I was recently playing around with modelling business growth using logistic equations, and I came upon a possible reason why large companies are unable to be ni

I was recently playing around with modelling business growth using logistic equations, and I came upon a possible reason why large companies are unable to be nimble and dynamic in the way small companies are. Note: The basic logistic equation is 1/(1 + e^-t) which one can extend to be S = M / (1 + e ^ (-rt-y)) where M is the maximum growth capacity, r is growth rate, y is number of years to the 50% mark. Anyway, it produces nice S-shaped growth curves that generally approximate growth in a limited environment. Anyway working with these a few things occurred to me. Near the bottom of the growth curve, growth is very slow. It then picks up suddenly, grows to a certain point, then growth rate declines and the market size tapers off. Lack of immediate success along these curves may be due to a growth rate that is too low or a market size that is too small (duh) but when we vary both maximum size (M) and growth rate (r) something really interesting happens. If we have a curve that successfully predicts two or three years of growth but then overperforms what we observe, this has exactly two causes: Either M is much bigger than expected and r is much smaller (meaning smaller growth now but much more growth later), or M is much smaller and y is much bigger (meaning the market is already saturated). You can't differentiate these just looking at how a project is performing. A small business can bet against the short term and for the future. A larger, publicly held business is often less able to do so, so getting over the slow growth in the lead-in of the logistic sigmoid is really tough in a larger corporate environment. This is probably a good part of the reason why big companies have a much harder time innovating.