Google got me this [0], which seems to fit what you want

[0] https://mpra.ub.uni-muenchen.de/901/1/MPRA_paper_901.pdf

there is some basic arithmetic in the article. imagine the cost was raised by $100, then prices of beans would be $101.5 and $103, i.e. pretty much everyone would go for higher quality. gradually decrease the premium, and you will gradually decrease the number of people who prefer the higher grade product in favor of lower price. this is pretty much it. quite simple and neat observation, actually.

"the harder the punishment, the harder the drug" is another very important non-trivial observation, missed by most people.

> quite simple and neat observation, actually.

Did you read my comment? That's exactly what I wrote. This is not a "theorem". Theorems live inside theories, they're logically implied by axioms of the theories. That basic arithmetic proves nothing of the sort.

Then it is a theorem, as it is tautologically implied by certain axioms imposed on preference relations or choice correspondences, such as completeness, transitivity and a notion of continuity.

Since the whole theory won't fit in one wikipedia article, I suggest you read the first chapters or either a) Mas-Collel, Whinston and Green or b) Kreps, Microeconomic Foundations I (not the old undergrad book from him)

This would provide you with the theory to understand this result in a more mathematical correct way.

"Theorems live inside theories" - sorry, didn't get that.

axioms: * given same price, consumer goes for higher grade product. * as relative price difference decreases, some consumers start going for higher grade product. * rules of arithmetic.

in any case, it seems that we have appreciation for different things. you prefer detailed verbosity, i prefer a simple idea that can be easily understood.

great and profound ideas are not necessarily complex, many of them are quite simple. let's keep them that way.