A community league operated in the neighbourhood in which I grew up. It was funded by the families living in the neighbourhood, and had a number of functions. One of them was to operate an outdoor skating rink each winter. Particular time slots were made available to figure skaters, hockey players, and recreational skaters, but if you were prepared to change into your skates outdoors, you could use the rink just about any time. This rink would certainly seem to fit the description of a congestible public good.

Some parents would also construct smaller rinks in their backyards, so that their younger children could skate without having to walk to the community rink. Since skating alone isn't much fun, these children generally had the company of other neighbourhood kids. Arguably, these parents were providing for their own benefit a good which had positive externalities for neighbouring families.

These projects are intrinsically very similar, and yet we do not hesitate to categorize one as a public good and the other as a good with positive externalities. We hope that the distinction between these two goods is a useful one, and indeed our analyses of the two goods have been quite different, but this example suggests that we might be making strong distinctions between quite similar goods.

One might argue that the backyard rink offers distinctly different benefits to the family that builds it than it does to other families, and that it should therefore be categorized as a good with externalities.

The theory of the second best states that if all of the distortions in the economy cannot be eliminated, all bets are off. Eliminating or reducing another distortion might raise welfare, but can just as easily reduce welfare. For example, Samuelson recognized that the optimal quantity of a public good would not be characterized by the Samuelson condition if the public good were financed through distortionary taxation. This condition assumes that expanded provision of public goods is costly to consumers only in that it requires scarce resources to be transferred from the production of other goods. However, if the production of public goods is financed through distortionary taxation, providing more public goods is also costly because it increases the amount of revenue that the government must raise, and hence increases the deadweight loss of the tax system. The optimal quantity of a public good when taxes are distortionary is generally (but not always) smaller than that dictated by the Samuelson condition.

This chapter looks at two important illustrations of the theory of the second best: the design of the tax system, and the pricing of goods produced by a regulated or government-owned monopoly.

OPTIMAL TAXATION

Every tax system that raises a significant amount of revenue will impose a deadweight loss upon the economy. The system that raises the required revenue with the smallest deadweight loss is said to be “optimal.”