Final answer:
Option A, regarding the private sector not producing a sufficient military for defense, is an example of a public good leading to market failure, as the private market may underprovide non-excludable and non-rivalrous goods.
Step-by-step explanation:
The question concerns examples of market failure, which occurs when a free market economy fails to allocate resources efficiently, leading to negative outcomes for society. Among the listed options, one example of market failure is clearly linked with the definition and description provided in the reference material.
In this context, public goods are a well-recognized form of market failure because they are often not supplied in sufficient quantities by the market due to their characteristics of non-excludability and non-rivalry. Given the information about externalities, such as pollution, where the private market fails to consider all social costs and benefits, we can identify the correct example of market failure.
Option A, which concerns a country's private sector not producing a large enough military to stop invaders, is an example of a public good that is not being sufficiently provided by the market. The defense provided by a military is non-excludable and non-rivalrous, which are characteristics of a public good leading to the free rider problem and market failure. Therefore, the correct option in the final answer is A.