How public goods lead to market failure, with an example

What a public good is. A public good has two features:

• it is non-excludable: once it exists, keeping anyone from enjoying it is extremely hard, or too costly to be worth doing;
• it is non-rival: one person's enjoyment does not reduce what is available to anyone else.

What market failure means here. We say the market fails when buyers and sellers, left to themselves, do not arrive at the efficient quantity of a good. For a public good, a market supplies an inefficient quantity, which is why such goods are usually left to the government.

How the market fails.

1. A seller cannot make users pay. A firm covers its costs by selling only to those who pay. With a non-excludable good, a person who refuses to pay still gets the benefit, so a private seller cannot collect enough to cover the cost.
2. Each user hopes to ride free. A free rider is someone who enjoys a good's benefit while avoiding payment for it. Since she gains whether or not she pays, each person waits for others to pay. The root is a positive externality: what one person pays for benefits others who give her nothing in return, and she leaves that benefit out of her decision.
3. True benefits stay hidden. People have a reason not to reveal how much they value the good, for instance because the figure might be used to tax them, so demand for it does not show in any market.
4. The outcome. Too little of the good is produced, or none, even when its total benefit to the community is larger than its cost. Society loses the excess of benefit over cost. The benefit each payer gives others is an externality, a benefit to someone else for which no payment is received and for which no market exists.

Example: a flood embankment. Our own example and figures. A village of 500 households on the Kosi in Bihar would be protected from yearly floods by an earthen embankment costing ₹30 lakh. Each household values the protection at ₹10,000, so the total benefit is ₹50 lakh, well above the cost.

• Once built, it shields every house behind it, whether the owner paid or not (non-excludable).
• One family's protection does not reduce any other's (non-rival).

A contractor offering to build it for a fee of ₹6,000 a house would find that many households refuse, reasoning that if enough neighbours pay they will be protected anyway. If, say, 300 households pay, only ₹18 lakh is raised, the cost is not met and the embankment is not built. A project worth ₹50 lakh to the village, against a cost of ₹30 lakh, is lost: the market has failed.

When the failure can be avoided.

• Compulsory payment. If every member must pay a set share, nobody can ride free. Governments do this through taxes and use cost-benefit analysis, going ahead when total benefit exceeds total cost. Here the state could build the embankment from taxes, since ₹50 lakh exceeds ₹30 lakh.
• Exclusion becoming possible. Where new methods allow non-payers to be cut off, a market can supply the good, as happened when private firms began to charge ports for lighthouse services and could switch the light off if a port did not pay.

Conclusion. Because a public good is non-excludable, users cannot be made to pay, each waits to ride free, and the benefit others receive goes unpriced. The market therefore produces less than the efficient quantity, as with the unbuilt embankment, unless payment is made compulsory or exclusion becomes possible.