complicate analysis. Briefly, electricity demand and supply must be kept in balance .... Any trajectory that meets the marginal cost schedule crosses it horizontally, turns down and eventually reaches the q-axis. 12. Fig. 1 illustrates this ...... price of -c), but suppose that demand has constant slope above this level. We can now.
Competition, Contracts and Entry in the Electricity Spot Market1 David M Newbery* Department of Applied Economics Cambridge, UK January 1997 (revised February 1998)
1. Introduction Until recently almost all electricity supply industries were vertically integrated statutory monopolies, operating either under state ownership or as regulated utilities. In 1989-90, the British government restructured the Central Electricity Generating Board, separating generation from transmission, allocating generation capacity between different companies, and creating a spot market for wholesale electricity to make generation competitive. In the following 7 years, Pollitt (1997) found that the electricity supply industry had been liberalised to some extent in 51 out of the 62 countries he studied, with privatization in 30 countries, and vertical separation either in place or planned in 27 countries. (See also IEA, 1997). The British model of vertical separation is rapidly becoming the reference model for reform, provided the system is large enough to support a number of competing generation companies (or has gas, which greatly reduces the minimum viable size of generation companies). Any government or regulatory commission contemplating such unbundling must address a number of structural questions, and needs to develop suitable tools for analyzing market power in the bulk electricity market, to make an informed choice between various options. This paper is directed to creating and applying such tools, and identifying and answering some of the questions that should be addressed before deciding how best to restructure the industry. Such questions include: How many generating companies are needed for effective competition - that is, competition that does not require regulation? What additional efficiency gains and price reductions flow from increasing the number of competing generation companies? What role do contracts play in increasing the intensity of competition between incumbents? How important is freedom of entry for effective competition? What effect do capacity limits have on the nature of competition? What determines equilibrium prices in the spot and contract markets for electricity when there is excess capacity and when there is inadequate capacity? Do entrants have a comparative advantage over incumbents in building any new capacity that is required to meet demand? The paper proceeds as follows. The rest of this section briefly summarises the English experience to show why these questions are important, why the answers are not self-evident, and what institutional facts need to be taken into account in modelling competition in the spot and contract markets. Section 2 sets out the theory of supply function equilibrium for a spot market without contracts or capacity constraints, and 1
This has been recovered from an earlier wordperfect 5.1 document and so the equations may need editing. The doi is http://www.jstor.org/stable/2556091 * Support from the British Economic and Social Research Council under projects R00023 1811 and R00023 3766 is gratefully acknowledged. An earlier version (Newbery, 1992a) was presented at the Royal Economic Society Conference 1992. This paper grew out of collaborative work with Richard Green, described in Green and Newbery (1992), and has benefited from extensive discussions with Edwin Kwok. I am indebted to two referees for helpful comments and to the editor, Robert Porter.
shows how to compute closed form solutions for the benchmark case of constant marginal costs and linear time-varying demand. Section 3 introduces contracts and shows how spot market equilibrium is affected, and whether it is made more competitive. Section 4 examines the effect of contracts on entry and of the threat of entry on the contract and spot markets. It shows that with sufficient competitors, entry will be blockaded, while with fewer it will be deterred, if the incumbents have sufficient capacity. Section 5 looks at the effect of limited capacity on the ability of incumbents to deter entry, and shows that if entrants compete in the price-setting part of the market, then they have a comparative advantage in building new capacity, but not if they enter on base load. The main findings of the analysis are that if incumbents have spare capacity and potential entrants can sign base-load contracts, incumbents will maximise their base-load contract cover while increasing the volatility in the spot market and deterring entry. If incumbents have inadequate capacity they will be forced to accept entry and increased competition. Additional competitors lower spot price volatility (in contrast to other types of markets), increase efficiency, and raise consumer welfare. 1.1 The English experience The pressures of the parliamentary timetable and the difficulty of finding the true costs of nuclear power resulted in a flawed restructuring of the English electricity supply industry. The original plan was to place the nuclear plant in a single large company with 70% of capacity, balanced by a single firm with the remaining conventional capacity. When the nuclear plant was belatedly withdrawn from the privatisation, the remaining fossil capacity was left unequally divided between two companies, National Power and PowerGen, with attendant concerns over their market dominance. National Power and PowerGen were sold as private generators, transmission was placed in National Grid Company, all of whose shares were held by the 12 Regional Electricity Companies (RECs) which were privatised. The nuclear plant remained in public ownership until mid 1996, when the modern stations were finally privatised.2 In the six years after privatisation, some 15 GW3 of new capacity were connected to the system, compared to the initial total generating capacity of 65 GW, and of this new capacity, 13 GW was in 19 combined cycle gas turbine (CCGT) stations. This new technology allows gas to be burned at high efficiency (over 50%, compared with 37-40% in conventional thermal stations), and at modest scale (nearly half the new stations had capacity in the range 168 MW to 500 MW, compared to the normal size of 2,000 MW for conventional coal or oil-fired stations). Over half of this CCGT capacity was built by independent power generators, though the rest has been built by the incumbents, National Power and PowerGen. The entry of new generators, the increased availability of existing nuclear stations together with 1.3 GW of new nuclear capacity, and increased imports reduced the market share of the two majors from 73% in 1990/91 to 54% in 1995/9. This fell to 46% in 1996/97 after National Power and PowerGen were persuaded, under regulatory pressure, to sell 6 GW of coal-fired plant to Eastern Group, and is expected to fall to 38% in 2
More details can be found in Newbery (1995) and Green (1996a)
3
Gigawatt, equal 1000 Megawatt (MW) or 1 million kW.
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2000/01 (MMC, 1996). Nevertheless, in the first five years, these two companies set the price of electricity in the pool nearly 90% of the time, and concerns over their market power continue.4 Those who argue that the generating industry is already adequately competitive argue that CCGTs have made generation contestable - new entrants were able to secure 15-year contracts to sell power, to buy gas, and to borrow the money needed to finance the building of CCGTs with performance guarantees. They have demonstrated their willingness and ability to enter the industry in the `dash for gas' that halved the demand for British coal for generation by 1994. Contracts not only facilitated entry, they have also greatly modified the exercise of market power of the majors. Electricity networks have special characteristics that constrain market design and complicate analysis. Briefly, electricity demand and supply must be kept in balance minute by minute to maintain frequency and voltage. These requirements are normally met by giving a system operator direct control over despatch of generation. In a vertically integrated system the operator minimises total system costs, but in the English system competing generators submit one day ahead a schedule of bids stating the price at which each generating set can be despatched. The despatcher then computes the least (financial) cost solution to meet forecast demand, and instructs suppliers which generating sets to have ready for despatch. If called upon to supply, they are paid according to the market clearing spot price (equal to the highest bid price accepted). The theoretical question is how to model this first-price sealed bid repeated auction. There are two contending models, the first based on Klemperer and Meyer's (1989) (KM) supply function equilibrium model, the second based on an explicit discrete bid auction model. The claim here is that any equilibrium of the first is also an equilibrium of the second, but not necessarily vice versa. KM explore the Nash equilibrium in supply functions that must be committed to before the realisation of uncertain demand. Green and Newbery (1992) noted that the uncertainty of demand was mathematically equivalent to the daily predictable time-varying demand, and they numerically solved a model calibrated to the 1990 English market. They examined issues of market power and the effects of the threat of entry, but not the important role played by contracts. The other approach is exemplified by von der Fehr and Harbord's (1992) model in which each generating company submits a single price for each generating set. This gives a step-like supply function rather than a continuous schedule. They showed that for some patterns of demand and allocation of capacity among generators there would be no equilibrium in pure strategies. Prices would be inherently unstable as in Edgeworth duopoly, and they claimed that observed pool price behaviour revealed such instability. They suggested that the correct way to think of the problem of setting up an electricity market was one of auction design, which is useful in identifying the relevant theoretical literature (eg McAfee and McMillan, 1987). Unfortunately, it is very hard to solve repeated auctions which lack pure strategy equilibria, leading to an apparent impasse there is a tractable modelling approach that assumes continuity of the supply schedules,
4
Evidence on bidding behaviour is provided by Newbery (1995), Wolak and Patrick (1996), and Wolfram (1996, 1997). In October, 1997, the Minister for Science, Energy and Technology called for a review of the Electricity Pool, in part prompted by these concerns (Newbery, 1997).
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which is subject to the criticism that the indivisibility of the generating sets rules out continuity and drastically affects the nature of the equilibrium. This conflict may be more apparent than real.5 Newbery (1992b) argued that the continuous supply function approach can be adapted to deal with discontinuities caused by the discreteness of each generating set. He noted first that the number of generating sets bid was large (over 200) and each set could submit bids for up to three specified tranches of the set's capacity (eg for the first 100 MW, the next 150 MW, and the final 80 MW). If the bids for each tranche are chosen appropriately, and the sizes of the tranches randomly chosen from an appropriate probability distribution, any monotonic supply function can be constructed which is continuous in expectation. Any equilibrium continuous supply function can thus be replicated by introducing a very small amount of randomisation. It remains an open question whether there are other plausible mixed strategy equilibria that cannot be found by the supply function approach, but discreteness of the individual sets is not an argument for rejecting the supply function approach.6 This paper shows how to solve for the simultaneous equilibrium in spot and contract markets in the case of a analytically tractable model - a task that remains incomplete because of the complexity of interactions between the spot and contract markets (e.g Green, 1992, 1996b; Powell, 1993). The natural approach to modelling electricity markets as supply function equilibria has the drawback that equilibrium is typically not unique. This paper proposes a unique equilibrium in the case where entry may be backed by contracts, and determines the level of contract sales that incumbent generators will sell to sustain this equilibrium. 2. Equilibrium in Supply Functions for a Duopoly The first step is to examine equilibrium in a spot market with no capacity constraints and no contracts. The English electricity generating industry was privatised effectively as a duopoly, as nuclear generation (and imports) are inelastically supplied. The case of a duopoly is an appropriate and natural starting point for model building, though it will be extended to the general n-firm case below. Each firm submits its supply schedule to the despatcher the day ahead as a sealed bid. The supply schedule must be a monotonically increasing continuous function of price, as the despatcher is required to choose generating sets to call up in order of increasing cost (the merit order), ruling out quantity discounts and backward bending supply functions (of the kind allowed by Bolle, 1992). In KM, the firms are uncertain about demand. Once demand is realised, the spot price is that which equates supply to demand (if one exists, otherwise the firms receive nothing). Just as the KM suppliers have to take account of possible variations in realised demand in different states of the world, in the electricity market generators have to take 5
Wolfram (1997) shows that many of the predictions of the two approaches are the same, as well as testing them empirically using English pool data. 6
Other objections are that it is hard to identify the supply function from any single day's price quantity observations, as there are constraints on the rate at which stations can be ramped up and down, and the fixed start-up costs are allocated over the hours the station is run. It has been claimed that the real bidding game lies in specifying the 30-odd technical parameters to derive advantageous despatch, eg by specifying a high minimum load for stations that will be forced to run to handle a transmission constraint. Inevitably this fine detail is lost in the kind of broad-brush modelling described here.
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account of reasonably predictable variations in demand over the day. With this modification, the notation and argument follows KM closely. 7 Suppose that the load-duration curve at any moment during the day is predictable with certainty and given by D(p, t), where 0 t 1 is `time', i.e. the fraction of the day that demand is higher than D, and p is the spot or pool price.8 (In this paper, following KM, p is defined as the spot price less the marginal cost of supplying an infinitesimal amount, shifting the origin so that the marginal cost schedule passes through the origin.) Assume that for all (p, t), - < D < 0, Dpp 0, and Dpt = 0. (This last assumption is required for the analytic solutions, but not for existence results.) The net demand facing firm i at moment t when the other firm, j, has supply schedule S (p), is D(p,t) - S (p). Let the effective generating costs of supplying q be C(q) with non-decreasing marginal cost C(q). 9 The strategy for firm i is formally a monotonically increasing function mapping price into a level of output independent of time, t: S : [0, ) [0, ), on the current assumption of no capacity constraints. The despatcher then determines the lowest price p(t) that equates supply to demand at each moment t, S (p(t)) + S (p(t)) = D(p(t),t), j i, provided such a price exists, and, if such a price does not exist, the firms are paid zero. On the assumption, justified by KM, that profit-maximising price-output pairs can be described by a supply function q = S (p),10 and given the assumptions on costs and demand, at any t, the choice of q implies a particular value of p, and so the profit maximising solution can be found by maximising profit, π = pq - C(q ) with respect to p: πi(p,t)=p.[D(p,t)-qj(p)]-CD(p,t)-qj(p),
iNEj,
(1)
iNEj.
(2)
so the first order condition can be written as dqj qi = dp p-C(qj) +Dp ,
Solving for the symmetric solution in which q = q = q gives
7
This section repeats the exposition in Green and Newbery (1992), which derived the differential equations as the first step to solving for equilibrium for a model calibrated to the cost schedules of the two thermal generators. That paper did not, however, consider the effect of contracts on equilibrium. 8
The assumption that instantaneous demand depends only on the current price is restrictive in ruling out intertemporal substitution in demand. Even the sophisticated computer scheduling system used in despatch finds solving intertemporal arbitrage problems extremely difficult, and on the demand side they seem to be of minor practical importance. Patrick and Wolak (1997) finds some evidence of arbitrage by water companies but remarkably low substitution elasticities for other firms within the day. With the change of origin, the effective cost is defined as C(q) C*(q) - qC*(0), where C*(q) is the true total cost of generating q. With constant marginal costs, the effective costs are then zero. 9
10
From now on, dependence of p on time, t, is not explicitly shown unless necessary.
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dq q dp = p-C(q) +Dp.
(3)
The result will be a Nash equilibrium in supply functions.11 The behaviour of the differential equation for the symmetric supply function equilibrium can be further analyzed (KM, p 1254). Consider points (q, p) such that q C(q)xi , p>0, qi =xi , i=1,2, p=0, qi =xi +Bp+bpln(-p), i=1,2, qi 0), and if there is no minimum economic scale of entry. This is approximately true of CCGT, which has constant unit average total costs, given base-load operation, and a small minimum scale (down to 60-75 MW, compared to a market of 50,000 MW), so is just the average total unit cost, given existing contract gas prices and interest rates. (Later we shall explore the consequences of relaxing the assumption of no minimum economic scale when discussing the number of entrants.) Entry deterrence will be feasible provided the incumbents have adequate capacity. In that case bidding to achieve the highest entry-deterring price is profit maximising because any higher price would induce entry that would drive Ep down to , (because CompCon
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more generators means more competition and lower prices, as demonstrated in Proposition 1). This would reduce sales without altering the average price, and hence would reduce incumbents' profit. Clearly a price below the entry-deterring price could be improved upon. The next step is to determine the upper price, p* and the level of contracts, X, which together fix the average price in (17). Proposition 3. The profit maximising entry-deterring strategy of under-contracted generators in a contestable market in which consumers are unwilling to be overcontracted is to set p* = p**, and X = X**, where P{X**,A(p**)} = , provided X** a , and otherwise to set X = X* = a , with p* such that P{a , A(p*)} = . Proof Define p as the minimum price, i.e. the solution to (13) and (14) when t = 1, a(t) = a . As dp(t)/dX < 0 it follows that both p/x < 0 and Ep/x < 0, for given p*. Differentiating (14) with respect to p* reveals that p/p* > 0 and Ep/p* > 0, for given X. So if p* < p**, and X < a , then p* and X can be increased to offset each other such that Ep remains constant. This will induce a mean-preserving spread to prices, and hence increase profits, as q(t) is positively correlated with p(t). Thus profits can be increased without inducing entry by holding Ep = and either raising p* to its maximum value, p**, or by increasing contracts to their maximum level of demand, a . QED. In general, the individually rational choice of total contracts, , say (as determined by Proposition 2), will not be equal to the joint profit-maximising choice, even if the generators coordinate on the best entry-deterring upper price, p** or p*, as the case may be. If > X**, then entry will be blockaded, to use the Bain's (1956) terminology, and prices in the industry will be kept below the entry-deterring level by `excessive' competition in the contract market. If < X** then entry would occur if the incumbents failed to realise that it was in their interest to increase contract cover. In that case their global profit-maximising strategy would be to increase contract sales to drive down prices to the entry-deterring level, and it would be individually rational for each generator to increase its contract cover. Proposition 4. Risk-neutral consumers would gain if generators in a contestable market reduced their level of contract cover. Proof The lower the extent of contract cover consistent with entry deterrence, the more elastic will be the net supply function and the lower will be the variance of prices around the mean (entry-deterring) price. Fig. 3 shows that consumers lose more consumer surplus by the higher price at peak demand of a more variable spot market than they gain from the lower price at off-peak demand. QED. 4.1. Contracting with more competitors It is straightforward to extend the analysis to the case of n identical incumbents by replacing q by q - x in equations (7) and (8). The aggregate Cournot schedule is CompCon
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Q = X + nbp, X = nx, and the highest price feasible aggregate supply schedule meets maximum demand on this Cournot schedule at p** = (a - X)/(n+1)b: Q=X+
n(n-1)bp** p 1(n-1) nbp - n-2 , n-2 p**
pp** .
(19)
The effect of increasing the number of competing generators and adjusting the level of contract cover to give the profit-maximising entry-deterring equilibrium is shown in fig. 4. The larger the number of generators, the more convex the supply function, and hence the lower the range of prices. To achieve the same average price, the upper price will therefore be lower and the lower price higher, the larger the number of competitors. This can be seen comparing 2, 3 and 5 generators in fig. 4. With 8 competing generators, entry is deterred with zero contracts for the parameters chosen, and any positive contract cover would reduce prices even further. If the generators are able to coordinate on a positive level of contracts and a maximum price to just deter entry, then the aggregate supply function is relatively insensitive to the number of competitors. As the number of competitors increases, it becomes increasingly likely that entry will be blockaded rather than deterred. In that sense a more competitive market is likely to have a lower average price than a less competitive market, provided that there is sufficient capacity to make further investment unnecessary. 5. Capacity constraints and entry deterrence Newbery (1992a) showed that capacity constraints modify the equilibrium supply schedules in a natural but significant way. As before, the supply schedules that satisfy the first-order condition for profit maximisation meet the Cournot schedule with dq/dp = 0, (i.e. dp/dq = ). Again, define p** as the price at which the aggregate Cournot schedule meets the maximum demand schedule. Given a choice of total contract cover, X, the aggregate Cournot schedule for n identical firms will meet the industry's full capacity output, K, at p (K,X) = (K-X)/nb, (eg. point E in fig. 5). The aggregate Cournot schedule will meet maximum demand at p (K) = (a - K)/b, (B in fig. 5). The maximum feasible price is p** = (a -X)/[(n+1)b]. Entry can be deterred if the average price can reduced to , and the average price can be reduced by increasing contract cover X or increasing the intensity of competition. Dividing total capacity among a larger number of firms, n, makes the aggregate supply schedule more convex, and in the limit it approaches a reverse L in which supply is elastic at marginal cost up to full capacity and is then completely inelastic. The average price in this competitive industry is a useful benchmark, because the average price with a finite number of firms will be higher than this. If the competitive benchmark average price is above the entry price, then there is no ambiguity in claiming that capacity is insufficient to deter entry. Even if a competitive industry had sufficient capacity to deter entry, an industry with fewer firms may be insufficiently competitive to drive the average price down to the entry-deterring level. In the latter case the incumbents would like to increase contract cover to minimise entry, but may be prevented by the unwillingness of consumers to be overcontracted. The average price p(t)dt can be determined as the area under the price-duration curve, defined as the plot of p(t) against t. Fig. 6 shows the price-duration curve (actually CompCon
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the net price-duration curve down to marginal cost) for the fully competitive industry (for which supply is completely elastic up to full capacity) and for a fully (baseload) contracted capacity-constrained triopoly, in which a(t) = a - (a - a )t, t [0,1]. The average competitive price with capacity K is Ep = (a -K) /{b(a -a )}, decreasing in total capacity. The amount of capacity required to deter entry will have to exceed a {2 b(a -a )} (solving for Ep = ). We can ask several questions of this contract-constrained industry unable to deter entry. Does the allocation of capacity between firms affect the equilibrium? Does the number of firms affect equilibrium? If incumbents and entrants have access to the same cost technology, does either have an advantage in investing? Define total capacity K = Σk , note that the largest total contract cover is X = a , and that highest price feasible aggregate supply schedule meets maximum demand on the Cournot schedule at p** = (a - a )/(n+1)b. The appendix shows that whether or not it is possible for the industry to reach full capacity output in equilibrium depends on whether or not p** > p (K,a ). This is equivalent to whether or not capacity K is less than a critical level, , or the number of firms above a critical number: na0 +a1 Kn a -K . 0
(20)
The appendix also shows that if K < , then there is a unique equilibrium supply schedule (for the chosen level of contract cover), and if K > , then there is a lowest equilibrium supply schedule, which will be chosen. Proposition 5. If generators wish to deter entry by lowering price, but are prevented by their inability to increase contract cover at equilibrium, then that equilibrium will be one of identical net supply schedules and independent of the allocation of capacity. Proof If each generator i sells contracts x = k - (K-a )/n, then each will supply along the same equilibrium net supply function, q - x . If the industry is capacity constrained, these supply functions will be uniquely specified and will reach full capacity simultaneously. If the industry is not capacity constrained, each generator will coordinate on the lowest price equilibrium supply function which will meet maximum demand simultaneously at the lowest feasible price. Total contract sales will be maximal (at a ), so that no generator can sell more contracts, nor lower the price any further. QED. 5.1 Entry with no technical progress If there is no technical progress then the new capacity will have the same (zero) marginal cost as existing capacity. The entry price is the overhead or capital cost per unit per day. Suppose that the minimum scale at which average unit cost reaches its minimum is s, that above s unit costs are constant, and that s is small in a sense to be made clear below. Proposition 6. A given increment of capacity (with the same marginal costs as that in the industry) when created by a new entrant will result in a lower average price than the same
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increment of capacity held by incumbents, providing firms are constrained (by consumer demand for contracts) from increasing contract cover to deter entry. Proof Equilibrium aggregate supply is uniquely defined under these conditions, and is an increasing function of the number of competitors (at any level of price). The number of competitors will be larger with entry as entrants are indistinguishable from incumbents and the allocation of capacity between firms is irrelevant in determining effective competition. More competitors leads to a lower average price. QED. Fig. 7 shows the effect of increasing the number of competitors on the average price, holding capacity and contracts constant. This suggests that a potential entrant could predict the post-entry average price, which would be lower were he to enter than were the incumbents to build the same quantum of capacity, Δk, and he would be therefore willing to sign an appropriate set of contracts Δk - (K+Δk-a )/(n+1) at this lower price. If s < Δk < 2s, and if Δk were sufficient to drive the price down to the entry-deterring level, the entrant could credibly undercut any incumbent's offer of additional contracts, and deter other potential entrants, who would not be able to enter profitably at any scale. More generally, if the amount of capacity, Δk, needed to drive down the average price to the entry-deterring level, satisfies ms < Δk < (m+1)s for some integer m, then m new entrants will enter. This appears to be what happened in the `dash for gas' in which a large number of small and medium scale independents entered the English market in the early 1990s. Another way to see the competitive advantage of new entrants is to note that without entry, the incumbents would need to install more capacity to drive the average price down to the entry-deterring level, and this would have higher cost than a more competitive industry. These higher costs would benefit consumers, not the incumbents, since the incumbents would now have less variable prices and the same mean as an industry experiencing entry (whose price duration curve in fig. 7 would be steeper and therefore higher than that of the incumbents after expansion). 5.2 Entry with technical progress If technical progress lowers variable costs compared to the incumbents (e.g the higher thermal efficiencies of later generation CCGTs), then new plant would run continuously on base-load and supply inelastically, with all the variation in output provided by the older plant. The effect on incumbents would be equivalent to a shift in the net demand facing them equal to the amount of new capacity invested. The number of price-setting firms would therefore remain unchanged whether an entrant or incumbent installed the investment needed to expand supply and drive down the average price to the entry-deterring level. In this case equilibrium in the industry is unaffected by the allocation of existing capacity or the ownership of new capacity.
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6. Conclusions If potential entrants can sign base-load contracts, then the generation market becomes contestable, as entrants can lock in the post-entry price without risk. If the industry has enough total capacity (given the number of firms) the incumbents can sell enough contracts to drive the price down to the entry-deterring level, and will find it most profitable to coordinate on the highest price, highest-contracted supply schedule that sustains this price. The resulting equilibrium is one in which the level of contract cover and bidding strategies are both uniquely specified. The threat of entry will, in most cases, cause the incumbents to increase their contract cover, which will make their behaviour in the spot market more competitive and reduce the average pool price. They will also maximise the variability of spot prices, and Newbery (1995) provides evidence that the two price-setting incumbents in the English electricity market, once they grasped the reality of entry threats (or after they had allowed in sufficient competitors to satisfy the regulator's desire for more competition), rapidly coordinated their bidding strategy in a way consistent with the story presented here. Increasing the number of competitors would reduce the maximum price reached in the pool, and this might also reduce the average price, depending on whether the equilibrium bidding behaviour ignoring the threat of entry were sufficiently competitive to keep prices below the entry level. If not, then the average price would again be set by entrants, but the variability of prices would be lower the larger the number of incumbent competitors, to the benefit of consumers, as shown by Proposition 4. Contracts in this model can deter entry, but, in contrast to Aghion and Bolton (1987), this only occurs when it is efficient to do so.19 The inefficiency created by market power arises because the incumbents may not be able to commit themselves through contracts to lower the price enough to deter excessive or inefficient entry. This occurs when the industry has insufficient capacity (given the number of firms). In that case the incumbents will only be able to deter entry if new investment has a lower marginal cost than existing capacity, and then only by undertaking all the required (and socially excessive) new investment. The amount of entry depends on the degree of competition and the number of price-setting firms, with less `excess investment' the more competitive the industry. If new capacity has the same variable costs as existing capacity, it will play an equal role in price-setting, and entrants, by credibly offering lower-priced contracts than incumbents, will be able to enter the industry and increase the degree of competition. The model set out here is simple, and reality will be more complex. Plants differ in their variable costs, so that marginal cost will vary with output. In this case net supply functions will not be independent of contract cover, as in this simple model, making it harder to find solutions. Nevertheless, the English market illustrated in fig. 1 has constant costs over a wide range of relevant output, while entry is replacing the right hand tail of higher cost plant, making the present model an ever closer approximation to this market. A more serious objection is that more complicated contracts than simple base-load contracts offer more complex hedging opportunities, and may allow the degree of contract cover to be increased, possibly enabling incumbents better to deter entrants. 19
Innes and Sexton (1994) and Ziss (1996) have pointed out that inefficient entry can be prevented in the Aghion and Bolton model of exclusionary contracts. Note that in the present model contracts are financial, not physical, and therefore not exclusionary, so the model is quite different.
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On the other hand, considerable entry by small independents has taken place, consistent with this simpler model. The main finding of the paper is that if entry remains contestable and the contract market is reasonably liquid and active, as seems likely to remain the case, then the inefficiencies of market power caused by too few generators are much reduced, and show up as more volatile prices than necessary. The other main finding is that limited capacity facilitates entry which increases competition, providing the new entrants compete in the price-setting part of the market. If the new capacity always runs on base-load, the incumbents can successfully deter entry, though they gain no advantage in so doing. Nor would entry affect the market power of the incumbents in this case.
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References Aghion, P. and P Bolton (1987) `Contracts as a barrier to entry', American Economic Review, June, 77(3), 388-401 Allaz, B. and J-L Vila (1993) `Cournot competition, futures markets and efficiency', Journal of Economic Theory, 59(1), Feb. 1-16 Bain, J. (1956) Barriers to New Competition, Cambridge, Mass: Harvard University Press Bolle, F. (1992) `Supply Function Equilibria and the Danger of Tacit Collusion: The Case of Spot Markets for Electricity', Energy Economics, April, 94-102 Green, R.J., (1992) `Contracts and the Pool: The British Electricity Market', mimeo, DAE, August. Green, R.J., (1996a), `Reform of the Electricity Supply Industry in the UK', Journal of Energy Literature, II(1), 3-24. Green, R.J., (1996b), `The Electricity Contract Market', DAE Discussion Paper 9616, Cambridge Green, R.J., and D.M. Newbery, (1992), `Competition in the British Electricity Spot Market', Journal of Political Economy, 100(5), October, 929-53. IEA (1997), Energy Policies of IEA Countries: 1997 Review, Paris: OECD Innes, R. and R.J. Sexton (1994) `Strategic Buyers and Exclusionary Contracts', American Economic Review, June, 84(3), 566-84. Klemperer, P. D. and M.A. Meyer, (1989), `Supply Function Equilibria in Oligopoly under Uncertainty', Econometrica, 57(6) Nov. 1243-1277. Laussel, D. (1992), `Strategic commercial policy revisited: a supply-function equilibrium model', American Journal of Economics, 82(1), 84-99. McAfee, R.P and J. McMillan, (1987) `Auctions and Bidding', Journal of Economic Literature, 25(2), 699-738. MMC, (1996), National Power PLC and Southern Electric plc: A Report on the proposed merger, London: HMSO, Cm3230. Newbery, D.M., (1992a), `Supply function equilibria: mixed strategy step functions and continuous representations', mimeo, Cambridge. Newbery, D.M., (1992b), `Capacity-constrained Supply Function Equilibria: Competition and Entry in the Electricity Spot Market', Cambridge: DAE Working Paper, 9208 Newbery, D.M., (1995), `Power Markets and Market Power', Energy Journal 16(3), 41-66. Newbery, D.M., (1997) `Pool Reform and Competition in Electricity', DAE Working Paper 9734, Cambridge, forthcoming in M. Beesley (ed.) Lectures on Regulation Series VII, \london: Institute of Economic Affairs Patrick, R.H. and F.A. Wolak, (1997) `Estimating the customer-level demand for electricity under real-time pricing', paper presented to POWER Conference, 14 March, mimeo, Stanford University. Pollitt, M. (1997) `The impact of liberalisation on the performance of the electricity supply industry', Journal of Energy Literature, 3(2), 3-31 Powell, A., (1993), `Trading forward in an imperfect market: the case of electricity in Britain', Economic Journal, 103, 444-53. von der Fehr, N-H. M. and D. Harbord, (1993), `Spot market competition in the UK electricity industry', Economic Journal, 103, 531-46. Wolak, F.A. and R.H. Patrick, (1996) `The time series behavior of market prices and output in the England and Wales electricity market' mimeo, Stanford. Wolfram, C.D., (1996), `Measuring Duopoly Power in the British Electricity Spot Market', mimeo, MIT. Wolfram, C.D., (1997), `Strategic bidding in a multi-unit auction: an empirical analysis of bids to supply electricity in England and Wales', paper presented to POWER Conference, 14 March, mimeo, Harvard University Ziss, S. (1996) `Contracts as a barrier to entry: Comment', American Economic Review, June, 86(3), 672-4.
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Appendix Over-contracting equilibria If X > a , then consumers will have bought more electricity on contract in periods of low demand than they require, and are no longer hedging but are actively speculating. If they are willing to do this, then (net) prices as defined (ie the price-cost margin) will become negative at sufficiently low demand, and generators will bid below cost. Suppose the actual unit cost is u, so that the actual price, P = p + u. It is likely that the demand schedule would become infinitely elastic at some positive (if low) price, u - c, (ie at a net price of -c), but suppose that demand has constant slope above this level. We can now ask how the ability to over-contract could increase profits in the case in which coordinating on p** with X = a would induce entry. The equation for aggregate supply for -c < p < 0 is given by the last equation in (11). The maximum level of contract cover can increase to = a + 3bc (for a duopoly) provided this is less than a , at which point the aggregate Cournot schedule would meet minimum demand at the minimum feasible price, -c, and the constant in (11) will be B = b(1 - lnc). The equation for aggregate supply in periods of over-contracting will be Q=a0 +3bc-2b(-p)[ln(c(-p))-1],
-c 0 is small. Define p as the maximum price reached at F in fig. 8: p = (a + d - nk)/b, and p by q(p ) = k - d as the price at which firm 1 first deviates from the schedule of the other firms, at H on OB in fig. 8. 21 With the appropriate change in the variable of integration, profits can be calculated for the deviation and compared with profits selling along the original non-deviating section. The advantage to deviating is p
1
p
p
2
2
D=Πd -Πo = (k-d)pf1(p)dp+ (k-d)pf2(p)dp- q(p)pf3(p)dp, p
2
p
(A2)
p
3
3
where f (p) remains to be determined. If the deviation d is small, the supply schedule q(p) can be linearised around p : q(p)Min[k,k+g(p-p2)],
1 k-a1n dq g dpp = n-1( p -b), 2 2
(A3)
where g is the slope of the supply schedule at p (i.e. angle kBH) whose value is found from (7) (replacing q by q - x, where x = a /n) evaluated at q = k, p = p . This in turn makes p = p + d/b (exactly, as angle BFG = b); and p = p - d/g (approximately, as angle GHB = g). If the demand schedule is a - μt - bp (where μ a - a ), then the equation for aggregate supply equals demand will be a0 -μt-bp=(n-1)q(p)+q*(p), i.e. μt=1-F(p)=a0 -bp-(n-1)q(p)-q*(p),
(A4)
where q(p) is given by (A3) and q*(p) is the deviation. It follows that μf1(p)=b;
μf2(p)=b+(n-1)g;
μf3(p)=b+ng.
(A5)
21
Note that fig. 8 is scaled for a single firm, facing 1/n total demand, in contrast to fig. 5, which shows aggregate supply and demand.
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Integrating the linearised supply function and ignoring terms in d and above, the condition for deviation to be attractive is that D > 0 in (A2), which is equivalent to k(b+g)-bp2(b+ng)>0.
(A6)
From (A3) k=p2[b+(n-1)g] +a1n,
so γ>0D>0 (n+1)k-a1n>a0 >nk.
(A7)
The condition for deviation to be attractive is that the slope of the supply function, g, is positive (and finite) at full capacity output. The condition a > nk is the condition that capacity be a constraint requiring positive prices, while the inequality (n+1)k - a /n > a is the condition that the supply schedule reaches full capacity below the Cournot schedule (at which point it would have infinite slope). If maximum demand at full capacity exceeds the Cournot output, the supply function equilibrium is the unique schedule meeting the intersection of the Cournot schedule with full capacity and no potentially profitable deviation is feasible. Step 2. To show the existence of a connected set of equilibria. Consider all solutions q(p) satisfying (5) or (8) as appropriate such that a0-nk a0-(n-1)k p* b q-1(k) 2b p**.
(A8)
If q(p**) = k, then bp** + (n-1)k = a - bp**, and there is no p > p** such that bp** + (n-1)k = D(p,t), so it is impossible for firm 1 to deviate to that part of the Cournot schedule that is the best response to the remaining firms selling at full capacity. For any p < p** the best response to q(p) is q(p). Thus supply functions satisfying (A8) are equilibria, with p* corresponding to the intersection of maximum demand with the Cournot schedule. In the duopoly case this range is defined by A [b + bln(k/b), 2bk/(a - k) + bln{(a - k)/(2b)}]. QED
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Fig 1
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