I will not take your bet but will offer you the opposite one--that the proportion will be not less that 10% HIGHER.
I believe that your signalling theory is correct, but woefully
incomplete. The demand for higher education is driven by a combination
of motives, including at least:
1. Education (human capital model)
2. Quality signalling (your model)
3. Credentialing (union card model)
4. Social signalling (status seeking model)
5. Consumption 1 (learning for its own sake model)
6. Consumption 2 (4-year party model).
Motive 1 has declined in relative (not absolute) importance as the
proportion of youth attending college has grown. (See Charles Murray.)
Motive 2 is very important but easy to exaggerate.
Motive 3 is even more important than 2. A 4-year degree has become
the While Collar Union Card: you can't get a "good" job without it,
regardless of how much you know or how good you are, and regardless of
how effectively you otherwise signal...
Motive 4 is also very important. As a 4-year degree has become the
prerequisite for a middle class career, it has also become the marker
for middle class social status.
Motives 5 and 6 are less important, but not to be overlooked.
All of these sources of demand tend to grow, along with technology
growth, income growth, and the usual downward diffusion of social
So, since I've added 4 sources of demand growth to your 2, I'll bet on the high side.
Care to take that bet?
Motive 3 is important for government (and possibly private non-profit) jobs; otherwise I don't buy it. But even so, a 10% gain is roughly what I expect, so I don't want to take this bet. I'll bet against you if you say that percent of 18-24-year-olds enrolled in 4-year institutions will rise by 20%.