This note provides an intuitive and simple proof of the existence of equilibrium in an incomplete ffnancial economy with numeraire assets, when the preferences are represented by concave, strictly increasing functions..

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...