and for the network service equates the consumer's marginal benefit to the price, where demand Qi = Di(p) solves equation (2). Total demand for network services is obtained by summing individual consumer demands: D(p)= In the short run, the capacity of the network is fixed, say at K. Then, given continual usage of network capacity, the price at which demand for and supply of capacity are equal solves (p*) = K, where p* = p*(K) solves equation (4). This solution is represented in Figure 3.1. A price above p* rations demand to the point where there is excess capacity, SO at P1, Networks in Telecommunications D(0) K Figure 3.2. The efficient price is equal to zero when demand at the zero price is less than network capacity. there is excess capacity K - D(P1). A price below p*, say at P2, allows excess demand D(P2) - K and results in unsatisfied customers. Regulated prices can miss the mark and lead to inefficient outcomes. The market-clearing price is also the efficient price. The equilibrium price shown in Figure 3.1 is strictly decreasing in capacity because demand for the network service is downward sloping. Conversely, outward shifts in demand increase the equilibrium price. In this setting, without congestion effects, increases in demand result in a higher equilibrium price. There is an important case of capacity pricing that occurs when demand at a zero price is less than capacity. This case is represented in Figure 3.2. In this case, the efficient price of capacity is the zero price. This corresponds to the situation of many fiber optic networks that have substantial amounts of transmission capacity, referred to as dark fiber. The price of capacity represents its per-unit economic scarcity rent. Economic rent per unit is positive with scarce capacity and zero with excess capacity. If variable costs are present, the pricing rule must be modified accordingly. Suppose that crepresents constant per-unit operating costs. If prices cover per-unit operating costs, then the firm should operate at those prices. If pri