The uproar over proposed federal legislation mandating a state takeover of county Medicaid costs in New York inspires a thought experiment: What if the mandate included New York City?

As proposed by U.S. Reps. Chris Collins and John Faso, the mandate carves out cities with a population of 5 million or more, a description that fits only New York City. Collins and Faso have justified this exception on grounds that the city has its own income tax, which better enables it to afford a share of Medicaid expenses.

Here is another possible explanation: The city’s Medicaid contribution is so large that including it in the mandate would reverse the political math.

A state takeover of local Medicaid costs that excludes New York City would tend to shift a greater share of the program’s financial burden onto the city and its taxpayers. But a takeover that encompasses New York City would tend to do just the opposite: shift the burden off the city and onto the counties of upstate and Long Island.

This is because the city’s share of Medicaid costs far outstrips its contribution to state revenues.

Of the $7.6 billion that county governments currently contribute to the Medicaid program, $5.4 billion, or 71 percent, comes from New York City. As of 2010, however, the city’s share of combined state tax revenues was either 40 percent 45 percent (if counted by where taxpayers live) or 45 percent 49 percent (if counted by where taxpayers work). If the full cost of Medicaid were shifted to the state, all else being equal, city taxpayers would stand to pay about almost $2 billion less.

Consider another scenario proposed by some county officials in the past: allowing the state to keep a larger share of sales tax revenue in exchange for taking over local Medicaid costs.

If such a swap were limited to the counties outside New York City (as discussed in a previous post), the state would need to take back 1.2 percentage points of the sales tax. The impact on county finances would be mixed: Poorer counties with high Medicaid populations and low sales tax revenues would save money; wealthier counties would lose money.

If, however, New York City were included in such a swap, the state would need to reclaim almost twice as much of the sales tax: 2.3 percentage points. And virtually every county in upstate and on Long Island would lose money on the trade –  while New York City would save almost $2 billion.

New York City’s outsized Medicaid costs are nothing new. They reflect a combination of relatively high poverty in the five boroughs and high costs among its hospitals and other healthcare providers. Traditionally, the city and other counties paid a fixed percentage of their residents’ Medicaid costs. The growth of this local contribution was capped at 3 percent a year under Governor Pataki, then frozen as of 2015 under Governor Cuomo.

Overall, the regional balance between tax payments and state spending is roughly a wash for New York City (only if calculated based on where taxpayers reside as opposed to where they work). In general, upstate counties see a net gain from the balance of payments, and taxpayers in New York City, Long Island and the suburbs north of the city are net losers.

UPDATE: Given the heated opposition to the Collins-Faso amendment from Governor Cuomo and others, it’s worth remembering that a state takeover of local Medicaid costs was once actively promoted by Cuomo’s father, the late Governor Mario Cuomo, who included a $110 million downpayment on the plan in his final budget proposal.

The circumstances were very different, of course: The elder Cuomo was acting on his own volition, not under the duress of a congressional mandate. His plan included a sales tax swap and was phased in more gradually. And his takeover did include New York City.