Power Laws in Economics: An Introduction

P aul Samuelson (1969) was once asked by a physicist for a law in economics that was both nontrivial and true. This is a difficult challenge, as many (roughly) true results are in the end rather trivial (for example, demand curves slope down), while many nontrivial results in economics in fact require too much sophistication and rationality on the part of the agents to actually hold true in practice.1 Samuelson answered, “the law of comparative advantage.” The story does not say whether the physicist was satisfied. The law of comparative advantage is a qualitative law, and not a quantitative one as is the rule in physics. Indeed, many of the insights of economics seem to be qualitative, with many fewer reliable quantitative laws. This article will make the case that a modern answer to the question posed to Samuelson would be that a series of power laws count as actually nontrivial and true laws in economics—and that they are not only established empirically, but also understood theoretically.2 I will start by providing several illustrations of empirical power laws having to do with patterns involving cities, firms, and the stock