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On the optimal control of the Vidale-Wolfe advertising model

✍ Scribed by Richard D. Edie

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
275 KB
Volume
18
Category
Article
ISSN
0143-2087

No coin nor oath required. For personal study only.

✦ Synopsis

The free endpoint infinite horizon problem (P) based on the Vidale -Wolfe advertising model 1 with a time-varying market is stated as follows:

-ρt d t over all measurable control functions u(t) 0 subject to the constraints

The Vidale -Wolfe advertising model describes the problem in economics of maximizing the profit J from the sale of a single product with a company sales rate x and a total market sales rate of m over time. This is done by controlling the rate of investment u in advertising. The change in sales rate for the product is determined by the rate of investment in advertising and the portion of the total sales rate (1x m) for the industry not controlled by the company. Then the term -βx is added to represent the rate at which customers would forget about the product if it were no longer advertised. In the profit function, Ax(t) represents revenue from sales. From this the rate of investment in advertising is subtracted to determine the actual profit at a given time, which is then multiplied by e -ρt to account for the time preference.

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