Assumptions for a Market Share Theorem
Name
OR-017-73.pdf
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631.75 KB
Format
Adobe PDF
Checksum (MD5)
ed96fe2c8b250d82c8bb31e240061279
Author(s)
Little, John D. C.
Bell, David E.
Date Issued
May 1973
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 017-73
Abstract
Many marketing models use variants of the relationship: market share equals marketing effort divided by total marketing effort. Usually, share is defined within a customer group presumed to be reasonably homogeneous and overall share is obtained by weighting for the number in the group. Although the basic relationship can be assumed directly, certain insight is gained by deriving it from more fundamental assumptions as follows: For the given customer group, each competitive seller has a real-valued "attraction" with the following properties: (1) attraction is non-negative; (2) the attraction of a set of sellers is the sum of the attractions of the individual sellers; and (3) if the attractions of two sets of sellers are equal, the sellers have equal market shares in the customer groups. It is shown that, if the relation between share and attraction satisfies the above assumptions, is a continuous function, and is required to hold for arbitrary values of attraction and sets of sellers, then the relation is: Share equals attraction divided by total attraction. Insofar as various factors can be assembled into an attraction function that satisfies the assumptions of the theorem, the method for calculating share follows directly.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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