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Department of Connections

1/6/2004
Railroadization

A study of the crash of the Viennese stock market in 1873 surrounding a very successful world's fair and the growth of atavistic sentiments like those of Greenberg, Prechter, Abelson, Buffet, Soros et al. has led me to the paper "Railroadization as Schumpeter's Standard Example." by Exben Sloth Anderson. He has a nice discussion of growth of a company in terms of the carrying path of the industry.

The standard equation a lotka verhulst curve can be found in any good book on ecology and leads to a growth equation

n(t+1)= n(t) + r n(t) ( 1-n(t)/k)

The last expression in parentheses gets progressively lower as n(t) comes near to k, leading to a lower growth rate that asymptotically approaches k in the continuous case or that chaotically fluctuates around k in discrete case.

For example if n(t) = 10% of k then the last factor is 90%. but if n(t) is 80% of k then the last factor is 20% and the growth rate is reduced accordingly.

"With this interpretation each established railroad unit may be seen as a starting point for further railroad construction. The effects of the pioneering railroad construction on further growth is only dependent on the potency of spread. n. But as the established railroad miles increase, the distance to the carrying capacity, k becomes smaller. This means that the effect on further growth of an established railroad unit becomes smaller and smaller since it is proportionate to the difference between k and n. 

In the early stages of the railroad diffusion, selection favors the fast action and spread, i.e. pairs of entrepreneurs and financiers able to provide high r values. This expansion is normally related to financial vulnerability. Later, when the railroad system is well developed, fastness is dangerous and does not lead to any results. What is needed is the fine turning which may give a lead vis-a-vis the competitors or which may marginally move the k frontier."

To what extent can the growth of IBM and Microsoft be understood within this framework? And, more generally, is there any profitable investment strategy related to the stages that companies are in relative to their own growth and the industries growth vis-a-vis the time to buy, and management decision-making?

When I visited Japan in 1993, they had seen a decline in the number of coffee shops by some 95% over the previous 10 years. How long will it be before the k limits such companies as Starbucks and will the growth rate of sales provide the signal? -- Vic