This article reconsiders the theory of existence of efficient allocations and equilibria when consumption sets are unbounded below under the assumption that agents have incomplete preferences. It is motivated by an example in the theory of assets with short-selling where there is risk and...

We address the fundamental issues of existence and efficiency of an equilibrium in a Ramsey model with many agents, where agents have heterogenous discounting, elastic labor supply and face borrowing con- straints. The existence of rational bubbles is also tackled. In the first part, we prove...