Hi there. Hoping someone can help me settle a debate I'm having with a friend.
We're discussing breakpoints and the application of a marginal rate at the breakpoint itself.
Let's say you want to have the following arrangement - a 5% tax rate applies to amounts up to $100. Anything above is taxed at 10%. My friend says that it's better (from the taxer's perspective) to say something to the effect of "the portion that is equal to or in excess of $100 is taxed at 10%."
I think that it fundamentally doesn't make sense to include "equal to" in that sentence. How do you have a portion that is "equal to" $100 and will be taxed 10%? What portion would that be? $1? 1 penny? 1/100th of a penny?
I think it only makes sense to apply the marginal rate to the amount "in excess of $100". That means that $100 is the breakpoint, and when you're at exactly $100... well - everything up to that point, and therefore the entire amount, is taxed at 5%.
So - what makes sense here? Can you apply a higher marginal rate directly AT the breakpoint?
To make it more concrete, my friend argues that if you had $100 on the nose, you'd tax 5% on $99 (or $99.99, or $99.9999999 - he thinks it all works / makes sense), whereas I argue that that arrangement is basically making a new breakpoint at $99 (or $99.99, or $99.9999999), and would be better described as "amounts in excess of $99 will be taxed at 10%.