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Author: | Feinberg, F. M. |
Title: | On Continuous-Time Optimal Advertising Under S-Shaped Response |
Journal: | Management Science
2001 : NOV, VOL. 47:11, p. 1476-1487 |
Index terms: | ADVERTISING MANAGEMENT OPTIMAL CONTROL THEORY |
Language: | eng |
Abstract: | Continuous-time monopolistic models of advertising expenditure that rely on strict response concavity have been shown to prescribe eventual spending at a constant rate. However, analyses of discrete analogs have suggested that S-shaped response (convexity for low expenditure levels) may allow for the periodic optima encountered in actual practice. Casting the dynamic between advertising and sales in a common format (an autonomous, first-order relationship), the present paper explores extensions along three dimensions: an S-shaped response function, the value of the discount rate, and the possibility of diffusion-like response. |
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