A public or collective good is defined as a good that is �non-rival�. This means: consumption of it by one person does not reduce the amount available to be consumed by others.

(The 'original' definition of Public Good by Samuelson ('The Pure Theory of Public Expenditure', Review of Economics and Statistics xxxvi nov 1954) is this:

each individual's consumption of such a good leads to no subtractions from any other individual's consumption of that good ...

hence 'it differs from a private consumption good in that each man's consumption of it, X12 and X22 respectively, is related to the total X2 by a condition of equality rather than of summation. Thus by definition X12 = X2 and X22 = X2.')

Eg. Bridge crossings, TV broadcasts. 'There is no limit to the number of sets that can costlessly tune in'. (F. Bator 'The Anatomy of Market Failure', Quarterly Journal of Economics 1958 - which goes into all these different types in great detail.)

Some, but not all, collective goods are also �non-excludable�. This means that if the good is provided, everyone in the group consumes it. It is not possible to exclude any individual from consumption. (Sometimes this is called a 'pur public good').

Eg. the perenial light-house example. All ships passing the lighthouse will see the light. So although someone who funds a light-house to protect their ships, gains from it; they don't get a competative advantage over anyone else. So the incentive is much reduced.

(See more on FabulousMonstersOfEconomicDebate/FundingLightHouses)

On the other hand, the TV broadcast could be made into a excludable public good which can be limited by eg. satellite subscription or pay-per-view.

The Public Good Problem is the problem of lack of incentives to supply the good.

In general, it is costly to produce a public good. Agents must 'contribute' by paying costs of its production. However, once a number of contributors have produced the good, there is enough of it for everyone to enjoy, whether or not they have contributed.

The common form of the problem involves non-excludable public goods. If you can consume the public good even if you haven't contributed, the best thing to do is consume but not pay the costs of contributing. (FreeRiding.)

Another form of the problem may still occur even with excludability. The 'market solution' to the pricing of public goods is to charge consumers according to their 'willingness to pay.' If this cannot be readily observed, consumers can misrepresent their willingness to pay. Misrepresentation games can also lead to inefficient provision.

CommonResources are not public goods, though they share many features and are often confused. (You're right Phil).

It seems the two problems of Commons and PublicGoods are sort-of mirrors of each other. Commons no one explicitly creates, but everyone destructively consumes. PublicGoods someone has to explicitly create but everyone non-destructively consumes. In both cases problems arise due to there being a disconnection between the payment and use. – PhilJones

Aside : I'd just like to award Darius a prize at this point for being the first guest to refactor a page from ThreadMode to EssayMode. :-) – PhilJones