On the boundary behavior of the excess demand function

I revisit thoroughly the standard boundary behavior satisfied by the excess demand function of a competitive economy, and I prove two implications of the boundary behavior. Then, I show that these implications lead to an alternative proof of the existence of competitive equilibria which is instructive, shorter and perhaps easier than the available proofs in the literature.

► Two implications of the boundary behavior of the excess demand function are proven.
► The implications lead to a new proof of the existence of competitive equilibria.
► The proof is shorter and easier than the existing proofs.
► The technique used in the proof is instructive from the pedagogical point of view.
► The technique is related to maximal elements and complementarity problems.