Criterios de exclusión

In the current literature three major models are in use for (imperfect) electricity markets: the Bertrand model, Cournot model and Supply Function Equilibrium (SFE) model. Cournot and Bertrand models constitute the two often used paradigms of imperfect competition.

4.2.1 Bertrand model

In the Bertrand (1883) model firms compete in price. They simultaneously choose prices and then must produce enough output to meet demand after the price choices become known. In the assumption that each firm has enough capacity to meet demand, the Nash equilibrium price in this model is the marginal cost which is the same as the case of perfect competition.

One of the reasons to introduce competition into power markets is to reduce the price of electricity. It was thought that under competition the prices would drop to the marginal cost level. It is generally admitted that the design of the British Pool was based on the assumption that Bertrand competition would prevail. However, this is not what happened.

A first example of the use of Bertrand competition in electricity was proposed by Hobbs [34] for studying the restructuring of the industry in the US. The rationale for retaining this paradigm is as follows. Electricity cannot be stored. If a generator has extra capacity it will be interested in selling electricity if and only if the price is above the cost of production. It will thus be subject to short-term price competition, hence leading to a Bertrand assumption. The latter is equivalent to perfect competition. It supposes marginal cost pricing when supply and demand curves meet in a single location and all producers have the same marginal costs. However, empirical studies (Wolfram [92]) have shown that prices in some imperfect markets are sustained well above marginal costs.

4.2.2 Cournot model

The other basic non-cooperative equilibrium is the Cournot (1838) model. In this model competition is in quantities. Firms simultaneously choose the quantities they will produce, which they then sell at the market-clearing price (the price for which demand is met by supply). An auctioneer will clear the market equating demand and production.

The point made by the proponents of this model (Borenstein and Bushnell [13], Bat- stone [10], Wen and David [87]) is that a large proportion of energy transactions are done by long-term contracts for which the price is fixed. Taking away the amount of electricity contracted, the remaining demand for electricity is much more elastic than that of the whole market. Small variations in price will produce large changes in demand. So firms will choose the quantities that optimize their profit. Under these situations the Cournot model is a more accurate representation of the market. Since generation capacities present significant constraints in electricity markets, the assumption underlying the Bertrand model that com-

petition is over prices and the firms have enough capacity to meet demand is not sustainable. Cournot models prevail over Bertrand models in the current literature on electricity markets.

4.2.3 Supply Function Equilibrium (SFE) models

A new model has been used in recent papers (Green and Newbery [32], Bolle [12], Newbery [52] [53], Rudkevich, Duckworth and Rosen [63], Visudhipan and Ilic [85] [86], Baldick, Grant and Kahn [5], Guan, Ho, and Pepyne [33], Baldick and Hogan [6], Baldick [4]). This approach is based upon the work of Klemperer and Meyer [43] and was applied to a pool model by Green and Newbery [32]. A supply function relates quantity to price. It shows the prices at which a firm is willing to sell different quantities of output. The SFE model applies very well to the market structure of many restructured electricity markets, such as New Zealand, Australia, Pennsylvania-New Jersey-Maryland Interconnection (PJM) and California Power Exchange. In these markets the bid format is precisely a supply function.

In this model competition is neither over price (as in Bertrand models) nor quantity (as in Cournot models) but in supply functions. Bertrand and Cournot models are limits ofSFE models. The Bertrand model is the limiting case in which the supply function is constant in price for any quantity, which means that the producer is bidding a price at which it is willing to sell any quantity. On the other hand, the Cournot model is the limiting case in which the supply function is constant in quantity for any price, meaning that the producer is bidding quantity that will be sold at the market-clearing price.

The problem with the use of SFE models is that in general there is not a unique equi- librium. There are often an infinite number of solutions lying between the Cournot and Bernard equilibria, which represent their upper and lower limits in price respectively. The existence of many equilibria makes it difficult to predict the likely outcome of strategic inter- action between players. There are some factors that reduce the range of feasible equilibria: uncertainty of demand and capacity constraints.

SFEmodels better explain the markups of electricity prices which empirical studies have shown to be above the Bertrand equilibrium but below the Cournot model. It is close to the Cournot equilibrium at peak time when capacities are almost saturated and close to the Bertrand equilibrium when there is a significant capacity excess.