Quasi Linear Preferences and Coase Theorem

We must note that amount of smoke depends on assignment of property rights i.e. distribution of rights but there exists a special case where outcome of externality is independent of property right. If preferences are quasi linear then every efficient solution must have same amount of externality. This result in which outcome of externality is independent of distribution of property rights is known as Coase Theorem.
Hence, reallocation of endowment does not affect efficient amount of externality. It also implies that Coase theorem is valid only when income effect is zero which happens only in the case of non-linear goods i.e. when Preferences are Quasi linear.