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Collaring the Risk of Real-Time Prices: A Merchant Strategy for Utilities

Fortnightly Magazine - October 15 1999

but no longer are earned by the merchant when demand slopes down.

Merchants need to be aware of price elasticity during peak high-demand hours and off-peak low-demand hours. If those elasticities differ from zero, the floor price for a given ceiling will have to increase as compared to the inelastic case. Merchants who face downward-sloping demands but ignore demand elasticity will lose money.

Because consumption varies with price, determination of the floor price is more complicated than in the fixed-quantity case. The approach is to compute earnings lost due to the price ceiling, then find the floor price that recovers the loss. From figure 2, earnings lost (EL) is derived by

EL = (Phs - Pc) *Qc.

Qc is derived from the peak arc elasticity condition:

(Pc - Phs)

(1 + ________ hc)

(Pc + Phs)

Qc = Qhs ____________ .

(Pc - Phs)

(1 - ________ hc)

(Pc + Phs)

In a similar manner, earnings desired (ED) to make up this loss is derived by

ED = (Pls - Pf) *Qf.

Qf is derived from the off-peak arc elasticity condition:

(Pls - Pf)

(1 - ________ hf)

(Pf + Pls)

Qf = Qls ____________ .

(Pls - Pf)

(1 + ________ hf)

(Pf + Pls)

Now Pf may be found by trial and error to achieve the equality of EL and ED. Table 2 displays Pf for several examples, as well as the earlier case of perfectly inelastic demands.[fn.7]

Note in example 2 that the merchant would lose $72 by continuing to set the floor at $0.04 per kilowatt-hour.[fn.8] For a large industrial customer with much greater consumption than in the example, losses could be substantial. It is important, therefore, that the merchant consider price-responsiveness during high- and low-temperature hours. In all cases where consumers respond to price, table 2 shows that the price ceiling must be higher than for the fixed-quantity case. An increase in (the absolute value of) elasticity in either period increases the floor price.

Change in Price Ceiling. Suppose the customer decided that these floor prices were too high and so decided to choose a higher price ceiling. Table 3 shows the price floors that correspond to a price ceiling of $0.25 instead of $0.20 per kilowatt-hour.

The price floor is now lower than in table 2 in all cases. Again, the price floor increases when demand is price-sensitive, but by a smaller amount than in the previous case.

The Free-Rider Problem: How to Keep

the Attractive Customers

A price collar effectively ensures the customer against high prices. As with insurance, however, the merchant must be aware of the potential problem of adverse selection. This problem occurs if the insurance policy attracts high-payout customers while discouraging low-payout customers.

The merchant offering a price collar also could lose money due to adverse selection, as mentioned. Customers with above-average demand elasticities would find a price collar developed with the assumption of an average elasticity more attractive than customers with below-average elasticities. For example, if hc=-1 (Qc=3,000) and hf=-0.45 (Qf=6,000), then the break-even price floor for a ceiling price Pc=$0.20