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By Schmalensee R., Willig R.

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If the market inverse d e m a n d curve is given by p l ( y ) , then the industry has been traditionally classified as a "natural monopoly". 24 Alternatively, if the market inverse demand curve is given by p 2 ( y ) , so that it intersects the competitive price level Pc at an output level, C, that is a large multiple of M, the industry is classified as structurally competitive. Finally, if C is a small multiple, then the industry is 23The determination of the relevant set of industry output levels can be a nontrivial exercise, especially in the multiproduct case.

T. y'yS = y0. Then k E C(y')= s=l k k E F { S s} + Y'~«(y'), s=l s=l where S c = { i ~ N: Y7 > 0}. Using the weak (strict) subadditivity of F, we have k k E c ( y ' ) >__(>)F(S} + E c(y'), s=l s=l where N ~ S = (i ~ N: ~y{ - yo > 0}. The result then follows from the strict (weak) subadditivity of c(-). D. 21The proof of both of these assertions can be found in Baumol, Panzar and Willig (1982, ch. 4, appendix I, p. 91). Ch. 1: Determinants of Firm and Industry Structure 33 This completes the present discussion of sufficient conditions for subadditivity.

E. one taust know C ( y * ) for every y* _< y. In the "familiar" single product case, natural monopoly has been associated with the presence of increasing returns to scale and falling average costs. However, this characterization is imprecise at best and can be seriously misleading. In order to examine this issue, we need Definition 15. Declining average costs Average costs are strictly declining at y if there exists a 8 > 0 such that C(y')/y' < C ( y " ) / y " for all y ' and y " with y - 8 < y " < y ' < y + 8.

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