244 CHAPTER | 8 Efficient Pricing of Electricity where P i is price in market I, c i is marginal cost, is a proportionality constant, and i is price elasticity of demand in market i (or customer class i). Also known as the inverse elasticity rule, this pricing rule is a well-known result in the literature on efficient public utility pricing. Formally, this rule states that the price that maximizes social welfare (TS) subject to a profit constraint will exceed marginal cost by an amount that is inversely proportional to elasti- city of demand. Another way of expressing Equation (8.10) is that (for a two-output market) (8.13) = ½ðP i - c i Þ P i * i = ½ðP j - c j Þ P j * j for j i. What this implies is that for any pair of markets (or customer classes), the percentage increase over marginal cost, weighted by the price elasticities of demand, should be equal to , which is known as the Ramsey number (Brown and Sibley, 1986). Example 8.1 (Continued): Marginal Cost Pricing in the Presence of Fixed Costs An electric utility has the following cost structure: TC = 1000 + 40*Q: Market demand for its electricity is P = 200 - 2Q: If price is set at marginal cost, what is the electric utility's profit? Solution: Setting the price equal to marginal cost implies that P = 40 and Q = 80. As such, Profit = Total Revenue - Total Cost or Profit = (200 - 2Q)*Q - 1000 - 40*Q. At Q = 80, then Profit = -$1000. (8.15) (8.14) Not surprising (due to the presence of fixed costs), the first-best optimal pri- cing (i.e., price equal to marginal cost) strategy does not allow the firm to recover all of its costs and a loss of $1000 occurs. This situation is displayed in Figure 8.4. ANOTHER OPTION: AVERAGE COST PRICING At first blush, one might think that a feasible solution is to set price at average cost; after all, this seemingly addresses the utility's need to recover all costs asso- ciated with providing service. Also, given the situation depicted in Figure 8.1, the price charged (and the quantity delivered) does not seem to diverge much