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...characterize Cournot equilibrium obtained as a function of price and cross-price effects and present a numerical illustration based on the Ontario (Canada) electricity market.
1. INTRODUCTION
The absence of price signals in retail markets has been identified as one of the main determinants of the crises that occurred in some deregulated markets such as those of California or Ontario (see, e.g., Sweeney (2002) for the California case and Trebilcock and Hrab (2005) for the Ontario one, as well as for a comparative perspective (1)). The necessity of developing pricing schemes that could provide incentive for consumers, in order to manage demand efficiently is by no means a new topic. Indeed, Boiteux developed the ideas of marginal-cost and peak-load pricing long ago (2) (Boiteux (1949)). Since then, other significant contributions have been made, notably by Steiner (1957), Williamson (1966) and Turvey (1968). For a review of more recent contributions, the interested reader may consult Crew et al. (1995). The institutional framework in this literature is, unsurprisingly, one of a regulated, vertically integrated monopoly utility. It is probably not an overstatement to say that the recommendations made in such context are of marginal relevance to players engaged in a competitive electricity industry. In the latter context, the level of investment in production capacity, as well as the prices are expected to follow a market logic, i.e., to be endogenous to consumer behavior and to the degree of competition.
The economics and operations research literatures have long traditions modeling interdependent firms' choices of production capacities and outputs (or prices) in oligopolistic industries. In the electricity context, the change of competitive structure, from a regulated monopoly to a (de facto) oligopoly, triggered literature on the new problems that appeared and helped to design the market mechanisms that were put in place. Competition in spot markets has undoubtedly been an important issue. Contributions in this area include, among many others, those of Bohn et al. (1984), Green and Newbery (1992) and Bolle (1992). Given the nature of the object under investigation, their models ignored investment decisions, which are actually relevant only in a long-term perspective. Murphy and Smeers (2005) and Pineau and Murto (2003) are examples of the long-term perspective, where the models deal with both production and investment decisions.
In these papers, the demands in different market segments, i.e., base-load and peak-load segments are independent. This amounts to saying that the cross-price elasticity is zero. Such an assumption is also made in some recent models of the long-term impacts of real-time pricing (e.g., Borenstein (2005)).
In this paper, we wish to study production capacity decisions in an oligopolistic electricity industry, in which players serve two market segments, namely, base-load and peak-load segments, with two different production technologies characterized by different cost structures. Our main objective is to shed light on production strategies when the demands in both segments are interdependent, and more specifically, when they exhibit positive cross-price elasticities. This assumption has been documented in the econometric literature dealing with time-of-use tariffs. Indeed, Lawrence and Aigner (1979), Manning et al. (1979), Tishler and Ye (1993), Aigner et al. (1994), Filippini (1995), Mountain and Lawson (1995) and Matsukawa (2001) all depicted significant positive cross-price elasticities between price periods (segments).
The reaction of consumption patterns to price clearly has an impact on technology choices and on investments, even if this is not yet fully understood in the new deregulated environment. These issues are of strategic importance to electricity firms in terms of the technology mix of base-load and peak-load capacities. They are also relevant to governments facing environmental constraints and politically sensitive to price levels.
In this paper, we present a model of an electricity market, characterized by n investors-suppliers, two technologies (base- and peak-load technologies) and two interdependent market segments (base- and peak-load) with different own-and cross-price parameters. Using this parsimonious model, we will characterize equilibrium output strategies and investigate their sensitivity with respect to key parameters. Our main contribution lies in the study of this equilibrium, both analytically and, when not possible, numerically. In particular, we illustrate the impact on capacities and prices of varying cross-price elasticities.
The rest of the paper is organized as follows: In Section 2, we introduce the model. In Section 3, we derive the unique Nash equilibrium in output strategies and present some comparative static results. In Section 4, we apply the model to the Ontario (Canada) market. In Section 5, we briefly conclude
2. THE MODEL
2.1 Demand Characterization
Consider n electricity producers (players) competing a la Cournot in a given market. Each player has at its disposal two types of production technology, to which we shall generically refer as base-load and peak-load capacities. Denote by [k.sub.ib],i = 1, ... ,n the base-load capacity of player i and [q.sub.ib],i = 1, ... ,n the quantity of energy produced during the base-load period. Similarly, [k.sub.ip] is the peak-load capacity and [q.sub.ip] is the quantity of energy produced during the peak-load period. Let [Q.sub.b] = [n.summation over (i=1)][q.sub.ip] and [Q.sub.p] = [n.summation over (i=1)[q.sub.ip] be the total quantities of energy (in megawatt hour, MWh) put on the market by all producers during the base-load and peak-load periods, respectively. [K.sub.b] and [K.sub.p] are the total capacities (in megawatt) of base- and peak-load capacities. The base-load capacity is used all the time during a reference period (e.g., a year), while the peak-load capacity is used only during a fraction of that period. We normalize the total time to 1 and denote by [tau] the percentage of time in which the peak load capacity is used. The relationships between capacities ([K.sub.b] and [K.sub.p]) and quantities of energy ([Q.sub.b] and [Q.sub.p]) are therefore
[Q.sub.b] = (1 - [tau]) [K.sub.b],
[Q.sub.p] = [tau] ([K.sub.b] + [K.sub.p]).
It is observed empirically that the peak-load capacity is only used "few" hours a day. Therefore, we assume in the sequel that [tau] < (1 - [tau]).
Denote by...
NOTE: All illustrations and photos
have been removed from this article.
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