The tax strategies can be its own mammoth thread.
One of the (many) factors to consider with the US progressive tax system is that the brackets are not linear. Sales taxes (say 7%) are linear and the tax applies the same to taxable items whether it costs $1.00 or $1,000,000.
With taxes, as the taxable income increases the amount of taxes *above* each threshold increases at a different rate. (Quick note: Taxable income is *not* the same as your income).
Percent Rates of 10, 12, 22, 24, 32, 35, 37 are the 2020 IRS values for taxable income.
For simplicity, let's suspend the concept of standard and itemized deductions, social security withholdings, retirement contributions etc. for now. Like in the hardware store kid example, you are simply wondering what happens of you get a raise.
*IMPORTANT* The actual math and tax calculations below are more complicated than what I am showing, but I wanted to keep it simple to help people understand the effects of progressive rates across brackets. There is a gross simplification that all money is being taxed and the tax levels are approximate for easy calculation.
Here we go:
Suppose you are single and you make $40,000 per year and are in the 12% bracket. That means $40,000 x 0.12 = $4800 is paid to IRS in taxes.
One day your boss offers to double your salary to $80,000.
Someone told you the next tax bracket is 22% for a single person making over $40,000 so you don't want to make more than that because you pay more taxes.
You might be thinking at 12% I would have payed $9600 in taxes. But now at 22% I have to pay $80,000 X 0.22 = $17,600. This is incorrect.
This is where some people get confused.
The 22% ONLY applies to the amount over the $40,000. So the first $40,000 is taxed at 12%, so you owe $4800 on that. The next $40,000 is taxed at 22% so you owe $8,800 on that portion for a grand total of $13,600.
You have paid $13,600 in taxes on a salary of $80,000. This amounts to $13,600/$80,000 = 17% of your income. (Sometimes this is referred to as an "effective rate").
You still have made more money than in the days you were making $40,000 !
Then you heard people talking about 6 figure salaries. So you decide to find a job that pays $100,000. You also found out that once you pass $85,000 you now move into the 24% bracket.
Using your newfound knowledge, you know that does not mean you pay $100,000 X 0.24 = $24,000. But you also know it is going to be more than you paid when you were making $80,000.
You will owe $85,000 X 0.22 = $18,700 on that portion and then another $15,000 X 0.24 = $3600, for a total of $22,300.
Your effective rate is $22,300/$100,000 = 22.3%
(Maybe you are thinking..I sure miss those 12% days).
Well, once you went past the 6 figure mark, you started dreaming it would be nice to say you are making a Quarter MIL per year. ($250,000)
A little research shows that puts you into the 35% bracket.
You would owe $207,000 X 0.32 = $66,240 on that amount and on the remaining $43,000 you owe $43,000 X 0.35 = $15,050 for a grand total of $81,290.
Your effective rate is $81,290/$250,000 = 32.5% which is almost 1/3 of your salary. Imagine if you only had to pay 12% on that 250K...
(Now it hits you: holy cow, I am paying more in taxes than I made in total back in the day when my boss doubled my salary to $80,000)
----end of examples----
As is hopefully clear, the more you make, the more that is taken and it is NOT LINEAR. Of course regardless of which bracket you end up in, you are still making more money. (This is the key concept)
The reality is that you are just not making as much (per dollar) as you were in the previous bracket. So rejecting a raise based on being in a higher bracket doesn't make sense for the average person.
If someone offers you more money for the same work, take it.
Now I will end this by saying there are tons more factors to consider and there are numerous ways to reduce your tax burden. The above is just meant to illustrate the math of the progressive tax bracket system.
Hope that helps someone.