We could all identify with the scene from “Peggy Sue Got Married,” in which Peggy Sue, transported back 30 years to her high school algebra class, tells the teacher (when he demands to know why she blew off a test), “Well, uh, Mr. Snelgrove, I happen to know that in the future, I will not have the slightest use for algebra. And I speak from experience.”
Well, today I needed algebra. And not Algebra I or II, but something I learned how to do in Algebra 5 (in Hawaii, they counted by semesters) or Analytical Geometry or Introduction to Calculus. Or maybe full-fledged Calculus. One of those.
I saw this Tweet from our anti-government friends at the SC Policy Council:
There is nothing “conservative” about a budget that’s grown nearly 40% over the past decade. http://bit.ly/1paA3HT #sctweets
So I immediately tried to calculate what that was annually. I knew it had to be less than 4 percent, but how much less?
I was pretty sure that I once knew how to set up an equation that would give me the answer, but I had no idea how to do it now. (I thought, Is this a “related rates” problem? I seem to remember that phrase vaguely. But no, I don’t think it is…)
So I guessed, trying several numbers that felt about right. And I found that adding 3.4 percent per year for ten years gave me an increase of a little under 40 percent. (I think I did that right.) So I replied to the Policy Council,
Or in other words, about 3.4 percent or so a year. That’s what you’re saying, right?
Now, I’ll grant you that 3.4 percent a year is nothing to sneeze at. That’s a healthy rate of growth, although not alarmingly high to your average observer.
However… I knew that that sounded WAY higher than what we actually experienced in SC over the last year. And I became immediately suspicious that the Policy Council wasn’t talking about state spending at all, but was throwing in increased federal spending — in other words, funds that our conservative Legislature was in no way involved in levying taxes to raise. So I followed the link, and I was right:
While the General Fund has only grown by 1.76 percent (again accounting for inflation), the bulk of budget growth has come from dependence on Other Funds (27.61 percent increase) and Federal Funds (36.77 percent increase). There is nothing “conservative” about an increasing budget, regardless of where the increases are coming from. Indeed, the budget is even less “conservative” now than ever since reliance on federal funds includes the loss of sovereignty by forcing the state to comply with the federal mandates attached to that funding. Moreover, there is nothing conservative about a budget that doesn’t return surplus money back to the taxpayers.
This reminded me of something that I didn’t realize about modern libertarians until I’d been exposed to Mark Sanford for several years.
I used to think that their objection was to paying for growing government. That they just didn’t like paying their taxes. And through the Reagan era and for a couple of decades after, I think that was to a large extent true — the supposed “pain” of paying taxes did indeed seem to lie at the emotional center of anti-government feeling.
But by the time we were done with Sanford’s battle to keep federal stimulus money out of SC, I had fully realized the extent to which the objection wasn’t to spending their money on government — it was to government itself. If a genie from a bottle made the wealth appear from thin air, the Sanford kind of libertarian would object to it being spent on government programs. Because of this quasi-religious belief that government itself, by existing, was an encroachment on the poor, beleaguered libertarian’s “freedom.”
Which reminds us once again that the policy council doesn’t want conservative government at all. It wants our legislators to be classically liberal.
Which is why, even if I remembered everything from every math class I ever took, I wouldn’t come up with the same answers the Policy Council does in trying to quantify “conservatism.”
The Legislature has been consistently “conservative” by the Reagan-era standard. They have held the line on taxes — cutting them at every turn — ever since Republicans first took over the House at the end of 1994. They have tightly contained the growth in funding sources that they control. And they’ve consistently starved essential functions of government to the extent that they’ve been at best marginally effective. (You can see this most dramatically when you look at our transportation infrastructure, but it’s true in the areas of education, law enforcement, public health, prisons, and so forth.)
But no, they haven’t quite shrunk it to the size that they’ve been able to drown it in a bathtub. Yet. And there are interest groups who won’t be happy until they succeed in doing that — no matter where the money is coming from.
Many years after completing my law degree, having fulfilled my undergraduate math requirement by taking symbolic logic in the Philosophy Department, I began to study psychology. Statistics was required, which required a significant background in math. I was glad I had taken through Calculus in high school, and even more that I married a mathematician.
You never know what you will need in the future, unless you are a work of fiction.
Seriously, though — how DO you set up an equation that will show how to calculate the annual rate that would give you an increase of just under 40 percent in 10 years? Or say 40 percent even, to make it easier?
So you say the budget 10 years ago was X. And you want to do ten operations that will arrive at an answer of 1.4 times X.
I found myself writing some pretty weird stuff trying to express that. So you start with X plus y/100 times X. And then you wrap that in parentheses, and you add to that an amount that is y/100 times that whole expression in parentheses again. And then you add to that y/100ths times the entire equation up to that point, wrapped in brackets…
Which just gets extremely unwieldy.
I think maybe there’s a sigma in it somewhere…
or an f for “function”…
Sigma is for adding a sequence of numbers. Let me aks the perfesser.
Or you can just Goal Seek in Excel. It’s far less brain-damaging than math.
The formula is ( (1+rate) to the 1/number of years)-1. (Sorry, typing on my phone so hard to write it). So it’s ( 1.4 to the .1 ) -1, or 3.42197 percent per year.
It’s similar to compounding interest on money and other related rate increase problems.
Yes.
Yes, that’s the ticket!
In Excel,
=RATE(10,0,-100,140,)
Gives you 3.422%
My peeps are wicked smaht…
Your other peeps may be wicked smaht. This just happens to intersect with what I do for a living, so I deal with these types of calculations all the time. Though, interestingly enough, when the problems get more complicated, we go back to using iterative methods, similar to what you did by hand (only we let the computer do the actual calculations of course).
Nice post, and you didn’t let the math or the rhetoric hide the underlying agenda.