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On Continuous-Time Optimal Advertising Under S-Shaped Response

Опубликовано на портале: 30-09-2003
Management Science. 2001.  Vol. 47. No. 11. P. 1476. 
Тематический раздел:
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. Supplementing the treatment by Mahajan and Muller (1986), a flexible class of S-shaped response models is formulated for which it is demonstrated that, in contrast to findings in the literature on discretized advertising models, continuous periodic optima cannot be supported. Further, a set of conditions on the advertising response function are derived, that contains and extends that suggested by Sasieni (1971). Collectively, these results both suggest a set of baseline properties that reasonable models should possess and cast doubt on the ability of first-order models to capture effects of known managerial relevance.

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См. также:
Michael J. Barclay, Clifford G. Holderness, Jeffrey Pontiff
Journal of Financial Economics. 1993.  Vol. 33. No. 3. P. 263-291. 
Paul Anthony Samuelson
Journal of Political Economy. 1964.  Vol. 72. No. 6. P. 604-606. 
Kevin Rock
Journal of Financial Economics. 1986.  Vol. 15. No. 1-2. P. 187-212. 
Ajay Kalra
Journal of Marketing Research (JMR). 1998.  Vol. 35. No. 2. P. 210-225. 
Luis M B Cabral
Aviv Nevo
[Учебная программа]