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Attention is focused on the theory concerning comparisons of single-firm market structures and certain multifirm alternatives to such structures. Firms are assumed to produce a single commodity with which is associated a price as well as a numerical index of quality. Considered first is the case in which the single firm is assumed to be profit-maximizing, and the price and quality of the commodity produced are compared with the corresponding quantities associated with a certain legislated-into-existence multifirm alternative consisting of a number of essentially identical profit-maximizing firms which produce the commodity at a uniform price and level of quality. Certain assumptions are introduced and it is proved, in a general and realistic setting concerning the number of possible solutions of the basic underlying optimization problems, that the single-firm structure outperforms the multifirm alternative in a significant sense having to do with prices and levels of quality. The remainder of the paper is concerned with the situation in which the alternative to the single-firm structure consists of a dominant firm (which sets the price and level of quality of the commodity) as well as a fringe of competitive firms whose combined total output capability is typically comparatively small. It is shown that if the single firm and dominant firm are profit-maximizing companies, and ifcertain other conditions are met, then the presence of the competitive fringe benefits the consumer in, for example, the following sense.