The digital economy and advertising diffusion models: Critical mass and the Stalling equilibrium

Feichtinger, G., Grass, D., Hartl, R.F., Kort, P.M., & Seidl, A. (2024). The digital economy and advertising diffusion models: Critical mass and the Stalling equilibrium. European Journal of Operational Research 10.1016/j.ejor.2024.05.043.

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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.

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