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The aim of this work is to examine the feasibility of applying the Economic Analysis of Law (EAL) to the institute of private property in Brazil in order to achieve efficiency in allocating assets to the hands of those who value them most, and also to promote sustainability, sustainable development and social welfare in the mould of the social function of property. To this end, the study addresses the development and concept of the Economic Analysis of Law, the various Schools of Thought, the economic instruments that are the foundations of EDA, Sustainability and its Dimensions, as well as the relativisation of private property and its social function in the light of Economic Analysis. Finally, it can be seen that by applying the Economic Analysis of Law to private property in Brazil, the clear definition of property rights means that the asset is allocated to the hands of those who value it most, thus promoting efficiency, sustainable economic growth and social welfare along the lines of the social function of property.