Although most of the theory to be developed in Chapters 4 through 8 is of recent origin, the concept of natural monopoly is not new. In this chapter I will review some of the tools that have traditionally been available to economists who studied natural monopoly. The first two sections describe the basic methodology common to almost all of microeconomic theory. The reader who is unfamiliar with this presentation may wish to review a standard economics text such as Samuelson (1980). The remaining sections describe more specialized results that will be used, or assumed, elsewhere in the book. References will be given when appropriate for a more detailed discussion of these conclusions. The primary function in collecting these results is to define a basic set of ideas upon which the remainder of the book will be built, rather than to teach the reader who is totally unacquainted with the material that is presented in this chapter.

Competitive equilibrium and monopoly equilibrium

One of the earliest formal models of competitive equilibrium is the analysis of supply and demand, due to Alfred Marshall (1927). Suppose that there are a large number of both potential buyers and potential sellers for a single well-defined product. On the supply side, each seller is assumed to have a cost curve defining the marginal cost of all possible units of output. Marginal cost for each seller is assumed to be an upward-sloping function of output.