01.14.06
New product adoption part 3: Mind your P’s and Q’s.
In the previous post we discussed a model for forecasting new product diffusion in a market. We discussed ways of finding values for its three inputs m, p, and q. Finally, we worked through an example using Seth’s Squid Soup. Now I would like to discuss the impact of price and advertising on this model (Because we’re marketers 
).
In its most simple form, the Bass model does not account for effects of price or advertising, but clearly this has to affect product diffusion. There is a more general form of the Bass model that allows one to scale based on parameters one thinks must impact diffusion, such as price or advertising.
S(t) = [p + q(Y(t-1)/m)] * [m – Y(t-1)] * Z(t)
Z(t) = 1 + α [% change in variable]
Where α is the elasticity of the measured variable, and %change is the percentage increase or decrease in the variable from the prior period. For price this is simply the percentage change in the price. However, it is a little bit more ambiguous for advertising, but dollar spend can be used…
In this equation, Z(t) is affecting both q and p, but it is also possible to scale one variable or the other as well. For example, p(t) = p(0) + α*Price(t). This alpha is not the elasticity, but some other scaling variable.
As an example let’s return to Squid Soup. We will leave price at 0 and only look at the effect of advertising. Initially advertising should be informational to persuade the innovators to adopt. Then as we move across the adoption cycle we should adjust the mix to be more persuasive to affect the imitators. For this example I will simplify, and just say “we’re advertising”…
I’ll set α at 0.8 and I will initially spend $1 on a sign that say’s “Squid soup is great for your health! It increases vitality by 15% and reduces cholesterol by 50%”. Then I will grow the ad budget by 100% each period for the first 5 periods (buying all the signs my budget will allow for $1) and continue at that spend for the remaining periods.
Z(t) will then be: 1 + 2(1) = 3 (for the first 5 periods) Giving us the following diffusion forecast:
NOTE: All sales figures are in thousands.
As you can see from the table, we have moved the inflection point forward three periods and accelerated adoption overall. Notice the effect of ceasing our advertising budget growth in period six.
Anyway… enough fun with Bass and Squid.
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