This week Elizabeth Warren proposed a fantastical entitlement program to provide free or affordable childcare to every single American family with a young child - suggesting that the program would cost $70 billion a year.

As Breitbart's John Carney notes - the whole plan is absurd; not because the price tag is so expensive, but because it's way too cheap.

Start with the basics. There are around four million babies born in the U.S. every year. That means there are approximately 20 million children under school age who could be enrolled in a national childcare program. Moody’s Analytics Chief Economist Mark Zandi and Sophia Koropeckyj, the economists behind Warren’s figures, estimate that the cost of each child in the Warren Centers—or Baby Warrens, as we would inevitably call them–would be $14,500. -Breitbart

At $14,500 times 20 million children, a national childcare program could cost up to $290 billion per year - or an extra 2 trillion per decade over her original estimate. That said, not every family qualifies, nor would every family take advantage of such a program as some people prefer to raise their own children or place them in the care of relatives.

That said, Warren's proposal promises free childcare to any family with an income under 200% of the poverty line - or around $51,000 for a family of four. All other families would pay no more than 7% of their income on childcare.

Zandi and Koropeckyj estimate that 1/3 of American households will choose to forego professional childcare; around the same percentage as today. This is magical thinking, suggests Carney - as it assumes that stay-at-home parents won't change their preferences in light of a massive government program.

Warren's plan assumes that the number of children in childcare centers would rise from 6.8 million to 12 million - however due to shifting preferences, that number would likely be much higher.

That said - the math behind Warren's plan is still wrong at 12 million children. At $14,500 per head, the program would cost approximately $174 billion per year, not $90 billion.

How they shave that $100 billion off the cost is partly redistribution and mostly voodoo economics, magical thinking disguised as macroeconomics. Because families earning more than 200 percent of the federal poverty level would have to pay for some of their childcare–but never really more than half–the cost would be reduced. But the size of the subsidy for even very wealthy families is large enough that this doesn’t shave much off the total cost. The heavy lifting here is in the rosy economic forecasts Zandi and Koropeckyj produce. They predict that the childcare for all program will “quickly lift economic growth” by transferring wealth from the rich—Warren wants to pay for the program with a tax on ultra-millionaires. In the longer term, they see it boosting economic growth because they foresee it boosting workforce participation and the number of hours worked. -Breitbart

In short, the plan only works if economic growth is "quickly lifted" because of a massive wealth transfer from ultra-millionaires, and if the free childcare results in more parents leaving the home in search of jobs amid already-low unemployment. The analysis fails to consider that a flood of additional workers who aren't at home raising their own kids would put downward pressure on wages.

"Cheapening labor costs while raising taxes on wealth would also diminish the return on capital investment, which would be a drag on productivity—the best driver of economic growth," notes Carney.

"In the end, we may end up with a diminished economy, families working more hours than before and spending less time with children, and an entitlement program that is much more expensive than anticipated (as entitlement programs tend to be)."

That said, encouraging Americans to have more children by making it more affordable is not a bad idea, concludes Carney. It should just be done in a way that doesn't require magical math - such as a much larger, fully refundable child tax credit, and allowing families to pay less in entitlement taxes when they have more than two children. After all, they will be supplying the next generation of workers who will pay for Social Security and Medicare, should it still exist by then.

"Childcare Deserts"

While Carney points out the crappy assumptions behind Warren's plan, there may be another major problem; accessibility. According to the Center for American Progress, more than half of American households live in what are known as "childcare deserts" - places where there are up to 3 children for every available childcare slot, or no childcare options at all.

Warren addresses this in a blog post, suggesting that her plan would "establish and support a network of locally-run Child Care and Early Learning Centers and Family Child Care Homes so that every family, regardless of their income or employment, can access high-quality, affordable child care options."

The problem, as New Republic reports, "There are simply not enough providers in operation, either in formal centers or in informal home settings, with enough openings to meet current demand."

That demand is only likely to increase if Warren’s plan makes childcare far more affordable and better quality than it is today. Significantly increasing the funding available to provide care and compensate providers adequately will certainly entice more people to jump into the business. But there is nothing in the plan that absolutely ensures that enough providers open up shop and create new slots so that all families can take advantage of it. -New Republic

In short, the federal government would need to become directly involved in solving the infrastructure problem - vastly expanding child development centers, which would add an entirely new set of costs to the proposal.

The Week's Ryan Cooper points out four flaws in Warren's plan.

The limitations of Warren's proposal are clearly driven in part by the desire to keep the headline price down, but somebody, in this case middle- and upper-class parents, will still have to make up the difference. Designing it in this way could easily increase the total cost (that is, including both state and private spending) of child care. The government could counter this problem by fixing prices, but there are no such controls mentioned in the proposal outline. Second is wasteful bureaucracy. Giving out subsidies based on income will require an administrative/surveillance apparatus to calculate payments and make sure that people aren't cheating the system. That's a lot of paperwork and very likely a lot of mistakes and headaches. Third is lower political durability. Families only eligible for smaller subsidies will be naturally resentful of the downscale families paying nothing, so there will be less resistance to a future Republican administration attempting to roll back the program. (Witness the last GOP Congress coming within a hair's breadth of repealing ObamaCare, but largely leaving Medicare alone.) A fourth problem is that families in the phase-out zone of the subsidy will potentially face a high effective marginal tax rate, as a large portion of any additional income will be eaten up by reduced subsidies — especially when combined with other proposals for means-tested tax credits that would phase out in a similar way, like Kamala Harris's LIFT Act.

Any way you cut it, Warren's plan - like so many before them, appears to be nothing more than a great sounding promise that would end up like California's ill-fated bullet train.