Epistemic status: extremely rough model, please don’t take too seriously, just trying to get ballpark estimates which someone might correct me on
It seems like there are a few considerations here:
Would this create a restaurant which would otherwise not exist, or a restaurant which would sell more meals than it otherwise would if it were in a different location?
If so, how many extra animals would be factory farmed?
For (i), if the rent you can get for a restaurant is higher than for a non-restaurant business then it seems like the market is implying the “best” (financial) use of the space is as a restaurant, suggesting the answer to (i) is at least in part yes.
For (ii), this suggests 12-15 sq ft per diner and assuming 70% of the area is dining space you get approx 300 diners at one time. Lets say 1000/day at capacity. If they eat more meat than they would at home (intuitively I guess they would but this is small, i can’t find any source on this).
Lets imagine you get an extra 100 people/day eating out once from this decision, and they eat 25% more meat than they otherwise would. Then the average person in the US eats 100kg of meat a year or 270g/day. An extra 25% is about 60g or about 0.06 chickens, 0.001 pigs or 0.0003 cows (based on numbers I got from a quick google) so you get ~2100 extra chickens, ~11 extra cows or ~35 extra pigs a year. If the restaurant is a chicken restaurant then this is clearly much more weighted towards chickens, and in fact if it causes people to eat chicken if they would’ve eaten beef at home, this is an underestimate. Let’s use 2100 chickens for now.
There are not very precise estimates available for how effective animal interventions are, but this by Rethink Priorities in 2019 suggests corporate campaigns such as those by the Humane League saved 120 chickens per dollar from broiler cages (with extremely wide error bars). If subsequent campaigns are 10x less effective (I don’t know what a good estimate is here but I’d guess future campaigns will be less effective than past ones as they hit diminishing returns) then you get 12 per dollar, or 2100 chickens with better quality of life for $175. If you think non caged lives are 10% better than caged lives this would be more like $1750 to offset the harm I estimate here.