city that is supplied is efficient because each consumer's marginal benefit equals the price, which in turn equals the marginal cost of capacity. Thus, the capacity level maximizes total benefits for consumers net of the cost of capacity. The solution is represented in Figure 3.5. The efficient price covers the costs of the firm if economies of scale do not exist at the market-clearing capacity level, that is, if marginal cost is greater than or equal to average cost: C'(D(p*))C(D(p*))/D(p*). 1 Define the net benefit of capacity by G(K), subject to . Then K* solves G'(K*) = 0 or B'(Q(*) = C'(K*),i= 1, ..,I, where . Pricing Network Services C'(Q) D(p*) = K* Figure 3.5. The efficient price and level of network capacity. Otherwise, if there are economies of scale, and prices must be constant per unit of output, then average-cost pricing is necessary: P**=C(D(p**))/D(p**) At this second-best price, the firm exactly breaks even. The firm supplies capacity that serves market demand at the average-cost price. A profit-maximizing firm adjust the price and sells the corresponding amount of network services such that marginal revenue equals marginal cost: R'(pm) = C'(D(PM)) Competition between profit-maximizing firms tends to lower prices below the monopoly level and raises the total amount of network capacity that is provided. With sufficient economies of scale, smaller numbers of firms provide capacity. Price competition tends to drive prices toward average costs. These results apply to network capacity in much the same way that they apply generally to productive capacity in practically any industry. More difficult issues arise in network industries due to uncertainty in demand for capacity. 2. Pricing Capacity under Uncertainty When demand is uncertain, the market-clearing price of capacity will vary. If the price of capacity is at the market-clearing level for the corresponding state of the world, then the price of capacity is the spot price. Let w be a real-valued random variable that represents the state of the world