66 rities, just as competition authorities, often resort to market shares only as the main determinant of a dominant market position.57 4.3 Criteria for judging competition in network industries The focus now turns to a normative discussion of how the competitiveness of a market can be assessed for the purpose of judging the need for government intervention into market processes. Since market characteristics and therefore also the characteristics of competition in a market depend on the particularities of the industry, such an analysis must be undertaken for a particular industry in question. The present section focuses on the special case of network industries. Competition policy for network industries is made difficult by the fact that network industries do not feature the typical characteristics of competitive markets. A main reason for this is that building a network infrastructure involves large fixed costs. On the physical layer of a network industry, there will therefore often be only one or very few active market players. The strong network externalities associated with the demand for network services may also favor fewer larger firms on the applications layer of network industries. The central characteristics of network industries therefore lead to a market structure in which only a few large competitors are far more likely to exist than many small firms. Does this imply that competition is not possible in network industries with large fixed and common costs? 4.3.1 Sufficient conditions for natural monopoly One critical concept for understanding the competitive forces in a market is the concept of natural monopoly. A market is considered a natural monopoly when a single firm can produce the relevant output at lower costs than several firms. A formal definition of natural monopoly employs the concept of strict subadditivity of the cost function in the relevant range of output (Baumol, 1977). The necessary conditions for subadditivity are different for single-product and multi-product production. In the case of a single-product firm, economies of scale, defined by the fact that a proportional increase in all inputs leads to an over-proportional increase in output, are sufficient to prove subadditivity of the cost function (Baumol, 1977: 810). Economies of scale are, however, not a necessary condition for subadditivity in the single-product case. It is possible that a cost function is subadditive in the relevant range of output even for output ranges in which the demand curve crosses the marginal cost curve in the range of increasing marginal costs. Given large fixed costs of production, it can be less costly to have a single firm produce in the range of increa- 57 See discussion in section 9.2.2 below. 67 sing marginal costs rather than to incur the fixed costs of production twice (Knieps, 2005a: 23). In the case of a multi-product firm, economies of scope are a necessary condition for subadditivity of the cost function. Economies of scope are defined by the fact that it is less costly to produce two or more product lines in a single firm rather than to produce any combination of the product lines in several firms (Panzar and Willig, 1981). Economies of scope are, however, not a sufficient condition for subadditivity of the cost function. Intuitively, to prove subadditivity it must be shown that the additional costs of producing an output vector z are lower when output vector x + y is already being produced by the firm than when only the output vector x is already being produced (Knieps, 2005a: 27): C(x+z) – C(x) ? C(x+y+z) – C(x+y), whenever x,y,z ? 0. This property of the cost function is called cost-complementarity. Costcomplementarity of production is a sufficient condition for subadditivity of the costs function in the multi-product case. The formal definition of strict and global subadditivity of a cost function, both for the single-product and the multi-product case, given by Baumol (1977: 810) reads: A cost function C(y) is strictly and globally subadditive in the set of commodities N = 1,…, n, if for any m output vectors y1, … , ym of the goods in N we have C(y1,…, ym) < C(y1) + … + C(ym). This is clearly the necessary and sufficient condition for natural monopoly of any output combination in the industry producing (any and all) commodities in N, for subadditivity means that it is always cheaper to have a single firm produce whatever combination of outputs is supplied to the market, and conversely. 4.3.2 Theories of monopolistic competition A long history of regulation in network industries is evidence to the fact that competition authorities in past times often doubted that effective competition is possible in these markets. A wave of deregulation in network industries since the 1980s demonstrates a changed perspective. Network sectors may not correspond to perfectly competitive markets. Economic theory does, however, offer models of monopolistic competition that allow for economies of scale, economies of scope and network externalities in competitive market environments. Using these models as reference models to judge competition in network industries increases the spectrum of observable market structures and market behavior that competition authorities can tolerate without calling for market intervention. Chamberlin’s theory of monopolistic competition (Chamberlin, 1933) is generally considered the forerunner of the models of monopolistic competition. When Chamberlin developed his theory he was looking for an explanation of competition in real markets. Chamberlin argued that competition in reality is characterized not by a large number of competitors producing homogeneous products; rather it is a struggle