# Natural Monopoly

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_762

## Abstract

An industry is a natural monopoly if total costs of production are lower when a single firm produces the entire industry output than when any collection of two or more firms divide the total among themselves. An industry can be a natural monopoly if production by a single firm is the outcome of unrestricted competition, or a natural monopoly may exist if competitive forces lead to a different industry structure. Generally a natural monopoly is characterized by subadditivity of a representative firm’s cost function. A cost function *c* is subadditive at an output *x* if \( c(x)\le c\left({x}^1\right)+c\left({x}^2\right)+\cdots +c\left({x}^k\right) \) for all non-negative *x*^{1},…, *x*^{k} such that \( {\sum}_{i=1}^k{x}^i=x \). If all prospective firms in the industry have the same cost function, or if one firm has a uniformly better technology, then subadditivity implies that industry costs are minimized if only one firm is active in the market. While subadditivity is a purely technical condition, it is also possible for natural monopoly to arise from purely economic forces if the imperfectly competitive outcome is inefficient. However, competition in a market with a small number of firms is inherently the domain of game theory and a unique equilibrium outcome is rarely found. Therefore it is generally acceptable to adopt the technical criterion of subadditivity as the defining characteristic of natural monopoly.

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