01.14.06
New product adoption part 2: A little Bass with your Squid Soup?
Frank Bass borrowed a model from immunology to describe how new products diffuse into a market. This model is very elegant, both simple and powerful. Using only three variables (coefficient of innovation, coefficient of imitation, and market size) it is able to fairly accurately model diffusion. It does this by recognizing that there are a few people in the market who act on their own and make decisions independently of others (the innovators) and a few people who are influenced by the installed base of adopters (the imitators), this is called an installed base effect. Bellow is the Bass equation in all its glory.
S(t) = [p + q(Y(t-1)/m)] * [m – Y(t-1)]
Where S(t) is the number of new adopters in time period t and Y(t-1) is the total number of adopters from the prior period. Essentially the first bracketed part of the equation is the probability of getting a sale, either through innovation or imitation. The second bracketed part is the remaining untapped market. Thus, if we multiply the probability of adoption by the number of people remaining we get the number of adopters for the current period.
Immediately one should ask, “Where do we get m, p, and q from?” Well, there are various methods for finding these numbers. First we can use analogy. By using p/q values from similar products we are able to infer a likely value for this new product. Second we can use historical data. Perhaps we have sales data from another, comparable, geographic region or early sales data from the product in question. Finding m is a little bit more of an art even than finding p and q. We want to try to start with the most inclusive market and systematically reduce it until we have found a best guess. For example, we could use the number of households in the US for the color TV market… Then we can perform sensitivity analyses on these data to see how affected our estimate is by error in our estimates of the values we arrived at for p, q, and m.
Once we have our values we can plug then into the bass model and estimate the diffusion process. One point to note is the point of inflection. This point represents maximum demand for the new product and is an important figure for production sizing. It also represents the point at which demand will begin decreasing.
A short example for Seth’s Squid Soup: I’m going to somewhat arbitrarily take our market size to be one million (I know it’s a big buffet). I will then take a slightly conservative value of p = 0.003 (Average value of p for all products studied is 0.03) and a slightly less conservative value for q = 0.7 (average value of q is 0.4). My reasoning for selecting these values is as follows: I have to imagine that squid soup will have a bit of a bad reputation from the get go (i.e. a lot of negative inertia) which is represented by the low value of p. However, assuming the soup actually does taste at least somewhat good, after those few innovators display their pleasure in eating squid soup it will have a strong influence on the remaining untapped market. (I chose to rely on taste for this example because this product suffers from observability issues. Meaning that Squid Soup is supposed to be healthy, and that is its benefit, but that feature is VERY hard for the untapped market to observe definitively, whereas people can readily observe and hear people’s enjoyment of the taste.)
S(t) is new adoptions for that year (We’re also simplifying the example by assuming that you only eat squid soup once, though the model can be modified to take into account repeat sales). Y(t) is total adoption up to that period. And “Trip” is what I am using for time period, i.e. trip to the buffet line.
NOTE: All sales figures are in thousands.
From the graph we can see this product starts very slowly but then once it reaches a “critical mass” of adopters the installed base effect takes over and growth is very rapid. Then we reach the inflection point (at trip11) where we have maximum demand for Squid Soup at 174,300 adopters. After the point of inflection demand begins to wane as the untapped market shrinks…
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