Borch's theorem, equal margins, and efficient allocation

The economic concept of margin guides or justifies the sharing of risks and resources. Broadly, by Borch's theorem, competing claimants, ends or users ought see equal margins along any efficient allocation.However helpful this maxim, its application is often hampered, and occasionally misguided, by concerns with the differentiability of objectives-or with the interiority of solutions. Circumventing such concerns, this paper introduces a quite applicable, generalized notion, called essential margin.Presuming transferable or quasi-linear utility, the coincidence of such margins supports efficiency, competitive equilibria, and core solutions. The said coincidence also defines deductibles and prioritized claims, seen in finance and insurance.