# tax brackets

consider the following table of tax rates.

`┌──────────────┬────────────┬────────────────┐`

│ Gross Income │ Net Income │ Effective Rate │

├──────────────┼────────────┼────────────────┤

│ 12,000$ │ 17,200$ │ -43.33% │

│ 20,000$ │ 22,000$ │ -10.00% │

│ 25,000$ │ 25,000$ │ 0% │

│ 40,000$ │ 34,000$ │ 15.00% │

│ 80,000$ │ 58,000$ │ 27.50% │

│ 160,000$ │ 106,000$ │ 33.75% │

│ 320,000$ │ 202,000$ │ 36.88% │

│ 640,000$ │ 394,000$ │ 38.44% │

│ 1,000,000$ │ 610,000$ │ 39.00% │

└──────────────┴────────────┴────────────────┘

for instance, a person whose gross income is 40,000$ pays 15% of their income in taxes. whereas someone who earns a million pays 39%. this sure does look progressive, doesn’t it?

in fact, people grossing below 25k actually have a *negative* tax bill — they receive a refund.

# surprise

but what if i told you this table represented a *flat* tax rate of 40% for all individuals, combined with a 10,000$ refundable tax credit. (“refundable” means that you get the difference back as a refund if it’s greater than your amount owed in taxes.)

you can easily verify this. for instance, 40% of 80k is 32,000$. now subtract that tax credit for a total of 22,000$. now subtract 22,000$ from the gross of 80,000$ and you get 58,000$.

# best of both worlds

what this example illustrates is the distinction between a *true flat tax* and a *marginal flat tax* and a *marginally flat tax*. our tax system described above isn’t truly flat, because the effective rates are indeed progressive. but it is *marginally* flat, because each additional dollars of earnings pays a flat rate. this structure gives us the benefits of flat taxes, such as administrative simplicity and minimal deadweight loss, while also retaining the social aim of reducing inequality.

# graphed

here are a few examples of these *effective* tax rates graphed, so you can see how progressive they are, even tho they use flat *marginal* rates.