The perils of being a math teacher

[omorka]

So moontyger posted a Link of the Day, in the comments of which the Laffer Curve was referenced.

Now, I've just started a unit on polynomials, and we just covered the review of all the function stuff they had back in Algebra II, so when someone mentions that the Laffer Curve has only two points - they said "zero and 100," but they really mean (0, 0) and (1.00, 0), where x is the tax rate and y is the tax revenue - I started coming up with questions:

Does the Curve have, as commonly assumed by economists and neocons, a single maximum? Or does it have multiple local maxima? If there are multiple local extrema, how would we know whether we were at the abolute maximum point rather than a local maximum? How many parameters are we talking about?

Is this thing polynomial or rational? Is there an asymptote anywhere? A flattening followed by an asymptotic fall-off? Is it even really a function?

Is it differentiable? Again, how many parameters are we talking about? There might be a whole family of potential Laffer Curves, and we might not be able to tell which one we're on. This might be a three-dimensional function in two variables, x and t, of which a given Laffer Curve - dare I say a curve in the Laffer family - is merely a cross-section at some time t?

What if it's sensitively dependent on initial conditions? What if it's *gasp* fractal?

Is it even continuous?


Then, as all mathematicians find their hopes of finding a new result dashed early in their careers by the realization that Gauss proved their particular result at the age of 17 or some such, I discover that Martin Gardner beat me to it.

Darn. :-/

Comments

[princejvstin.livejournal.com]

Its hard to compete with Martin Gardner :)

[brezhnev.livejournal.com]

One of my pals (not sure if you've met him, but he goes by pastorofmuppets here) was going to grad school for economics. One of the things that disillusioned him was the stochastic factor -- the fact that there's an unknown fudge factor underneath it all made it all too fuzzy for his tastes ultimately.

Ireland's experiment with tax reduction turned out well, though they did end up with a good bit of inflation. But I imagine that it's not quite so neat as one can describe easily on a graph. We do have lots of data points, though -- the highest I've ever heard of was 80%, the upper bracket in Norway at least at one time, and (so I'm told) 90% in 1980s Yugoslavia. I'd imagine that if tax rates get too exorbitant, then anyone in the upper brackets is probably going to start working through the underground economy or move everything offshore.

[awbryan.livejournal.com]

Oh, that's so purrfect. I just met a woman who's a politically liberal economics major; she'll love this cartoon.

It illustrates the main problem with all of classical economics: the assumption that humans are rational actors just because that assumption makes the math work out nicely. Physics has a similar problem: we call it "approximating the cow by a sphere".

Neither system is very accurate :-P

[greeneyes-rpi.livejournal.com]

This post is so totally sexy.

:)

[bibulb.livejournal.com]

"...First, assume a perfectly spherical chicken..."