Congress originally enacted the alternative minimum tax (AMT) to make sure that high-income folks would pay at least a minimum amount of income tax. Sound familiar? It seems awfully similar the “Buffett rule,” the principle that those with incomes above $1 million should pay at least 30 percent of their income in taxes.

As currently constructed, the AMT adds enormous complexity to the tax code and increasingly burdens middle-class families. So it seems natural to ask: why not just replace the AMT with a version of the Buffett rule?

To help answer that question, the Tax Policy Center estimated what it would cost to scrap the AMT and enact the Fair Share Tax, a recent legislative proposal that would impose a 30 percent minimum tax on individuals earning more than $1 million. (The tax would phase in so its full force wouldn’t hit taxpayers as soon as their income topped $1 million.)

We found that the Fair Share version of the Buffett rule wouldn’t come close to paying for AMT repeal. Scrapping the AMT would lose a whopping $1.2 trillion relative to current law between now and 2022. The Fair Share Tax would only recover about $100 billion of that revenue, for a net loss of $1.1 trillion.

What would it mean relative to current policy – a more realistic baseline under which the AMT would be permanently patched and the 2001/2003/2010 tax rates extended? The AMT fix would reduce revenue by $550 billion over the decade while lower rates would boost the amount the Fair Share tax would bring in by about $150 billion. The net: the swap would still lose $400 billion over 10 years.

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Why does the AMT generate so much more revenue than the Fair Share tax? The biggest reason is that the AMT simply hits a much bigger chunk of taxpayers. By design, the Fair Share tax wouldn’t affect anyone making less than $1 million. Yet 96 percent of AMT taxpayers have incomes under $1 million, accounting for 77 percent of all AMT revenue. The Fair Share tax would need to start at a much lower income level to make up the lost revenue from the AMT.

The AMT may be a mess, but it would be awfully costly to replace.