The implication seemed to be that the Shapley value would be significant in accounting for monopoly power if it turned out that the Shapley value turned up no disadvantageous monopolies. The examples of [4, 7] lend credence to this expectation, [7] in a production context, [4] in an exchange context. There it turned out that in a large economy monopoly, as appraised by the Shapley value, definitely was advantageous. The major result of this paper is that, when these examples are generalized, it is no longer necessary that every monopoly conceivable in a given situation have a higher Shapley value than its competitive counterpart. In accounting for monopoly power, the Shapley value appears to have a limited success.