There are two things that have come up during the debt limit battle that deserve some mathematical analysis, and as a former math professor, I'm just the guy to do them for you.
First is the discovery by someone -- trumpeted yesterday by none other than our Hero of the Revolution Rush Limbaugh -- that the CBO would score a ten year clamping of spending at last year's level as a $10T cut in spending over ten years.
Now here's the mathematical theorem: some such fact is the unremarkable consequence of the need to allow for inflation in budgeting processes -- something everyone should do in their own budget -- and assuming some initial spending. The particular value of $10T over 10 years is a mathematical consequence of assuming 3% inflation and the current spending of $3.7T.
A mathematical result is one that is true because you can check it for yourself, so in this case you can either trust me or "Do the math!" Here's an outline of the proof: no matter what spending you assume for last year, letting it increase by an inflation of 3%/year will result a total increase in spending over ten years of a little less than three times that value. Assuming the base is $3.7T gets you a $10T inflationary increase in spending. Cap spending at last year's level and that increase is what you do away with.
Note that every single proposal to cap spending -- even Colorado's famed Taxpayer Bill of Rights (TABOR) -- uses a base like a state or national domestic product that will increase due to inflation, just as every calculation every businessman does about the future is corrected for inflation, sometimes by using the "constant dollar" assumption.
To put it another way -- and this is much more important -- if you hold spending constant for the next ten years, while the GDP increases by 3%/year, spending falls from it's current 25% of GDP to 18.5% of GDP, a very desirable goal.
That's the mathematics. The politics of holding spending constant one year at a time for each of the next ten years are another thing entirely.
The second fact is something no one else has said throughout this entire battle.
Here it is: if you want the deficit to shrink to a very small amount while tax rates remain constant and growth is restored -- or under any other economic assumptions for that matter -- all you have to do is to cut spending every year by your favorite fixed fraction of the increase in the debt.
If you do that every year, then the deficit heads toward zero in a number of years equal to 1 / (your favorite fixed fraction). That's a formula which means divide one by your favorite fraction. Your calculator knows the way. If you get "low battery" you made a mistake.
For example, if you insist that the spending for the next ten years be cut by an amount equal to any debt ceiling increase, then you are cutting next year's spending -- the only year that matters -- by one tenth of the debt increase, and, assuming constant revenue and that you have the will to do that each of those years, the deficit will decline toward zero over ten years.
In other words, John Boehner and the House Republican's opening salvo in the debt limit battle back in May -- spending cuts equal to any debt limit increase -- was exactly the right plan to balance the budget in some number of years. They couldn't have sold the period as one year, or three, or five, so the discussion has naturally settled on the CBO ten-year budgeting period, just as I predicted it would months ago.
The proof? Oh,... well,... it appears I'm out of time today, so I'll have to leave that as exercise for the reader.
I told you I was a former math professor.
