inty. In a deterministic setting, net- works can use prices to ration capacity while avoiding problems of either congestion or excess capacity. Later, we address the problem of random demand. Suppose that there are Iconsumers, i = 1, I. Each consumer obtains a bene- fit from consuming network capacity, Bi(Qi), where Qi is both the network service and the amount of capacity required to deliver the network service. Assume that the consumer's income does not affect the consumer's benefit from network services and that consumption of network services does not affect the consumer's marginal utility of income. These assumptions are made to simplify the presentation by rul- ing out income effects on the demand for network services. Suppose that network services require a small portion of income. In practice, consumer demands for network services are affected by income. For our purposes, these differences can be modeled by allowing differences in consumer benefit functions. Assume also that the consumer's purchases of goods other than network ser- vices need not be specified explicitly. As noted in Chapter 1, the demand for network services is a means to an end. Consumption of network services such as telecommunications depends on the demand for communication and the value of other economic transactions. Because many forces drive the consumer's needs for telecommunications services, it is sufficient to specify a benefit function for network services. It can be assumed that the purchases of other goods are adjusted optimally Pricing Network Services p*=p*(K) D(p2) Figure 3.1. Allocating scarce network capacity and the market-clearing price. by the consumer and that the benefit function for network services is a reduced form that incorporates related consumption decisions. The benefit function can be considered separable from some other types of consumption decisions. Let P be the price of the network service. The consumer's demand for the network service maximizes net benefits: Vi(p) )=max 0B'(Q) - PQ = The consumer's dem