Notes

Why public good leads to market failure:
Firstly, public good is said to be non-rivalrous. Non rivalrous means that the consumption of one good by a person does not diminish the quantity available for another person. In the context of singapore, national defense enhances the overall security of the country. When one person enjoys the benefits brought about by national defense, he does not reduce the benefits to another person and national defense available for consumption remains unchanged regardless of the number of users.
Secondly, a public good is said to be non-excludable, which means to say that it is technically impossible to exclude anyone from using the good once it is produced. An example would be national defense. The social security brought about by a robust national defence system is shared by everyone within the nation, regardless of nationality or whether they pay taxes or not. A tourist would feel the same sense of security as a citizen who has paid 20 years worth of taxes. As such, national defense is non-excludable.
As a result of non-rivalry, no additional units of public goods need to be produced for additional unit of consumption since no units have been diminished. This results in the marginal cost for an additional unit of consumption to be zero.
For example, the cost expended to make 5 million people feel safe is the same as the cost needed to make 5.5 million people feel safe. In the traditional theory of firms, a firms's profit maximising output is where MC=MR. Since MC=0 in the case of non-rivalry, the condition would result in MC=MR=O. To achieve allocative efficiency, a rational firm would price its good at P=MC=0 in this case. It is not possible for private sector to supply the good if P=0 since private firms are assumed to be profit-motivated, thereby leading to a missing market.

The problem of non-excludability would lead to "free-rider" problem. Since there is no expression of demand, it is not possible to charge a market price for the good and hence, unprofitable for private firms to supply the pure public good. This is exemplified by the tourists who enjoy the sense of security from national defense without paying regular income tax. Since anyone can enjoy the benefits of a pure public good without paying for it, there will be an absence of a price signal and thus producers will not supply this good.

As a result, if public goods were left to the market, they would not be provided at all. There is hence a missing market for public goods, thus leading to complete market failure. The market has failed because no resources will be allocated to their production. As a result, consumers in the society will not get to consume the goods at all.