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Predicting California Deman Response

How do customers react to hourly prices?
Fortnightly Magazine - July 1 2003

Own price elasticity. The own price elasticity is simply the percentage change in consumption due to a percentage change in price in either the peak or off-peak time period. For example, if the price doubles-an increase of 100 percent-and usage declines by 30 percent, then the own-price elasticity equals -30 percent/100 percent, or -0.30. Note that elasticities are expressed as fractions and have no units.

Elasticity of substitution. Many analyses have focused on a single parameter that characterizes customers' load shifting from one time period to another (e.g., from the peak to off-peak period). Known as the elasticity of substitution, this is the primary parameter of the constant elasticity of substitution (CES) demand model. The elasticity of substitution represents the negative of the percentage change in the ratio of electricity consumption in two time periods that occurs in response to a given percentage change in the relative price between those two periods. For example, in the case of a time-of-use rate, the peak to off-peak elasticity of substitution represents the negative of the percentage change in the ratio of peak to off-peak usage that occurs in response to a given change in the ratio of peak to off-peak prices, all other factors held constant:

s = - [% D (Qp/Qo)] / [% D (Pp/Po)],

where s is the elasticity of substitution, Qp and Qo are peak and off-peak usage, and Pp and Po are peak and off-peak prices, respectively. A s value of 0.10 implies that a peak to off-peak price ratio of 150 percent (e.g., with peak and off-peak prices of $0.25 and $0.10/kWh respectively, and calculating the percent change as the natural logarithm of the price ratio) will produce a reduction in peak to off-peak usage of 15 percent relative to the case for a flat price (i.e., -0.10 * 150 percent = -15 percent). Own price elasticities and substitution elasticities may be compared when the necessary data are available. Caves and Christensen (1980) showed that an elasticity of substitution of 0.17 was consistent with a peak-period own-price elasticity of approximately -0.30.

An Open Letter From 11 Energy Experts:

The Time Has Come for Real-Time Pricing

We write to express our strong support for dynamic pricing of electricity to retail customers. An important missing ingredient in all wholesale electricity markets in the United States is active demand-side participation in the price-setting process. Dynamic pricing at the retail level provides retail customers with the incentive and ability to make efficient consumption and risk-management decisions reflecting their own individual preferences. It is the least-cost way to achieve active demand-side participation in the wholesale market. Active demand-side participation limits price volatility in a competitive wholesale electricity market. In an imperfectly competitive wholesale market, it also limits the ability of suppliers to exercise unilateral market power, and thereby leads to significantly lower average wholesale electricity prices that benefit all retail customers.

We define dynamic prices as retail prices that vary with hourly system conditions. There are a number of ways to accomplish this, but the essential feature of all such pricing plans is that