1. Assume that you've got a population with varying levels of natural academic/intellectual ability. Hard to imagine, I know. But bear with me.
2. Assume that N% of the age-appropriate members of that population attend college.
3. Let x be the number of Professors needed to teach classes to that N%. Within certain variation limits, we can imagine that x is a function of n that is not inverse in any way, so that the more students you have, the more professors you require.
4. Now, while there will be some latitude, generally x will be drawn exclusively from some definable upper reach of the population in terms of academic/intellectual ability. Let's define that reach as the top Z%.
5. This population will also want high school teachers. But while some of those high school teachers will come from the top Z% (remember, there's some latitude there because not all smart people become professors), the range from which the high school teachers is going to be drawn is going to be much larger. Let's call that the top Y%, where Z>Y. Now because teaching college is, in general, such a better lifestyle choice than teaching high school, HS teachers are generally going to be drawn from the range between the top Z% and the top Y%. So the two general rules are (with exceptions, of course):
1. Professors come from the top Z%.6. So that's our baseline. Now let's assume that somewhere along the line, it is decided that everyone should go to college. That's unrealistic, of course. But let's imagine that the push results in a tripling of n. So now we're sending 3N% of the age-appropriate population to college.
2. Teachers come from the top Y%, but generally from the range between Y% and Z%
7.An increase in n is going to require an increase in x. So x will go up as well.
8. The relationship between x and Z%, however, is going to be inverse in some way or another. The more professors you need, the "deeper" into the intellectual bullpen you need to go. So as x increases, Z% is going to DECREASE by some amount, call it B.
9.As Z% decreases, the number of people in the gap between Y% and Z% decreases. So unless more of those people start teaching high school (and why would they? they've got other jobs already), in order to keep the same number of high school teachers, Y% is going to have to drop as well. Because the distribution of academic/intellectual ability is somewhat normal, the decrease will be smaller than B. Let's call it A, where (A < B). So two new rules:
1. Professors come from the top (Z-B)%.Conclusion: The more college professors you employ, the lower the range of academic/intellectual ability from which you must hire your high school teachers. In other words, as college demand expands, it eats up the good instructors who would otherwise be teaching high school.
2. Teachers come from the top (Y-A)%, but generally from the range between (Y-A)% and (Z-B)%
We can plausibly imagine that similar effects take place with respect to junior high school and elementary school teachers.
So am I crazy?