It's amazing what can be accomplished if nobody cares who gets the credit.

Saturday, November 20, 2010

On math

Not too many people like math, I think. It can be opaque sometimes, very hard to understand even for somebody who is "good at math," quotes read aloud, would you kindly. Even harder than the abstract concept of math as something you do in a class, from a textbook, sometimes while drinking, is the application of mathematics to real life.

Economics is a strange intersection of mathematics and human psychology, or perhaps macro-scale sociology. If politics is America's favorite sport, then economics is America's favorite part of America's favorite sport. On the internet, it's not a rare thing to hear a call of, "read an economics textbook," to indicate that somebody thinks their opponent doesn't know anything about it. (I rank this right up there with "most Americans think" as a way to disguise the phrase "I think"). The truth is, very few people know anything about economics, economists included. If it's the intersection of social science and mathematical science, it's definitely near the social science border. It is, to say the least, inexact, and anytime anybody tells you, "I read an economist who was positive that xxxxxx," that economist is lying. Being positive of anything in economics is a good indicator of overconfidence and little else.

That is what baffles me about the new rallying call, which states that the only way to fix the deficit is to cut taxes. The argument is that if taxes are lower, people spend more, the economy grows, and we collect more in revenue. There is some precedent for this: In southern Ireland, in 1997, a reduction from 40% to 20% of the capital gains tax resulted in a huge increase in revenue, almost 300%. Of course, those of us with analytical minds may seek to ask, "what else was happening around that time," and indeed, there was a credit bubble present in the country at the time, but even so, the dramatic impact of this move cannot be denied, and it seems clear that to some greater or lesser degree, the tax rate does impact revenues collected, and it is possible to lower the tax rate and increase revenue.

However, here is where math enters. You cannot simply say, "lower taxes result in increased revenues," because this language implies that this is always the case, and that there is therefore a linear relationship between taxation and revenue. This is absurd. Were this the case, the government would achieve the highest revenues at a 0% tax rate, which mathematically simply does not work. (Any amount of money multiplied by 0% is 0.) Similarly, it cannot be argued that higher taxes result in higher revenues, because this implies another linear relationship, in which a 100% tax rate produces the highest possible government revenues. This is also absurd. (If all money leaves the economy due to taxes, then there is no economy, which means there is no flow of money, which means there are no taxes collected.)

Clearly there must be a more complicated relationship between taxation rates and government revenues, which means that any such relationship must be modeled using a polynomial equation whose degree is AT LEAST two. (For those of you who don't know math: a 2nd-degree polynomial is a quadratic equation, wherein the highest exponent to which the variable is raised is 2, for example x^2+2x+1). This, in fact, represents an economic concept known as a laffer curve. While the specifics of the laffer curve are frequently debated, the idea that there is a point of taxation which will minimize burden and maximize revenues should not be surprising. The curve is not as simple as a 2nd-degree polynomial, and finding the "sweet spot," the very top of the curve, where dr/dt = 0, will more than likely never occur, (we would need an extended period of economic stability, and we would have to play with the tax rate every year, adjusting everything just so) but it is for this that we should strive. Saying that "more taxes increases/decreases revenue collected," is a drastic oversimplification of the matter, and is not at all how we can or should effectively pursue this debate. An in-depth discussion of historical precedent, into which is incorporated notes about the current levels of saving versus spending, and how increased or decreased taxation is likely to affect them, as well as a discussion about who would be least and most impacted by any adjustment in taxes, and how this would impact the economy as a whole, is necessary. Saying that you know exactly what will happen if you increase or decrease the tax rate, just as saying you know exactly what will happen in any economic situation, is simply wrong.

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