stallation of additional switchboards interconnected through trunk lines, which in turn caused switching to become more complex. For example, in an exchange with two switchboards, one-half of all calls would require the participation of two operators to set up and take down each call, whereas calls to exchanges with three and four switchboards would require multiple operators for two-thirds and three-quarters of all calls, respectively. In addition, the presence of multiple switchboards increased the organizational problem considerably. Operators had to keep track of the board on which each customer resided and which trunk lines were open at any particular time. The problem becomes all the more difficult after one considers, as we point out in Chapter 2, that the number of connections increases quadratically with the number of users. Thus, increases in the subscriber base drastically increased both the cost of service and the complexity of the organizational problem. The diseconomies of scale in switching became a major problem for the Bell System, which had to seek rate increases as its subscriber base grew. It also became a trap for the independents, who often entered based on the promise of lower rates, only to find that their very success in attracting business away from the Bell System rendered those rates unsustainable. 12 The result was that duplication of networks did not necessarily cause costs to increase. Although the deployment of mechan- ical switches eventually caused switching to become less important as a source of Verizon, 535 U.S. at 475-76 (noting that at the time of the breakup of AT&T, local telephone service was "thought to be the root of natural monopoly in the telecommunications industry"); United States V. W. Elec. Co., 673 F. Supp. 525, 537-38 (D.D.C.1987), aff' d, 894 F.2d 1387 (D.C. Cir. 1990) (concluding that local telephone service "is characterized by very substantial economies of scale and scope" and that "[t]he exchange monopoly of the Regional Companies has continued because it i