What's the relationship between public goods and externalities?

Public goods and externalities are both concepts in economics that deal with market inefficiencies.

Public goods are commodities or services that are provided without profit to all members of a society, either by the government or a private individual or organisation. They are characterised by two main properties: non-excludability and non-rivalry. Non-excludability means that once the good is produced, no one can be excluded from using it. Non-rivalry means that the use of the good by one person does not reduce its availability to others. Examples of public goods include street lighting, public parks, and national defence.

Externalities, on the other hand, are the indirect effects of consumption or production activity that affect the welfare of a third party, and are not reflected in market prices. They can be either positive or negative. Positive externalities occur when the consumption or production of a good causes a benefit to a third party. For example, the education of an individual can benefit society as a whole, as it can lead to lower crime rates and higher productivity. Negative externalities occur when the consumption or production of a good causes a cost to a third party. For example, pollution from a factory can harm the health of people living nearby.

The relationship between public goods and externalities lies in the fact that they both represent situations where the market fails to allocate resources efficiently. In the case of public goods, the market may fail to provide them at all, as private firms may not find it profitable to do so. This is because they cannot exclude non-payers from using the good, and one person's use of the good does not reduce its availability to others. In the case of externalities, the market fails to account for the full social costs or benefits of production and consumption, leading to overproduction in the case of negative externalities, and underproduction in the case of positive externalities. Therefore, both public goods and externalities often require government intervention to correct these market failures.