You don't need a larger building when there are less people in it, and you don't need more teachers when there are less students.
The argument you described is very different from mine. Mine is more like "schools say books are worth $10, but the prices of books raise to $11. Nevertheless, schools continue buying books"
If you don't believe this, there's data on the subject of minimum wage increases and percent employment. Look at this comment and my explanation below it: