The most obvious answer is Coasian bargaining. What Coase showed in his famous "The Problem of Social Cost" is that if there are no transaction costs and if utility is transferable then it suffices to allocate property rights—i.e. to give one party the right either to engage in the externality-causing activity or to prohibit it. The two parties will then engage in bargaining with the result that the socially efficient level of the activity is undertaken. The idea is that if an activity has private value $v$, but imposes external social cost $c$ on others then
if the private individual has the right to participate in the activity then others would collectively be willing to pay up to $c$ to persuade him not to. This offer will be accepted only if $c>v$ so the activity takes place only if it is optimal.
if others have the right to prohibit the activity then the private individual would pay up to $v$ for them not to do so. This offer will be accepted only if $v>C$ so again the activity takes place only when it is optimal.
This example assumes a negative externality, but the same approach works in the case of a positive externality. For example, if the private benefit is $v$ (which may be negative if the activity is very costly) but there is an external benefit of $u$ then third parties would collectively be willing to pay up to $u$ to encourage the private individual to engage in the activity. Thus, the activity takes place only if $v+u>0$---i.e. exactly when it is efficient.
This solution is an important element of carbon trading schemes, which are one of the main ways that countries are attempting to tackle the problem of anthropogenic global warming.
The Coasian solution has the attractive feature that it is relatively decentralised (there is no need for a central planner to accurately determine the size of the externality). Although this solution appears to work very well, it has a couple of important drawbacks:
The zero transaction cost assumption is strong. This is particularly true when an activity imposes a small externality on a large number of people so that there is potentially the need for a large number of bilateral payments.
If the externality falls on a large number of individuals then paying a subsity creates a public good problem: each individual could try to free ride and hope that a large enough subsidy is paid by others.
The Coasian solution therefore works best when either
- the externality falls mostly on a single 'large' agent who can therefore engage in Coasian bargaining without the fear of free riding and only incurring transaction costs once.
- agents are able to use contracts, their government, or some other device to act collectively as if there were the single large agent in 1.