Efficient Industry Structure 27 Multiproduct Natural Monopoly While single-output scale economies imply single-output natural monopoly, this is not necessarily the case for multiple-output (or multiproduct) firms. The subadditivity conditions for a multiple-output natural monopoly are far more complex than those of a single-output monopolist. In this case, economies of scale are not equivalent to decreasing average cost, as the firm may not oper- ate along a linear expansion path. For a multiproduct firm, cost analysis requires the examination of not one but several concepts. Ray Average Costs Ray average costs (RACs) describe the behavior of the cost function as output is expanded proportionally along a ray emanating from the origin. Baumol et al. (1982) offer the following definition: in the two-product case, one considers the behavior of costs along a cross section of the total cost surface. Defining a composite good, this measure allows a calculation of the average cost of this particular bundle and is given by RAC = CðtY 0 Þ/t, (2:18) 0