The problem of public goods. What is a “public good”? Without going into technical details, as a first approximation a public good is something which provides benefits to people even if they did not voluntarily contribute to producing it. Or, to put it slightly differently, a public good is something which, if produced, is difficult to exclude people from consuming. The classic example is national defense. Suppose national defense was paid for by voluntary contributions rather than taxes. The national defense that was provided by this means would benefit those people who did not contribute, not just those who did. Public sanitation and public health, public broadcasting, clean air, education, and many other things have this character. Some of these may also provide private benefits to particular individuals: education does provide specific benefits to those who receive it, but it also contributes to higher overall economic productivity which benefits the society as a whole. And here is the problem: in general, the level of public goods provided through unconstrained free capitalist markets will be far below the socially optimal level.
A few examples will make this clear. Suppose that education was only provided by the market. Private firms offered educational services and parents would buy these services for their children’s education. There would be no subsidies and no public provision. In such a world, a large proportion of poor people would fail to get even minimal education. Or consider public health and sanitation. Suppose that sewers, water treatment and human waste disposal were provided only by the market; there was no public provision of these services. This would be a disadvantage even to those who could afford those services, since poor sanitation would be a breeding ground for diseases that would affect everyone. Markets are good at producing things in which most of the benefits are captured by those who directly pay for the good or service, but not public goods whose value is diffuse to a wide variety of people. Markets will underproduce public goods, and this is inefficient.