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The Theory of Natural Monopoly

      Natural monopoly is a market structure wherein a single seller (the natural monopolist) can, owing to the importance of economies of scale, supply the socially optimal quantity of output at the lowest possible total cost.

bulletThe structural condition of natural monopoly is generally thought to be applicable in the case of services that are provided to a large number of users. The firm must incur massive costs in constructing a delivery infrastructure. Once the service delivery plant is in place, additional users can be accommodated at low marginal cost. Examples: water, natural gas, electricity, cable TV, telephone.
bulletThe conventional illustration of natural monopoly in principles textbooks shows the market demand curve intersecting the long run average cost schedule (LAC) in the region of increasing returns to scale.

    Viscusi, Vernon, and Harrington define temporary natural monopoly as a case in which the growth of demand over time (as represented by a rightward drift of the demand function) pushes the demand function into the region of constant returns to scale. That is, given growth in the market, the socially efficient market structure has more than one seller.

Example: AT&T needed only 800 circuits to accommodate the demand for long distance telephone service between New York and Philadelphia in 1946. By the late 60s demand had grown to a level requiring 79,000 circuits.

The modern view of natural monopoly (also called the "New Learning") is based on the concept of subadditivity. That is, the salient feature of natural monopoly is a cost function that is subadditive.

Sharkey [see William Sharkey. The Theory of Natural Monopoly, 1982] defines subaddivity as follows:

If q1, q2, . . ., qk are output bundles that sum to q, then a single firm is superior on efficiency grounds to a multifirm industry if the following condition holds:

C(q) < C(q1) + C(q2) + . . . + C(qk)               (1)

C(q1) can be interpreted as the cost of producing commodity bundle q1. If inequality (1) holds, then a single firm can jointly produce bundles q1, q2, . . ., qk more cheaply than if the bundles were produced separately, or if they were produced by two or more firms.

 Think of subadditivity as an extension of the concept of economies of scale to the multiproduct case.

Subadditivity: The single product case.


The conventional view holds that the efficient industry structure has only one firm, so long as output is less than that corresponding to minimum efficient scale or Q' in the graph.


It can be demonstrated, however, that the socially efficient industry structure has one firm even if economies of scale have been exhausted--so long as the cost function is subadditive at the relevant output level.


To see this, view the graph. Notice that the cost function is subadditive up to output level Q*, even though economies of scale are exhausted at output level Q'. If, however, the demand function touches LAC at an output level exceeding Q*, the industry is not a natural monopoly based on our definition.

Subadditivity: The multiproduct case

    There is no obvious reason why the electic utility industry is not a multimarket industry. Suppose, for example, that we have cost functions for power generation and power distribution as illustrated in the following diagram


Notice that economies of scale are exhausted quickly in power generation; whereas power distribution meets out principles definition of natural monopoly.


The issue: are there economies of scope between power generation and power distribution. If so, then a single firm is more efficient than a multimarket industry.Let:

q1 = 1000 MWHs of power generation

q2 = 1000 MWHs of power distribution

q = q1 + q2

There exist economies of scope between power distribution and power generation if the following inequality holds:

C(q) < C(q1) + C(q2)

Economies of scope are derived from technological complementarities in production or distribution of goods and services.



Joint production of cars and trucks.


Joint distribution of cable TV and high speed internet service.


Joint production of gasoline and fertilizer.

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