The US library system far supposes India's. There would a few library's near me without public funds. But, most of them would shut down so an equivalent private option does not actually exist.
Is it the cheapest way to prevent crime? Is a leading question. Where I live we spend a lot of money on a wide range of things from beat cops to parks and street lights that prevent crime. And library's provide many other services than just crime prevention.
A more realistic question might be; Assume 10% of their useful function to me was crime prevention would reallocating 10% of their funding to something else above and beyond what we already spend on it prevent more crime? And the answer to that question is no.
PS: In theory we might be able to say use subliminal messages to prevent crime more cheaply. But, of the options that are actually being considered Library's are surprisingly cost effective.
No, the issue isn't their useful function, the issue is their public benefit.
The cost/benefit to evaluate public subsidies is (public benefits) / (public costs). If 90% of the benefits of a library are gained by the users, then it's highly likely that this will be negative.
In such cases, a mixed model is best - i.e., if 10% of the benefits are public, 90% private, then a 10% subsidy for libraries might be justified.
But, Public Benefit always = Sum of all Private Benefits. You may be thinking direct benefit vs external benefit, but as everyone utility functions are separate their share of the public benefit is different. I specifically mentioned my personal cost (as a share of the public cost) and my personal (indirect) benefit to help clarify the issue, but I think you missed that point.
Cost and benefit are also independent. It possible for a Polio vaccine to provide 100,000 times the public benefit relative to it's cost (eliminating a disease for all time can easily be worth vaccinating people on the other side of the planet). Research can also easily have that magnitude benefit ratio's.
And (public benefits) / (public costs) is only negative if public benefits or public costs are negative you might be thinking Benefits - Costs but that does not really fit the rest of your equations either. Anyway, the idea that public subsidy's should not exceed the ratio of (individual benefit) / (public benefit) sounds good until the public benefit exceeds the cost at which point there is little for an individual to pay the costs.
PS: There is a reason people get PHD's in economics it's a lot more complex than you might think. Just consider adding different levels of diminishing returns to all of those cost benefit equations and your still barely scratching the surface.
Is it the cheapest way to prevent crime? Is a leading question. Where I live we spend a lot of money on a wide range of things from beat cops to parks and street lights that prevent crime. And library's provide many other services than just crime prevention.
A more realistic question might be; Assume 10% of their useful function to me was crime prevention would reallocating 10% of their funding to something else above and beyond what we already spend on it prevent more crime? And the answer to that question is no.
PS: In theory we might be able to say use subliminal messages to prevent crime more cheaply. But, of the options that are actually being considered Library's are surprisingly cost effective.