example (1, 2), (2, 3), and (3, 4). Then the total cost function of the network is C(Q12, Q13, Q14, Q23, Q24, =3f+c(Q12 + Q23 + Q34) + 2c(Q13 Q24) + 3cQ14. The total cost function has economies of scale due to the presence of fixed costs that come from the links. The main point of the preceding example is that economies of scale in compo- nents of the network can imply the need to concentrate traffic. The use of central switching in hub-and-spoke configurations and the establishment of trunk lines in backbone networks take advantage of economies of scale in nodes and links, including high-capacity switches and transmission lines. Concentration of traffic to achieve economies of scale is a particularly interesting aspect of network design. Economies of scale in networks also derive from standard sources (Spulber 1989, 1995). (1) Networks have joint and common fixed costs that can be spread across units of output or across multiple outputs. Such joint and common fixed costs include the overhead costs of designing and managing the network, as well as fixed costs of construction and maintenance. Telecommunications companies main- tain extra transmission capacity, known as dark fiber, because the cost of installing additional fiber during the initial installation is lower than the cost of later additions to capacity. With greater output of a service or of a set of services, companies can spread out the fixed costs. (2) Economies of scale are present in telecommunications, as in other industries, because with a higher output it becomes possible to switch technologies. For example, fiber optic transmission lines, although expensive, reduce unit costs of transmission relative to copper or coaxial systems for a sufficiently high output Networks in Telecommunications level. Similarly, high-capacity switches lower unit costs for a sufficiently high output level. (3) Networks benefit from volume-surface relationships. Pipeline companies can scale up the volume of a pipeline without the same increase in surface area and thus 