Chapter 6. The Dynamics of Growth from Diffusion

• Stocks and Flows in New Product Adoption – A Conceptual Diffusion Model

• The Bass Model – An Elegant Special Case of a Diffusion Model

• A Variation on the Diffusion Model: The Rise of Low-cost Air Travel in Europe

• Strategy and Simulation of Growth Scenarios

• Conclusion

• Appendix: More About the Fliers Model

Now we turn our attention from goal-seeking feedback and cyclicality to reinforcing feedback and the dynamics of growth. We begin with a product diffusion model responsible for S-shaped growth-and-stagnation in the sales lifecycle of new products and services. The model applies to a wide range of consumer goods from VCRs and DVDs to web-sites, microwave ovens and mobile phones. We examine the structure and dynamics of the well-known Bass diffusion model (Bass, 1969) and then propose a variation on this model to investigate growth strategy in the airline industry.

S-shaped growth appears in many guises. It is found in biological and ecological systems where for example exponential growth of a species runs up against a natural limit such as available land or food. A typical pattern of behaviour over time is shown at the top of Figure 6.1. Consider the qualitative features of the trajectory. In the early years, there is very little movement in the state of the system as exponential growth covertly gathers pace. In the middle years, the doubling power of exponential growth becomes dramatically apparent with a huge absolute change in the state of the system. In the final years, growth tails off and the state of the system settles into equilibrium. On the lower left is the corresponding feedback structure made up of two interacting feedback loops: a reinforcing loop, which is the growth engine, and a balancing loop as the limiting effect. The state of the system accumulates whatever is growing. It could be elephants in Uganda, nesting birds in Britain or visitors to a popular new ski resort. The more elephants, birds or visitors, the greater the net growth rate, though for elephants and birds growth is through births whereas for skiers growth is through word-of-mouth. The carrying capacity of habitat is important too: national parks for elephants, hedgerows for nesting birds and infrastructure for skiers. As the population grows, the state of the system approaches its carrying capacity and resource adequacy falls thereby reducing the fractional net increase. Eventually, a time comes when the state of the system is equal to the carrying capacity and the net growth rate falls to zero.

Figure 6.1. Feedback loops for S-shaped growth

On the lower right, the same feedback loops are re-labelled to represent sales growth and market saturation. The growth engine is powered by cumulative sales. The more units sold, the more visible the product and the greater the net sales rate. This kind of reinforcing effect applies to many fashion or lifestyle items such as Apple's iPod or Sony's PlayStation. The limiting effect comes from market saturation (cumulative sales in relation to maximum market size). When the product is new then market saturation is low and the fractional net increase is high (perhaps as much as 0.5, or 50 per cent, per month for the iPod). As market saturation approaches 100 per cent then the fractional net increase falls to zero because every consumer in the target market already owns the product.