$10 a person is naive math, sure, there would be reduced demand which means that some of that cost would be bourne by other purchasers to keep industry revenue stable, and there would be a reduction in production which further compounds this. But it's not a doubling in cost, I think the true number would be between 20 and 30 dollars per person (10-20% of their monthly food budget) that continues eating as much meat, per month, and close to that percentage in production decline. A big deal, but not a complete upheaval in the meat industry.
The subsidies aren't really about keeping meat costs down for consumers so that meat producers can remain profitable. They're more about manipulating the global meat market to compete against other producers and ensure domestic food security.
I'm sure that if the subsidy went away, McDonalds would reformulate the big mac so that it's only $5.50. It's gross, but that's what fast food companies do.
