In "The Problem of Social Cost", Coase (1960) used a simplified conception of property rights as the outcome of mere contracting in independent exchanges. This conception has been suitable for successfully analyzing many important issues, including that of externalities related to the use of assets and public goods. However, its implicit assumption that exchange in property rights does not affect future transaction costs provides an inadequate basis for understanding property institutions and has caused confusion on the efficacy of private ordering and the role of the state and legal institutions. It has thus limited the scope of most of the economics of so-called property rights to analyses of political interactions and contract rights in personal exchanges. In the real world, property is defined by interaction between multiple exchanges which cause exchange-related non-contractible externalities among market participants. When such exchange-related externalities are considered, property becomes inherently linked to public and legal interventions, which are indispensable to reach true property—that is, in rem—enforcement and truly impersonal—asset-based—exchange.