Failure of the free market system means that the market mechanism is unable to allocate scarce resources for social benefit.
Factors cause Market failure
Externalities
Imperfect competition
Imperfect information
Non provision of public goods
Inefficiency in the provision of quasi public goods
Provision of demerit goods
Public Goods
Public goods are the goods and services which have not affected the consumption of one person by the consumption of another person and there is no competition in consumption in which the consumption can not be avoided for non payment.
Since a price cannot be changed and a profit cannot be obtained from public goods, they are not provided by a market system.
Quasi Public Goods
Quasi public goods are the goods and services from which non payers of the price can be restricted though there is no competition in consumption.
Merit Goods
Merit goods are the goods in which social benefits are higher than the private benefits.
Ex:
Education
Health services
Sanitary services
Demerit Goods
The goods and services in which social benefit is lower than the private benefit are demerit goods.