Thanks so much for putting this together! I hadn’t thought of the cross-price elasticity effects across types of animal products, but of course it’s an important thing to incorporate.
Two extensions of this sort of analysis that I would be interested to see:
Are there any important cross-price elasticity effects between animal and non-animal (including non-food) products? For instance, if the worst type of meat is beef, as you estimate, then it could be good to buy products that use the same inputs as beef—a type of grain that grows best on the types of land suitable for cattle, say—because that will push up the price of beef and push people into less harmful meat products. (It makes sense that cross-price elasticity effects would tend to be largest within kinds of meat, but other products may still worth considering, if this hasn’t already been done.)
Just as the substitution effects across kinds of meat are presumably stronger than between meat and other things, the effects are presumably strongest within brands of a particular animal product. That is, maybe buying (less in-)humanely raised chicken or environmentally (less un-)friendly beef pushes up the price of that product in general, which causes people to consume less of it, leading to an improvement overall, even though the purchased product itself still does net damage. How much would these within-product considerations change things?
Obviously there’s no end to the possible extensions, until we have a complete model of the entire economy that lets us estimate the general equilibrium impact of switching from one product to another. But maybe there are a few more elasticities that would be relatively important and tractable to consider.
I did estimate high cross-price elasticity effects between free range and cage eggs. If you add other free range/humane products to the spreadsheet then you will have to estimate CPE effects with this sort of thing in mind. The model has capacity for it, just add more rows and columns in the matrices and interpolate the formulas. You can also include different plant products if you like, but I think you are really just adding needless complexity and noise at that point, those differences seem small and nearly impossible to estimate. I lumped all plant products together with average emissions and the assumption of equal-or-nonexistent elasticity effects.