Coase's theorem explains one way of solving market failure with regards to externalities. It states that the problem of externalities can be solved without outside intervention, if parties are allowed to bargain without cost. In order to understand what this means for the economy, it is necessary first to examine what externalities are, and furthermore, how and why Coase's theorem is a route to solving them.
An externality can be defined as the product of one party's action that affects another, such as noise, pollution, or research. Externalities can either be positive or negative in the way in which they affect others: the knock-on effect of technological research, for example, is a positive externality, as the new knowledge developed benefits the whole of society's quest for new technology. Air pollution is a negative externality as it affects the quality of life of the people who continuously breathe polluted air. Common to both examples is that the actor is not affected by the externality in the sense that the researcher recieves no added benefit for the knowledge contributed to society, and the polluter is not penalised for the negative effect that is being created. In this way, there is a difference to the cost or benefit to society as a whole of the action, and the cost or benefit to the private actor. The cost of polluting, for example, is higher for society as a whole, as many people suffer as a result of it. There is no market for pollution so the producer does not have to pay for it, hence the private cost being lower.
The situation in which externalities are not being taken into account is one in which the market is inefficient: it has failed to maximise benefit to buyers and sellers as it does not consider bystanders, whereas society does. It is therefore necessary to solve this inefficiency by dealing with the externality. This is done by changing the quantity of production. Naurally, as the free market does not consider externalities as they do not constitute part of that market, to change will not take place without some kind of incentive. These can be public - government orientated, or private. Public solutions tend to rely on either regulating output, such as a law on levels of pollution output; or using market-based policies - taxing and subsidising: placing a tax on pollution per unit would reduce pollution as the polluter now has to consider the value of pollution, so called "Pigovian taxes". This is similar to Coase's solution: that actors can come to an agreement between themselves to solve the externality. A polluter of a river which is regularly used downstream by anglers, for example, could be solved by the anglers paying the factory not to pollute the river, or alternately, the factory paying the anglers compensation for the pollution they produce.
The issue of who pays whom is decided by the "property rights" involved in the affair. These create the market for the exhange to take place: if the anglers own the river then the polluter owes them compensation for damaging their river. If the polluters own the river, then the anglers need to bribe them to stop polluting it so they can still use it. The negotiations would be redundent if neither party had any claim to a right over the river as the flow of money or otherwise could not be determined: this is often the situation in which government intervention is required to solve the externality, as clear property rights are required for Coase?s theorem to function properly. Of course it is possible that the externality would not be solved at all if the benefit of polluting the river was greater to the polluter than the value of what was offered by the anglers; however this would mean that polluting at that level is efficient. Coase's theorem has a second stumbling block when it comes to transaction costs. These are the costs of bargaining and making the agreement. It is necessary to have low transaction costs for the theorem to work, otherwise it is possible that the externality will not be resolved. High legal costs to resolve situation, costs of coordinating many parties - gathering many anglers together to bargain with the factory, for example; translation costs if the parties speak different languages and so on, all make it increasingly unlikely that the negotiations between actors actually take place.
It is thus demonstrated that Coase's theorem is not always appropriate to solve externalities: it can occur that property rights are not clearly defined in order for one party to bargain with another; or that the price of this bargaining itself is too high to make it worthwhile for the parties involved. In ideal conditions however, it is suitable for private parties to act in the way the theorem describes to solve the externality in the most efficient manner: moving the equilibrium of production or comsumption to the level most beneficial to society as a whole.