16 CHAPTER | 2 The Theory of Natural Monopoly and Literature Review which is characterized both by economies of scale and by those of network planning, and as such, yields a natural monopoly. Because this network leads to externalities, vertical integration has traditionally yielded the most efficient organization of the industry, especially for larger firms. But it is due to the ver- tical nature of electricity production that questions have arisen concerning whether any aspect of the production process may not be a natural monopoly. If this is the case, questions then become: would the market be better served by allowing competition into that component and would the gains from compe- tition exceed the lost economies that would result? This is the critical element that needs to be explored. Things are not always so clear, however. While there has been little work done in the areas of testing whether the transmission and distribution processes are natural monopolies, they are usually assumed to be so, as both are charac- terized by what is known as network economies. Network economies arise due to the interconnectedness of the national transmission grid so that significant saving in inputs and direct routing yield both economies of scale and economies of scope. These are defined later in this chapter, along with a review of the relevant literature. DEFINING NATURAL MONOPOLY Older industrial organization theory cited that the presence of scale economies determined whether an industry was a natural monopoly. It is important to note that much of the theory of natural monopoly is concerned with the precise meaning of "increasing returns" or, equivalently, decreasing average costs. Scale economies exist when a proportionate increase in output leads to a less-than-proportionate increase in cost. Mathematically, a cost function (one output) is said to exhibit global (local) economies of scale if CðqÞ < CðqÞ (2:1) for > 1, q 0. According to Marshall (1927), increasing returns can be either internal or external to the firm and, similarly, internal or external to the industry. A natural monopoly tends to arise due to high fixed costs, which tend to be asset specific and, as such, are largely sunk. As a result, average cost tends to decline as out- put is expanded over a large range, thus rendering a single provider socially optimal. In addition, economies of scale can be either technical (relating to the production process) or pecuniary, that is, related to the prices paid for inputs. One of the difficulties in testing for natural monopoly is the practical applica- tion of testing for subadditivity of a firm's cost function, which is critical, as local (global) subadditivity is a necessary and sufficient condition for local (global) nat- ural monopoly (Evans, 1983). In addition, it is necessary to distinguish between single-output and multiple-output natural monopolies, which is done next.