On the relation between the equilibrium set and the demand functions

It is shown that, in pure exchange economies, the individual demand functions can be recovered from the equilibrium set regardless of the way we evaluate wealth. Following Balasco (2004), the demand functions do not have to be differentiable, not even continuous nor utility maximizing. Thus, the set of equilibria does not necessarily carry the structure of a manifold. Further, it is proved that the inner product structure is redundant in the sense that the result holds true even if wealth is being evaluated by means of a more general function on the price commodity space satisfying minimal requirements.