As previously mentioned, the theory of natural monopoly has a long history. Before proceeding to set out in mathematical terms the conditions for that theory, I will survey part of that history in Section 2.1. The purpose of such a survey is twofold. First, it will enable readers to place the present effort in the proper context. Although the theory to be developed in this book is more formal and mathematical than work that has preceded it, many of the important ideas were originally suggested by earlier writers. Second, the literature survey will help those readers who are unfamiliar with the mathematical approach used throughout the volume to understand the most significant concepts.

In addition to the survey, this chapter contains, in Section 2.2, an examination of some recent empirical work that has attempted to test for natural monopoly conditions — primarily economies of scale — in the railroad industry. The major implication of these studies is that the railroad industry is inherently a multiple output industry and that simple measures such as economies of scale are not adequate to answer the relevant policy questions. Much of the complexity in later chapters is due to the need to develop a theory of natural monopoly that is relevant to multiple output firms and markets.

Finally, I will briefly discuss in Section 2.3 the interrelationship between the theory of natural monopoly and the possibility of destructive competition.