Power Curves

A small number of companies have achieved huge scale, while a large number of companies are quite small. A small number of internet users/sites have many connections, while many other internet users/sites are connected to only a few others. A small number of external shocks to an economic or biological system have huge implications, while many small shocks have hardly any impact at all. All of these relationships follow what’s called a “Power Law.” A power law distribution generally talks about the relationship between the size of an occurrence and its rank (I know this isn’t mathematically correct – let’s skip the details of how the power law is different from Zipf’s law and Pareto’s law …). But just to stay with math for a while: If you replace the nominal scale on the y axis with a logarithmic scale in a power curve graph, you basically get a straight downward-sloping curve.



Power laws and power curves are helpful to understand industry structures. Studies have shown that the concentration of players in specific industries follow power laws, and that if anything, the inequalities increase over time. Chris Anderson in “The Long Tail” (amazon.com)has argued that there is a lot of money to be made reaching niche consumers, particularly in industries where electronic distribution is feasible. (A recent HBR article questioned some of his findings.)

Why do power curves exist? They are linked to intangible assets (brands, talent, intellectual property) leading to increasing returns. A McKinsey study shows that labor and capital intensive industries (e.g. chemicals or machinery) have flatter curves than industries such as software or biotech.

One of the most intriguing discussions of power laws is the book “Why Most Things Fail” by Paul Ormerod(amazon.com). I just loved this book. Ormerod talks a lot about biological systems, and shows how exogenous shocks have lead to extinctions of species over the last 500 million years. Not surprisingly, there is a power law here: A few large shocks killed a lot of species, many others had very limited impact. He then applies these findings to the economic world: How do external shocks lead to the disappearance of companies, and what can firms do to “improve their strategic fitness level? But that’s a whole separate discussion …