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

Fortnightly Magazine - October 15 1999

familiar product. Utilities offer flat rates through equal pay plans to avoid summer and winter monthly spikes. Future electricity markets will see third parties with long histories in risk management offer these new pricing products at competitive rates.

Collar Pricing:

How to Allow for Demand Response

In the following examples, demand and cost conditions are simplified for presentation purposes; however, the concepts should provide direction for pricing collars in a competitive market.

Inelastic Demand. Figure 1 presents a price collar contract with the assumption that demand is not price-responsive. The price ceiling is Pc and the floor is Pf. For simplicity, it is assumed that the collar is for a summer day with only one hour during the high-priced peak period and one hour during the low-priced off-peak period. Notice that demand shifts with temperature, so that consumption (Q) is higher during the peak period when prices are high due to hot temperatures. In this initial case, quantity demanded is perfectly inelastic with respect to price.

In figure 1, Pl s and Phs are the probabilistic low and high spot prices, Ql and Qh are corresponding quantities consumed, and A and B are the supplier's probabilistic loss and gain depending on the actual price.

If it is assumed that the entire contract is represented by figure 1, where the customer selects a price ceiling of Pc , then the merchant would set the price floor, Pf, by equating the area represented by loss A to the area represented by the desired gain, B. Using this equality, the price floor that allows the supplier to break even is[fn.6]

Pf = Pl S +(Ph S - PC)(Qh __Ql ).

With inelastic demand, the only unknown in this equation is Pf. Off-peak quantity does not change even though Pf exceeds Pls.

Elastic Demand. Figure 2 depicts downward-sloping demands. For a given price ceiling, the merchant's loss (A) is larger than for the inelastic case. The per-unit loss is unchanged, but the merchant now loses on a larger number of units. For a given price floor, the merchant now gains less (B'). Per-unit gain would be the same as before, but the gain is now for a smaller number of units. So in order to break even, the merchant must increase floor price to increase per-unit gain. But the increase in per-unit gain will have to more than offset the decrease in quantity that accompanies the higher price.

In figure 2, the merchant's loss increases for a given price ceiling. Total loss A' is the sum of the original loss A and the additional loss of rectangle C. The additional loss is due to an increase in quantity demanded when the customer purchases at price ceiling Pc instead of the higher spot price Phs. Similarly, total gain is now B'. To make up for the larger loss, the merchant must increase price floor Pf. But because demand Df is downward-sloping, the increase in floor price causes a decrease in quantity sold at the floor price. Rectangle D represents revenues that were earned when demand was inelastic,