[robjan]

That doesn't make sense. Once you hit a threshold, usually the amount of money below the threshold is taxed at 0% or a lower percentage, then anything earned on top is taxed at a higher rate. You still earn more money by earning above the threshold.

[mrob]

That's still a discontinuity in the marginal value of income. You don't need the slope of the post-tax income:pre-tax income graph to go negative for there to be inefficiency. Any sharp change in the curve is enough.

[robjan]

Where's the incentive to fiddle your taxes? Yes you can donate your money to bring yourself into a lower tax band but you will still never have more in your bank account by doing so. e.g if there is a system where tax is 10% then it goes up to 20% at a $100 income. If I earn 99 then my take home is 89.1 (99 * 0.9) if I earn 101 then my take home is 90.8 (100 * 0.9 + 1 * 0.8). Yes, the effective tax rate is higher but I can never take home more by deliberately earning less money.

[O_H_E]

Note: I am note defending any previous arguments, just trying to make a fact clearer.

Your calculations was right in that idealistic tax system, but the real world is really messy with lots of exceptions, Tax credits, Benefits, and such.

Building on your example, I will add a little Child Benefit to make a slightly less ideal idealistic-scenario.

Assume If earning < 100: child_credit = 3

Assume 1 Child

If earning 99: take_home = (99 * 0.9) + 3 = 92.1

If earning 100: take_home = (100 * 0.9 + 1 * 0.8) = 90.8

-----

I chose this example because I remember vividly a story about a family in the UK that avoided getting promoted because their take-home would decrease. Of course it have to be a very small promotion in order to not be worth it. I don't know if cases like this is rare in the US, but it is generally a thing.

[pashamur]

You're forgetting benefit cliffs which are a large chunk of the discontinuity problems. Any benefit that does not have a gradual phase-out (like subsidized health care plans) will lead to these discontinuity problems.

https://www.zerohedge.com/news/2012-11-27/when-work-punished...

[enragedcacti]

is a 1% change sharp?