Question

Two individuals have different demand functions for a public good. Explain how to find the aggregate demand for that public good. How does government provision of public goods solve the free rider problem?

Answer 1

The aggregate demand for a public good is found by vertical summation of individual demand curves (instead of horizonatal summation as in the case of private goods). The individual demand curves show the price someone is willing to pay for an extra unit of each possible quantity of the public good. Due to vertical summation of individual demand curves, the market demand curve for public goods gives the price society is willing to pay for a given quantity. Thus the aggregate demand for a public good is the sum of marginal benefits to each person at each quantity of the good provided.

A public good is a good that is both non-excludable and non-rivalrous. This means that individuals cannot be effectively excluded from its use, and use by one individual does not reduce its availability to others. Consumers can take advantage of public goods without paying for them, that is, people have an incentive to let others pay for the public good and then to “free ride” on the purchases of others. This is called the free-rider problem. If too many consumers decide to free-ride, private costs to producers will exceed private benefits, and the incentive to provide the good or service through the market will disappear. The market will thus fail to provide enough of the good or service for which there is a need.

The key insight in paying for public goods is to find a way of assuring that everyone will make a contribution and to prevent free riders. A common solution to the problem is for governments to impose taxation to fund the production of public goods. Thus the government provision of public goods solves the free rider problem as governments can enforce mandatory tax collection and use the revenue to provide public goods.