This document summarizes Ronald Coase's theorem on the allocation of resources between parties when transaction costs are zero. It discusses that Coase believed private negotiations between parties could lead to an efficient allocation of resources to address externalities, rather than relying on government intervention. It provides an example of how a factory and fishermen could negotiate an efficient solution to pollution without government regulation if transaction costs were zero. The document also outlines the assumptions of the theorem and provides analysis of an example case related to Coase's work.