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 68 for market shares, fought on the basis of product differentiation, price differentiation and investments into reputation. In real markets buyers choose between combinations of price and quality. As long as consumers view products as potential substitutes, they can be considered to be in the same relevant market. Because buyers have preferences for particular product characteristics, however, the demand facing each firm is not perfectly elastic. Through product differentiation each firm has a degree of price-setting competency. Firms can therefore charge prices which exceed marginal costs of production. The theory of monopolistic competition assumes free market entry. As long as economic profits are being made, new firms enter into the industry. The theory assumes that the effect of entry is spread evenly across all firms already active in the market. With more products available on the market, the demand curve for any particular product shifts back towards the origin and demand for this product becomes more elastic (the slope of the demand curve decreases). Once price is equal to average costs of production, no economic profit is made and entry into the market ceases. In equilibrium, monopolistically competitive markets therefore feature fewer firms, prices that exceed marginal costs, and product differentiation. The equilibrium is not characterized by stable market power since no firm is able to make positive economic profits over a substantial time period. The theory of monopolistic competition was subsequently refined in various models of product differentiation.58 These models build on a theory of consumer behavior, which puts the spotlight on consumer valuation of product diversity. Consumers derive utility not directly from goods and services, but rather from the characteristics of these goods and services. Products represent bundles of characteristics and depending on individual preferences a consumer will choose her optimal bundle (Lancaster, 1966). This can be represented in a theoretical model by using a spatial setting as in Hotelling (1929). In a spatial model, consumers choose between those bundles closest to their preferred bundle as represented by proximity in geographic space (Lancaster, 1975). The valuation of product diversity has alternatively also been modeled by an explicit treatment of the value of product diversity in the utility function of a representative consumer. In such a model the representative consumer’s utility depends positively on the number of goods produced in the market and all products are potentially substitutable (Dixit and Stiglitz, 1977). One central theme of the theory of product differentiation is that in markets featuring economies of scale, there is a trade-off between taking advantage of these economies of scale and offering product diversity in the market. A first-best equilibrium, in which prices equal marginal costs, would require transfers to firms making losses and would have a tendency to lead to too little product diversity in the market. The monopolistically competitive equilibrium allows firms to charge prices above marginal costs such that transfers for losses are no longer required. Whether this equilibrium corresponds to a second-best optimum which maximizes social welfare under the restriction that revenues must be sufficient to cover all fixed and variable 58 For an overview see also Knieps (2005a: Chapter 9). 69 costs of production is not clear (Carlton and Perloff, 2005: 230; Dixit and Stiglitz, 1977: 301). The monopolistically competitive equilibrium could be biased either in the direction of too much product diversity or of too little product diversity in the market, depending on the preferences of consumers for product variety and the extent of the economies of scale. Because divergence from a second-best optimum is not systematic, it is difficult, if not impossible, for policy makers to correct the monopolistically competitive result towards a second-best optimum. Monopolistically competitive markets therefore offer no justification for government intervention. 4.3.3 Entry barriers The central characteristic common to the models of monopolistic competition is that their positive equilibrium properties depend on the assumption of free market entry. The theories of monopolistic competition show that the question of when competitive forces are sufficient to restrain market power can be approached by analyzing the possibilities for market entry. As long as economic profits in a market entice market entry, firms in this market cannot be said to have market power. Only when economic profits are realized over an extended time period without inducing market entry is market power present. There are different traditions with respect to defining barriers to market entry. The traditional industrial economic theory on entry barriers is represented by Bain (1956). Embedded in the structural approach, which explains market outcomes by a given market structure, Bain formulated a broad theory of market entry barriers that includes variations of economies of scale, product differentiation advantages of incumbents, and capital requirements (Schmalensee, 1989: 968). In essence, Bain considers all market characteristics that lend cost advantages to an incumbent firm to be barriers to entry, even if these cost advantages are only temporary. For example, if economies of scale allow the installed firm to produce a higher level of output at lower average costs of production, then, according to Bain, this must be looked at as a barrier to market entry. Potential entrants would initially produce less output at higher costs. Also, when product differentiation by the incumbent forces potential entrants to spend more on advertising than the incumbent is currently spending, then this is considered a barrier to market entry. A far more narrow definition of barriers to entry was formulated by Stigler, a representative of the Chicago School. Stigler defines: “A barrier to entry [...] as a cost of producing (at some or every rate of output) which must be borne by a firm which seeks to enter an industry but is not borne by firms already in the industry” (Stigler, 1968: 67). This definition focuses on long-run cost asymmetries between an incumbent firm and firms willing to enter the industry. The foremost reason for long-term cost advantages held by incumbents is the irreversibility of investments necessary for production. When the incumbent has already made these investments, their costs are no longer decision-relevant to him. They are, however, relevant to a firm contemplating entering the industry. Other reasons for asymmetric cost advantages can