One of the basic principles of economics is that, in most cases, allowing private parties motivated by personal greed and a motive for profit to make decisions makes for the best results. If you are trying to sell your car, and I'm attempting to buy said car, we can both get what we want by coming together and agreeing to a price for your car. No need for outside intervention; since we are both selfish people, we'll do everything we can to get maximize the benefits from our buying and selling.
However, not all transactions are limited to affecting only the participants. If our agreement has effects on others, others who are not part of the transaction process, we might end up making a decision that affects them and is NOT the most efficient outcome. Such an effect on outsiders to a financial transaction is known in economics as an externality, since these effects are related to those external to the financial transaction, the bystanders.
Externalities can be either positive or negative, depending on whether the bystanders benefit or are harmed by the transaction. Positive externalities include spillover benefits from advancing technologies. One example would be this blog; the Internet started as a way for the government to preserve information in case of an attack, back in the days of the ARPA-net, and now it's changed how we communicate and gain information.) Negative externalities are things like pollution, which affects many people who are not benefiting from the pollution-generating enterprises. (If it sounds like negative externalities are similar to the Tragedy of the Commons, well, they are related concepts; in both cases, the market fails because not everyone who is affected has a hand in making the decision.)
How are externalities resolved? Well, the easiest way is by having all the parties involved sit down to negotiate a solution that benefits everyone according to how much value they place on the solution. This is the heart of the Coase theorem, which states that when there are no transaction costs and trade is possible, a market-based solution to an externality is possible, no matter how the property rights are initially distributed. If a town is worried about pollution in a nearby lake, the townspeople can negotiate with the polluters and work out a solution that meets everyone's needs, perhaps by paying a stipend to the company if it is able to reduce pollution below a particular limit.
The Coase Theorem is one method of solving externalities, but it has its limits; high transaction costs (the expense of creating and enforcing a contract, for example), difficulty in performing a trade, or simply a large number of potentially affected parties with different ideas of what constitutes a solution can make a market based trade impossible. In such a situation, one solution is to internalize the externalities (usually through government action). Positive externalities can be internalized by allowing those who create benefits for outsiders to capture some of the profits, for example with patents that allow the inventors to market their new developments. Methods like pollution taxes enable negative externalities to be internalized, forcing a person or business that generate adverse effects on surrounding individuals to consider the costs of those adverse effects in the price of doing business.
Of course, not every externality can be so easily internalized. Take the effect of a property's condition on the neighboring house prices. A well-maintained, beautiful property can prop up the prices of other houses in the neighborhood, while a run-down or ramshackle house can drag down property values through out the neighborhood. But internalizing the effects of your house's condition on other houses would be difficult; unless you cut a check for all your neighbors next time you sell your house, there's few ways for you as an individual to motivate your neighborhood to keep clean and well maintained. Here again, the government can be a solution, rather than the problem. Passing ordinances requiring houses to be kept up to a certain standard of cleanliness is one way that governments are able to improve the results of the market.
The moral of the story: while the government is not always the solution, it can play a role in making the market work as efficiently as possible.
