This week’s “Daily Journal” guest columnist is Mitch Kokai, associate editor of Carolina Journal.

It’s hard to convince some people that lowering tax rates can increase government revenue. The degree of difficulty climbs when the skeptical taxpayer doesn’t understand the tax system.

A recent letter in the monthly journal First Things highlights the problem. The writer, complaining about “some hoary Republican tropes” and “fuzzy-math calculations,” dismisses the argument that cutting the top income tax rate from 70 percent to 28 percent could lead to increased government revenue. “That would mean someone making $100,000 a year would have to instantly vault up to making at least $250,001,” the critic calculated.

The good news for our letter-writing friend? He understands arithmetic. The bad news? He displays a complete ignorance of tax brackets.

He assumes that applying a 70 percent tax rate to an income of $100,000 would yield $70,000 in tax revenue. He then computes that income of $250,001 would yield that same sum — plus some spare change — with a 28 percent tax rate.

If only our tax system were that simple.

It would be easy to laugh at this letter writer’s mistake, but one suspects many other taxpayers fall victim to the same error. It’s no laughing matter if that collective ignorance prevents taxpayers from understanding worthwhile reforms.

More on reform in a moment. First, let’s address the error.

Government taxes different levels of income at different rates. We call our income-tax system “progressive” not because the political Left celebrates it, but because it assesses higher rates at progressively higher incomes. The income range subject to a particular tax rate is the “bracket” associated with that rate. Beyond the last income threshold sits the top marginal rate.

When we last coped with a top marginal rate of 70 percent in the 1970s, the government split taxpayers’ income into 15 different brackets. In other words, those who earned the highest incomes saw their income taxed at 15 different rates. Only the income beyond the highest threshold faced a 70 percent tax rate.

Once the top marginal rate fell to 28 percent in the late 1980s, the tax man separated income into just three brackets. Today we have six brackets and a top marginal rate of 35 percent. A single taxpayer with taxable income of $100,000 faces a top rate of 28 percent and actually pays a little less than 22 percent of her income to the I.R.S.

There’s no need for most of us to know details about the brackets. But we do need to understand the concepts of “brackets” and “marginal rates.” Without that understanding, it’s hard to follow debates about tax cuts, tax hikes, and tax reform.

Take the flat tax. Supporters take for granted the notion that most people understand a flat tax means a flat tax rate. Choose one rate, and apply it to every taxpayer. That sounds fair.

But what if taxpayers don’t get that distinction? It’s entirely possible that some believe a flat tax means one flat assessment charged to everyone — regardless of income. Sales clerk or CEO, you would pay the same dollar figure to the government.

People operating under that misconception would not see that a flat tax rate forces those with higher incomes to pay proportionally higher taxes. Apply a 10 percent tax rate to every taxpayer, and the CEO with $1 million in taxable income pays $100,000. That’s 50 times more tax than the $2,000 assessed the sales clerk with taxable income of $20,000.

It’s even possible, as my colleague Dr. Roy Cordato demonstrates in his latest research on tax reform, to make higher earners pay higher percentages of their incomes with a flat tax rate. Just exempt a certain amount of income from any taxation — in other words, create a zero-tax bracket — then apply the flat rate to all other income.

Let’s say the flat rate is 10 percent, and it kicks in for all income above $20,000. Make less than $20,000, and you pay no income tax. The taxpayer with income of $30,000 pays $1,000, or 3.3 percent of her income. The effective tax rate hits 5 percent with a $2,000 tax at $40,000 of income. By the time taxable income hits $100,000, the effective tax rate is 8 percent.

Whether the government should tax income at all before it’s used is a topic for another discussion. What’s clear is that taxpayers need to know the basics of the current tax system before they can judge the merits of proposed reforms.