Merit goods
Merit goods are also things that are 'good' for you, but unlike public goods they can be provided privately. The problem is that if they are provided solely by the private sector then they tend to be under-consumed, so, again, the government has to step in to correct the market failure.
The best two examples are health and education. Both of these goods can be provided privately. Some of you may be at a private school (or independent school, as they are called), or your family may have a private health insurance scheme. But, if the government did not step in and provide state schools and the NHS, then numerous families would not be able to afford either. This would cause increased crime and reduced productivity from an underclass of the non-educated, and increased health problems which can also cause problems for the labour market.
There may also be another section of people who can afford to pay for, say, health insurance, but just feel that it is a waste of money. They are young, fit and healthy - why bother? Of course, if they get knocked down by a bus they need the cover pretty quickly, but it is too late. Also, if they have survived the bus and feel they need cover as they get older, they may find that the premiums are higher than they would otherwise have been, or they are not covered for various ailments they have picked up on the way (like a bad back, for example).
In other words, people find it difficult to think long term. A £30 a month premium may seem a lot when you're young and healthy, but it will save you a lot of money over the long term.
Pensions are another example. Although the UK is moving towards a system where everyone has to think of putting something away privately, many people don't start until they are in their 40s, and this is often too late. The earlier you start, the longer your initial premiums have to grow with the stockmarket. So, because 'pensions' tend to be under-consumed, the government