This paper aims to provide a representation theorem for consumption stream in the simplex in continuous time, by using the weaker axiom of ”Agree with,” the strong axiom of ”Preferential Independence”, and the axioms of ”Separability” and ”Measurability” on the simplex,...

This work aims to provide a representation theorem for consumption in simplex in continuous time by using a weaker axiom of ’Agree with’, a strong axiom of ’Preferential Independence’,[10, 9], and axioms of ’Separability’ and ’Measurability’ on Simplex provided by Qin and...

We solve the problem of a social planner who seeks to minimize inequality via transfers with a fixed public budget in a distribution of exogenously given incomes. The appropriate solution method depends on the objective function: If it is convex, as in the case of the absolute mean deviation, it...