# Is there a well known name for a class of functions where a proportion varies according to the size of the whole.

As a lay person I apologise if this is the wrong forum please let me know if it isn't.

In flat taxation regime you pay x% of some value (income for arguments sake). This remains at x% as value decreases or increases.

In a progressive taxation regime you pay a varying % dependant upon some variables bases on a function of the 'some value'.

So for example the rate may be y% (where y < x) for where some value is less than the above or possibly be z% (where z > x) for some value is greater than in the able example.

What I'm trying to find is if there is name for a function where a proportion varies according to the size of the whole. If you see what I mean.

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I think that what you're describing is the differential equation

$$\frac{dL(x)}{dx} = ax$$

Using your example, $L$ would be the tax liability and $x$ would be the income. $\frac{dL(x)}{dx}$ is just code for "how your tax liability depends on your income." The solution in this case is just

$$L(x) = \frac{ax^2}{2} + c$$

Where $c$ is the amount of money that you charge someone with no money.

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