The famous economist Ronald Coase proposed the following possible solution to the problem of externalities: Say there is a factory which pollutes a river that provides drinking water to a local village. The government can allocate private property rights over the use of the river to one of the parties (either to the factory owner or to each of the local villagers), and then the respective parties can simply trade (buy/sell) the right to use the river. 

Is this an effective solution to the externality problem? Explain your answer.