 T time periods, representing both times of day and days of the week. The consumer purchases network services in each time period, as represented by the vector = (Q1,..., QT). The consumer takes into account the relative benefits of consuming services in the different time periods and the relative prices across the time periods. Consumers choose demand to maximize net benefits, SO that Qi = Dj(p1,..., PT) represents consumer i's demand in time period t,t= 1, Total demand in period t is D(p1, PT). The set of time-of-use prices can be adjusted to increase the quantity of services demanded in some periods and to reduce the quantity of services demand in others. Time-of-use pricing makes more efficient use of capacity by matching demands to capacity. For a given level of capacity K, the market-clearing time-of-use prices solve T equations, t = 1, T. To illustrate the solution, suppose that there is a single consumer with a quadratic benefit function and only two time periods,2 B(Q1, - Then, because marginal benefit equals the price in each period and capacity is the same, the price in period t is simply * = a - b,K - y K, t=1,2, which is well defined if a/(bt +y) > K. Let the price equal zero otherwise. The time-of-use prices are lowered in all periods by increases in the substitution para- meter y. Consider time-of-use pricing in the long run when the network firm chooses the level of capacity. Suppose that there is a single representative consumer. Then the optimal level of network services in each time period and the optimal level of network capacity satisfy the following condition:3 2 Assume that b1 > y and b2>y. Assume also that the two goods are substitutes, y > 0. 3 The network service in each period is limited by capacity, Qt < K*. If Qt < K*, aB/aQt = 0. If Qt = aB/dQt 0. Networks in Telecommunications The sum of marginal benefits of network services across time periods equals the marginal cost of capacity. To understand this fundamental result, notice that capacity acts as a public good across the time peri