Children will be children, and Coase will always be Coase.

An article in the BBC News ( Selby School Cancels Outside Break In Row Over Noise ) reports that a school in North Yorkshire England has cancelled its afternoon outside breaks following neighbour's complaints to environmental health officials. The school has also put up a sound proof fence because it fears a noise abatement order.

So why are these parents so upset at the school for paying for such an expensive fence? If you ask an economist (ceteris paribus) they will tell you that the cost of the fence must have been exactly equal to or less than the cost of the noise abatement order. So in a sense, it was a pareto optimal solution for the school to bear the burden of the cost of the fence. The school is no worse off (they would otherwise have had to pay the more expensive noise abatement order), the children can still yell, and the neighbours can sit in peace.

They did. in fact, still cancel afternoon breaks. The Coase theorem tells us that when externalities are present, if we ignore transaction costs, bargaining can lead to an economically efficient allocation, regardless of initial property rights.

So no matter who has the right to a quiet neighbourhood here, a solution is possible. If the parents put such a high value on letting their children have outside breaks, they can finance more fencing, or pay for the neighbours to re-insulate their houses.

Cancelling afternoon breaks  tells us something about the school administration's value on afternoon play time. They must value it less than what they are willing to pay in order to compensate the neighbours during that time.

So the children sit inside.