## What is the power law?

A power law is a relationship in which a relative change in one quantity gives rise to a proportional relative change in the other quantity, independent of the initial size of those quantities. An example is the area of a square region in terms of the length of its side.

## Who invented power law?

The theory is named after psychophysicist Stanley Smith Stevens (1906–1973). Although the idea of a power law had been suggested by 19th-century researchers, Stevens is credited with reviving the law and publishing a body of psychophysical data to support it in 1957.

**What is the power law equation?**

A power law is often represented by an equation with an exponent: Y=MX^B. Each letter represents a number. Y is a function (the result); X is the variable (the thing you can change); B is the order of scaling (the exponent), and M is a constant (unchanging). If M is equal to 1, the equation is then Y=X^B.

**What is the power law in economics?**

A power law (PL) is the form taken by a remarkable number of regularities, or laws, in economics and finance. It is a relation of the type Y ¼ kXa, where Y and X are variables of interest, a is the PL exponent, and k is typically an unremarkable constant.

### Why do power laws arise?

Power laws also arise from preferential attachment phenomena. In economics this is manifested as the rich get richer; in internet studies as the tendency of highly linked sites to get ever more links and hits.

### How do you fit a power law?

This Help Article tells you how to fit a power law or an exponential to a set of points. The power law has the form y = a x^b, and the exponential models y = a exp(b x). The power law or exponential increases faster than a linear function, and a simple least-squares method will fail to converge.

**What is the power law curve?**

Power laws, or L-curves, are another useful growth curve, as they tell us how learning or performance increases in closed systems, temporary environments of fixed complexity. Power laws have similarities to the saturation phase of S-curves, though they are likely each due to different physical mechanisms.