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The Bass diffusion model was developed by Frank Bass and describes the process how new products get adopted as an interaction between users and potential users. The model is widely used in forecasting, especially product forecasting and technology forecasting. Mathematically, the basic Bass diffusion is a Riccati equation with constant coefficients. Image File history File links Bass_diffusion_model. ...
Prof Dr. Frank M. Bass is a leading academic in the field of operations research, and is considered to be among the founders of Marketing science. ...
Look up forecast in Wiktionary, the free dictionary. ...
Product forecasting is the science of predicting the degree of success a new product will enjoy in the marketplace. ...
Technology forecasting is forecasting the future characteristics of useful technological machines, procedures or techniques. ...
In mathematics, a Riccati equation is any ordinary differential equation that has the form It is named after Count Jacopo Francesco Riccati (1676-1754). ...
Frank Bass published his paper "A new product growth for model consumer durables" in 1969 [1] Prior to this, Everett Rogers published Diffusion of Innovations, a highly influential work that described the different stages of product adoption. Bass contributed some mathematical ideas to the concept. [2] Everett M. Rogers (1931 in Carroll, Iowa - Albuquerque, New Mexico, 21 October 2004), communications scholar, pioneer of diffusion of innovations theory, writer, and teacher. ...
This model has been widely influential in marketing and management science. In 2004 it was selected as one of the ten most frequently cited papers in the 50-year history of Management Science [3]. It was ranked number five, and the only marketing paper in the list. It was subsequently reprinted in the December 2004 issue of Management Science.[3]
Model formulation
[1] Where: is the rate of change of the installed base fraction is the installed base fraction is the ultimate market potential is the coefficient of innovation is the coefficient of imitation Sales is the rate of change of installed base (i.e. adoption) multiplied by the ultimate market potential :
[1] The time of peak sales [1]
Explanation The coefficient p is called the coefficient of innovation, external influence or advertising effect. The coefficient q is called the coefficient of imitation, internal influence or word-of-mouth effect.
Typical values of p and q:[4]
- The average value of p has been found to be 0.03, and is often less than 0.01
- The average value of q has been found to be 0.38, with a typical range between 0.3 and 0.5
Image File history File links Bass_adopters. ...
Image File history File links Bass_new_adopters. ...
Extensions to the model
Generalised Bass model (with pricing) Bass found that his model fit the data for almost all product introductions, despite a wide range of managerial decision variable, e.g. pricing and advertising. This means that decision variable can shift the Bass curve in time, but that the shape of the curve is always similar.
Although many extensions of the model has been proposed, only one of these reduces to the Bass model under ordinary circumstances.[3]. This model was developed in 1994 by Frank Bass, Trichy Krishnan and Dipak Jain:
where is a function of percentage change in price and other variables
Successive generations Technology products succeed one another in generations. Norton and Bass extended the model in 1987 for sales of products with continuous repeat purchasing. The formulation for three generations is as follows:[3] where is the incremental number of ultimate adopters of the ith generation product is the average (continuous) repeat buying rate among adopters of the ith generation product is the time since the introduction of the ith generation product It has been found that the p and q terms are generally the same between successive generations.
Relationship with other s-curves There are two special cases of the Bass diffusion model. Use in online social networks The rapid, recent (as of early 2007) growth in online social networks (and other virtual communities) has led to an increased use of the Bass diffusion model. The Bass diffusion model is used to estimate the size and growth rate of these social networks. In probability theory and statistics, the exponential distributions are a class of continuous probability distribution. ...
In probability theory and statistics, the logistic distribution is a continuous probability distribution. ...
A virtual community is a group whose members are connected by means of information technologies, typically the Internet. ...
References - ^ a b c d Bass, Frank (1969). "A new product growth for model consumer durables". Management Science 15 (5): p215-227.
- ^ Management Science 50 Number 12 Supplement, Dec 2004 ISSN 0025-1909 p1833-1840
- ^ a b c d Management Science 15(5) p215
- ^ Mahajan, Vijay; Muller, Eitan and Bass, Frank (1995). "Diffusion of new products: Empirical generalizations and managerial uses". Management Science 14 (3): G79-G88.
Prof Dr. Frank M. Bass is a leading academic in the field of operations research, and is considered to be among the founders of Marketing science. ...
External links - Relationship between the Bass and the logistic market adoption models
See also The study of the diffusion of innovation is the study of how, why, and at what rate new ideas spread through cultures. ...
Look up forecast in Wiktionary, the free dictionary. ...
External links - http://www.pdma.org/visions/oct02/diffusion.html
- http://www.utdallas.edu/~mzjb/bass.ppt
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