The second welfare theorem and the core-equivalence theorem have been proved to be fundamental tools for obtaining equilibrium existence theorems, especially in an infinite dimensional setting. For well-behaved exchange economies that we call proper economies, this paper gives (minimal)...

It is well known from the work of S. Ross that a securities market is complete if and only if each call option can be replicated using available securities. The present short note announces the following surprising complementary result to Ross' important contribution. . If the number of...