from joint production of the two sets of products. There are potential cost gains from The Design and Costs of Networks handling multiple forms of traffic (peak and off-peak), multiple origin-destination pairs, or multiple types of transmission (voice and data). An example of economies of scope is the sharing of a fixed cost between two or more goods: C(Q1,Q2)=F+c(Q1)+c(Q2) Such a cost function exhibits economies of scope because producing the two goods separately would require paying the fixed cost twice. Another source of economies of scope in networks is sharing facilities that exhibit increasing returns to scale, such as high-capacity transmission lines. Suppose that a network can carry two types of traffic, Q1 and Q2, and that the common transmission line has a cost function c(Q) with economies of scale. The economies of scale of the transmission line mean that average cost declines with output: Adding these two conditions together implies that d(Q1) + c(Q2) c(Q1 + Q2). This implies that the network has economies of scope: (30) C(Q1, Q2) = c(Q1 + Q2) < c(Q1) + c(Q2) = C(Q1, 0) + C(0, Q2). This sharing of a high-capacity trunk line to achieve economies of scale is illustrated in Figure 2.13. Another source of economies of scope is the benefits from handling multiple types of random traffic. Suppose that 2* = A1 + 22 is the combination of two types of traffic. Then the capacity requirements for a combination of two types of traffic are less than the capacity requirements for handling the two types of traffic separately: <21/2+((21)2/4+11/2 + 22/2 +[(22)2/4+22W]1/2 = + M2. Let the cost of the service capacity have a constant unit cost, d(u) = CU. Then the total cost function has economies of scope: C(21,22) = CUI + CU2 = C(A1, C(0, A2). This result readily generalizes to multiple independent traffic flows. Simply separate one traffic flow at a time to obtain the result. Thus, networks have economies of scope that result from efficiencies in serving multiple independent traffic flows. The concept of economies of