رقابت با توابع عرضه و تقاضا
|کد مقاله||سال انتشار||تعداد صفحات مقاله انگلیسی||ترجمه فارسی|
|8163||2001||25 صفحه PDF||سفارش دهید|
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Energy Economics, Volume 23, Issue 3, May 2001, Pages 253–277
If economic agents have to determine in advance their supply or demand in reaction to different market prices we may assume that their strategic instruments are supply or demand functions. The best examples for such markets are the spot markets for electricity in England and Wales, in Chile, in New Zealand, in Scandinavia and perhaps elsewhere. A further example is computerized trading in stock markets, financial markets, or commodity exchanges. The functional form of equilibria is explicitly determined in this paper. Under a certain condition, equilibria exist for every finite spread of (stochastic) autonomous demand, i.e. demand from small, non-strategically acting consumers. Contrary to competition with supply functions alone, however, there is no tendency for market prices to converge to 0 if the spread of autonomous demand increases infinitely. Lower bounds of market prices can be computed instead.
On 1 April 1990, a spot market for electricity was established in England and Wales. This is probably the best example for competition with supply functions. The three big suppliers, National Power, PowerGen, and (former) Nuclear Electric1, as well as some small ones are required to submit bids for each of their generators2. The ranked bids of every supplier form a staircase supply function and can be integrated into an aggregate supply function. Every half-hour a price is determined so that supply meets demand which in turn may depend on the spot price (see Fig. 1) and which has a stochastic component. For further details of the British electricity system and its performance, see Green (1994) and Littlechild (1994). The theoretical implications of competition with differentiable supply functions were independently derived by Klemperer and Meyer (1989) — who had other examples in mind3 — and Bolle (1992) who was explicitly concerned with electricity markets. Further studies stem from Green and Newbery (1992) and Newbery (1991). The alternative to smoothing the staircase supply function is to regard the market as a multiple-bid auction (Bolle, 1997).4 Although the British electricity market had a predecessor in Chile, it was the British example which made the Scandinavian countries, New Zealand, California and Spain introduce a similar market and makes other southern and eastern European countries prepare one. In the United States as well as in Germany, electricity markets still depend on Third Party Access or similar rules; but in both countries spot markets may be introduced later on. In Norway, New Zealand, California, and from autumn 2000 on also in England and Wales (Power in Europe, 1999) the bids are extended to include demand-side bids. So, in addition to the aggregate supply function there is an aggregate demand function resulting from those bids. The spot market price is determined by the cutting point of the gross excess supply (supply-bids minus demand-bids) and autonomous demand by small consumers5 (see Fig. 2). This would be the case if just the big users of electricity were invited to submit bids. In New Zealand and Norway, however, the distributors of electricity, as well, submit demand bids, either themselves or via a common agent such as the Powerbuy Group in New Zealand, so that practically all demand is covered by bids. The class of purchasers, however, who buy for consumers with given tariffs (possibly also spot-price tariffs) cannot really bid strategically. In the end, they buy what their autonomous consumers require. So strategic incentives are limited to exploiting differences between ex ante-pricing (on the basis of announced demand and supply) and ex post-pricing (on the basis of real demand and supply). In New Zealand, there are special rules for pricing these differences between announced and real demand supply which try to keep such incentives small (never zero, however!). In Norway, there is an additional market for deviations from the announced quantities. This market has the character of the market described in Fig. 2. So, in reality, there is a two-stage market but, in spite of this, I hope to grasp the decisive structural implications by analyzing the one-stage market below. What we will do in the following is a game theoretic analysis of competition with supply and demand functions where there is additional autonomous demand. Our point of view is to handle demand bids by agents of autonomous consumers as autonomous demand. Strategic bidders are often identical to big industrial users of electricity who can really determine their final demand. Further examples of competition with supply and demand functions are those developing computerized trading possibilities in other spot markets, cf. stock markets, financial markets, and commodity exchanges. As in the case of competition with supply functions alone it does not make much sense to investigate this market with deterministic autonomous demand because ‘almost every’ strategy vector of functions is in equilibrium (see Klemperer and Meyer, 1989 and Bolle, 1992). The out-of-equilibrium regions of the functions can be used to express arbitrary threats. With stochastic autonomous demand, an interval of possible spot prices results and, within this interval, supply and demand functions have to take equilibrium values. In spite of this, there is still a continuum of equilibria. In the next section, we will derive the equilibrium aggregate supply and demand functions under a simplifying assumption: constant (zero) marginal costs of the suppliers and constant gross profit6 per kWh by ‘big users’. Special cases are discussed in Section 3 and constraints are considered in Section 4. In Section 5, results are discussed under policy aspects. Although the language of the electricity market is employed, the model can also be used as well to describe other commodity or financial markets where multiple bids are submitted or where conditional decisions have to be made in advance of the market day. The differences of market organizations will often be mirrored in different constraints imposed on the space of feasible solutions. The main result of this paper is that such restrictions may be decisive for the existence of pure strategy equilibria.
نتیجه گیری انگلیسی
The result of our investigation may make us uneasy about the possible success of the New Zealand and other countries’ electricity markets. If autonomous demand is large we either get prices which possibly are considerably bounded away from marginal costs (see Table 1) or we get mixed strategies. High prices cause losses of consumers’ surplus, if the participants of these markets play mixed strategies we should expect some instability, i.e. fluctuations of supply and demand which cannot be explained by changes of market parameters. Table 1 shows that it might be advantageous for the big customers to collude (as those customers in the Powerbuy Group in New Zealand). Or does all this mean that we should not allow demand side bids at all in order to be back in the relatively simple market of competition with supply functions alone? It is always dangerous to derive policy guidelines from a model as simple as ours. First, electricity markets do not consist of a spot market only; there are futures and forward contracts as well as long-term contracts. As the joint analysis of the interacting markets usually turns out to be too difficult, different models are used to investigate the influence of single market segments. The existence of a futures market in connection with an oligopolistic spot market, e.g. is shown to be advantageous for consumers by Bolle (1993), Powell (1993), Allaz (1992) and others, but only on the basis of a rather simplified spot-market model. Secondly, for the purpose of this model, the real electricity spot market is further simplified in some respects, for example by omitting transmission restrictions, line losses, the possibility of generator break-downs, the pricing of reserve capacity, fees, etc. In addition, the assumptions of the above model allow for arbitrarily large demand and supply and also arbitrarily large consumers’ and producers’ surpluses. In reality, however, we have to take into account capacity restrictions; even more realistic but far more difficult to handle would have been non-identical increasing marginal costs and non-identical decreasing marginal gross profits w. Such a model, however, would require one to analyze a system of k+r differential equations in (9) and (12) instead of (11) and (14). As the restrictions to the solutions turned out to be crucial in our simple case, such an analysis can be expected to be rather complex. Intuitively, one should expect the largest effect from capacity constraints for the customers, i.e. by assuming ‘small’ customers. Only in such a more realistic model would it make sense to determine the value of ‘large autonomous demand’. Excluding the big users from the auction procedure is a good measure only at first glance. In this case, strategic bids are substituted by demand which is part of ‘autonomous demand’. Does this mean that the big users no longer determine their demand strategically? Certainly not! Staying in the above model and assuming that the big users pay spot prices11 and use demand functions as their strategic device, their demand is still a best reply to the excess demand of all others (however, with less uncertainty than those suppliers have who are required to stick to their schedules for 24 h). What seems to be crucial for the absence of pure strategy equilibria with low prices is the existence of strategic demand, i.e. the existence of big customers who are relatively free to switch on and off their electricity-using devices. At the moment, these are mainly large industrial firms which have the possibility to produce their own electricity12 at high-price periods or to postpone13 their production. The latter might be facilitated by buffer stocks-usually not of electricity but of products like chemicals or heat or pump water (a private pump storage generator could profit from temporal arbitrage). In the near future, new metering may be introduced even for households. This might be the appropriate foundation of competition for small customers.14 In England and Wales as well as in New Zealand this competition has already started. A lot of innovative contracts can be expected (as everywhere in deregulated industries). Electricity trading is becoming a business of its own. Specialized firms buy electricity (on the spot market or under long-term contracts) and sell it to households and small firms under a variety of contracts. Possibly, some day these traders will also decide when to switch on storage heating as well as the washing machine and the dish-washer. All in all, this development might increase the amount of strategic demand with two counteracting consequences: temporal arbitrage of any kind smoothes the variance of spot prices (and is thus the basis for lower production costs); the increase of strategic demand, however, may increase prices and/or make the temporal development of prices less predictable. What remains to be done? Firstly, one might look empirically for indications that mixed strategies be used. Secondly, one should theoretically investigate cases with increasing marginal costs of electricity production, capacity constraints, and other ‘realistic’ improvements of the model. This should settle the question of whether or not our negative results were induced by an oversimplified model. Thirdly, one should theoretically investigate mixed-strategy equilibria. The main difficulty for such an investigation, however, is the determination of those supply and demand functions which should be mixed.