Albany Democrats never got the memo that there’s no such thing as a free lunch. They’re peddling a universal health-care plan they claim would not only cost nothing more, but leave the state $45 billion richer.

The plan might as well be signed by a Nigerian prince.

The seemingly magical solution is a “single-payer” law called the New York Health Act. Authored by longtime Assembly Health Chairman Richard Gottfried of Manhattan, the legislation would shift all 20 million New York residents into one health plan, operated by the state and financed by taxpayers.

AlbanyCare would cover everything for everyone — theoretically enabling people to see the highest-priced specialists, check in to the highest-tech hospitals, receive the costliest procedures. All without paying a dime in premiums, copayments or deductibles.

The new plan would seek federal permission to take over for Medicare, Medicaid, the Veterans Administration and every other existing form of coverage. Private insurance would be effectively outlawed.

Few would shed tears for the paperwork-burying, claim-denying, premium-soaring status quo — other than the tens of thousands of insurance workers put out of work.

Also much to be desired is the promise of blanket coverage for 1.3 million New Yorkers who remain uninsured, and the prospect of never again holding a bake sale for a cancer patient who has coverage but still can’t pay the astronomical bills.

But how could Albany possibly afford to absorb one-sixth of the economy? The Democrats’ answer: Single-payer would cost dramatically less than the status quo.

That far-fetched claim is based on the say-so of Gerald Friedman, an economist at the University of Massachusetts at Amherst, who wrote an analysis of Gottfried’s bill two years ago.

Friedman asserts that single-payer will save so much — mostly by eliminating insurance-related bureaucracy and squeezing deep discounts on drugs — that AlbanyCare could spend $25 billion more on medical care and other expenses and still come out $45 billion ahead.

Friedman acknowledged Albany would have to hike taxes by $92 billion — more than doubling New York’s heaviest-in-the-nation state burden — to make up for the premiums companies and their employees would no longer be paying. But he insists most New Yorkers would be better off, in large part because the new taxes on payroll and investment income would be steeply progressive, conveniently shoving most of the cost onto a wealthy minority.

Friedman is an unabashed booster of the single-payer concept. He has written similarly rosy assessments of proposed single-payer systems in other states, including one for Vermont that even the governor who was its chief sponsor ultimately rejected as fatally expensive.

Likewise, Friedman’s AlbanyCare study is seriously flawed. It relies on a high-ball estimate of administrative savings, assumes the state can get away with chopping drug prices by 37 percent and fails to account for the cost of non-New Yorkers who would flock to the state for free care.

His conclusions conflict with those reached by more sober analysts, including at the left-of-center Urban Institute, who have projected that single-payer systems would increase overall health-care spending, not reduce it. A more conservative study by the Foundation for Research on Equal Opportunity estimates that AlbanyCare would quadruple the state’s tax burden and destroy 175,000 jobs.

Yet Friedman’s too-good-to-be-true numbers were cited as gospel by Gottfried and most of his fellow Democrats in the Assembly as they voted 94-46 to pass the New York Health Act for a third year in a row.

It’s as if the House Republicans had outsourced the cost-benefit analysis of their health plan to Rush Limbaugh instead of the Congressional Budget Office.

Lest anyone dismiss last Wednesday’s vote as empty grandstanding: The bill has 30 cosponsors in the 63-member Senate, which will almost certainly rise to 31 after a special election this month. That leaves it just one vote, and one governor’s signature, shy of becoming law.

It’s true other countries with single-payer-style plans, such as Canada and the United Kingdom, provide universal coverage while spending far less than the United States does. But those systems achieve their savings by doing more than simply reducing red tape: They pay lower salaries to their doctors and nurses and restrict access to high-cost care — methods that supporters of single-payer in Albany avoid bringing up.

The reality is that no conceivable health-care system will give New Yorkers something for nothing, and Albany lawmakers should stop pretending otherwise.