Bass, F. M. (1969)

Management Science, Vol. 15, No. 5, p215-227.
A growth model for the timing of initial purchases of new products is developed and tested empirically against data for eleven consumer durables. The basic assumption of the model is that the timing of a consumer's initial purchase is related to the number of previous buyers. A behavioral rationale for the model is offered in terms of innovative and imitative behavior. The model yields good predictions of the sales peak and the timing of the peak when applied to historical data. A long range forecast is developed for the sales of color television sets.

This paper concerns itself with developing a growth model. A theory for when a consumer makes their first purchase of new consumer products.

The practical reality is this is a mathematical model underpinning the adoption/diffusion of innovations. It is an evolution from Bass’ imitation model that he developed in 1962, shortly before Rogers published his book on Diffusion of Innovations.

The probability that an initial purchase will be made at time T given that no purchase has yet been made is a linear function of the number of previous buyers

Bass’ work is extremely useful in understanding (and potentially predicting) sales of new consumer products based on two coefficiets – one for innovators (those consumers who will purchase a product based on external to a social system influences) and one for imitators (those consumers who are influenced internally to a social system, such as by word of mouth).

Included in the paper are graphs of sales for several consumer products with a fitted line of the model.  Products such as home freezers, black and white tvs etc. It is interesting to observe how close the model predicts actual sales over the observed years.

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