 32.3
6 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 537.0 3205.0 26.9
Table 13: Cournot Equilibrium with reduced hydro flows (E=-1/3)
t qth1# qth2 QRth qh1 # qh2 QRh QR Qthfringe Qtot Price
1 614.3 944.4 1558.7 1029.6 0.0 1029.6 2588.3 453.2 3403.2 57.6
2 607.0 944.4 1551.4 826.8 0.0 826.8 2378.2 448.6 3188.4 53.5
3 527.4 944.4 1471.8 787.1 0.0 787.1 2258.9 445.9 3066.5 51.2
4 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 438.5 2942.8 44.9
5 426.4 944.4 1370.8 743.6 0.0 743.6 2114.4 430.9 2906.9 38.3
6 341.7 902.7 1244.4 743.6 0.0 743.6 1988.0 427.4 2777.1 35.3
# denotes multiple equilibrium. Values reported are averages over 400 different simulations.
Table 14: Welfare Analysis, Model with reduced hydro flows
Index (Perfect Competition = 100)
Elasticity Firm 1’s
Producer
surplus
Firm 2’s
Producer
surplus
Fringe’s
Producer
surplus
Producer
surplus
Consumer
surplus
Welfare
E = -0.1 123.4 147.9 144.6 135.3 77.7 96.7
E= -1/3 107.6 115.4 109.7 110.0 87.1 98.7
E= -1/2 103.7 107.4 103.1 104.4 92.2 99.3
E= -2/3 102.5 105.3 101.4 102.8 93.3 99.4
E= -1.0 101.4 103.2 99.9 101.4 94.5 99.4
35
Table15: Demand Indicators
Total
demand
(GWh)
Demand - qMR
(GWh) *
Inflows
(GWh)
Inflows
(demand – qMR)
Average Net
demand per
day (GWh)
Max demand
Min demand
Average Elasticity
Residual Ddand
January 2733.43 2293.80 1058.98 46% 74.0 2.20 0.49
February 2520.23 2139.77 996.86 47% 76.4 1.90 0.47
March 2911.54 2532.46 1333.09 53% 81.7 1.85 0.51
April 2768.74 2484.73 1118.05 45% 82.8 2.00 0.48
May 2885.11 2587.79 1294.28 50% 83.5 1.69 0.45
June 2794.75 2466.61 1561.06 63% 82.2 1.82 0.50
July 2820.53 2487.82 1475.91 59% 80.3 1.79 0.49
August 2799.88 2478.86 1384.18 56% 80.0 1.75 0.49
September 2649.14 2307.95 1262.55 55% 76.9 1.94 0.48
October 2770.69 2399.68 1478.88 62% 77.4 1.93 0.40
November 2751.61 2328.93 1385.07 59% 77.6 1.90 0.40
December 2859.66 2410.97 1279.78 53% 77.8 1.98 0.40
* qMR
includes production from must run thermal plants and hydro production from ROR plants.
Table 16: Marginal Value of Water (MVW)
E = -0.1 E = -1/3 E= - 0.5 E = -2/3 E = -1.0
January 0.00 11.13 11.13 13.91 17.90
February 0.00 11.13 11.13 13.54 17.75
March 0.00 10.62 11.13 13.36 17.75
April 0.00 11.13 11.89 15.78 19.85
May 0.00 9.53 11.13 12.78 17.29
June 0.00 0.00 7.78 11.13 14.21
July 0.00 1.92 10.08 11.13 15.41
August 0.00 6.45 11.13 11.13 15.78
September 0.00 8.47 11.13 11.98 17.03
October 0.00 0.00 9.82 11.13 15.78
November 0.00 2.21 11.13 11.13 17.01
December 0.00 9.88 11.13 14.61 20.28
36
Table 17: Marginal Value of Water under different price elasticity assumptions.
(1) (2) (3) (4) (1) (2) (3) (4) (1) (2) (3) (4) (1) (2) (3)
Jan 11.13 10.08 0.00 0.00 0.49 0.49 0.15 0.15 0.10 0.0 0.03 0.0 46% 110% 46%
Feb 11.13 9.33 17.75 17.25 0.47 0.47 1.36 1.36 0.08 0.0 0.23 0.0 47% 25% 47%
Mar 10.62 8.88 0.00 0.00 0.51 0.51 0.15 0.15 0.08 0.0 0.03 0.0 53% 131% 53%
Apr 11.13 11.13 15.78 15.45 0.48 0.48 0.94 0.94 0.10 0.0 0.19 0.0 45% 35% 45%
May 9.53 7.85 9.53 7.85 0.45 0.45 0.45 0.45 0.06 0.0 0.06 0.0 50% 63% 50%
Jun 0.00 0.00 0.00 0.00 0.50 0.50 0.50 0.50 0.09 0.0 0.09 0.0 63% 84% 63%
Jul 1.92 1.14 1.92 1.14 0.49 0.49 0.49 0.49 0.08 0.0 0.08 0.0 59% 81% 59%
Aug 6.45 5.32 11.13 11.13 0.49 0.49 0.73 0.73 0.09 0.0 0.13 0.0 56% 60% 56%
Sep 8.47 7.02 11.98 11.13 0.48 0.48 0.92 0.92 0.09 0.0 0.16 0.0 55% 45% 55%
Oct 0.00 0.00 11.13 11.13 0.40 0.40 0.72 0.72 0.06 0.0 0.11 0.0 62% 50% 62%
Nov 2.21 1.08 17.01 16.62 0.40 0.40 1.00 1.00 0.06 0.0 0.12 0.0 59% 35% 59%
Dec 9.88 7.90 14.61 14.02 0.40 0.40 0.72 0.72 0.06 0.0 0.09 0.0 53% 44% 53%
Average 6.87 5.81 9.24 8.81 0.46 0.46 0.68 0.68 0.08 0.0 0.11 0.0
stdev 4.55 4.16 6.93 6.83 0.04 0.04 0.35 0.35 0.02 0.06
Corr MVW 0.24 0.27 0.88 0.89 0.26 0.77 -0.93 -0.22
MVW Average Elasticity of
residual demand
St dev intra-month
elasticity
Inflows/ net demand
37
Figures
Figure 1
Marginal cost functions
0
20
40
60
80
100
120
140
0 200 400 600 800 1000 1200
Adjusted capacity, MW
US$/MW
Firm 1
Firm 2
Firm 3
Figure 2
Marginal cost functions
(US$/MW)
0
20
40
60
80
100
120
0 200 400 600 800 100 120
Adjusted capacity, MW
Firm 1 Firm 2 Fringe
38
Figure 3
Figure 4
Load per hour (April 2000)
2000
2500
3000
3500
4000
4500
5000
5500
1 101 201 301 401 501 601 701
Hour
MW
Anchor price/quantity
10
15
20
25
30
35
2500 3000 3500 4000 4500 5000
Output (MW)
price
t=1
t=2
t=3
t=4
t=5
t=6
39
Figure 5
Figure 6
Fringe's MC if 2 strategic producers
0
10
20
30
40
50
60
0 100 200 300 400 500
Capacity, MW
$/MW
Peak shaving results (April 2000)
0
1000
2000
3000
4000
5000
6000
1
40
79
118
157
196
235
274
313
352
391
430
469
508
547
586
625
664
703
Ranking (hour)
MW
Loadcurve
Shaveddemand
Hydro generation
40
Figure 7
Figure 8
Residual Demand E=0.33
0
5
10
15
20
25
30
35
40
1000 2000 3000 4000 5000 6000
MW
US$/MW
1 2 3 4 5 6
Peak shaving results (April 2000)
0
1000
2000
3000
4000
5000
6000
1
48
95
142
189
236
283
330
377
424
471
518
565
612
659
706
Ranking (hour)
MW
Load curve
Hydro
generation
Shaved demand
Entire system
41
Figure 9
Figure 10
Price
25
30
35
40
45
50
1 2 3 4 5 6
$/MW
Cournot, E= -1/3
Cournot, E=-2/3
PC, E=-2/3
PC, E=-1/3
Total production
2500
3000
3500
4000
4500
5000
1 2 3 4 5 6
MW
Base, E= -1/3
Base, E=-2/3
PC
42
Figure 11
Figure 12
Firm 1's hydro production
0
500
1000
1500
2000
2500
1 2 3 4 5 6
MW
Base, E=-1/3
Base, E=-2/3
PC
Firm 2's thermal production
600
700
800
900
1000
1 2 3 4 5 6
MW
Base, E= -1/3
PC
Base, E=-2/3
43
APPENDIX # 1 - TABLES
1. Base Model, Same slope approach
A. Competitive Equilibrium (Same slope approach)
Table A1.1: Competitive equilibrium (E=-0.1)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 665.94 944.40 1610.34 2133.1 0 2133.1 3743.4 690.03 394.46 2406.49 4827.9 26.0
2 665.94 944.40 1610.34 1802.6 0 1802.6 3412.9 600.43 394.46 1986.36 4407.8 26.0
3 665.94 944.40 1610.34 1564.1 0 1564.1 3174.4 600.43 394.46 1747.87 4169.3 26.0
4 665.94 944.40 1610.34 1116.3 0 1116.3 2726.6 600.43 394.46 1300.08 3721.5 26.0
5 645.03 944.40 1589.43 764.7 0 764.7 2354.1 600.43 394.46 948.48 3349.0 26.0
6 454.60 944.40 1399.00 743.7 0 743.7 2142.7 595.43 394.46 927.52 3132.6 21.7
Table A1.2: Competitive equilibrium (E=-1/3)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.1 944.4 1617.5 2133.1 0.0 2133.1 3750.6 693.9 394.46 2406.49 4839.0 29.4
2 673.1 944.4 1617.5 1802.6 0.0 1802.6 3420.1 604.3 394.46 1986.36 4418.9 29.4
3 673.1 944.4 1617.5 1564.1 0.0 1564.1 3181.6 604.3 394.46 1747.87 4180.4 29.4
4 673.1 944.4 1617.5 1116.3 0.0 1116.3 2733.8 604.3 394.46 1300.08 3732.6 29.4
5 673.1 944.4 1617.5 764.7 0.0 764.7 2382.2 603.9 394.46 948.48 3380.5 28.9
6 566.2 944.4 1510.6 743.7 0.0 743.7 2254.4 600.4 394.46 927.52 3249.3 26.0
Table A1.3: Competitive equilibrium (E=-0.5)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.10 944.40 1617.50 2133.1 0 2133.1 3750.6 694.61 394.46 2406.49 4839.7 29.9
2 673.10 944.40 1617.50 1802.6 1 1803.6 3421.1 605.01 394.46 1986.36 4420.5 29.9
3 673.10 944.40 1617.50 1564.1 2 1566.1 3183.6 605.01 394.46 1747.87 4183.0 29.9
4 673.10 944.40 1617.50 1116.3 3 1119.3 2736.8 605.01 394.46 1300.08 3736.2 29.9
5 673.10 944.40 1617.50 764.7 4 768.7 2386.2 604.69 394.46 948.48 3385.3 29.7
6 673.10 944.40 1617.50 743.7 5 748.7 2366.2 600.79 394.46 927.52 3361.5 26.3
Table A1.4: Competitive equilibrium (E=-2/3)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.1 944.4 1617.5 2133.1 0.0 2133.1 3750.6 694.9 394.46 2406.49 4840.0 30.2
2 673.1 944.4 1617.5 1802.6 0.0 1802.6 3420.1 605.3 394.46 1986.36 4419.9 30.2
3 673.1 944.4 1617.5 1564.1 0.0 1564.1 3181.6 605.3 394.46 1747.87 4181.4 30.2
4 673.1 944.4 1617.5 1116.3 0.0 1116.3 2733.8 605.3 394.46 1300.08 3733.6 30.2
5 673.1 944.4 1617.5 764.7 0.0 764.7 2382.2 605.1 394.46 948.48 3381.7 30.0
6 673.1 944.4 1617.5 743.7 0.0 743.7 2361.2 602.2 394.46 927.52 3357.8 27.5
Table A1.5: Competitive equilibrium (E=-1.0)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.10 944.40 1617.50 2133.1 0 2133.1 3750.6 695.28 394.46 2406.49 4840.3 30.5
2 673.10 944.40 1617.50 1802.6 0 1802.6 3420.1 605.68 394.46 1986.36 4420.2 30.5
3 673.10 944.40 1617.50 1564.1 0 1564.1 3181.6 605.68 394.46 1747.87 4181.7 30.5
4 673.10 944.40 1617.50 1116.3 0 1116.3 2733.8 605.68 394.46 1300.08 3733.9 30.5
5 673.10 944.40 1617.50 764.7 0 764.7 2382.2 605.53 394.46 948.48 3382.2 30.4
6 673.10 944.40 1617.50 743.7 0 743.7 2361.2 603.56 394.46 927.52 3359.2 28.7
44
B. Cournot equilibrium (Same slope approach)
Table A1.6: Cournot equilibrium (E=-0.1)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 0.0 944.4 944.4 1612.3 0.0 1612.3 2556.7 500.3 394.46 274.6 3726.1 98.1
2 0.0 944.4 944.4 1447.7 0.0 1447.7 2392.1 488.6 394.46 183.8 3459.0 88.1
3 0.0 944.4 944.4 1328.4 0.0 1328.4 2272.8 480.2 394.46 183.8 3331.3 80.9
4 0.0 854.9 854.9 1149.3 0.0 1149.3 2004.2 467.6 394.46 183.8 3050.0 70.0
5 0.0 730.7 730.7 1025.1 0.0 1025.1 1755.9 458.8 394.46 183.8 2792.9 62.4
6 0.0 636.6 636.6 931.0 0.0 931.0 1567.7 452.2 394.46 183.8 2598.1 56.7
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.7: Cournot equilibrium (E=-1/3)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 133.7 944.4 1078.1 1743.0 0.0 1743.0 2821.1 441.2 394.46 274.6 3931.4 47.2
2 140.1 944.4 1084.5 1572.0 0.0 1572.0 2656.5 437.5 394.46 183.8 3672.3 44.0
3 120.3 944.4 1064.7 1472.6 0.0 1472.6 2537.3 434.9 394.46 183.8 3550.4 41.7
4 122.0 944.4 1066.4 1247.0 0.0 1247.0 2313.4 429.9 394.46 183.8 3321.5 37.4
5 127.0 867.7 994.7 1094.1 0.0 1094.1 2088.8 426.6 394.46 183.8 3093.6 34.6
6 131.9 773.6 905.4 995.1 0.0 995.1 1900.6 424.5 394.46 183.8 2903.3 32.8
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.8: Cournot equilibrium (E=-0.5)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 341.7 944.4 1286.1 1759.9 0.0 1759.9 3046.0 431.7 394.46 274.6 4146.8 39.0
2 341.7 944.4 1286.1 1595.3 0.0 1595.3 2881.4 429.3 394.46 183.8 3888.9 36.9
3 341.7 944.4 1286.1 1476.0 0.0 1476.0 2762.1 427.5 394.46 183.8 3767.8 35.3
4 341.7 944.4 1286.1 1252.1 0.0 1252.1 2538.2 424.1 394.46 183.8 3540.6 32.4
5 341.7 941.5 1283.2 1067.3 0.0 1067.3 2350.5 421.4 394.46 183.8 3350.1 30.1
6 341.7 847.4 1189.1 973.2 0.0 973.2 2162.3 420.0 394.46 183.8 3160.5 28.9
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.9:Cournot equilibrium (E=-2/3)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 377.7 944.4 1322.1 1768.1 0.0 1768.1 3090.2 429.0 394.46 274.6 4188.3 36.6
2 376.0 944.4 1320.4 1605.2 0.0 1605.2 2925.6 427.1 394.46 183.8 3930.9 35.0
3 378.3 944.4 1322.7 1483.6 0.0 1483.6 2806.3 425.8 394.46 183.8 3810.3 33.9
4 375.8 944.4 1320.2 1262.2 0.0 1262.2 2582.4 423.2 394.46 183.8 3583.9 31.7
5 379.6 944.4 1324.0 1072.2 0.0 1072.2 2396.2 421.1 394.46 183.8 3395.6 29.9
6 378.2 944.4 1322.5 932.5 0.0 932.5 2255.0 419.6 394.46 183.8 3252.8 28.5
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
45
Table A1.10: Cournot equilibrium (E=-1.0)
t qth1# qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 454.6 944.4 1399.0 1768.2 0.0 1768.2 3167.2 426.3 394.46 274.6 4262.5 34.3
2 454.6 944.4 1399.0 1603.6 0.0 1603.6 3002.6 425.0 394.46 183.8 4005.8 33.2
3 454.6 944.4 1399.0 1484.3 0.0 1484.3 2883.3 424.1 394.46 183.8 3885.7 32.4
4 454.6 944.4 1399.0 1260.4 0.0 1260.4 2659.4 422.4 394.46 183.8 3660.1 31.0
5 454.6 944.4 1399.0 1074.2 0.0 1074.2 2473.2 421.0 394.46 183.8 3472.4 29.8
6 454.6 944.4 1399.0 933.0 0.0 933.0 2332.0 420.0 394.46 183.8 3330.2 28.9
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.11: Lerner Indices
E=-0.1 E=-1/3 E=0.5 E= -2/3 E=-1.0
t Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2
1 100% 59% 76% 38% 70% 31% 57% 25% 42% 18%
2 100% 65% 75% 41% 68% 33% 55% 26% 40% 18%
3 100% 71% 73% 43% 66% 34% 53% 27% 39% 19%
4 100% 74% 70% 48% 63% 38% 50% 29% 36% 20%
5 100% 71% 68% 48% 60% 40% 47% 31% 33% 21%
6 100% 68% 66% 45% 59% 38% 45% 32% 31% 21%
46
2. Base Model, Different slope approach
A. Competitive Equilibrium (Different slope approach)
Table A1.12: Competitive equilibrium (E=-0.1)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 665.94 944.40 1610.34 2133.1 0 2133.1 3743.4 690.0 394.46 2406.49 4827.9 25.98
2 659.02 944.40 1603.42 1802.6 0 1802.6 3406.0 600.4 394.46 1986.36 4400.9 25.98
3 655.09 944.40 1599.49 1564.1 0 1564.1 3163.6 600.4 394.46 1747.87 4158.5 25.98
4 647.72 944.40 1592.12 1116.3 0 1116.3 2708.4 600.4 394.46 1300.08 3703.3 25.98
5 620.67 944.40 1565.07 764.7 0 764.7 2329.7 600.4 394.46 948.48 3324.6 25.98
6 454.60 931.31 1385.91 743.7 0 743.7 2129.6 591.1 394.46 927.52 3115.2 17.92
Table A1.13: Competitive equilibrium (E=-1/3)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.1 944.4 1617.5 2133.1 0 2133.1 3750.6 693.9 394.46 2406.49 4839.0 29.4
2 673.1 944.4 1617.5 1802.6 0 1802.6 3420.1 604.1 394.46 1986.36 4418.7 29.2
3 673.1 944.4 1617.5 1564.1 0 1564.1 3181.6 604.0 394.46 1747.87 4180.0 29.1
4 673.1 944.4 1617.5 1116.3 0 1116.3 2733.8 603.7 394.46 1300.08 3732.0 28.8
5 673.1 944.4 1617.5 764.7 0 764.7 2382.2 602.8 394.46 948.48 3379.4 28.0
6 469.5 944.4 1413.9 743.7 0 743.7 2157.7 600.4 394.46 927.52 3152.6 26.0
Table A1.14: Competitive equilibrium (E=-0.5)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.10 944.40 1617.50 2133.1 0 2133.1 3750.6 694.6 394.46 2406.49 4839.7 29.93
2 673.10 944.40 1617.50 1802.6 0 1802.6 3420.1 604.9 394.46 1986.36 4419.4 29.81
3 673.10 944.40 1617.50 1564.1 0 1564.1 3181.6 604.8 394.46 1747.87 4180.8 29.74
4 673.10 944.40 1617.50 1116.3 0 1116.3 2733.8 604.6 394.46 1300.08 3732.8 29.58
5 673.10 944.40 1617.50 764.7 0 764.7 2382.2 604.0 394.46 948.48 3380.6 29.02
6 551.59 944.40 1495.99 743.7 0 743.7 2239.7 600.4 394.46 927.52 3234.6 25.98
Table A1.15: Competitive equilibrium (E=-2/3)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.1 944.4 1617.5 2133.1 0.0 2133.1 3750.6 694.9 394.46 2406.49 4840.0 30.2
2 673.1 944.4 1617.5 1802.6 0.0 1802.6 3420.1 605.2 394.46 1986.36 4419.8 30.1
3 673.1 944.4 1617.5 1564.1 0.0 1564.1 3181.6 605.2 394.46 1747.87 4181.2 30.1
4 673.1 944.4 1617.5 1116.3 0.0 1116.3 2733.8 605.0 394.46 1300.08 3733.3 30.0
5 673.1 944.4 1617.5 764.7 0.0 764.7 2382.2 604.5 394.46 948.48 3381.2 29.5
6 633.6 944.4 1578.0 743.7 0.0 743.7 2321.7 600.4 394.46 927.52 3316.6 26.0
Table A1.16: Competitive equilibrium (E=-1.0)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.10 944.40 1617.50 2133.1 0 2133.1 3750.6 695.3 394.46 2406.49 4840.3 30.51
2 673.10 944.40 1617.50 1802.6 0 1802.6 3420.1 605.6 394.46 1986.36 4420.1 30.45
3 673.10 944.40 1617.50 1564.1 0 1564.1 3181.6 605.6 394.46 1747.87 4181.6 30.42
4 673.10 944.40 1617.50 1116.3 0 1116.3 2733.8 605.5 394.46 1300.08 3733.7 30.33
5 673.10 944.40 1617.50 764.7 0 764.7 2382.2 605.1 394.46 948.48 3381.8 30.05
6 673.10 944.40 1617.50 743.7 0 743.7 2361.2 601.9 394.46 927.52 3357.6 27.26
47
B. Cournot equilibrium (Different slope approach)
Table A1.17: Cournot equilibrium (E=-0.1)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 0.0 944.4 944.4 1612.3 0.0 1612.3 2556.7 500.1 394.46 274.6 3725.9 98.0
2 0.0 944.4 944.4 1426.7 0.0 1426.7 2371.1 496.3 394.46 183.8 3445.6 94.7
3 0.0 944.4 944.4 1295.5 0.0 1295.5 2239.9 491.1 394.46 183.8 3309.2 90.2
4 0.0 860.7 860.7 1091.1 0.0 1091.1 1951.8 484.9 394.46 183.8 3014.9 84.9
5 0.0 738.4 738.4 947.3 0.0 947.3 1685.8 480.7 394.46 183.8 2744.7 81.3
6 0.0 645.7 645.7 838.4 0.0 838.4 1484.1 476.8 394.46 183.8 2539.2 77.9
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.18: Cournot equilibrium (E=-1/3)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 61.2 944.4 1005.6 1815.6 0.0 1815.6 2821.2 441.2 394.46 274.6 3931.5 47.2
2 59.0 944.4 1003.4 1608.1 0.0 1608.1 2611.5 440.0 394.46 183.8 3629.8 46.2
3 49.7 944.4 994.0 1472.7 0.0 1472.7 2466.8 438.6 394.46 183.8 3483.6 45.0
4 31.4 944.4 975.7 1219.2 0.0 1219.2 2194.9 435.5 394.46 183.8 3208.6 42.2
5 21.1 833.9 855.0 1058.6 0.0 1058.6 1913.6 434.0 394.46 183.8 2925.8 40.9
6 9.0 733.3 742.3 949.6 0.0 949.6 1691.9 432.9 394.46 183.8 2703.1 40.0
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.19: Cournot equilibrium (E=-0.5)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 248.6 944.4 1193.0 1882.4 0.0 1882.4 3075.4 431.3 394.46 274.6 4175.7 38.6
2 241.2 944.4 1185.6 1657.7 0.0 1657.7 2843.2 430.5 394.46 183.8 3852.0 38.0
3 242.8 944.4 1187.2 1498.5 0.0 1498.5 2685.7 429.6 394.46 183.8 3693.5 37.1
4 232.2 944.4 1176.6 1213.3 0.0 1213.3 2389.9 427.5 394.46 183.8 3395.6 35.3
5 259.0 871.2 1130.2 977.1 0.0 977.1 2107.3 426.1 394.46 183.8 3111.6 34.1
6 206.6 767.5 974.1 894.8 0.0 894.8 1868.9 425.4 394.46 183.8 2872.5 33.5
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.20: Cournot equilibrium (E=-2/3)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 341.7 944.4 1286.1 1933.0 0.0 1933.0 3219.1 427.5 394.46 274.6 4315.7 35.4
2 341.7 944.4 1286.1 1688.1 0.0 1688.1 2974.2 426.9 394.46 183.8 3979.3 34.9
3 341.7 944.4 1286.1 1523.2 0.0 1523.2 2809.3 426.2 394.46 183.8 3813.8 34.3
4 341.7 944.4 1286.1 1213.8 0.0 1213.8 2499.9 424.7 394.46 183.8 3502.8 32.9
5 341.7 944.4 1286.1 956.4 0.0 956.4 2242.5 423.0 394.46 183.8 3243.7 31.5
6 341.7 848.2 1190.0 809.3 0.0 809.3 1999.3 422.4 394.46 183.8 2999.9 30.9
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
48
Table A1.21: Cournot equilibrium (E=-1.0)
t qth1 # qth2 QRth qh1 # qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 454.6 944.4 1399.0 1969.6 0.0 1969.6 3368.5 424.8 394.46 274.6 4462.4 33.0
2 454.6 944.4 1399.0 1711.2 0.0 1711.2 3110.2 424.4 394.46 183.8 4112.8 32.7
3 454.6 944.4 1399.0 1538.8 0.0 1538.8 2937.7 423.9 394.46 183.8 3939.9 32.3
4 454.6 944.4 1399.0 1215.0 0.0 1215.0 2614.0 422.8 394.46 183.8 3615.1 31.3
5 454.6 944.4 1399.0 945.7 0.0 945.7 2344.6 421.8 394.46 183.8 3344.6 30.4
6 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 420.7 394.46 183.8 3141.5 29.5
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.22: Lerner Indices
E=-0.1 E=-1/3 E=0.5 E= -2/3 E=-1.0
t Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2
1 100% 59% 76% 38% 71% 32% 62% 26% 48% 19%
2 100% 66% 76% 43% 71% 35% 62% 29% 47% 21%
3 100% 73% 75% 47% 70% 38% 61% 31% 47% 22%
4 100% 79% 74% 56% 69% 45% 60% 36% 45% 25%
5 100% 78% 73% 56% 67% 48% 58% 42% 43% 29%
6 100% 77% 72% 55% 67% 47% 57% 42% 42% 33%
49
3. Base Model, Same slope approach, Reduced Hydro Flows
A. Competitive Equilibrium (Same slope approach)
Table A1.23: Competitive equilibrium (E=-0.1)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 860.0 1101.3 1961.3 833.4 0.0 833.4 2794.7 629.9 242.4 952.7 3666.9 107.0
2 779.2 1101.3 1880.5 808.2 0.0 808.2 2688.7 606.1 242.4 927.5 3537.1 86.5
3 779.2 992.9 1772.1 808.2 0.0 808.2 2580.3 596.2 242.4 927.5 3418.9 78.0
4 705.2 992.9 1698.1 808.2 0.0 808.2 2506.3 566.8 242.4 927.5 3315.4 52.6
5 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 546.2 242.4 927.5 3214.3 34.8
6 535.8 944.4 1480.2 808.2 0.0 808.2 2288.4 536.0 242.4 927.5 3066.7 26.0
Table A1.24: Competitive equilibrium (E=-1/3)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 779.2 992.9 1772.1 833.4 0.0 833.4 2605.5 572.6 242.4 952.7 3420.4 57.6
2 673.1 992.9 1666.0 808.2 0.0 808.2 2474.2 566.0 242.4 927.5 3282.6 51.9
3 673.1 992.9 1666.0 808.2 0.0 808.2 2474.2 560.6 242.4 927.5 3277.2 47.2
4 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 551.5 242.4 927.5 3219.6 39.4
5 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 543.3 242.4 927.5 3211.3 32.3
6 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 537.0 242.4 927.5 3205.0 26.9
Table A1.25: Competitive equilibrium (E=-0.5)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.1 992.9 1666.0 833.4 0.0 833.4 2499.4 564.0 242.4 952.7 3305.7 50.2
2 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 558.7 242.4 927.5 3226.8 45.6
3 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 555.1 242.4 927.5 3223.2 42.5
4 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 548.4 242.4 927.5 3216.4 36.7
5 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 542.8 242.4 927.5 3210.9 31.9
6 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 538.6 242.4 927.5 3206.6 28.2
Table A1.26: Competitive equilibrium (E=-2/3)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.1 944.4 1617.5 833.4 0.0 833.4 2450.9 559.0 242.4 952.7 3252.3 45.9
2 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 554.5 242.4 927.5 3222.6 42.0
3 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 551.8 242.4 927.5 3219.9 39.7
4 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 546.8 242.4 927.5 3214.8 35.3
5 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 542.6 242.4 927.5 3210.6 31.7
6 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 539.4 242.4 927.5 3207.5 29.0
Table A1.27: Competitive equilibrium (E=-1.0)
t qth1 qth2 QRth qh1 qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.1 944.4 1617.5 833.4 0.0 833.4 2450.9 553.3 242.4 952.7 3246.5 40.9
2 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 550.3 242.4 927.5 3218.4 38.4
3 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 548.5 242.4 927.5 3216.6 36.8
4 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 545.2 242.4 927.5 3213.2 33.9
5 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 542.4 242.4 927.5 3210.4 31.5
6 673.1 944.4 1617.5 808.2 0.0 808.2 2425.7 540.2 242.4 927.5 3208.3 29.7
50
B. Cournot equilibrium, Same slope approach, Reduced Hydro Flows
Table A1.28: Cournot equilibrium (E=-0.1)
t qth1 # qth2 QRth qh1 # Qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 486.8 992.9 1479.8 1041.5 0.0 1041.5 2521.2 524.4 242.4 119.3 3407.4 119.0
2 488.9 983.0 1472.0 834.2 0.0 834.2 2306.2 510.0 242.4 119.3 3177.9 106.5
3 455.6 944.4 1399.9 767.8 0.0 767.8 2167.7 502.9 242.4 119.3 3032.3 100.4
4 341.7 944.4 1286.1 743.6 0.0 743.6 2029.7 481.1 242.4 119.3 2872.5 81.6
5 231.8 863.9 1095.7 743.6 0.0 743.6 1839.3 468.2 242.4 119.3 2669.2 70.5
6 137.7 769.8 907.5 743.6 0.0 743.6 1651.1 461.6 242.4 119.3 2474.4 64.8
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.29: Cournot equilibrium (E=-1/3)
t qth1 # qth2 QRth qh1 # Qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 614.3 944.4 1558.7 1029.6 0.0 1029.6 2588.3 453.2 242.4 119.3 3403.2 57.6
2 607.0 944.4 1551.4 826.8 0.0 826.8 2378.2 448.6 242.4 119.3 3188.4 53.5
3 527.4 944.4 1471.8 787.1 0.0 787.1 2258.9 445.9 242.4 119.3 3066.5 51.2
4 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 438.5 242.4 119.3 2942.8 44.9
5 426.4 944.4 1370.8 743.6 0.0 743.6 2114.4 430.9 242.4 119.3 2906.9 38.3
6 341.7 902.7 1244.4 743.6 0.0 743.6 1988.0 427.4 242.4 119.3 2777.1 35.3
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.30: Cournot equilibrium (E=-0.5)
t qth1 # qth2 QRth qh1 # Qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 662.7 944.4 1607.1 1046.3 0.0 1046.3 2653.4 442.2 242.4 119.3 3457.3 48.0
2 662.7 944.4 1607.1 836.3 0.0 836.3 2443.4 439.0 242.4 119.3 3244.1 45.3
3 618.9 944.4 1563.3 760.9 0.0 760.9 2324.1 437.3 242.4 119.3 3123.1 43.8
4 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 433.3 242.4 119.3 2937.6 40.3
5 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 427.7 242.4 119.3 2932.0 35.5
6 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 423.5 242.4 119.3 2927.8 31.9
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.31:Cournot equilibrium (E=-2/3)
t qth1 # qth2 QRth qh1 # Qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.1 944.4 1617.5 1055.0 0.0 1055.0 2672.4 437.1 242.4 119.3 3471.3 43.7
2 673.1 944.4 1617.5 844.9 0.0 844.9 2462.4 434.8 242.4 119.3 3258.8 41.6
3 673.1 944.4 1617.5 743.6 0.0 743.6 2361.1 433.2 242.4 119.3 3156.0 40.3
4 477.5 944.4 1421.8 743.6 0.0 743.6 2165.4 430.4 242.4 119.3 2957.5 37.8
5 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 426.4 242.4 119.3 2930.7 34.4
6 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 423.3 242.4 119.3 2927.5 31.7
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
51
Table A1.32: Cournot equilibrium (E=-1.0)
t qth1 # qth2 QRth qh1 # Qh2 QRh QR Qthfringe qMR qhPS Qtot Price
1 673.1 944.4 1617.5 1055.0 0.0 1055.0 2672.4 432.3 242.4 119.3 3466.4 39.5
2 673.1 944.4 1617.5 844.9 0.0 844.9 2462.4 430.7 242.4 119.3 3254.8 38.1
3 673.1 944.4 1617.5 743.6 0.0 743.6 2361.1 429.7 242.4 119.3 3152.4 37.2
4 607.8 944.4 1552.2 743.6 0.0 743.6 2295.8 426.8 242.4 119.3 3084.3 34.8
5 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 425.2 242.4 119.3 2929.4 33.3
6 454.6 944.4 1399.0 743.6 0.0 743.6 2142.6 423.0 242.4 119.3 2927.3 31.5
# denotes multiple equilibrium. Values reported are averages over 400 simulations.
Table A1.33: Lerner Indices
E=-0.1 E=-1/3 E=0.5 E= -2/3 E=-1.0
t Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2
1 78% 51% 55% 32% 46% 25% 38% 21% 28% 16%
2 76% 56% 51% 34% 43% 27% 35% 22% 26% 16%
3 74% 57% 49% 35% 41% 28% 34% 23% 25% 16%
4 81% 70% 51% 40% 38% 30% 31% 24% 25% 18%
5 84% 75% 59% 47% 43% 34% 34% 27% 23% 18%
6 83% 72% 59% 49% 48% 38% 37% 29% 25% 19%
52
Appendix #2
A simple 1-year Cournot model for Chile’s Electricity Industry
The model that was used to analyze the exercise of market power in Chile’s electricity
industry assumed that the hydro producer was able to allocate its hydro production over a
1 month planning horizon. In addition, in that model no value was given to the water left
in the reservoir at the end of the month. Accordingly, even though Firm 1, the hydro
producer, was “allowed” by the model to use only a fraction of the water available,
incentives pushed more in the direction of using it all.
In real life, however, producers usually maximize over a longer time horizon, and thus it
is reasonable to expect them to store a fraction of their hydro flows available in a
particular month in order to use them in a later period. An interesting question is whether
the hydro scheduling pattern that resulted in the 1-month period model would also be
observed when a longer planning horizon is assumed. If so, generators would exploit
differences in demand elasticity across months by shifting water from low demand
elasticity months to high demand elasticity months. According to the data reported in
Table 15, this means that water should be stored in October, November and December
and released in April, March, January and the winter months62
. In the paper I report
evidence based on MVW analysis suggesting that Firm 1’s incentive to exercise market
power by shifting hydro production from one month to another depends on how large are
the inter-month differences in demand elasticity/ The smaller the fluctuations, the closer
is the hydro scheduling strategy to the traditional competitive supply-demand or valuemaximizing
optimization analysis’ conclusions (i.e. water is stored when it is relatively
abundant and released when it is relatively scarce).
The MVW analysis is helpful in that one can draw conclusions regarding how hydro
flows would be allocated across months, but it does not provide information regarding the
size of the flows that are stored and later released. In addition, it is not possible to
compare the market equilibrium when market power is and is not exercised. In order to
address these issues, a very simple 1-year model was estimated. This model will still
suffer the omission of re-allocation across years but will probably shed lights of the reallocations
that happen within a year.
Given that the estimation of this model was computationally intensive, I had to use many
simplifying assumptions. In addition, information on many variables was required but not
available; as a consequence, additional assumptions were required.
62
Market demand was parameterized as before, and thus it was assumed that price elasticity was –1/3 at the
peak anchor point. Residual demand is not constant throughout the year because must run production and
the fringe’s production fluctuates over the different months.
53
The Model
The model is basically the same than the 1-month model. I assumed that there are only
two periods per month (rather than 6 as in the 1-month model): a high demand period and
a low demand period (t=1 and t=2 respectively). Each of them lasts for 360/372 hours.
Notice that by reducing the number of periods to only two, I am implicitly reducing the
demand variability. Given that Firm 1 is allowed to store hydro flows one month and
release them in a later period, a state variable, namely the reservoir level, is introduced.
Water inflows are assumed to get to the reservoir at the beginning of each month.
Each period, Cournot producers face a residual demand given by:
DR
(Pt) = D(Pt) – S f
(Pt) – qMR
t - qPS
ht
where D(P) is expected market demand, DR
(P) is expected residual market demand, S f
(P) is the Fringe’s (thermal) supply function (adjusted by transmission losses), qMR
is
must-run units’ generation and qPS
h is the Fringe’s hydro production from reservoirs
distributed across periods according to a Peak shaving strategy.
Firm 2’s optimization problem remains basically the same than in the 1-year model. Firm
1’s optimization problem is modified to take account of the reservoir level, and the
corresponding minimum and maximum capacity constraints.
Firm 1’s Optimization problem
Max ∑t { Pt (q t)*(q1ht + q1Tht) – CT1 (q1Th t) } (1)
s.t.
(2) q1Th MIN ≤ q1Th t ≤ q1Th MAX ∀ t (thermal production min/max constraints)
(3) q1h MIN ≤ q1h t ≤ q1h MAX ∀ t (hydro production min/max constraints)
(4) Sm = Sm-1 + Fm – q1hydro m ∀ m (Reservoir’s level evolution)
(5) SMIN ≤ Sm ≤ SMAX ∀ m (Reservoir’s min/max capacity constraint)
(6) S0 = SINI (Reservoir’s initial level)
(7) S12 = SEND (Reservoir’s level at the end of the year)
where:
m = month index; m = 1,2,..12. m=1 for the first month of the hydrological year
assumed.
t = index for each period of 360/372 hours. Since I assumed that there are only two
periods per month, t = 1,2, …24. The periods are set in chronological order (t=1 for
the high period, month 1; t=2 for the low period, month 1; t=3 for the high period,
month 2, and so on).
P t (qt) = is the inverse function of the expected residual demand in period t
54
Qt = is total production by firm 1 and 2 in period t, (Qt = q1t + q2t ),
qit = qiTh t + qih t is total production by Firm i in period t,
qiTh t = total energy produced by Firm i out of thermal plants, period t
q1h t= total energy produced by Firm 1 out of hydro-storage plants, period t
CTi(qiTh t) = Total Cost function, thermal plants, firm i
qiTh MIN = Minimum thermal production, Firm i, period t
q1Th MAX = Maximum thermal production, Firm i, period t
q1h MIN = Minimum hydro production, Firm 1, period t
q1h MAX = Maximum hydro production, Firm 1, period t
q1h tot = available hydro production for the whole period
Sm = reservoir level at the end of month m, measured in terms of energy.
SINI = initial reservoir level.
SEND = end of year reservoir level.
Fm = water inflow expected to get to the reservoir at the beginning of month m.
Measured in terms of energy.
q1hydro m = total energy produced by Firm 1 out of hydro storage plants, month m.
q1hydro m = q1h(2m-1) + q1h(2m)
63
The objective function is basically the same than in the 1-month model except for the
residual demand, which is in terms of expectation. Constraints (2) and (3) are the same
than in the 1-month model and thus need no further explanation. Constraint (4) states that
the hydro energy available in the reservoir at the end of each month is equal to the hydro
energy available at the end of the previous month plus the water inflows (in terms of
hydro energy) received at the beginning of the month and less the hydro energy that was
produced during the month. Constraint (5) states the minimum and maximum bound for
the reservoir level. Finally constraints (6) and (7) are initial and end conditions.64
This version of the model takes into the account the incentives Firm 1 has to re-allocate
water from one month to another (but always within a year). This is a good assumption
for all the Chilean reservoirs except for El Laja (the biggest one) that is so big that its
water can be allocated from one year to another. For the moment it is not possible to
estimate a model with such a long planning horizon because the information requirements
cannot be fulfilled.
This model’s treatment of uncertainty is certainly simplistic and incomplete. Only
expected values of water inflows and demand per period are considered. Variability is not
taken into account because there was no information available. This omission is
important, especially with respect to hydro inflows, as hydro producers are likely to
manage their reservoirs taking into account the probability of the hydrological year being
normal, dry or rainy. Under the current regulation, generators are required to ensure the
power supply even under the driest conditions. As a consequence it is reasonable to
expect them to manage the reservoirs less aggressively. The exercise of market power is
not likely to be the unique goal producers pursue as this model implicitly assumes.
63
q1hydro m= 1 = q1h(t=1) + q1h(t=2), q1hydro m= 2 = q1h(t=3) + q1h(t=4), and so on.
64
The model will be estimated under two versions: with and without constraint (7).
55
I assumed that the discount rate was equal to zero.
Model estimation
The model was estimated under two different market assumptions: i) the market is
perfectly competitive and ii) producers are able to exercise market power.
Market demand was assumed to be linear. Each month’s slope was calculated such that
the elasticity at the peak demand level is –1/3. Anchor quantity to parameterize demand
was set to the average load (augmented by spinning reserves) of the highest/lowest
360/372 hours. Anchor price was given by each month’s nodal price. Table A2.1 reports
the data used to parameterize the market demand and to estimate the residual demand.
Capacity and marginal cost functions are the same than in the 1-month model.
Hydro inflows are given by the average hydro generation per month reported by the CNE
for “normal” hydrological year (See Table A2.2). In this sense, water inflows can be
interpreted as “expected flows”. These inflows were used to allocate hydro production
according to a peak shaving strategy, when needed. In the model where Firms 1 and 2 are
supposed to be able to exercise market power, I allocated the Fringe’s hydro production
according to this approach. In this case, I assumed that its water inflows were not large
enough to store a portion of them given the min and max production constraints. As a
consequence, its hydro production per period was calculated by allocating hydro
resources over a 1-month time period. When perfect competition is assumed, water
inflows of the entire system are allocated according to the peak shaving strategy.
As expected, results of the model turned out to be sensitive to the starting month of the
one-year period (i.e. hydro scheduling for the year Jan – Dec was slightly different than
for April – March, and so on). The longer the planning horizon, the less important the
starting point is. Unfortunately, my data set is too short to further increase the time
horizon. In addition I do not have information that could be used to simulate water
inflows for a longer period. In an attempt to overcome this problem, I estimated the
model and the competitive equilibrium for the 12 possible starting points. I will report
results for each estimation and will look for general trends.
I assumed that minimum and maximum capacity of the reservoirs were not restrictive, as
I did not have information for many of them. This assumption should not introduce too
many distortions as in the past years the reservoir level reached its maximum or
minimum capacity only a few times, and most of them took place in very rainy or dry
years, and thus in periods in which inflows were different from the ones used to estimate
this model.65
65
The problem to this argument is that all the observations are from periods in which the management of
hydro resources is supposed to have been competitive.
56
The reservoir level at the end of the year may be important too, being this another
consequence of the short time period used. In order to analyze how important this
constraint is, I estimated two versions of the model:
- Reservoir level at the end of the year restricted to be equal to the initial level; in this
way, Firm 1 is constrained to use all the water available in the year (“bounded
estimation”).
- Reservoir level at the end of the year restricted to be within min/max bound limits
(Constraint (7) is not included). Firm 1 is implicitly allowed to use only a fraction of
the water available for the whole year (“unbounded estimation”)
It is worth to mention that even though results from these two versions of the model
differ, the differences are rather small. In particular, any change in the amount of hydro
production is usually compensated at least in part by a change in Firm 2’s thermal
production.
Results
I do not intend to exhaustively analyze the results of this model’s estimation, as many of
the results are similar, in qualitative terms, to what was found in the 1-month model and
additional insights are beyond this paper’s reach. I will focus on the question that
motivated the estimation of this model: Would Firm 1 store water in low price-elasticity
of demand months and release it in high price-elasticity of demand months as it could be
extrapolated from the 1-month model? The analysis will be made in comparative terms.
In particular, I will compare each month’s rate of use of water inflows that results in the
Cournot and in the competitive model. Results are reported in Tables A2.3, A2.4, A2.5
and A2.6
The assumption for the reservoir level at the end of the year turned out not to be
important, as results from the “bounded” and “unbounded” almost coincide.
The starting month assumption is more important for the competitive equilibrium than for
any of the Cournot models estimated. In the latter, the pattern of hydro scheduling is
almost always the same (but magnitudes differ), no matter what month was assumed to
be the first. In particular, water is stored in June and July (winter months) and October
and November. Water from June and July is completely shifted to August and September,
while water stored in October and November is allocated to the first half of the year. In
the case of the competitive equilibrium, when the model was estimated assuming that the
initial month was any of the first 5 months, all the water available was exhausted in every
1-month period. Results start to change as June and the months in the second half of the
year are assumed to be the “initial month”, as there is enough water to be stored and used
in a later period.66
In a perfectly competitive industry, water would be stored in the
second half of the year, the rainy and melting season, and released in the first half of the
next year. This allocation is in line with the availability of hydro production relative to
demand as power is “saved” in the periods when it is relatively abundant and it is
released when it is relatively scarce.
66
In line with this result is the greater standard deviation that resulted in the competitive model.
57
As I mentioned, a Cournot producer would store power in June, July, October and
November. According to these results, it could not be argued that water is allocated from
low elasticity months to high elasticity months. Indeed, as Table A2.6 reports, the
correlation coefficient between the average price elasticity of demand and the rate of use
of available hydro flows is positive, as expected, but relatively small (0.37). Firm 1’s
hydro scheduling strategy is closer to the conclusions of the traditional competitive
supply-demand analysis, where water is stored in those periods in which it is relatively
abundant and released when it is relatively scarce. This conclusion is supported by the
correlation coefficient between the rate of use of available hydro flows and the
inflows/demand monthly ratio (-0.89). See charts A2.1 and A2.2 for a graphic support of
the relative importance of each of the alternative explanations for the hydro scheduling
strategy.
In order to understand why Firm 1 does not inter-month differences in demand elasticity,
two alternative hypotheses are formally analyzed.
1. Intra-month differences in demand elasticity are big enough and water can be
allocated within a month in order to exercise market power. In order to analyze
this hypothesis, I estimated the model assuming no intra-month differences in
demand elasticity and keeping constant inter-month differences. A priori, this
explanation does not sound plausible as I assumed that there are only two periods
in each month and therefore, demand variability is considerably reduced. If this
hypothesis is true, then we should observe that given that producers cannot
exploit intra-month demand variability, greater inter-month reallocation should be
observed. As it is reported in Table A2.6, column (2), the resulting correlation
coefficient between the use rate of available inflows and price-elasticity of
demand is still positive, but considerably smaller. At the same time, the
correlation with the inflows/demand ratio is still high and thus the relationship
strong. Accordingly, intra-month variability seems not to be a good explanation.
2. Inter-month differences in demand elasticity are relatively small. As a result, the
incentive to exploit them is also small. In order to test for this hypothesis, I
estimated the model assuming that price elasticity of market demand was not –1/3
at the peak anchor point, as I did in the previous exercise, but could take different
values (E=-0.1, -1/3, -1/2, -2/3, -1.0) which were randomly allocated to each
month. Consequently, inter-month variability of price elasticity of demand was 7
times higher. Results are fully supportive of this hypothesis. Indeed, the
correlation coefficient is very high (0.95) and it is almost unaffected when no
intra-month variability is assumed (column (4)).
Observe that the larger are inter-month differences in price elasticity, the more incentives
Firm 1 has to allocate its hydro resources in order to exercise market power and the less
relevant is the traditional competitive supply-demand analysis in order to understand the
hydro scheduling strategy (See Charts A2.3 and A2.4). Preliminary evidence from a 1year
model is in line with the MVW analysis: producers’ incentive to exercise market
power by shifting water from one month to another depends on how large inter-month
differences in price elasticity are. The smaller the difference, the closer is the hydro
58
scheduling strategy to the traditional supply-demand analysis’ conclusions (i.e. more
water to periods in which water is relatively scarce).
I would like to conclude this analysis by emphasizing that this model is just an attempt to
address the issue of hydro scheduling over a longer planning horizon when firms have
market power. It is clear that an additional modeling effort is needed in order to have
more definitive answers. In particular, it is necessary to improve the treatment of
uncertainty and to further increase the planning horizon (in order to reduce the
importance of the starting and final points).
Table A2.1 : Data to estimate residual demand (E=-1/3)
Month t Average
Load
(MW)
Price
(US$/MW)
A B qPS qMR
Jan 1 4169.4 31.14 5559.2 44.6 180.7 590.9
Jan 2 3178.6 31.14 4238.1 34.0 137.8 590.9
Feb 3 4008.4 31.14 5344.6 42.9 148.6 566.2
Feb 4 3492.2 31.14 4656.3 37.4 144.0 566.2
Mar 5 4386.8 31.14 5849.1 47.0 489.2 509.5
Mar 6 3439.9 31.14 4586.6 36.8 372.3 509.5
Apr 7 4176.0 31.10 5568.1 44.8 259.9 394.5
Apr 8 3300.8 31.10 4401.1 35.4 137.8 394.5
May 9 4321.9 31.10 5762.5 46.3 406.9 399.6
May 10 3433.8 31.10 4578.4 36.8 137.9 399.6
June 11 4398.8 31.10 5865.1 47.1 489.2 455.7
June 12 3364.4 31.10 4485.9 36.1 387.6 455.7
July 13 4286.3 31.10 5715.0 45.9 489.2 447.2
July 14 3295.8 31.10 4394.4 35.3 313.0 447.2
Aug 15 4224.6 31.10 5632.7 45.3 489.2 431.5
Aug 16 3302.0 31.10 4402.7 35.4 396.4 431.5
Sept 17 4179.9 32.74 5573.2 42.6 489.2 473.9
Sept 18 3178.8 32.74 4238.4 32.4 368.9 473.9
Oct 19 4228.5 37.26 5637.9 37.8 489.2 498.7
Oct 20 3219.6 37.26 4292.9 28.8 322.0 498.7
Nov 21 4298.8 37.26 5731.7 38.5 489.2 587.0
Nov 22 3344.6 37.26 4459.4 29.9 317.4 587.0
Dec 23 4334.2 37.26 5778.9 38.8 489.2 603.1
Dec 24 3353.1 37.26 4470.8 30.0 249.7 603.1
59
Table A2.2 : Expected water inflows (GWh)
Month Firm 1 Fringe Total
January 940.5 118.5 1059.0
February 898.6 98.3 996.9
March 1012.6 320.5 1333.1
April 974.9 143.2 1118.0
May 1091.5 202.7 1294.3
June 1245.4 315.7 1561.1
July 1177.5 298.4 1475.9
August 1054.8 329.4 1384.2
September 953.7 308.9 1262.5
October 1177.1 301.8 1478.9
November 1094.7 290.4 1385.1
December 1004.9 274.9 1279.8
Table A2.3: Cournot model, “bounded version”
Hydro production / hydro production available
Starting
month ↓ Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Jan 100% 99% 99% 102% 100% 90% 97% 107% 109% 93% 98% 111%
Feb 117% 100% 98% 102% 100% 89% 95% 105% 108% 90% 95% 108%
Mar 115% 113% 98% 102% 100% 88% 94% 103% 106% 89% 94% 107%
Apr 114% 112% 110% 100% 100% 87% 93% 102% 105% 88% 93% 106%
May 113% 110% 109% 112% 100% 86% 92% 101% 103% 87% 92% 105%
Jun 112% 109% 108% 112% 106% 85% 91% 100% 103% 87% 91% 104%
Jul 111% 108% 106% 110% 104% 100% 90% 98% 101% 86% 90% 103%
Aug 109% 106% 105% 109% 103% 97% 104% 97% 99% 85% 89% 102%
Sep 109% 106% 105% 108% 103% 93% 99% 109% 99% 84% 89% 101%
Oct 109% 106% 105% 108% 103% 90% 97% 107% 109% 84% 89% 101%
Nov 106% 103% 102% 106% 100% 90% 97% 107% 109% 100% 87% 99%
Dec 103% 100% 99% 103% 100% 90% 97% 107% 109% 97% 103% 96%
Ratio > 100% use > monthly inflow, ratio < 100% use < monthly inflow (water is stored).
Table A2.4: Cournot model, “Unbounded version”
Hydro production / hydro production available
Starting
month ↓ Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Jan 100% 99% 99% 102% 100% 90% 96% 106% 108% 91% 96% 109%
Feb 117% 100% 98% 102% 100% 89% 95% 105% 108% 90% 95% 108%
Mar 115% 113% 98% 102% 100% 88% 94% 103% 106% 89% 94% 107%
Apr 114% 112% 110% 100% 100% 87% 93% 102% 105% 88% 93% 106%
May 113% 110% 109% 112% 100% 86% 92% 101% 103% 87% 92% 105%
Jun 112% 110% 108% 112% 106% 85% 91% 100% 103% 87% 91% 104%
Jul 111% 108% 106% 110% 104% 90% 90% 98% 101% 86% 90% 103%
Aug 109% 106% 105% 109% 103% 90% 96% 97% 99% 85% 89% 102%
Sep 109% 106% 105% 108% 103% 90% 96% 106% 99% 84% 89% 101%
Oct 109% 106% 105% 108% 103% 90% 96% 106% 108% 84% 89% 101%
Nov 106% 103% 102% 106% 100% 90% 96% 106% 108% 91% 87% 99%
Dec 103% 100% 99% 103% 100% 90% 96% 106% 108% 91% 96% 96%
Ratio > 100% use > monthly inflow, ratio < 100% use < monthly inflow (water is stored).
60
Table A2.5: Competitive model
Hydro production / hydro production available
Starting
month ↓ Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Jan 100% 100% 100% 100% 100% 92% 96% 101% 102% 92% 100% 113%
Feb 124% 100% 100% 100% 100% 90% 94% 99% 100% 91% 99% 112%
Mar 121% 121% 100% 100% 100% 89% 92% 97% 98% 89% 97% 110%
Apr 120% 120% 108% 100% 100% 88% 92% 96% 97% 88% 96% 109%
May 118% 118% 107% 118% 100% 87% 90% 95% 96% 87% 95% 107%
Jun 117% 117% 106% 118% 107% 86% 90% 94% 95% 86% 94% 106%
Jul 117% 117% 106% 106% 100% 100% 90% 94% 95% 86% 94% 106%
Aug 117% 117% 100% 100% 100% 98% 102% 94% 95% 86% 94% 106%
Sep 117% 108% 100% 100% 100% 96% 100% 105% 95% 86% 94% 106%
Oct 117% 102% 100% 100% 100% 94% 98% 104% 105% 86% 94% 106%
Nov 100% 100% 100% 100% 100% 95% 100% 105% 102% 100% 94% 106%
Dec 100% 100% 100% 100% 100% 95% 99% 104% 104% 96% 104% 100%
Ratio > 100% use > monthly inflow, ratio < 100% use < monthly inflow (water is stored).
Table A2.6: Rate of use of Inflows under different price elasticity assumptions.
PC (1) (2) (3) (4) (1) (2) (3) (4) (1) (2) (3) (4)
Jan 114% 110% 111% 66% 70% 0.46 0.46 0.14 0.14 0.10 0.0 0.03 0.0 0.39
Feb 110% 106% 106% 138% 137% 0.42 0.42 1.22 1.22 0.05 0.0 0.14 0.0 0.40
Mar 102% 104% 105% 76% 75% 0.47 0.47 0.14 0.14 0.09 0.0 0.03 0.0 0.46
Apr 104% 106% 96% 118% 119% 0.52 0.52 1.02 1.02 0.12 0.0 0.23 0.0 0.40
May 101% 102% 104% 95% 96% 0.43 0.43 0.43 0.43 0.06 0.0 0.06 0.0 0.45
Jun 92% 91% 91% 79% 78% 0.48 0.48 0.48 0.48 0.10 0.0 0.10 0.0 0.56
Jul 95% 95% 96% 80% 81% 0.47 0.47 0.47 0.47 0.09 0.0 0.09 0.0 0.52
Aug 99% 103% 104% 101% 99% 0.47 0.47 0.70 0.70 0.09 0.0 0.14 0.0 0.49
Sep 99% 105% 106% 113% 110% 0.45 0.45 0.87 0.87 0.10 0.0 0.18 0.0 0.48
Oct 90% 89% 90% 98% 97% 0.37 0.37 0.68 0.68 0.07 0.0 0.12 0.0 0.53
Nov 96% 92% 93% 129% 133% 0.38 0.38 0.95 0.95 0.07 0.0 0.14 0.0 0.50
Dec 107% 104% 105% 113% 110% 0.37 0.37 0.69 0.69 0.06 0.0 0.10 0.0 0.45
Average 0.44 0.44 0.65 0.65 0.08 0.0 0.11 0.0 0.47
stdev 0.05 0.05 0.34 0.34 0.02 0.06 0.06
Corr
Elasticity 0.11 0.37 0.12 0.95 0.94
Corr
Inflows /
Net
demand -0.92 -0.89 -0.73 -0.23 -0.25
Ratio > 100% use > monthly inflow, ratio < 100% use < monthly inflow (water is stored).
Hydro production / Inflows
(Bounded version)
Average Elasticity of
residual demand
St dev intra-month
elasticity
Inflows/ net
demand
61
Figure A2.1
Figure A2.2
Average use of hydro flows / elasticity of demand
Base case
80%
90%
100%
110%
120%
0.30 0.35 0.40 0.45 0.50 0.55
Elasticity of residual demand
averageusoofavailablehydro
flows
1 2 PC
Average use of hydro flows vs Inflows/ddand
Base Case
80%
90%
100%
110%
120%
0.30 0.35 0.40 0.45 0.50 0.55 0.60
Inflows/demand
averageusoofavailable
hydroflows
1 2 PC
62
Figure A2.3
Figure A2.4
Average use of hydro flows / elasticity of demand
(Larger inter-month difference)
60%
70%
80%
90%
100%
110%
120%
0.00 0.50 1.00 1.50
Elasticity of residual demand
averageusoofavailable
hydroflows
3 4 PC
Average use of hydro flows vs Inflows/ddand
(Larger inter-month difference)
60%
70%
80%
90%
100%
110%
120%
0.30 0.35 0.40 0.45 0.50 0.55 0.60
Inflows/demand
averageusoofavailable
hydroflows
3 4 PC