In response to my "Tamerlane" post, commenter Josh writes:
How are schools public goods?
Good question. I will give you the answer that I gave in my Public Finance field course.
Schools are public goods because of their function as jails. Young boys who are not closely supervised by their parents will tend to form violent gangs; the violence perpetrated by these gangs imposes costs that spill over into every segment of society and the economy (go watch the movie City of God for a demonstration of how this works). By forcing boys into a structured environment for most of the day, public schools keep them off the street, creating huge spillover benefits for third parties. Schools are therefore a public good. Incidentally, this is why your junior high probably felt like a state prison - it was one.
BUT, the public good-ness of schools is not why we spend a lot of government money on them. We spend government money on schools because of an incomplete markets problem.
Human capital is extremely valuable. Some people estimate the return to human capital investment as being around 15% (good luck getting that return from your retirement account!). But human capital suffers from an incomplete markets problem, because the crucial time frame for the purchasing of human capital (i.e. childhood) comes at a time when the owner and main beneficiary of the capital (i.e. the child) is not legally empowered to make his or her own investment decisions. Since as a toddler you can't possibly pay to educate yourself, anyone who does end up footing the bill for your education will probably end up not seeing a positive return on their investment. So if education is purely private, we will probably end up with a lot less human capital investment than is optimal (or than your grown-up self will wish you'd received as a toddler).
Note that this incomplete markets problem, though not a public goods problem in the classic Lindahl-Samuelson sense, nevertheless looks a lot like one. The transaction between whoever pays for your early childhood education (the govt., your parents, the Catholic Church, etc.) and whoever provides the education (teachers) has very important benefits to a third party (you). So it's a similar kind of issue.
What are the solutions to this incomplete markets problem? Well, we could solve it the Coasian way, by giving some older person(s) - e.g. your parents - the right to the proceeds from your future labor. But this would mean you would be born into slavery. It is therefore a solution that society, and also a large number of libertarians, will be unwilling to accept. (Note for all you sci-fi economists out there; when "superbaby" technology comes around, parental rights will be a much bigger and more uncomfortable issue!)
The modern solution to the incomplete markets problem has been to have government step in and buy little kids an education. We've fixed an arbitrary cutoff for legal adulthood (albeit one that we now know is loosely supported by science), and we've decided that before that cutoff, the government will invest in your human capital. So far, the system of universal public education has been a resounding success, and has probably been a huge factor in the development of rich modern economies. It's not hard to see why. Before universal public education, there were some private schools, but most parents opted to keep their kids around the house to do labor for the family. It was a perfectly rational equilibrium. Socialization of education solved the incomplete markets problem and created the vast literate workforces that undergird every moden nation's prosperity.
So I hope that answers the question.
As a final note, I want to point out that this is just one more reason to be wary of the modern American libertarian movement. The philosophy has never had a good answer to the question of children's rights. And yet the question of whether or not the government and/or or your parents can make you go to school is of crucial importance to the wealth of nations...and hence of crucial importance to our ability to guard our future liberty against Tamerlane.
Update: Lots of EconLog love today. Arnold Kling asks why government needs to provide education instead of just subsidize it. My answer: No reason in principle, but in practice government contractors seem quite hard to monitor. David Henderson says that innocent kids shouldn't be sent to prison/school. My 12-year-old self certainly agreed with him...but society fears gangs more than it loves perfect child liberty. Henderson also asks why people are more willing to vote for public schools than they are to pay for them. The answer to this is simple: people gain a lot from other people's kids being educated, since systemic underinvestment in education makes the country as a whole much poorer (and thus lowers parents' real wages). So they agree to pay taxes to have their kids educated, as long as everyone else does so as well, and the net benefit they receive is far more than if only they themselves were paying to have their own kids educated. So government solves a coordination problem, similarly to the public goods case.