For Public Goods, however, my use, consumption or enjoyment does not deny you the use, consumption or enjoyment of the good - we are not rivaling each other for the use of the good (or service), so they are non-rival in consumption. An example is a football game or theatre performance - where, if anything, the more people who are enjoying or watching the performance, the greater the enjoyment of each person. So, how might we think if the total demand for a football game or theatre performance? Instead of adding up the quantity (1 or the length or the performance, game) for each person, we need to add up the price each person is willing to pay for the performance - we add up individual demands vertically, up the price axis, accumulating then total amount the audience is willing to pay for the same performance.
This example, however, illustrates that "non-rivalness" is not the only characteristic which separates public goods from private goods. In these cases, it is simple and easy to exclude people from the game or performance - we can stop people who have not paid from getting into the ground or theatre, and exclude them. For a public good, however, this is not possible - public goods are non-excludable as well as being non-rival. Examples include street lighting, lighthouses, national defence, public health (cleaner air, disease control etc.,) radio and TV broadcasts [though note here that it is possible, though expensive, to exclude people - or at least fine them if they do not have the appropriate receiver license), and, importantly, the natural (or urban) environment. There are also such things as public bads - pollution is the classic example, which we will deal with below.
The market problem of public goods and a possible solution.
Why is the non-excludable characteristic a problem? Because if private (non collective) companies or organisations cannot charge people for their use, how are they going to raise enough revenue to pay the costs of providing these public goods? They cannot, other than relying on charitable (altruistic) donations from people who care about these goods. So, a simple-minded economist (who believes that people only do things for their own narrow self-interest) might argue that these public goods can never be provided by a free market. An "economically rational" individual would not spend hard earned income on public goods, since s/he would reason that others will provide the good anyway, and cannot exclude him or her from consumption or enjoyment once they do, so there is no point in contributing - better to "free-ride" on other (less economically rational) peoples' charity. If everyone behaved like this, no-one would get any public goods.
There must be something wrong here, though. People do organise themselves to provide for at least some public goods. The lighthouses in the UK are run by Trinity House, which is an independent (private) organisation, paid for by contributions from mariners. The Royal National Lifeboat Institution (RNLI) is similarly a private charity supported solely by voluntary donations. Public service television stations in the US also exist and are succesful on the same principle. A lot of people are not quite so narrow-minded and stupidly selfish as the purely self-interested economically rational man - thank goodness.
Nevertheless, free-riding is a problem for many public goods. Unless everyone is forced to make a contribution (through taxes), the chances are that less of the public good will be provided than is socially optimal - that is, less than everyone is really willing to pay for the good, and hence a smaller or lower supply of the good than everyone really wants. Thus, many public goods are paid for and provided by the Government, through coercion on the public's (yours and my) behalf. What do we mean by socially optimal?
Imagine, as a simple case, two people (households) interested in getting streetlights put into their private street (of just two houses). Both households have their own ideas about how much they are willing to pay for this common (public) service. One household (the most interested) could discover how much streetlighting would cost, and realise that it alone was not willing to pay the full amount. It might then approach the other and ask for a contribution towards the total cost. What would be the outcome of such negotiations?
The following diagram explains this and shows how (honest) negotiation between people could provide for the right amount of the public good that people want. This diagram may look seriously off-putting - but it is really quite straightforward - spend a little time and thought following through the explanation in the boxes - just get your brains into gear! The outcome is that both households each contribute what they are willing to pay for street lights, and the combined amount is enough to cover the costs of supplying the amount (number) of streetlights that both households (collectively) are willing to pay for. This is socially optimal for this community of two households. If the costs were greater than the households willingness to pay, then too many street lights would be provided. If the costs were lower than the combined willingness to pay, then too few lights would be provided, since the users are willing to pay for more.
The major problems with this concept of voluntary collective negotiation for the supply of public goods should be obvious (with a little thought). The solution requires that all the people interested in and benefiting from the public good are fully committed to the idea of collective action, and recognise that the solution will not work if people free-ride. This might be expected amongst a relatively small and coherent community (such as mariners for lighthouses and the RNLI for instance). Otherwise, as with the Royal Society for the Protection of Birds (RSPB), which (among other things) buys or rents wildlife reserves for the conservation of birds and thus related environments - as public goods -with voluntary donations and subscriptions, the organisation must put up with the near-inevitability that there will be substantial free-riding. Although the RSPB can, of course, exclude all but it own members from particular wildlife reserves, the general public cannot be excluded from the general good of encouraging wildlife. The National Trust is another example, albeit helped by the Her Majesty's Treasury in that large estates or country houses etc. can be left to the National Trust in lieu of estate duties, which would otherwise accrue to the Treasury as taxes.
Although the formal logic of this solution suggests that each contributor will pay a different price according to their own willingness to pay, the difficulties with this differential solution in practice normally result in a standard contribution (membership fee, annual subscription etc.), though always allowing for the seriously altruistic or enthusiastic to contribute more if they like.
In some cases, it may be that a particularly rich or concerned member of the public might be prepared to pay for the public good on their own. This would follow from the above diagram if Dy intersected the supply curve (at C=MC=AC) - then the intersection would indacate the quantity Y would buy on his/her own, without support from the rest of the community. There is one classic case of this - the American media tycoon Ted Turner was so impressed with public service broadcasting (PSB, no adverts) that he bought his own PSB station in his home city of Atlanta. Once he had done so, of course, he was able to raise additional voluntary contributions from other residents, and thus extend the quality of the service. But this is a non profit making enterprise.
In general, however, for many public goods (National Parks, Environmentally Sensitive Areas, Areas of Outstanding National Beauty, national defence) it has been considered that the problem of free-riding is too great, and these public goods are provided by the Government and paid for out of general tax revenue, to which everyone is obliged to contribute according (roughly) to their means.
The issue here is that the market mechanism is capricious in the income (and wealth) distribution that it generates between people. The accidents of birth, personalities, family circumstances and local conditions all combine with the operation of the market system itself to ensure that incomes are never equal. Although most governments seek to rectify this somewhat with social security and progressive taxation systems (where the rich are supposed to pay more than the poor), the fact remains that some people will be richer than others, and thus have a generally greater willingness to pay. Social justice and equity demand, however, that some things are too important to be left to the market (even given that the poor are supported through income supplements of various sorts).
There are, however, some clear overlaps between merit goods and public goods. Some of our public goods (especially, perhaps, the natural environment in the form of National Parks etc.) are also considered to be merit goods. Our major merit goods (health, education) also have public good aspects - the better educated and the more healthy the population, the better-off everyone is, regardless of the indivudal level of health or education of each of us, simply because the economy and society is likely to work and perform better.