Marketing: Bass Model Equation

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Slide 9 of 22

Bass Model (Basic Version)

Bass, F. M. (1969). A new product growth for model consumer durables. Management

science, 15(5), 215-227.

1. A customer either adopts in a specific period or waits to adopt, and all potential customers eventually adopt

2. There is a maximum potential number of buyers

3. No repeat or replacement purchases occur, only first-time purchases

4. The impact of word-of-mouth communication on product adoption is the same, regardless of when a customer adopts the product

5. The effect of imitation is always positive

Assumptions

Slide 10 of 22

Bass Model Concept

n t

= p × �� ���� ������� � � − � � + � × �������� � �

× �� ���� ������� � (� − � � )

N = Market potential

n(t) = number of adopters at time t

p = “coefficient of innovation” – what kind of effects are these?

q = “coefficient of imitation” – what kind of effects are these?

N(t) = total adopters up to t, such that N(t) = n(0) + n(1) + n(2) + … + n(t)

What if q > p? What if p > q?

Intuition

Adoptions due to external influence

Adoptions due to internal influence

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Slide 11 of 22

n(t) = p × N + (q – p) × �(� − 1) − �

� × � � − 1

Where N(t-1) is total number of adopters up to time t-1

Assuming p = 0.01 and q = 0.41, and market potential is 16,000 adopters

(assuming 1 unit per adopter)

What are the sales forecasts (aka predicted values) for Quarters 1, 2, and 4?

How do the forecasts compare with actual data?

Applying the Bass Model Equation: How to Forecast Sales

Actual Equation for Forecasting in Discrete Time Periods

Slide 12 of 22

n(t) = p × N + (q – p) × �(� − 1) − �

� × � � − 1

n(t) = a + b × �(� − 1) − ! × � � − 1

When n(t) = 0, total adoption has reached potential as N(t - 1) � N(t) � N

N = #$ # $%#&'(

)

(

p = a/N

q = p + b

Applying the Bass Model Equation: How to Estimate p, q, and N

Actual Equation for Forecasting in Discrete Time Periods