Thursday, February 3, 2011

Say I have Four Numbers...

"I have four numbers..." Call them N, D, R, and T.

I know that N/D=R.

And I know that T is close in value to R, perhaps a little above or a little below.

Let me take as an example N=12 and D=3. Then R=4. And T is close to 4, so, maybe 6.

Now I create a new number X such that N/X=T.

In my example, T > R. Therefore (N/X) > (N/D).

I think -- I'm out of school a long time now, but I think that if N/X > N/D, then X/N < D/N.

And I think I can multiply both sides of the inequality by N, so X < D.

So, if T > R then X < D. And conversely, if T < R then X > D.

N is the numerator: Gross Federal Debt.
D is the denominator: Gross Domestic Product.
R is the ratio N/D: Gross Federal Debt as a Percent of GDP.
T is my exponential trend value, calculated to be very close to R for the years 1955 through 1973.

This line

So, if T > R then X < D. And conversely, if T < R then X > D.

means:

If the Exponential Trend value is more than the "Gross Federal Debt as a Percent of GDP" value, then my value X -- which is the Gross Hypothetical Product or GHP -- is less than the Gross Domestic Product. And conversely, if the Exponential Trend value is less than "Gross Federal Debt as a Percent of GDP" then GHP is more than GDP.

In other words, it means that if this graph shows the two lines crossing:

then this graph also must show the two lines crossing:

But it doesn't.