Most reports about the recently passed federal tax plan have included a line about the near doubling of the standard personal income tax deduction. Few have gone on to explain how that change benefits those at the lowest end of the income scale.

That shouldn’t surprise us here in North Carolina, where increases in the standard deduction — also referred to as the “zero tax bracket” — have become a standard element of near annual tax changes. Media accounts of tax policy in the Tar Heel State have focused much more on declining rates than on increased amounts of income removed from the tax man’s consideration.

It’s a simple change. But it takes a little thought to grasp the striking impact a higher standard deduction can have on a family’s income tax bill.

Before taking a closer look at the federal change, let’s revisit the most recent increase in North Carolina’s standard deduction.

Under current state law, North Carolina individual income taxpayers pay a 5.499 percent flat rate. For those who take the standard deduction, the first $8,750 is exempt from that flat rate for individual filers. Married couples filing jointly can deduct twice as much: $17,500. (Those numbers jumped by $500 per person in 2017).

In 2019, the flat tax rate drops again to 5.25 percent, while the standard deduction increases to an even $10,000 for individual filers and $20,000 for married couples. In other words, the rate itself drops by roughly 4.5 percent, while the standard deduction increases by more than 14 percent.

The relative impact is greater for those with the lowest amounts of taxable income. To illustrate, we’ll turn to three hypothetical married couples with a single income earner. One family features a bank teller earning $25,000. The second has a bank president making $120,000. The third is led by a corporate CEO with a $1 million income.

Under the current law, the $25,000 household owes roughly $412 in state income taxes. That’s 1.6 percent of the household’s income. The $120,000 household pays $5,636 (4.7 percent). The $1 million household pays $54,027 (5.4 percent).

The bank president earns 4.8 times as much as the teller but pays close to 14 times as much income tax. The million-dollar taxpayer earns 40 times as much income as the teller but pays 131 times as much income tax.

Now for the caveats: These calculations assume all income is taxable and that none of the households chooses to itemize deductions. Remove these assumptions, and it’s likely that each household is likely to see its tax bill decrease. Those with higher incomes are likely to enjoy a larger decrease, though they’ll still end up paying much more in income taxes than those at the lower end of the income scale.

The calculations above also assume that none of the households has children. A child tax credit drops the tax bill to an even greater degree, and the state tax code’s treatment of children works to the lower-income earner’s advantage.

It’s not necessary to our discussion of the impact of the standard deduction to try to account for these caveats. If other exemptions skew the tax system in favor of higher earners, blame those exemptions. Don’t blame either the flat tax rate or the standard deduction.

How does the picture change under the increased state standard deduction planned for 2019? The bank teller’s tax bill drops to $262 (1 percent). The president now pays $5,250 (4.4 percent). The million-dollar earner forks over $51,450 (5.1 percent).

The bank president will pay 20 times as much as the teller. The million-dollar earner will pay 196 times as much. The increased standard deduction makes the overall system more progressive, meaning higher earners surrender a higher share of their income to the tax man, even as the flat tax rate continues to drop.

Now let’s turn our attention from Raleigh to Washington. The federal income tax includes even more complicating exemptions and deductions, so isolating the impact of the standard deduction and tax rate alone offers a less accurate picture of the real-world impact of tax changes. Still, there is value in computing the higher standard deduction’s impact.

A $25,000 married household sees its income taxed today under two different rates: 10 percent and 15 percent. The $120,000 household also faces a 25 percent tax rate. The $1 million household sees income taxed at four additional rates: 28, 33, 35, and 39.6 percent.

Using the same caveats we employed before, the current $13,000 standard federal deduction means that the $25,000 household owes $1,200 in federal income tax (4.8 percent of household income). The $120,000 taxpayer owes $18,057 (15 percent). The $1 million household owes $334,996 (33.5 percent).

Earning 4.8 times as much income, the bank president pays 15 times as much income tax as the teller. Earning 40 times as much income as the teller, the corporate CEO pays 283 times as much income tax.

Yes, other exemptions, credits, and deductions in the federal code undoubtedly change these calculations. Any million-dollar earner who actually pays a $335,000 tax bill needs a new tax accountant. But these are the bills one would see from a system based solely on current tax rates and the current standard deduction.

Under the newly passed tax bill, five of the seven marginal tax rates go down. Before factoring in the change in the standard deduction, two of our three hypothetical households would fare better with the new rates. The bank teller still would owe $1,200, or 4.8 percent of household income. The bank president would see his bill drop to $15,419 (12.8 percent). The corporate CEO sees her bill drop to $304,569 (30.5 percent).

It looks as if the higher-income households are getting a better break from lower rates. But the new federal tax bill also raises the standard deduction for married filers from $13,000 to $24,000. That’s an 85 percent increase in the value of that deduction.

Now the hypothetical $25,000 bank teller’s family owes tax on just $1,000 of income. The tax bill drops to $100. That’s 0.4 percent of household income. It represents a 92 percent decrease in the tax bill charged under current law.

The bank president’s income tax bill drops to $12,999 (10.8 percent). That’s a 28 percent decrease from current law. Now, the president pays 130 times as much income tax as his teller.

Meanwhile, the $1 million taxpayer sees her tax bill drop to $300,499 (30 percent). That’s a 10 percent cut in the overall income tax bill. But the CEO pays more than 3,000 times as much income tax as the bank teller. The CEO also pays 23 times as much tax as the bank president, even though she earns about eight times as much income.

In other words, the combined effect of lower rates and a higher standard deduction has a much greater relative impact on those at the lower end of the income scale — whether at the state or federal level.

That’s a fact worth repeating.

Mitch Kokai is senior political analyst for the John Locke Foundation.