| Sumario: | This article presents an elementary proof of existence, making use of special features of the excess demand functions when gross substitution is assumed. This assumption has been extensively used in investigating uniqueness and stability properties of competitive equilibrium. However, to the best of the author's knowledge, there has been no attempt to introduce this assumption in order to simplify the existence proof. Justification of the loss of generality of result by the transparency of the proof and the elementary mathematics involved; namely, that a continuous function over a compact set attains its minimum in the set. In essence it is a classroom note. The study of competitive equilibrium, and especially the proof of existence theorems in various market models, has played a central role in the development of mathematical economics. Yet the method of proving these theorems has remained uniform on the whole; the application of either a separating hyperplane theorem or a fixed point theorem.
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