In the insurance market, information asymmetry can lead to adverse selection and moral hazard. Adverse selection occurs when those seeking insurance have better information about their risks than the insurance company. For instance, a person with a known health issue might be more inclined to buy health insurance, leading insurers to face higher than expected claims. Moral hazard arises post-insurance purchase, where the insured party might take on greater risks because they know they're covered. For example, someone with car insurance might drive more recklessly. Both these issues can lead to higher premiums for everyone and might even result in insurers exiting the market if they can't accurately price the risks.

Public goods and common resources are both non-excludable, meaning it's difficult to prevent people from using them. However, they differ in terms of rivalry. Public goods are non-rivalrous, meaning one person's consumption doesn't reduce its availability to others. Examples include street lighting or national defence. On the other hand, common resources are rivalrous; one person's consumption reduces the amount available for others. Examples include fisheries or forests. Overconsumption can lead to the 'Tragedy of the Commons', where individuals, acting in their own interest, deplete or degrade the common resource.

The free-rider problem arises when individuals benefit from a good without paying for it, especially prevalent with public goods due to their non-excludable nature. Governments can address this in several ways. Direct provision and financing through taxation is a common method. Since everyone pays taxes, the government can use this revenue to provide the public good, ensuring its availability to all. Another approach is regulation, where the government sets rules or standards for the provision and consumption of the good. Lastly, governments can sometimes convert the public good into a club good, where access is restricted to paying members, though this isn't always feasible or desirable.

Setting the 'right' level of tax or subsidy is challenging because it requires precise knowledge of the external cost or benefit associated with the externality. Governments need to determine the exact difference between the social and private costs or benefits, which is often difficult due to the dynamic nature of markets and external factors. Moreover, measuring the magnitude of externalities is complex, especially when they have long-term implications or affect large populations. Additionally, political pressures, lobbying, and other non-economic factors can influence the decision-making process. Lastly, unintended consequences might arise from the intervention, necessitating further adjustments.

Governments, despite their best intentions, might not always succeed in correcting market failures due to various reasons. Firstly, there's the issue of imperfect information. Governments might not have complete or accurate data to make informed decisions. Secondly, political pressures and lobbying can lead to policies that favour certain groups over the greater good. Thirdly, administrative costs and bureaucracy can make interventions inefficient. Lastly, there's the risk of government failure, where the intervention itself causes a new market failure or exacerbates the existing one. For instance, a subsidy meant to boost a certain industry might lead to overproduction and resource misallocation.