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So you and Gunz are right that investing in education is a good idea. The issue is who should be doing the spending. Try as I might, I can't come up with any convincing arguments for why an auto mechanic, soldier, or construction worker should have to pay for my kids to attend college.
The auto mechanic, soldier, and construction worker don't benefit from living in a society with a higher standard of living both directly and indirectly?
Pointing to spillover benefits without taking their magnitude into account isn't very helpful.
Say I'm considering a project that won't do me any good, but will generate $100 worth of benefits to the community. In a case like that, it makes sense for the government to heavily subsidize this project. Otherwise nobody would do it and society would lose out on the potential benefits.
By way of contrast, suppose instead that I'm considering a project that will generate $100 worth of benefits to me personally, and $1 worth of benefits to the community. There's still a good case for subsidizing this project a little bit, but it would be silly to suggest that the government should pick up most or even a significant part of the tab.
Going to college or a tech school is much more like the second case than the first. Nobody has ever said "I'm not going to blow four years going to college -- I'd rather just free ride off those who do." People go to college because they know that they stand to reap very large personal gains from doing so. To the extent that my education benefited others, that's more than already covered by federal and state financial aid programs and direct state support for public universities. What Obama is proposing goes light-years beyond any possible appeal to positive externalities and is just a transfer to the middle class.