Public Goods: Public goods are goods and services that are non-excludable (it is impossible to prevent people from consuming the good, even if they don't pay for it) and non-rivalrous (one person's consumption does not diminish the amount available for others). National defence clearly exhibits both of these characteristics. It's impossible to exclude anyone from the protection offered by a nation's armed forces, and one person's safety doesn't reduce the safety of others.

External Benefits: External benefits occur when the consumption of a good or service benefits someone who is not directly involved in the transaction. National defence generates significant external benefits. A strong defence protects not only the country that spends on it but also potentially protects trading partners, allies, and even global stability. These benefits are not reflected in the private cost incurred by the nation.

Why Market Failure Occurs: Because national defence is a public good, the free market will under-provide it. Individuals have an incentive to be 'free-riders' – benefiting from the defence without contributing to its cost. This leads to a situation where the quantity of national defence provided is less than the socially optimal quantity. The market fails to allocate resources efficiently because the private benefit to an individual is less than the social benefit.

Monopoly: A monopoly exists when there is a single seller in a market, and there are no close substitutes for the product. This gives the monopolist significant market power to control the price.

Market Failure due to Monopoly: A monopoly leads to market failure for several reasons:

• Higher Prices: A monopolist will restrict output and charge a higher price than would prevail in a competitive market. This means consumers pay more for the good or service.
• Lower Quantity: The monopolist will produce a lower quantity than would be produced in a competitive market. This means there is less of the good or service available to consumers.
• Reduced Consumer Surplus: Consumers experience a reduction in consumer surplus because they pay higher prices and have access to a smaller quantity of the good or service.
• Inefficient Resource Allocation: Monopolies tend to be less efficient than firms in competitive markets. They have less incentive to innovate and reduce costs because they face less competitive pressure. This can lead to resources being misallocated, as the monopolist doesn't have to respond to consumer demand signals as effectively. The monopolist may also restrict output to artificially inflate prices, leading to a deadweight loss – a loss of economic efficiency for society.

In summary, a monopoly results in a loss of consumer welfare (due to higher prices and lower quantities) and an inefficient allocation of resources, both of which are characteristics of market failure.

The non-provision of a public good results in a misallocation of resources because the market mechanism fails to allocate resources efficiently. Public goods, by definition, are non-excludable (it's impossible to prevent people from benefiting) and non-rivalrous (one person's consumption doesn't diminish the availability for others). This leads to a situation where the private sector is unwilling to provide these goods because they cannot easily charge for them and therefore cannot generate sufficient revenue to cover the costs.

As a result, resources that could have been used to produce the public good are instead allocated to other, potentially less valuable, uses. This represents a misallocation. For example:

• National Defence: Without government provision, resources (e.g., skilled labour, capital) might be diverted to private industries, potentially leaving a nation vulnerable to external threats. The benefits of national defence are enjoyed by everyone, so a market-based approach would under-provide it.
• Clean Air: Businesses might pollute the air because they don't bear the full cost of the pollution (the cost to society). Resources used in polluting activities are misallocated away from cleaner production methods. The social cost of pollution is not reflected in the price of goods produced.
• Street Lighting: Without government intervention, private companies would struggle to profit from providing street lighting because everyone benefits regardless of whether they pay. Resources would be misallocated to more profitable ventures.

The government's role in providing public goods is crucial to correct this market failure and ensure resources are allocated in a way that maximizes overall societal welfare.