Some goods can switch between being public goods and being private goods depending on the circumstances. For example a fireworks display is a public good if performed in a town with many residents. Yet if performed at a private amusement park, such as Disney World, a firework display is more like a private good because visitors to the park pay for admission.
Another example is a lighthouse. Economists have long used lighthouses as an example of a public good. Lighthouses mark specific locations so that passing ships can avoid treacherous waters. The benefit that the lighthouse provides to the ship captain is neither exclusive nor rival in consumption so each captain has an incentive to free ride by using the lighthouse to navigate without paying for the service. Because of this rider problem private markets usually fail to provide the lighthouse that ship captains need. As a result most lighthouses today are operated by the government.
In some cases, however lighthouses have been closer to private goods. On the coast of England in the 19th century for example some lighthouses were privately owned and operated. Instead of trying to charge ship captains for the service, however the owner of the lighthouse charged the owner of the nearby port. If the port owner did not pay the lighthouse owner he turned off the light and ships avoided that port.
In deciding whether something is a public good, one must determine who the beneficiaries are and whether these beneficiaries can be excluded from using the good. A free rider problem arises when the number of beneficiaries is large and exclusion of any one of them is impossible, if a lighthouse benefits many ship captains it is a public good. Yet if it primarily benefits a single port owner it is more likely to be a private good.
The difficult Job of cost benefits Analysis:
So far have been that the government provides public goods because the private market on its own will not produce an efficient quantity. Yet deciding that the government must play a role is only the first step. The government must determine what kinds of public goods to provide and in what quantities.
Suppose that the government is considering a public project, such as building a new highway. To judge, whether to build the highway it must compare the total benefits of all those who would use it to the costs of building and maintaining it. To make this decision the government might hire a team of economists and engineers to conduct a study, called a cost benefits analysis the goal of which is to estimate the total costs and benefits of the project to society as a whole.
Cost benefits analysts have a tough job. Because the highway will be available to everyone free of charge there is no price with which to judge the value of the highway. Quantifying benefits is difficult using the results from a questionnaire and respondents have little incentive to tell the truth. Those who would use the highway have an incentive to exaggerate the benefits they receive to get the highway built. Those who would be harmed by the highway have an incentive to exaggerate the costs to them to prevent the highway from being built.
The efficient provision of public goods is, therefore intrinsically more difficult than the efficient provision of private goods. When buyers of a private good enter a market they reveal the value they place on it by the prices they are willing to pay. At the same time, sellers reveal their costs by the prices they are willing to accept. The equilibrium is an efficient allocation of resources because it reflects all this information. By contrast cost benefits analysts do not have any price signals to observe when evaluating whether the government should provide a public good and how much to provide. Their findings on the costs and benefits of public projects are rough approximations at best.
Source: Principles of Economics.