Peak-load pricing

The theory of peak-load pricing originated in work by Boiteux (1949) and Steiner (1957), and was further developed by Hirshleifer (1958). Their seminal work showed that peak-load pricing led to better use ofinstalled capacity and to smaller capacity requirements as compared to average cost pricing. These results were derived in models based on several simplifying assumptions. One is that the load within two periods of equal length is uniform. In reality the load changes continuously over time.

Another is constant returns to scale. Williamson (1966) presented a method for dealing with periods of unequal length and an easy way to handle more than two periods. Turvey (1968 b) stressed the need to take supply variations into account when identifying peaks and off-peak periods, Pressman (1970) developed a formal analysis where any number of demand periods could be considered; he also incorporated the pos-sibility of cross elasticities between subperiods and the use of a more general cost structure than the one used so far. Gravell (1976) and Nguyen (1976) considered how the peak load solution is affected by storage possibilities. Panzar (1976) analyzed peak load pricing using a neo-classical cost function. Crew and Kleindorfer (1971,1976 and 1979) and Wenders (1976) took into account the existence of different tech-nologies i.e., one for base loads, another for intermediate loads and a

third kind for extreme peak situations. A survey of peak load pricing in theory and practice is given in Mitchell-Manning-Acton (1978) and in Crew-Kleindorfer (1979).

By taking diverse technology and positive cross elasticities between subperiods into account, while retaining many of the other simplifying assumptions, we can illustrate the essence of the theory of peak-load pricing.

Prices,

Marginal costs

G

Gas turbines

Hydro power otherwise waste water

Nuclear pciWr

C

P^e = uniform price, PN = off-peak price, PD = peak price In = original short-run demand, summer nights En - original short-run demand, winter days

= short-run demand, summer nights after substitutions

= short-run demand, winter days after substitutions

Figure 3.1. Social benefits of a switch from uniform pricing to price differentiation.

First, in a system of uniform pricing, the price is set excessively high during off-peak periods. By comparison, price differentiation gives rise to social benefits (illustrated by the triangle ABC in Figure 3.1). Second, the peak price is set too low under uniform pricing. As a result, the

demand which is met during peak periods is higher than in the case of price differentiation when costs exceed the willingness-to-pay. In this instance, price differentiation implies social benefits (illustrated by the area EFGH in Figure 3.1).

But this reduction in the off-peak price and increase in the peak price will, of course, affect the price ratio between the subperiods. The con-sumers will respond to this change by moving part of this peak demand to the off-peak period, This is illustrated in Fig. 3.1 as a shift from £>?

to £>2 in peak and the corresponding shift from In to D$ in off-peak. As these shifts according to the Slutsky condition, will ce of the same magnitude, we can calculate the savings in operating costs as

&q • PD-Aq pN = &q fpD - PNYillustrated by the area IDKJ in Fig. 3.1).

In the longer run the demand for electricity may be more responsive to price than the short-run demand. The reason is that in the short run prices provide signals for the consumption of electricity for some given stock of consumers' appliances. In the long run, households can adapt through investments in new appliances and industrial customers through changes in production technology. As a consequence planned capacity expansion may be postponed which also is a benefit of a peak-load pricing scheme. Thus the benefits of a change from average to peak-load pricing will be greater over a longer than over a shorter period.

Savings in terms of what may otherwise be regarded as expansion of extra reserve power stations should, of course, also be included as a benefit of price differentiation. This should be kept in mind when such pricing reforms are under evaluation and when drawing conclusions from pricing experiments.

The benefits of a given peak-load pricing scheme net of production costs have been reviewed above. But, there are other costs associated with peak-load pricing. These include the costs of more complicated and therefore more expensive meter equipment and administration. For different reasons (e.g. a lack of cheap sophisticated meters), only a very limited number of prices can be used in a peak-load pricing scheme for customers. Determination of a peak-load pricing scheme involves several practical problems, such as

• How many prices should be used?

• What are the optimal differentials between them?

• Where should the limits for the different rating periods be set?

Many public enterprises still regard the solution of these problems as a challenging task; see Rees (1976) and Fishe (1982). Some large con-sumers of high-voltage power already have the equipment necessary for this kind of pricing system. But most subscribers of low-voltage electricity could have to supplement their meters or obtain new ones.

The optimal frequency of price changes cannot be determined without first ascertaining the size of additional costs for administration, infor-mation, meters, measurement and charging with respect to more far-reaching price differentiation based on the differences in SRMCs; see Bohm (1974), Capehart-Storin (1983) and Andersson (1984).