Some Numbers

As the chart above shows, the population of California has more than doubled since the days of the 1960 Master Plan.* UCLA has become notorious for being hard to get into. What was UCLA's undergraduate enrollment back then? Yours truly poked around on the web and it turns out getting data on that issue takes some doing. I ended up looking at the Master Plan itself. That document gives data on the entire UC System as it was in 1958 and on total student enrollment. You never find undergraduates-only by campus. But with some estimating, it appears that UCLA probably had about 11-12,000 undergrads at most. It now has around 31,000 undergrads, so the undergrad population has come close to tripling. In short, UCLA undergraduate enrollment has outpaced overall population growth. Now, you would have to look at college-age population rather than total to get a more legitimate comparison. And you might want to look at the comparative growth of northern vs. southern California. And there is the sensitive issue of out-of-state admissions. But putting it all together suggests (to me, at least) that what has happened over the long-term is that a) more folks out of the general population want to go to college than was the case circa 1960, and b) UCLA's reputation as a desirable university to attend has gone up. If anyone out there has more to say about this matter, please add a comment.

I suspect there is some analogy to the freeways, which were also being expanded at the time of the Master Plan. When you first build them, there is lots of capacity and traffic flows freely. But since access is subsidized, they eventually fill up and become congested.
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*http://www.lib.berkeley.edu/uchistory/archives_exhibits/masterplan/MasterPlan1960.pdf