TL:DR - Assuming utility functions, if you value animals above the meat they produce, the utility from paying people not to eat them and not eating them yourself is always greater than paying people to eat meat and eating it yourself.
Here is why a person following a utility function couldn't get out of fulfilling these types of moral responsibilities by paying for them -
Killing an animal [K utils]
Eating an animal [E utils]... and the cost of acquiring the animal is included in this
So, for a "vegetarian", the relevant information is that util losses from killing an animal outweigh util gains of eating one. In other words...
K+E<0
To want to eat meat, you need to make K+E greater than 0.
Now, you're essentially proposing paying some money in order to Save an animal. Let S be the utility generated from not Killing an animal, as a function of how much you money you Pay.
S = -PK-P
Now it is true that you can generate a net positive utility by Paying sufficient money to offset K+E, and that's why this intuitively seems like a good idea...
K+E+S > 0 if P is large enough...
But here is the problem: since K+E is a negative number, not killing and eating is always better than killing and eating. In math terms -
K+E+S < S
for all "vegetarians". Therefore, no utility-maximizing agent who is currently a vegetarian is going to choose to start eating meat and paying others not to eat it.
At best, if they value animal lives above all other causes they might donate to, they would continue not eating meat and also not pay others to eat it.
The only person who would eat meat and pay for others to not eat it would be a person who 1) valued meat more than animals 2) valued animals more than all other causes they could donate to. This would be a very small set.
Still - this approach does work for humans, for the purpose of guilt-alleviation. It would probably be a net good if people started doing it - it is akin to carbon offsets,.
I agree that killing a cow is K utils no matter who does it, but eating a cow is E_me utils if I do it and E_other utils if a stranger does it. If E_me > K > E_other, then my utility function supports paying for other people to not eat meat.
I notice that a large fraction of Effective Altruism people are vegetarian. This makes sense: in general Effective Altruists take moral issues seriously, even when that means changing your lifestyle. I'm not sure it's a good balance, though.
One way to think about this is to convert it into money. How much would I need to be paid to give up eating meat? All animal products? How much money would I need to spend on myself to be about as happy as I would be with less money but continuing to eat animals? I'd probably be willing to go vegetarian for about $500/year, vegan for maybe $2000/year.
It turns out you can probably pay to convince other people to be vegetarian much more cheaply than that. I estimate the cost of a vegetarian-year at $4.29 to $536 while Brian Tomasik estimates $11 with better methodology (which I looked at). This is by placing ads on facebook for a site where people can watch an animial cruelty video and ideally become vegetarian or vegan.
If you would get more than $11/year worth of enjoyment out of continuing to eat meat, why not give $11/year to convince someone else to not eat meat for you? Or give $50/year and be on the safe side?
(While you're giving money, you should probably give it to the organization that you think will do the most good with it, which I think is probably one of GiveWell's top charities. The nice thing about money as opposed to actions is that it's easy to redirect.)
I also posted this on my blog.