Talk:Laffer curve/Archive 3
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unused illustration
There seems to be an unused resource: https://wiki.riteme.site/wiki/File:Neo-Laffer_curve.svg which nicely illustrates how the real "curve" would be wildly more complex. It seems it could compliment the similar plot that's already in the section: #Use_in_supply-side_economics (which lacks a visual reference to the "curve" presumption the article is nominally about). DKEdwards (talk) 01:22, 24 November 2019 (UTC)
Trivial information with complicated language
I wonder whether we need this passage:
- Under the assumption that the revenue is a continuous function of the rate of taxation, the maximum illustrated by the Laffer curve is a result of Rolle's theorem, which is a standard result in calculus
Yes, a standard result indeed. It effectively says that a curve between two points has a point (or several points) where it takes a maximum value. That should be thought self-evident by any non-mathematician once they understand the question.
Mathematicians think: "Hm. That seems to be trivial, but are there cases where it is not true?" And the point for them is to prove it also for the weirdest of cases. Economists seldom bother even to discuss why they think the function can be regarded as continuous (which it mostly isn't, strictly speaking).
Citing mathematical theorems in the intro makes many readers think that the article is about a complex technical term, not the simplifying pedagogic aid it is. All of the points in the article should be understandable with no training in mathematics beyond the basics.
- The reference to Rolle seems inapposite, given that the hypothesis of that theorem is differentiability on the open interval, not mere continuity. Perhaps economists do assume that the function is differentiable, but if so, then it is necessarily continuous, and continuity is all that is needed, by the Extreme Value Theorem. Heck, even continuity can be dispensed with: all that is really needed is boundedness: Economists understand that more cannot be taken in taxes than is generated in income, even if governments sometimes do not. There must be a maximum by the Least-upper-bound property, if it's not at 100%, it must be somewhere else.
- Of the two citations, I cannot find a full text version of Gahvari, Firouz available to me, so can't comment on it. The linked page of L.H. Meyer is so garbled that I can't consider it a reliable source, on this point at least. First, you don't need to assume that G'(0) > 0 - you can have a perfectly fine Laffer curve with G'(0) = 0, or even undefined. The required (additional) assumption (beyond the hypotheses required for Rolle) is that G(t) be > 0 for some t in the (open) interval. Secondly the reference to b being "infinity" is unclear at best. — Preceding unsigned comment added by 93.97.176.246 (talk) 02:42, 11 March 2020 (UTC)