oduction function must be defined that specifies the inputs needed to produce unbundled network element services q and final customer services Q: H(Q,q, N, K, X, Y, Z) =0. It should be evident that additional network services will generally require more inputs to the network if the same level of final customer services is to be main- tained. This is because the network production function is the efficient combination of inputs needed to produce a given level of services subject to the underlying engi- neering specifications and technology. Alternatively, if the inputs to the network are fixed, particularly capital equipment and facilities, the modified production function will not sustain the same level of outputs. Also, it is likely to differ from the technologically efficient production function, which requires all inputs to be vari- able. Instead, with some inputs already fixed, the production function is a short-run production function that is suboptimal relative to the long-run production function. The production function having been redefined, it is necessary to redefine the network firm's cost function to handle both final services and the services of unbundled network elements. The modified cost function CU(Q, is the minimum level of expenditures needed to produce network outputs (Q, q) subject to the modified production function. With all inputs variable, CU(Q, q) is a long-run cost function. Then, notice that the standalone cost of final outputs equals the original cost function: C"(Q,0)=C(Q). The Design and Costs of Networks For the modified long-run cost function, the incremental cost of the services pro- vided by a network element is calculated in the same manner as any type of incre- mental cost. For ease of illustration, suppose that there is only one final output Q and only one service from the unbundled network element q. Then, because CU(Q, q) is a long-run cost function, that is, with all inputs variable and chosen optimally, the long-run incremental cost of the service provided by the network 