Characterizing the efficient points without closedness or free-disposability

Many multicriteria problems in economics and finance require that efficient solutions be found. A recent contribution to production theory established a characterization of efficient points under closedness and free-disposability (Bonnisseau and Crettez in Econ Theory 31(2):213–223, 2007, Theorem 1). However, as will be shown using a number of examples, these results cannot be applied to simple and plausible production sets, nor can they be extended to other classic multicriteria problems such as those arising in optimal portfolio theory and bargaining theory. To address these limitations, a reformulation of the above theorem without closedness or free-disposability is proposed. This enables efficient solutions for a wider range of multicriteria problems to be identified.