First have a regressive (fixed amount) flat-tax per year per child, something like $15,000. That reflects the government's cost in education and healthcare. Then have a progressive (percentage) tax deduction or credit per year per child, e.g. your taxable gross income is reduced by 10% per child. Reducing your AGI 10% reduces your taxes by more than 10% if the tax system is bracketed or curved.
Say also that an ordinary family typically takes \$10k/year of other deductions (standard deduction and all that). The \$15k/kid/year is also tax deductible since governments don't tax tax.
Income 0 kids tax 3 kids tax extra kept income per kid
$40k 4k 40k (all) -12k
$100k 22k 46k -8k
$1M 400k 300k 33k
$10M 5M 3.5M 500k
For the very rich: the proportions stay about like this, letting them keep 5 more % of their income per kid.
You make \$40k/year, no kids. Minus the \$10k, you're in a 15% bracket so paying ~$4000 in tax.
You make \$40k/year, 3 kids. You are underwater because your $45k 3-kid tax > your income.
Make \$100k/year, 0 kids. Taxable income is \$90k/year putting you in a 30% bracket, tax is ~22,000 figuring for the curve. You keep $78,000.
Make \$100k/year, 3 kids. Taxable income is 30% less (-\$30k) - the 10k standard - the \$45k tax you pay, or \$15k. That's in a 10% bracket so \$1500. Total tax is \$46,500, you keep $53,500, or about what an American nets after also paying state tax, FICA, healthcare and higher education.
Make \$1M/year, 0 kids. You're in a 45% tax bracket, so \$400,000ish tax, you keep \$600k.
Make \$1M/year, 3 kids. Deduct \$10k, \$300,000 for the 3 kids, and the \$45,000 kid tax you paid, giving \$645,000 taxable income. Taxed at 45%, about \$255,000.
With the kid tax that's \$300k, so \$700k you keep. You're being paid $100k to raise 3 kids.
Make \$10M/year, 0 kids. Taxable income is \$9.990M, putting you in a 50% bracket for almost all of it. Tax is \$5,000,000, you keep \$5,000,000.
Make \$10M/year, 3 kids. Deductions are the 10k standard, 30% (\$3M) for the kids, and the \$45,000 tax you paid for the kids. That's \$3,055,000. Net income is \$7M, back in the 50% bracket so \$3.5M. Add the \$45,000 kid tax you paid, tax is $3.545M, you keep \$6.455M. You are literally being paid \$1.455M to have kids.
Make \$10M/year, 9 kids. Deductions are 10k, 90% (9M) for 9 kids, and $135,000 kid tax you paid. That's \$9,145,000, leaving \$855,000 taxable at 45% or ~\$370,000 plus the kid tax. You keep \$9.5 million. You are literally being paid \$4.5M to have 9 kids.