Long term supply curves are different than supply curves. They are similarly named, but different concepts.
Supply curves measure supply at a price.
Long term supply curves measure market equilibrium supply as demand changes over time.
The elasticity measurement is the derivative of supply with respect to price. It cannot be applied to long term supply curves.
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You seem to compare different models of supply in demand, each based on different assumptions, and each expected to work on different time scales, and declare one of them "incorrect". Presumably what you mean by a more "correct" model is that it explains existing data and predicts future events better than the alternatives. If so, one should take your outline, make it into a proper simulation, plug in the available data, tweak the free parameters to match, then check if its predictions match the data not used to calibrate the model. Only after that you will have an argument for correctness. And only then, say, make a recommendation to the EA community re ways to decrease farm animal production.
To be fair, this bias towards theorizing instead of modeling and testing is a common pitfall of this community. I find it pretty disappointing, but maybe it's just me.
What do you recommend if good data is too costly to collect?
I think that if someone has made a claim but failed to use good data or an empirical model, it should not require good data or an empirical model to convince that person that they were wrong. Great if you have it, but I'm not going to ignore an argument just because it fails to use a model.