The Bass Diffusion Model. Model designed to answer the question: When will customers adopt a new product or technology?. History Published in Management Science in1969, “A New Product Growth Model For Consumer Durables”. Working Paper 1966.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Model designed to answer the question:
When will customers adopt a new product or technology?
Working Paper 1966
Peak in 1968
Industry Built Capacity For
14 million units
Growing Software Applications
Cumulative Probability of Adoption up to Time t
Introduction of product
f(t) = d(F(t))dt
Density Function: Likelihood of Adoption at Time t
1983 1 2 3 4 5 6 7 8 9
Years Since Introduction
Source: Cellular Telecommunication Industry Association
St = p ´ Remaining + q ´ Adopters ´ Potential Remaining Potential
Innovation Imitation Effect Effect
St = sales at time t
p = “coefficient of innovation”
q = “coefficient of imitation”
# Adopters = S0 + S1 + • • • + St–1
Remaining = Total Potential – # Adopters Potential
Innovation Imitation Product/ parameter parameter Technology (p) (q)
B&W TV 0.028 0.25
Color TV 0.005 0.84
Air conditioners 0.010 0.42
Clothes dryers 0.017 0.36
Water softeners 0.018 0.30
Record players 0.025 0.65
Cellular telephones 0.004 1.76
Steam irons 0.029 0.33
Motels 0.007 0.36
McDonalds fast food 0.018 0.54
Hybrid corn 0.039 1.01
Electric blankets 0.006 0.24
A study by Sultan, Farley, and Lehmann in 1990 suggests an average value of 0.03 for p and an average value of 0.38 for q.
The Bass Model proposes that the likelihood that someone in the population will purchase a new product at a particular time tgiven that she has not already purchased the product until then, is summarized by the following mathematical.
L(t): Likelihood of purchase at t, given that consumer has not purchased until t
f(t): Instantaneous likelihood of purchase at time t
F(t): Cumulative probability that a consumer would buy the product by time t
Once f(t) is specified, then F(t) is simply the cumulative distribution of f(t), and from Bayes Theorem, it follows that:
L(t) = f(t)/[1–F(t)] (1)
Solution to Differential Equation
Bass Model can also be expressed as
Sales = S(t) = m f(t)
Cum. Sales = Y(t) = m F(t)
Or, Estimate Directly with this:
a=p.m, b=(q-p) and c = -q/m.
p = a/m
As a function of product price, reduction in uncertainty in product performance, and growth in population, and increases in retail outlets.
Coefficient of innovation (p) as a function of advertising
p(t) = a + b ln A(t).
Effects of price and detailing.
Awareness è Interest è Adoption è Word of mouth
x(t) = 1+[(dPr(t)/dt)/Pr(t)]b1 + [(dADV(t)/dt)/ADV(t)]b2
X(t) = t+ Ln(Pr(t)/Pr(0)) b1 + Ln(ADV(t)/ADV(0)) b2
“Carry-Through” Effects for GBM
“In Forecasting the Time of Peak It is Helpful to Know that a Peak Exists”
By Frank Bass