A Market Share Theorem

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A Market Share Theorem
David E Bell
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In fact, one could consider A^, A^... , A^ to be the attractions of a number of different product classes which compete with each other for consumers. For instance, A^ may represent the total attraction of radios, A^ televison sets, A3 stereo systems, and so on. One might postulate a different model for computing the share of the electronic media market held by each of these product classes. Combining this with our model for individual sellers within a segment provides a more sophisticated comp...etitive model.
Assumptions Al - A4 essentially make a(-) an unnormalized probability function on the set of sellers. For an alternative axiomation that closely parallels probability, see the Appendix. Market share, on the other hand, satisfies all the axioms of probability theory and so, mathematically speak- ing, is a probability function defined on the set of sellers. The statement of the assumptions and results is in terms of market share, but the term "prob- ability of purchase" could clearly be substituted without affecting the mathematical 15.


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