UNITED STATES OF AMERICA FEDERAL ENERGY REGULATORY COMMISSION

Transcription

1 UNITED STATES OF AMERICA FEDERAL ENERGY REGULATORY COMMISSION San Diego Gas & Electric Comany, ) EL Comlainant, ) ) v. ) ) ) Sellers of Energy and Ancillary Services ) Docket Nos. Into Markets Oerated by the California ) Indeendent System Oerators Cororation ) and the California Power Exchange, ) Resondent. ) ) Investigation of Practices of the California ) EL Indeendent System Oerator and the ) California Power Exchange ) REPORT ON COMPETITIVE BIDDING BEHAVIOR IN UNIFORM-PRICE AUCTION MARKETS DR. PETER CRAMTON MARCH 20, 2003

2 Peter Cramton 1 Professor of Economics, University of Maryland President, Market Design Inc. March 20, 2003 Cometitive Bidding Behavior in Uniform-Price Auction Markets 1. Introduction (1) I have been asked by Duke Energy to resent the economic theory of cometitive bidding in uniform-rice auction markets, such as the markets administered by the California Indeendent System Oerator ( CAISO ) and the California Power Exchange ( CalPX ). I have also been asked to discuss the imlications of this economic theory for the norms of cometitive conduct, the design and enforcement of market rules, and an assessment of market failure. (2) The cornerstone of cometitive market behavior is that each sulier seeks to maximize rofits. It is this rofit maximizing behavior by individual market articiants that steers Adam Smith s invisible hand, leading to efficient outcomes for the market as a whole. The benefits of indeendent rofit maximizing behavior occur in theoretical erfectly cometitive markets, but such benefits also arise in the a wide range of real-life markets, including cometitive wholesale electricity markets such as those oerated by the CAISO and the CalPX. 1 Peter Cramton is Professor of Economics at the University of Maryland and President of Market Design Inc. Over the last 19 years, he has conducted research on auction theory and ractice. This research aears in the leading eer-reviewed economics journals (see During the last 10 years, Cramton has alied this research in the design and imlementation of auction markets in the U.S. and abroad. He has led the design and imlementation of several high-stake auction markets in telecommunications, electricity, and other industries. He has advised numerous governments on market design and has advised dozens of bidders on bidding strategy in high-stake auction markets. Since 1998, he has advised ISO New England on market design. In California, Cramton served on the Blue Ribbon Panel examining ricing rules for the California Power Exchange. He currently is advising EPRI on agent-based simulation methods to evaluate market reforms in California

3 (3) In reaction to the crisis in the California electricity markets in , much attention has been focused in the economic literature on whether suliers in the California markets have violated cometitive norms by bidding resources at rices in excess of marginal costs. 2 As a matter of economic theory and sound market design for wholesale electricity bid-based auction markets, there is and should be no cometitive norm stiulating that suliers bids should equal marginal costs. The lack of marginal cost bidding is not evidence of anticometitive or maniulative behavior by market articiants, nor is it evidence even that cometition is failing or that markets are broken. In any real-world market in which suliers are not forced by conditions or rules to be rice takers, bidding above marginal cost is consistent with and, indeed, is imelled by indeendent, non-collusive, rofit maximizing behavior. Bidding above marginal cost should be viewed as an inevitable and desirable resonse of indeendent, rofit maximizing decisions in real-world markets where the ideal conditions of a erfectly cometitive market do not revail. (4) Bidding behavior in the California electricity markets should not, therefore, be assessed against a norm of marginal cost bidding, which alies only in the theoretical extreme of erfect cometition. While some may use this extreme oint as a convenient benchmark, it is not the norm for rational, rofit maximizing behavior by indeendent cometitors. In real bid-based electricity markets oerating under a range of suly and demand conditions, individual suliers should be bidding to maximize their rofits, which, as this aer exlains, will inevitably involve bidding above marginal cost. Bidding above marginal costs is and should be the cometitive norm in uniform-rice electricity auction markets. (5) Bidding above marginal cost is an inevitable consequence of rofit maximizing decisions whenever at least one sulier has some unhedged caacity. In these circumstances, which characterize most bid-based markets, including electricity markets, each sulier exects to maximize its rofits by offering its unhedged outut at rices above marginal cost. Bidding above marginal cost to maximize rofits should characterize all suliers in all cometitive, bid-based electricity markets. In articular, rational bidding above marginal cost does not entail or require: (1) the resence of one or more large bidders, (2) extreme suly scarcity, (3) demand that is unresonsive to rice, or (4) collusion or other bid coordination among suliers. Rather, any sulier with unhedged caacity maximizes rofits by offering suly at bid rices higher than marginal cost. 2 For examle, Sheffrin (2001); Borenstein, Bushnell and Wolak (2002); and Joskow and Kahn (2002)

4 (6) A main theme of this aer is to demonstrate that marginal cost bidding is an abstract, ideal characteristic of erfectly cometitive markets, but it should not be considered the norm for cometitive wholesale electricity markets. A corollary is that bidding above marginal cost in cometitive wholesale electricity markets is consistent with nonmaniulative, non-collusive, rofit maximizing behavior. Bidding marginal cost maximizes rofits only for caacity that is already sold in forward markets. Suliers of all unhedged caacity have an incentive to bid above marginal cost. It is for this reason that one commonly observes ricing above marginal cost in most real markets. Hotels, arking, rental cars, airlines, and electricity are all examles of markets where suly is rationally offered at rices above marginal cost. (7) A sulier that bids above marginal cost to maximize rofits does not have unlimited ower to charge whatever it wants. The sulier s bids are limited by the cometitive resonse of other suliers as well as any resonse by demand. As the sulier raises its rice it runs an increasing risk that either another sulier will ste in to serve demand or that buyers will curtail demand. At the same time, the resonse by demand and other suliers is not unbounded. Demand may have a limited ability to curtail quantity in resonse to higher rices and other suliers may be limited in their ability to ste in to meet demand. These limits imly that suliers are not rice takers, but face a fundamental, marginal tradeoff between the quantities they offer to sell and the rices that they would exect to receive. (8) In auction markets, suliers develo bid curves, which normally have higher rices bid for higher quantities of outut offered. A rofit-maximizing sulier in develoing its bid curve balances the marginal gain from bidding a higher rice for a given quantity of outut, with the marginal loss from selling a smaller quantity at such higher rice. The sulier is limited in the rice that it offers by the exectation and reality that as it raises its bid rices, the quantity it is able to sell falls, either because other suliers fill in additional quantity at lower bids, or demand itself falls in resonse to the higher rice. (9) In the idealized extreme of a erfectly cometitive market, suliers would have absolutely no decision to make at all with resect to their bid curve. Each and every sulier is resumed to be a rice taker, which imlies that rofits are maximized by bidding marginal cost. In real-world cometitive markets, in which suliers come to each market with some unhedged caacity, suliers are not rice takers and should not be exected to act like one. Suliers will choose their bid curves so as to maximize their rofits, which will entail making indeendent decisions trading off marginal gains from a - 4 -

5 higher bid curve against marginal losses from foregone outut. This is the essential rofit maximizing decision exected of each sulier, acting indeendently, in bid-based electricity markets. This rofit maximizing behavior will, as this aer demonstrates, result in bid curves above marginal cost, some suly being unsold or withheld, and clearing rices in excess of rices hyothesized in a theoretical erfectly cometitive market. (10) Profit maximizing bidding is the norm we exect of suliers in bid-based electricity markets. Following this norm does not mean that market clearing rices will necessarily be just and reasonable under all market structures and under all suly and demand conditions. Nor does it mean that regulators should eschew market rules that will decrease ressures on clearing rices under certain conditions. The key is that market rules need to be designed around the normative exectation that suliers in bid-based auction markets will not submit bid curves at their exected marginal costs, but, instead, will make rofit maximizing decisions that trade off marginal gains from raising bids against marginal losses in foregone outut. 2. Preliminaries (11) Terminology matters. To avoid confusion, it will be useful to define a few terms. (12) Marginal cost is the sulier s oortunity cost of roducing an additional unit of outut. It includes the sulier s marginal roduction cost, but also includes oortunity costs, such as the sale into a higher riced market, and incremental costs from constraints, such as those arising from emission limits or caacity limits. When an electric generator is not oerating, its ertinent marginal costs include costs associated with start-u and no-load oerations. The sulier, all else being equal, is indifferent to selling an additional unit at marginal cost or not. Electric generators marginal costs tyically increase with outut, and increase steely as full caacity is reached. This is the bidder s marginal cost curve its marginal cost at each ossible quantity. (13) Oortunity costs arise in interrelated markets. A hydroelectric resource fed from a limited ool of water is a good examle of oortunity costs, since generating ower today imlies less available generating caacity tomorrow. Therefore, even though today s rice is above the hydro generator s variable cost (zero), the generator has an incentive to bid at least its oortunity cost based on its rediction of future rices

6 (14) Oortunity costs are not confined to hydro generation. Gas-fired generation, articularly in California, is subject to NOx constraints. In some locations, these reresent hard constraints: a lant may have a fixed amount of NOx ermits er year, and once those are used, the lant cannot be run further. Similarly, even in the resence of tradeable NOx ermits, roducing today has an added cost equal to the ermit rice. (15) Perhas the biggest source of oortunity cost in ower markets arises from the sequential clearing of related markets. Selling in the day-ahead market forecloses the otion of selling in the real-time market; selling in the day-ahead energy market recludes selling in the ancillary services (AS) market; and selling in the California market recludes selling in a neighboring market. The bids of a rofit maximizing generator will reflect these oortunity costs. (16) In a bid-based auction market, a sulier submits a bid rice for each quantity indicating its offer to suly. This is called the bidder s as-bid suly curve, or simly its suly curve. (17) In a uniform-rice auction, also called a single-rice auction, the auctioneer takes the asbid suly curves of each bidder and adds them together in the quantity dimension to form the aggregate suly curve, as shown below for an auction with two bidders with suly curves exressed as ste functions. A common alternative is for bidders to exress suly as a iecewise linear function. Each bidder s as-bid suly curve is required to be non-decreasing in quantity as rices rise a bidder cannot reduce its quantity in resonse to higher rices. Figure 1. The aggregate suly curve Bidder 1 Bidder 2 Aggregate suly + = q 1 q 2 q (18) Similarly, the auctioneer aggregates the rice-quantity bids of each demand-side bidder to form the aggregate demand curve. The auctioneer then determines the market-clearing - 6 -

7 rice as the rice where the aggregate suly and demand curves intersect (the oint (q 0, 0 ) in the figure below). All suly offers below the clearing rice are winning bids and are asked to suly the quantity bid, with each sulier aid the clearing rice 0 ; all demanders receive the quantity they bid above 0 and ay the clearing rice 0. Figure 2. The uniform-rice auction Price Demand Suly (as bid) 0 (clearing rice) q 0 Quantity (19) In the figure above as well as subsequent figures, demand and suly are drawn as straight lines. This is for convenience only. In ractice, the curves are nonlinear and discontinuous. More imortantly, the figures as drawn do not reflect the inherent uncertainty in both demand and suly. A sulier knows its own suly bid, but it must estimate its own marginal cost curve, the aggregate demand, and the suly curves of the other bidders based on incomlete data. This grahical reresentation of bidding behavior simlifies the sulier s actual rofit maximizing decision. One can interret the figures as one ossible realization. In actuality, each sulier decides on its bid-curve based on its araisal of all ossibilities and the associated likelihoods of these ossibilities. Each oint on its suly curve is chosen to maximize rofits for instances in which the bid is on the margin. (20) The imortance of uncertainty is highlighted by the fact that the sulier submits a whole suly curve. If there was no uncertainty, the sulier could instead submit just a single oint: Firm i will suly q i at the clearing rice of 0. Rather, the sulier submits a continuum of rice-quantity airs, exressing its rofit-maximizing quantity choice for the domain of all rices that can occur under all ossibilities. (21) In making its decision on the quantity to suly at all relevant rices, the sulier needs to estimate both demand and the suly rovided by others at all ossible rices. These - 7 -

8 estimates give the sulier an understanding of how much of the aggregate demand will remain, once the suly of the other bidders has been netted out. The sulier s estimate takes into account not only how resonsive demand is to rice, but also how resonsive the suly of the other bidders is to rice. From this analysis, the sulier calculates a critical inut to its bidding decision its estimate of the residual demand curve. Formally, the residual demand curve is constructed by taking the aggregate demand and subtracting the suly of the other bidders, as shown below. Figure 3. Residual demand removes the suly of the other bidders 0 Demand q 0 Suly Suly of others = q q i q q i Suly firm i Residual demand q (22) Notice that even if the demand curve is nearly vertical (inelastic), the residual demand curve tyically is much more resonsive to rice (elastic), since it includes the resonse to rice of all the other suliers. Throughout, firm i will reresent a tyical sulier, with as-bid suly S i and marginal cost MC i. Let i denote the set of all suliers other than i, and let S -i and MC -i denote the aggregate suly and marginal cost of the bidders other than i. The residual demand curve for sulier i is denoted D i. The quantity q i sulied by bidder i is determined from the intersection of its suly S i and residual demand D i, as shown below

9 Figure 4. The residual demand curve Price As-bid suly S i () 0 Residual demand D i () = D() j i S j () q i Quantity (23) One common economic model that is alied in analyzing electricity markets is erfect cometition. Perfect cometition assumes that there are an infinite number of sellers and buyers, so that no market articiant can affect rice. As a consequence, all buyers and sellers are rice takers: each seller offers to suly the market with a quantity of the roduct at a rice just equal to its marginal cost of roduction, and each buyer offers to urchase a quantity of the roduct at a rice equal to the marginal value it laces on the roduct. Under erfect cometition, no bidder on either the suly side or the demand side is able to affect the market-clearing rice through its bids. (24) The model of erfect cometition is simle to aly to electricity markets. The assumtion that no sulier is able to imact the market-clearing rice imlies that each bidder faces a horizontal residual demand curve, as shown below. The market will accet any quantity from the bidder at the clearing rice 0. As a result, no bidder has an incentive to bid above its marginal cost curve. The rofit-maximizing bidder simly bids its marginal cost curve, S i () = MC i (). Increasing the bid above marginal cost would eliminate some rofitable sales without any corresonding gain from a higher rice

10 Figure 5. Bidding strategy with erfect cometition Price As-bid suly S i = MC i 0 Residual demand D i q i Quantity (25) Marginal cost bidding has the further benefit of efficient disatch. Energy is sulied by the least-cost units. As a result of its simlicity and desirable efficiency roerties, marginal cost bidding often is used as a benchmark to comare with actual market erformance (Borenstein et al. 2002, Bushnell and Saravia 2002). It even is sometimes asserted that suliers should bid marginal cost in a cometitive electricity market. This rescrition for behavior, however, is only aroriate in the extreme and unrealistic case of erfect cometition as we will see next. Only under erfect cometition a setting that requires that no firm suly more than one MWh of energy in any hour is marginal cost bidding consistent with rofit maximizing behavior. 3 Such an assumtion is inconsistent with the ractical realities of electricity generation. (26) Economists define market ower as the ability of a sulier to affect the market-clearing rice. Under economic theory, the only markets in which suliers do not have the ability to affect the market-clearing rice are erfectly cometitive markets. Each sulier in a erfectly cometitive market is hyothesized to be a rice taker its bidding decisions would have no affect on the market clearing rice. In real-world cometitive markets, economic theory recognizes that a sulier faces a downward-sloing residual demand and, therefore, its bidding decisions have the otential to affect the market clearing rice. Thus, in economic terms, the exercise of market ower amounts to nothing more than a sulier s ability to construct a rofit-maximizing as-bid suly curve that is above its 3 Forward contracts, which are examined later, will rovide an excetion to this result

11 marginal cost curve. In the context of electricity markets, such behavior can be called economic withholding, but such a label does not make the conduct anticometitive, maniulative, or otherwise imermissible. Physical withholding failing to submit a bid for all available caacity when the rice is above its marginal cost is another variant of exercising market ower, but such conduct also is not anticometitive, maniulative, or otherwise imermissible. (27) The exercise of market ower does not imly that a sulier unilaterally moves the market rice above a cometitive level. Rather, the exercise of market ower reflects an individual sulier s construction of a bid curve based on its calculations of rofit maximizing bids. The resulting market clearing rice reflects the demand curve and the as-bid suly curves submitted by all suliers acting indeendently in a rofit maximizing manner. I will use the economists definition of market ower throughout. Under this definition, the exercise of market ower by itself is not anticometitive or maniulative. (28) The law uses the term market ower in a different way from economists. Market ower is often defined to mean anticometitive or maniulative conduct that is not accetable under legal norms and has direct and sustained effects on market rices. Illustrative of the legal concetion of market ower is this definition embraced recently by a FERC administrative law judge: Market ower is the ability to rofitably sustain elevated rices through the unilateral restriction of suly by a dominant firm or by the restriction of suly arising from the coordinated (e.g. collusive) restriction of suly decisions by multile firms acting in a coordinated fashion. 4 I view the legal aroach to market ower as being focused on conduct that violates legal norms. Among the norms in the antitrust laws are strictures against collusion among suliers (rice-fixing or bidrigging), or anticometitive conduct such as creating artificial barriers to entry, or, in some cases, by seeking to obtain too much market dominance through acquisition of another seller. Violation of legal norms that results in a sustained distortion of market rices might, in aroriate contexts, be considered an unlawful, abuse of market ower. The economist s definition of market ower assumes neither that conduct violates legal norms nor that market results are distorted. 4 PacificCor. v. Reliant Energy Services, Inc., 102 FERC 63,030 at. 32 (emhasis in original)

12 3. Indeendent rofit-maximizing behavior is the basis for market rices (29) A cornerstone of markets is indeendent rofit-maximizing behavior. It is recisely this behavior that steers Adam Smith s invisible hand to roduce efficient market outcomes: It is not from the benevolence of the butcher, the brewer, or the baker that we exect our dinner, but from their regard to their own interest. (Smith 1904) As in any market, cometitive suliers in electricity markets are motivated by rofits. Indeendent rofitmaximizing behavior should not only be exected but encouraged by regulators, rovided the behavior is consistent with the market rules. In restructured ower markets, the role of market-based rates is to allow suliers to ursue rofit maximization in submitting bids or negotiating rices in a bilateral transaction. A FERC administrative law judge, who rejected challenges to certain long-term contracts entered into in the West, recently exressed the economist s rincile that rofit maximization is the norm for sellers with market-based rate authority: 5 So far as the record shows, the Resondents [suliers] did not violate any oerative norm in their dealings with PacifiCor. They did not mislead PacificCor. They did not defraud PacifiCor. They did not collude to increase rices in the marketlace. They did not unduly exercise market ower. True, they were after the Main Chance and sought to maximize their rofits through every lawful device they could. But that is exactly what businessmen are suosed to do and what the Commission contemlated they would do when it authorized the Resondents to sell electricity at wholesale and in interstate commerce at market-based rates. (30) The role of regulators is to design and monitor a set of market rules that relies on the indeendent rofit-maximizing behavior of the market articiants to achieve the objective of roviding consumers with low-cost, reliable ower. In certain contexts, resulting rices may be deemed unjust and unreasonable by regulators and, accordingly, market rules may be modified so as to influence future market clearing rices roduced by individual rofit maximizing bidding decisions. 4. Cometitive bidding in real markets (31) Since the time of Adam Smith, economists have develoed several economic models with which to analyze the behavior of buyers and sellers in markets. The most tractable economic models relate to the olar extremes of erfect cometition and monooly. 5 PacificCor. v. Reliant Energy Services, Inc., 102 FERC 63,030 at. 88 (emhasis added)

13 Under erfect cometition, each firm is a rice taker its actions cannot imact the market rice, and so its decisions take rice to be fixed. Under monooly, the firm has no cometitors, and so in develoing a strategy the monoolist need not factor in the likely behavior of its cometitors. Almost all actual markets, and certainly all ower markets, are somewhere between these two extremes. In bid-based wholesale ower markets, each firm has the otential to affect the market clearing rice through its indeendent rice and quantity bidding decisions, but the best rofit maximizing actions by one firm will deend on its exectations of the rofit maximizing actions chosen by its cometitors. This is the realm of imerfect cometition, where strategy and uncertainty lay imortant roles. (32) The use of the model of erfect cometition stems from its simlicity, not its universal validity or alicability to real world markets. Economists understand that erfect cometition is a convenient olar extreme, which although rarely observed in ractice, does rovide a useful aroximation of outcomes in some markets. As a consequence, the model of erfect cometition can rovide general guidance for regulators and other architects of market design, but it does not rovide a useful norm of cometitive behavior. (33) Real markets are not erfectly cometitive. Even in highly cometitive markets with no entry barriers, firms tyically find that their individual behavior can affect the market rice. Certainly for current electricity markets characterized in almost all geograhic locations by large caacity investments and moderate to high concentration of ownershi, as shown in the table below it would be unreasonable to suose that the ideal of erfect cometition should revail. 6 In each of the regional electricity markets, the largest suliers oerate a substantial share of the generation caacity, but each sulier also faces cometition from numerous other suliers. In markets like this, esecially in the resence of transmission constraints, erfect cometition is likely a oor model either normative or descritive of ricing behavior. 7 6 Paul Joskow (1997) writes, Creating a reasonably cometitive generation market is certainly an imortant olicy goal. However, creating a erfectly cometitive generation market is not a realistic goal. The satial attributes of generation markets and changing network conditions virtually assure that generation markets will never be erfectly cometitive under all system conditions Interestingly, among the four restructured markets in Table 1, the California electricity market is, if anything, less concentrated than other electricity markets

14 Table 1. Generation shares in several regional electricity markets California New York PJM New England Owner Share Owner Share Owner Share Owner Share PG&E 17% NYPA 17% PSE&G 20% PG&E NEG 17% AES 9% NRG Power 12% PECO 17% NRG 8% Reliant 8% LIPA 12% PP&L 16% Sithe 7% Mirant 8% Reliant 7% GPU 13% Notheast Util 6% Duke 7% Keysan 6% PEPCO 11% Northeast Gen Serv 6% SCE 6% Constellation 5% BG&E 11% FP&L Energy 5% Dynergy 6% Entergy 5% Connectiv 9% Mirant 5% Other 39% Mirant 5% Other 3% Caline 4% Dynergy 5% Wisvest 4% AES 4% Duke Energy 4% Sithe 3% Other 33% Other 20% Total MW 44,682 Total MW 36,342 Total MW 65,067 Total MW 26,441 as of July 1999 as of January 2002 as of January 2000 as of January 2001 Sources Borenstein et al. (2002) NYISO Load and Caacity Data Singh and Jacobs (2000) Bushnell and Saravia (2002) (34) Yet many observers, including the California ISO, have resented the lack of marginal cost bidding as evidence of anticometitive behavior or an abuse of market ower by firms in California sot electricity market (Sheffrin 2001). Bidding above marginal cost is not evidence of bad behavior; rather it is evidence of rofit maximizing behavior. Only in the theoretical extreme oint of erfect cometition is marginal cost bidding consistent with rofit maximization. Bidding above marginal cost is an inevitable consequence of rofit maximization whenever there is a ositive robability that a sulier s bid may imact the market clearing rice. In this lausible case, alicable to most actual markets, individual rofit-maximizing behavior results in submitting bids above marginal cost. (35) The theory of bidding in uniform-rice auctions under conditions of imerfect cometition has been develoed extensively in the economic literature (Klemerer and Meyer 1989, Ausubel and Cramton 2002). In this theory, each sulier submits a bid function to maximize its rofits given its marginal cost curve, its exectations about market demand, and its exectations of the suly curves of the other bidders. The theory has several imortant imlications: (1) so long as there is some robability that the sulier s bid may affect the clearing rice, the rofit-maximizing bid curve exceeds its marginal cost curve; (2) the sread between its otimal bid and marginal cost increases with the quantity that the bidder is sulying; (3) the sread between its otimal bid and marginal cost increases the less resonsive the suly of the other bidders is to rice; (4) the greater incentive for larger bidders to inflate bids above marginal cost imlies a shortrun inefficiency too little of the market is served by the largest bidders; and (5) forward

15 contracts have the effect of mitigating incentives to bid above marginal cost. I now rovide a simle demonstration of each of these imlications as well as some intuition. Profit-maximizing suliers bid above marginal cost (36) Each bidder in a uniform-rice auction faces a fundamental tradeoff between rice and quantity. By offering to suly at a lower rice, the bidder increases the likelihood that it will suly a larger quantity; whereas, by offering to suly at a higher rice, the bidder increases the likelihood that it will suly a smaller quantity but at a higher rice. A rational bidder otimizes this tradeoff to maximize rofits. This involves setting its bid at each quantity at the oint where the marginal gain from bidding a little bit higher (a higher rice on the quantity sold) exactly balances the marginal loss (failure to get the sread between the bid and marginal cost on the exected available quantity that will go unsold as a result of the higher bid). (37) As a simle examle, consider the ricing decision of a firm oerating a 1,000 MW unit with a marginal cost of $49/MWh at caacity. Rational behavior tyically will lead this firm to bid the last MW of caacity at the rice ca of, say, $250/MWh. To see this, consider the decision of the firm to raise its bid on the last MW from $249 to $250. The marginal gain from such a bid is 1,000 multilied by the robability that the last MW sells at $250; whereas, the marginal loss is equal to the foregone rofit on the last MW ($249 49) multilied by the robability that the market clearing rice is $249 (and not $250). Bidding the rice ca is the best strategy for the firm, rovided the marginal gain exceeds the marginal loss. In this examle, the marginal gain will exceed the marginal loss, so long as the robability of a $249 market clearing rice is less than 5 times the robability of a $250 market clearing rice. Hence, the $250 bid is otimal, unless the bidder believes that raising its bid by the last $1 will reduce its chance of selling the last MW by more than a factor of 5. The intuition for this result is straightforward: by raising its bid by $1, the bidder achieves the $1 higher rice on all 1,000 MWs when the bid sets the rice; whereas the $200 loss ($249 49) only occurs on the last MW when the increase revents the MW from being sold. (38) This calculation does not imly that the sky s the limit with resect to the firm s rice and quantity bids. Profit-maximizing bidders face a real danger from bidding too high. They run the risk that their caacity will go unsold as a result of offering a rice that is too high some other bidder may ste in front of them in the merit order, or the quantity demanded may fall as a result of offering a rice that is too high

16 (39) The incentive to bid above marginal cost is seen in the figure below. Imerfect cometition imlies that the bidder s residual demand curve is downward sloing. By raising its bid above marginal cost, it achieves a high rice on all of its quantity. The marginal gain is reresented by the green rectangle. The marginal loss (the loss of roviding some quantity at marginal cost) is given by the red triangle. Whenever the residual demand curve is downward sloing, the marginal gain will exceed the loss for small enough uward shifts in the as-bid suly curve beyond the marginal cost curve. Figure 6. Incentive to bid above marginal cost As-bid suly S i MC i 0 Gain Loss Residual demand D i q i q (40) To maximize rofits, the bidder continues to increase its bid curve above its marginal cost curve until the equilibrium oint is reached. At the equilibrium oint, a slight increase in the bid leads to a marginal gain (a higher rice on the quantity sold) that exactly balances the marginal loss (the rofit lost as a result of the reduced quantity). This is seen in the figure below, in which the marginal gain is given by the green rectangle and the marginal loss is given by the red area. Offering q i at the clearing rice 0 just balances the marginal gain and loss

17 Figure 7. The otimal bid balances the marginal gain and the marginal loss As-bid suly S i 0 Gain MCi Loss Residual demand D i q i q (41) This incentive to bid above marginal cost is not the result of coordinated action among the bidders. Rather, each bidder is indeendently selecting its bid to maximize rofits based on its estimate of the residual demand curve it faces. To see this, suose that there are eleven suliers in the market, each with the same marginal cost curve. Consider the bidding incentives of one firm (firm i) when the other ten are all bidding marginal cost. This is shown in the figure below. Since each of the ten other firms is bidding marginal cost, the others would suly the entire market demand at a rice of -i. Firm i then is facing the residual demand D i, which begins at the rice -i. Since the residual demand is downward sloing, firm i otimally bids S i, which is above marginal cost. As a result, firm i sulies q i, ushing the clearing rice down to

18 Figure 8. A firm still bids above marginal cost when others bid marginal cost Other bidders Firm i S i S -i =MC -i MC i -i 0 0 D i D 0 q -i 10 GW 0 q i 1 GW (42) The behavior described above reresents one firm s rofit-maximizing resonse to all the other firms bidding marginal cost. However, this is not an equilibrium, since none of the other firms have an incentive to bid marginal cost. 8 Like firm i, each of the others has an incentive to bid above marginal cost. The equilibrium bidding behavior is deicted in the figure below, where each of the similarly situated firms is doing exactly what firm i is doing: bidding above marginal cost to otimize the exected rice-quantity tradeoff. In equilibrium, firm i s bid above marginal cost is such that the marginal gain from the higher rice is exactly offset by the marginal loss of some rofitable quantity. This calculation is made assuming a residual demand curve that correctly anticiates that each of the other bidders is also bidding to maximize its own rofits and hence bidding in a similar way, as shown below in the suly curve S -i of the other bidders. 8 The only excetion to this, as we will see, is when all of the other firms have sold forward 100% of their energy caacity. In this event, it will be an equilibrium for each of the others to bid marginal cost, but firm i s incentive to bid above marginal cost will remain, unless it too is 100% hedged

19 Figure 9. Equilibrium bidding behavior Other bidders S -i Firm i S i MC -i MC i -i 0 0 D i D 0 q -i 10 GW 0 q i 1 GW (43) In ractice, determination of the otimal suly function is comlicated by the firm s uncertainty about its residual demand curve. The firm faces uncertainty about both the aggregate demand and the suly functions adoted by its cometitors. As a result, the firm selects each oint on its suly function to otimize the tradeoff between rice and quantity given the distribution of residual demand curves the firm faces. The introduction of uncertainty comlicates the firm s decision roblem, but does not alter the fundamental tradeoffs that are resented in the figures. Physical withholding is analogous to bidding above marginal cost (44) Discussions relating to ower markets frequently invoke the concet of sulier withholding behavior. (45) Economic withholding is identical to bidding above marginal cost: a sulier decides to roduce less than is economically feasible at a given rice level, because the higher rice level associated with the lower outut maximizes the sulier s rofits. Here, economic feasibility is based on the sulier s marginal cost, including any oortunity costs. These oortunity costs are esecially imortant when the roduct is sold in a sequence of related markets, as is the case in ower markets. (46) Physical withholding, in which firms fail to bid in their economically feasible caacity above a certain amount, is often described as a searate strategy from economic withholding. However, the two are closely related. Both result in outut that is less than

20 the quantity that could be economically roduced at the revailing rice, as shown in the figure below. Figure 10. Economic and hysical withholding S i S i MC i MC i 0 0 D i D i q i q e q q i q e q (47) The difference between economic and hysical withholding arises from the uncertainty in the residual demand curve the sulier faces. With hysical withholding the sulier is more at to regret its suly bid in the event that its residual demand is higher than exected. Why then would a sulier choose to hysically withhold caacity? One reason has to do with nonconvexities in the sulier s cost function that it is unable to exress in its bid. For examle, as a result of start-u and no-load costs, the sulier may exect to be better off hysically withholding a unit, rather than including the unit in its suly bid. Start-u and no-load costs may not be justified for a unit that is exected to run only a short eriod of time. The incentive to bid above marginal cost increases with quantity (48) In the figure above, the sread between the as-bid suly and the bidder s marginal cost curve increases with quantity. This is a characteristic of a rofit-maximizing suly function. The reason is simle. The marginal gain from an increase in the bid is roortional to the quantity sold. As more quantity is sold, the buyer has a greater incentive to increase the as-bid suly curve above the marginal cost curve. Likewise, as the quantity sold falls to zero, the sread between the otimal suly bid and the firm s marginal cost goes to zero. There is no incentive to increase the rice if doing so results in no quantity sold

21 The equilibrium rice falls as cometition increases (49) The fact that a bidder s incentive to bid above marginal cost increases with its quantity has an immediate imlication: the equilibrium market clearing rice falls as the market becomes less concentrated. In a less concentrated market, bidders are smaller and hence have a reduced incentive to bid above marginal cost. In terms of the residual demand curve, a smaller bidder faces a flatter residual demand curve. Other cometitors are better able to cover the caacity of a smaller bidder withholding some of its quantity. Hence, the rofit-maximizing bidders in a less concentrated market bid a smaller margin above marginal cost, resulting in a lower clearing rice. Demand and suly resonse mitigates incentives to bid above marginal cost (50) A rimary determinant of how much to bid above marginal cost is the resonsiveness of the residual demand to changes in rice. If the residual demand curve is not too resonsive to rice as in the figure above, then the otimal bid requires a large margin above marginal cost. If instead the residual demand curve is resonsive to rice as in the figure below, then the margin above marginal cost is less. Figure 11. Residual demand resonse reduces incentives to inflate bids As-bid suly S i MC i 0 Gain Loss Residual demand D i q i q (51) The resonsiveness of the residual demand curve comes from either: (1) load reducing demand in resonse to higher rices, or (2) other suliers exanding suly in resonse to higher rices. Current electricity markets have suffered from a lack of demand resonse. Over time, as demand becomes more rice resonsive, the incentives for suliers to submit bids in excess of marginal costs will be reduced. Suly resonse

22 tyically deends on how close the system is to caacity. When there is amle excess caacity, then other suliers ste in when one sulier curtails roduction the rice imact of the curtailment is minimal. In contrast, when caacity is scarce, then substantially higher rices may be needed to attract sufficient suly to make u for the curtailment of suly by one bidder. (52) The resonsiveness of the residual demand curve also deends on how close the market is to real time. As markets aroach real time, articiants lose the ability to resond to rice changes. For examle, units with substantial start-u times or low ram rates are unable to offer additional energy on short notice. As a result, both suly and demand become steeer more inelastic as the market aroaches real time. Hence, real time markets tend to be the most vulnerable to the exercise of market ower, as defined by economists. As the aggregate demand and suly curves become more inelastic, individual suliers are faced with increasingly inelastic (steeer) residual demand curves, roviding increased incentives for bidding their remaining caacity above marginal costs. Large bidders serve too little of the market (53) Each sulier faces a different residual demand curve. The shae of the residual demand curve deends on the size of the individual sulier. Tyically, the residual demand curve will be steeer for a larger sulier and flatter for a smaller sulier. In the figure below, the large bidder has 10 times the caacity of the small bidder. As a result, the large bidder s ability to affect rice is much greater: a dro in suly of 5,000 MWh leads to a much larger rice imact than a dro of 500 MWh. Hence, the residual demand of the large bidder aears about 10 times as stee as the small bidder. (Actually, the sloes may be identical, but the residual demand of the large bidder aears 10 times steeer, since the large bidder has 10 times the generating resources.)

23 Figure 12. Residual demand is steeer for a larger bidder Large bidder Small bidder S l S s 0 0 D s D l 0 q l 10 GW 0 q s 1 GW (54) The imlication of a steeer residual demand is that the large bidder otimally increases its bid above marginal cost more than the small bidder, as shown below. As a result, at the clearing rice 0, the large bidder has a lower marginal cost than the smaller bidder. The large bidder is economically withholding some of its caacity, which enables its smaller rivals to roduce more. This result imlies the introduction of inefficiency into the disatch: the smaller rival sulies caacity to the market, even though more efficient caacity from the larger bidder is available and unused at the market clearing rice. Figure 13. Large bidder makes room for its smaller rivals Large bidder Small bidder S l S s MC s 0 0 D s MC l D l 0 q l 10 GW 0 q s 1 GW

24 (55) Although the disatch is inefficient, the imact of the inefficiency is to enable smaller firms to oerate relatively more efficiently than larger firms, since the smaller firm is using a larger ercentage of its available caacity than it would in the absence of withholding by the large bidder. In the long run, this encourages entry and growth of smaller firms and an imroved market structure, flattening the residual demand curves for all firms including the large bidder and thereby reducing over time the sread between the as-bid suly curve and the marginal cost curve. Profit maximizing behavior in a uniform-rice auction corrects roblems of market structure absent barriers to entry. Thus, the short-term inefficiencies caused by imerfect cometition send the right rice signals to induce long-term efficient outcomes. Forward contracts mitigate incentives to bid above marginal cost (56) The analysis above assumes that the bidders do not have any forward contracts going into the market. In ractice, forward ositions are common, so it is imortant to examine how incentives change as a result of forward contracts. Indeed, forward contracts lay a critical role in mitigating the incentive to bid above marginal cost. (57) To see this, consider a sulier that has sold 100% of its generation forward. Such a sulier is fully hedged and has no incentive to bid above marginal cost. The sulier already knows the rice it will receive from the terms of the forward contract. The sulier has no interest in distorting the clearing rice either uward or downward. Its incentive is to bid its marginal cost, so that it can satisfy the forward contract with its own generation whenever it is the least-cost sulier. If instead the sulier s marginal cost at full caacity is above the clearing rice, then the sulier will roduce only to the oint where its marginal cost is equal to the clearing rice, and it will then satisfy the remainder of the forward contract with urchases from the sot market. Marginal cost bidding maximizes rofits for a sulier that has sold 100% of its generation forward. (58) A firm that sells most, but not all, of its generation forward alters its bidding incentives in a similar way. For examle, if a large firm with 10 GW of caacity, sells 80% of its caacity forward, then its bidding incentives in the sot market are the same as a small bidder with 2 GW of unhedged caacity. The large firm has no incentive to bid above marginal cost on the first 8 GW of caacity; it only begins to bid above its marginal cost on its last 2 GW of caacity. In this way, the sulier satisfies its forward obligation at least cost, and maximizes its rofits on its remaining 2 GWs. Thus, the imlications of forward contracting are that caacity sold forward will be bid in at marginal costs, and

25 the remaining unhedged caacity will be offered at lesser margins above marginal cost than if the sulier had no or less hedged caacity. This is shown below, where the dashed suly curve assumes no forward contracting and the solid suly curve assumes that the quantity q F was sold in forward markets. Figure 14. Forward contracts mitigate incentive to bid above marginal cost S i no forward S i with forward MC i 0 Forward sale q S Residual demand D i q i q F q i q (59) Fortunately, both generators and load have strong incentives to engage in forward contracting. Both generators and load benefit from locking in long-term rices to avoid the volatility of the sot market. However, erhas the biggest benefit from forward contracts is the reduction or elimination of incentives to affect sot rices. As a result of forward contracts, bidding in sot markets is much closer to marginal cost, resulting in a more efficient disatch. Incentives for hedged suliers to bid at or near marginal cost will tend to kee rices at cometitive levels excet in extreme circumstances. On these occasions, say in resonse to a large forced outage, the ISO will need to draw on unhedged caacity. This caacity will be bid above marginal cost, but the extent of overbidding will be damened by forward contracts. (60) We have seen that forward contracts lay a critical role in mitigating market ower in sot markets. But what determines rices in forward markets? Since buyers and sellers in forward markets always have the otion of waiting and urchasing or selling in the sot market, the forward rice tends to be influenced by the exected sot rice. The main difference between forward and sot rices is that sot rices are more volatile, since suly or demand shocks often occur close to real time, ushing the sot rice either high

26 or low. Hence, in addition to mitigating market ower in sot markets, forward contracts enable buyers and sellers to hedge risks associated with suly and demand shocks. 5. Emirical observation is consistent with theory (61) The theory resented above has imortant ractical ramifications. Indeed, in my exerience advising dozens of bidders in electricity and other markets, I have found that bidders, either exlicitly or imlicitly, develo their bid curves by taking into account the rice-quantity tradeoff from incremental increases in bid rices. In some cases, I have observed ower comanies exlicitly comute the residual demand curves in order to determine their otimal rice-quantity bids in ower markets. In other cases, I have observed the comanies ursue a more exerimental aroach, where strategies are based more on intuition and exerience, which are then adjusted in resonse to erformance. Although this exerimental aroach does not exlicitly aly the theory, as Milton Friedman observed, it matters less whether firms actually follow the secific calculus of bidding outlined above, as long as they act as though they do. So long as the bidders engage in some amount of exerimentation and adjust strategies toward those with better rofit erformance, behavior should converge to the theoretically redicted behavior. Such a convergence is observed in numerous laboratory exeriments, where student subjects are asked to make suly bids into a realistic model of an energy market. In all cases, the behavior confirms the tendency to bid above marginal cost (e.g., Rassenti et al. 2002). Actual industry data also confirms this tendency to bid above marginal cost (Borenstein et al. 2002; Bushnell and Saravia 2002; Sheffrin 2001; Wolfram 1998). (62) Some observers have resented common features of as-bid suly curves as evidence of market maniulation, such as the common occurrence of discontinuities in a firm s suly curve. This behavior, however, is not evidence of maniulation, but rather evidence of rational bidding in the resence of the natural discontinuities that occur in a tyical firm s marginal cost curves. Most firms oerate a variety of generating units. The low-cost baseload units oerate almost all the time, the mid-load units oerate in shoulder and eak eriods, and the high-cost eaking units only oerate at eak times or in resonse to forced outages. Inevitably there are discontinuities in a firm s marginal cost curve, whenever the firm reaches the caacity of a lower-cost unit and begins to use a higher-cost unit, as illustrated below. The as-bid suly curve drawn is an entirely lausible rofit maximizing resonse to the equally lausible marginal cost curve