Existence, uniqueness and determinacy of Arrow–Debreu equilibria in finance models

We characterize the Arrow–Debreu equilibria of a pure exchange one good economy where agents have additively separable utilities. It is then shown that under gross substitution hypotheses on utilities (or if relative risk aversion is smaller than one), the excess utility has gross substitute properties. Uniqueness of equilibria thus follows. It is finally proved that generically equilibria are determinate.