tput relationships have complicated effects on the underlying engineering processes. Because a production function is constructed from engineering processes, it is difficult to extract particular inputs from a production process. Input requirements can stem from many different engineering processes. The resources, labor, and capital equipment in a production function are aggregates. This means they are added up from the requirements of the many individual engineering processes used to produce final outputs. Removing some amount of one input or another, say a computer or some other piece of capital equipment, can have far-reaching effects in an optimized engineering system. The network engineer must compensate for removal of the input by necessary reductions in output, not to mention rebalancing of potentially all affected engineering processes to best produce the lower level of output. Accord- ingly, engineering processes that support production create connections between inputs that are not easily broken. Providing unbundled access to inputs in a pro- duction process thus is likely to have complex effects throughout the underlying engineering processes. 8 This approach is based on the classic analysis of Chenery (1949). See also Wibe (1984). The Design and Costs of Networks 2. Production Functions for a Single-Output Network Networks generally require capital equipment. The nodes and links of a network can be associated with specific capital equipment, such as the switches and lines of a telecommunications network. Let N = {1, , n} be the set of nodes of the network and let L be the set of m links that connect these nodes. For the purpose of this section, let N and L represent the services of capital equipment that are respectively associated with the nodes and links of the network. Typically, a production function for a firm also depends on land and other resources, labor services at various skill levels, and additional parts, components, and materials. In what follows, let X represent land and resources, let Y