Can power laws be used as a tool to gain advantage in the real world by helping choose what to focus on?

My current understanding is that a power law is a relationship between two variables $Q$ and $q$ such that $Q = q^k$ for some $k$.

For example, let $Q$ be the area of a square, and q the side length of the square. Then $Q = q^2$. The important thing to understand here (in my opinion) is that if we for example double the side length $q$, then $Q = (2q)^2 = 4q^2$, so $Q$ has quadrupled. That's a big increase.

How I think this could be applied in the real world, is if you have some variable $Q$, then if you can find another variable $q$ that is in a power law with $Q$, you should allocate resources towards increasing $q$, rather than some other variable?

Like, if there are multiple variables that can increase $Q$, you should try to find one that is in a power law to $Q$.


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This will always depend on a context and its impossible to cover all possible instances of use of power laws in economics.

One famous example of use of power law is Ramsey rule for optimal taxation that uses it indirectly. It can be shown that Marginal Excess Burden of taxation (Jacobs Principles of Public Finance pp 153; Ramsey 1927) increases roughly quadratically as tax rate increases. This power law then implies that its optimal to smooth tax rates over comedies rather than have some commodities with very high tax rate and some with small tax rate.

This has significant real world consequences, and is routinely used as a justification for roughly uniform VAT and sales tax rates.


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