Assumptions for a Market Share Theorem
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...
| Main Authors: | , |
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| Format: | Working Paper |
| Language: | en_US |
| Published: |
Massachusetts Institute of Technology, Operations Research Center
2004
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| Online Access: | http://hdl.handle.net/1721.1/5345 |
| _version_ | 1826200150658252800 |
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| author | Little, John D. C. Bell, David E. |
| author_facet | Little, John D. C. Bell, David E. |
| author_sort | Little, John D. C. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:31:57Z |
| format | Working Paper |
| id | mit-1721.1/5345 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:31:57Z |
| publishDate | 2004 |
| publisher | Massachusetts Institute of Technology, Operations Research Center |
| record_format | dspace |
| spelling | mit-1721.1/53452019-04-12T08:16:27Z Assumptions for a Market Share Theorem Little, John D. C. Bell, David E. 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. 2004-05-28T19:34:51Z 2004-05-28T19:34:51Z 1973-05 Working Paper http://hdl.handle.net/1721.1/5345 en_US Operations Research Center Working Paper;OR 017-73 1746 bytes 646911 bytes application/pdf application/pdf Massachusetts Institute of Technology, Operations Research Center |
| spellingShingle | Little, John D. C. Bell, David E. Assumptions for a Market Share Theorem |
| title | Assumptions for a Market Share Theorem |
| title_full | Assumptions for a Market Share Theorem |
| title_fullStr | Assumptions for a Market Share Theorem |
| title_full_unstemmed | Assumptions for a Market Share Theorem |
| title_short | Assumptions for a Market Share Theorem |
| title_sort | assumptions for a market share theorem |
| url | http://hdl.handle.net/1721.1/5345 |
| work_keys_str_mv | AT littlejohndc assumptionsforamarketsharetheorem AT belldavide assumptionsforamarketsharetheorem |