a type of residual demand that is contingent on the pricing policies of rival firms. If competing firms offer fixed levels of capacity, then the firm's demand can be interpreted as a residual demand function, that is, as the market demand function net of the quantities offered by rival firms. Accordingly, in what follows, we allow the demand function D(p) to represent a variety of such situations. Let = pD(p) be total revenue and let (p) = pD'(p) + D(p) be marginal revenue. A profit-maximizing firm with capacity K compares the revenue- maximizing output with available capacity. The revenue-maximizing price solves R'(PR) = 0. The revenue-maximizing output is thus QR = D(PR). If there is sufficient capacity K to serve QR, the firm will set the price at PR, which is greater than p*; see Figure 3.3. Otherwise, if the firm is capacity-constrained SO that K < QR, the firm will choose the price at which all capacity is used, which is exactly p*; see Figure 3.4. The monopolist will not have excess demand but may have excess capacity. With increased competition, firms have incentives to lower prices and there is less incentive for firms to have excess capacity. In the long run, capacity is variable. If the network is to be newly established, the firm can choose capacity to reflect the expected requirements of customers over some period of time. If the network already exists, the firm considers the costs of constructing additional capacity and the adjustment costs of integrating that Networks in Telecommunications R'(Q) Figure 3.4. The constrained revenue-maximizing price equals p* if K < QR. capacity within the network. To represent these situations, let C(K) represent the cost of providing capacity K. Assume that there are no other costs of providing network services. Then the efficient price equals the marginal cost of capacity evaluated at total demand: p*=C'(D(p*)). This price clears the market because total demand for network services equals the amount of capacity that is supplied: K*=D(p*). = Also, the level of capa