Titel
The digital economy and advertising diffusion models: Critical mass and the Stalling equilibrium
Autor*in
Gustav Feichtinger
TU Wien
Autor*in
Dieter Grass
International Institute for Applied Systems Analysis (IIASA)
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Abstract
In the digital economy it is frequently observed that products become more valuable the larger is the number of people that use it. To account for such network effects, we introduce a new diffusion equation in a dynamic model of the firm with the aim to obtain the advertising policy that maximizes firm profits. Also an advertising budget is introduced. First, we find that introduction of the network effect leads to a critical mass of the sales level. Only if the sales are greater or equal to this level, is it optimal for the firm to have a substantial sales level in the long run. Second, introduction of an advertising budget could result in the existence of a Stalling equilibrium. This new type of equilibrium, at which the advertising amount is at its upper bound, serves as the critical mass threshold separating growth and decline. Third, the advertising policy is continuous in the sales level either when the discount rate is large and the rate of forgetfulness is low, when the Stalling equilibrium exists, or when the rate of forgetfulness is that high that the firm is always in decline. Furthermore, existence of the Stalling equilibrium involves an important message to the management of the firm in that a slight increase of the advertising budget would open up an avenue of growth in sales.
Stichwort
OR in marketingNetwork effectsCritical massOptimal control
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
European Journal of Operational Research
Band
318
Ausgabe
3
ISSN
0377-2217
Erscheinungsdatum
2024
Seitenanfang
966
Seitenende
978
Publication
Elsevier BV
Erscheinungsdatum
2024
Zugänglichkeit
Rechteangabe
© 2024 The Authors

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