(Brendan Mcdermid/Reuters)

When I wrote about Social Security’s $80 billion cash-flow deficit and soon-to-shrink trust fund recently, I left out lots of stuff for two reasons.

First, I didn’t have unlimited space. Second, you don’t have unlimited reading time.

So today, let’s look at some of Social Security’s nittier and grittier details that I omitted last week and why those generally unrecognized details show that the solution proposed by many of my correspondents and online commenters to solve Social Security’s financial problems — removing the salary cap on which Social Security tax is paid — is a terrible idea.

Why? Because removing the cap would undermine Social Security by turning it from an earned benefit, which it is now, into mass welfare. Welfare doesn’t play very well these days.

Okay, here we go.

Workers and their employers pay a combined 12.4 percent of a worker’s salary of up to the current cap — $132,900 a year — in Social Security taxes. (I’m assuming, as most competent economists do, that the employer’s half of the tax is money the employee would otherwise get.)

A 12.4 percent tax on the entire salary earned by most people falls far more heavily on the less-well-paid than on the mega-high-paid, for whom the Social Security tax is little more than a rounding error.

But that regressive tax is offset by Social Security’s progressive benefit structure. Your retirement benefit, under the numbers in force this year, consists of 90 percent of your first $11,112 of salary; 35 percent of the next $55,884; and 15 percent of everything over $66,596.

So the more you pay in Social Security tax, the bigger the benefit you get. But the lower your benefit is compared to the Social Security tax you paid.

You still with me? Good.

Now, let’s assume that instead of a max tax of $16,479.60 for Social Security — that’s 12.4 percent of today’s $132,900 limit — there was no cap. That means that someone earning, say, $1 million a year would be paying $124,000 of Social Security tax.

When this big earner retired, under the current formula she’d be entitled to a retirement benefit of more than almost $160,000 a year — about nine times today’s average benefit. I can’t imagine her getting anything like that much because I’m sure that in addition to taking off the cap, the benefit structure would be changed to provide little or nothing in the way of higher benefits for her.

That radical tax change from the current everyone-pays-and-everyone-gets would transform Social Security from a politically invulnerable earned-benefit program into a politically vulnerable welfare program. And, in my not-so-humble opinion, that would undermine its long-term viability.

John Rother, AARP’s longtime Social Security expert and the chief executive of the National Coalition on Health Care, says earnings caps have been part of Social Security ever since President Franklin Delano Roosevelt got the program enacted in the 1930s.

“It was designed as an earned benefit; it’s contributory, and your benefit depends on how much you contributed,” he told me.

That combination, Rother added, is a major reason Social Security became widely-embraced rather than being regarded as a charity program.

Another Social Security maven, Gene Steuerle, agrees. “If you remove the earnings cap, you fundamentally change the nature of the program and turn it into a welfare system,” says Steuerle, a co-founder of the Tax Policy Center (and co-author of a Social Security column with me last year).

Steuerle makes another point that’s well worth considering. To wit: If we enact a 12.4 percent tax increase on upper-income people by uncapping Social Security, it will exacerbate the current pattern of devoting increasingly large portions of federal revenue to retirement and medical care. That disproportionately benefits older people, like Steuerle and me.

In addition, Steuerle says, uncapping the Social Security tax would make it more difficult for the government to raise money to pay for things like infrastructure, education and social programs that we need to help younger people and prepare our country for the future.

Two final things. First, I’d love to find a way to apply Social Security tax to capital income, which is a big deal for the better-off among us but small beer for most people. But I can’t figure out how to do that without impinging on the federal income tax.

Second, I’ll offer my thoughts, which reflect conventional thinking among Social Security wonks, on how to fix the program.

You gradually raise the retirement age a bit; increase the earnings cap (but not hugely); tweak the benefit formula in various ways; and adopt some of the changes that Steuerle and I proposed.

I wish I could offer you a simple, one-step Social Security solution like “remove the earnings cap.” But as I hope I’ve shown you, removing the cap won’t make Social Security more secure. It will make it less secure.

And that, my friends, is the bottom line.