The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Natural Monopoly

  • William W. Sharkey
Reference work entry


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 x1,…, xk 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.

This is a preview of subscription content, log in to check access.


  1. Baumol, W.J., and D.F. Bradford. 1970. Optimal departures from marginal cost pricing. American Economic Review 60(3): 265–283.Google Scholar
  2. Baumol, W.J., E.E. Bailey, and R.D. Willing. 1977. Weak invisible hand theorems on the sustainability of prices in a multiproduct natural monopoly. American Economic Review 67(3): 350–365.Google Scholar
  3. Boiteux, M. 1956. Sur la gestion des monopoles publics astreints à l’équilibre budgétaire. Econometrica 24(1): 22–40.CrossRefGoogle Scholar
  4. Clark, J.M. 1923. Studies in the economics of overhead costs. Chicago: University of Chicago Press.Google Scholar
  5. Faulhaber, G.R. 1975. Cross-subsidization: Pricing in public enterprise. American Economic Review 65: 966–977.Google Scholar
  6. Ramsey, F. 1927. A contribution to the theory of taxation. Economic Journal 37: 47–61.CrossRefGoogle Scholar
  7. Sharkey, W.W. 1982. The theory of natural monopoly. Cambridge: Cambridge University Press.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • William W. Sharkey
    • 1
  1. 1.