# Bass Model of Diffusion

Friday December 31, 2021

A large number of research studies have estimated parameters p and q of the Bass model for many product categories.
(1) Using these data, estimate the values of p and q for the hybrid power vehicle. The Harvard notes by Ofek provide details on the estimation process. The process is also summarized in the lecture notes. You should follow that process, but need to make several important judgments such as what analogous product categories to use, the similarities between the innovation and the analogous categories, and the weights of the attributes. In your assignment, provide details of these steps and the assumptions you make.

(2) After you estimated p and q values, assume a market size of m=1,000,000 units. Then use the first equation in Ofek’s Appendix to estimate the annual sales. This equation is a critical part of the Bass model:
St = p⋅m + (q – p)⋅Nt-1 – (q/m)⋅(Nt-1)2
St is the annual sales of year t, Nt-1 is the cumulative or aggregate sales from year 1 to year t-1. Obviously for year 1, t=1 and Nt-1 = 0. For year 2, t=2 and Nt-1 = S1. For year 3, t=3 and Nt-1 = S1 + S2. And so on. You should start from year t=1, and continues the calculation until three years after the sales peak.
You can estimate the annual sales with an Excel sheet, by computing Nt-1, (Nt-1)2 and St, starting from year t=1. In constructing the Excel formula, it is useful to recognize that Nt-1 = Nt-2 + St-1.
To show the work, you can describe how you conducted the estimates, and provide the Excel sheet that you used (you can copy and paste the sheet to WORD).
Highlight the year when the sales peak. Discuss the forecast results in terms of diffusion speed, the number of cars that could be potentially sold, etc.

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