- Non-excludable: You cannot stop anyone from using the good.
- Non-rival: If you use the good, it is equally available to others who want to use it as well.
Examples: Street lights, national defense
How public goods are a form of market failure
If a public good is provided to a market, e.g. national defense, the social benefits are greater than the private benefits, creating a positive externality (notes on positive externalities can be found here, as are the notes on merit goods which cause positive externalities of consumption, or you can take a look at separate merit goods notes. Also, you can take a look at negative externaility if you want, only try not to confuse yourself! See here). This means that people know that the benefits to them if they join the army is that the country can be at an advantage during war. However this is the same benefit people will receive if they don't join the army, so people are inclined not to join the army because the cost is too high (risk of death) and there are mutual benefits to those who have joined with those who haven't. This is called the free-rider problem. People benefit from goods/services that they haven't paid for. This is market failure because there is no market incentive for people to join the army, or for the private sector to provide national defense.
Public goods can be a form of market failure if the price mechanism breaks down. If the provision of street signs and road signs requires people to pay (i.e market provision), some people will pay and some people won't (free rider problem). Businesses providing road signs will not check who has and hasn't paid because too many people are benefiting from them (due to the properties of a public good, see above). Thus by the creation of a positive externality, the private sector does not see it profitable to continue providing road signs, leading to market failure.
Government provision of public goods financed through taxation. This ensures everyone pays for it and everyone benefits from it.