Intertemporal Time Preference on a Simplex in Continuous Time

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, consistent with the spirit of Koopman’s work between 1960 and 1972, and Epstein’s work in 1983 and 2003. We consider a model containing discontinuous trajectories on the simplex, which is another departure from previous research because it is a subset of the product space with an empty interior