Market failure in the case of a public good

Market failure and the public good. Market failure, in the sense used here, means that the market left to itself does not produce the efficient quantity of a good, so society could gain from a different quantity. A public good is both non-excludable (it is extremely hard to keep anyone from enjoying it) and non-rival (one person's use does not reduce what is available to others). If its supply is left to the market, it is provided in an inefficient quantity.

Why the market fails.

• No seller can charge users. A private seller earns revenue by refusing the good to those who do not pay. A public good does not allow this, since a non-payer cannot be kept out, so a seller has little prospect of covering the cost.
• Buyers wait for others to pay. Each person hopes to enjoy the good on others' payments. This is the free rider problem, and it arises from a positive externality: a contribution benefits others who do not pay for that benefit.
• People hide their true benefit. The benefit each person gets is not revealed through a purchase, and people may understate it, so demand for the good does not show up in the market. The government cannot read it from a price either.
• The result. The good is supplied too little or not at all, even when its total benefit to society is greater than its total cost. Society loses the excess of benefit over cost that the good would have produced.

Example: a flood-warning system. Our own example. A district in Assam could install river gauges and sirens to warn villages of rising water. Everyone within earshot benefits (non-excludable), and one family's hearing the siren does not reduce another's warning (non-rival). The total benefit in lives and goods saved is far above the cost. But no private firm could collect fees from each household, since a family that refused to pay would still hear the siren. So no firm installs it, and each village waits for another to pay: the market has failed, as a project worth more than it costs is not undertaken.

The remedy. Public goods are therefore provided by the government, which raises the money through compulsory payment and uses cost-benefit analysis to decide which projects are worth doing: a project goes ahead if its total benefit exceeds its total cost.

Conclusion. The market fails for a public good because non-payers cannot be excluded, so private sellers cannot earn revenue and buyers free ride. The good is under-supplied unless the government provides it.