The purpose of this paper is to investigate the structure of the class of market excess demand functions which can be generated by aggregating individual utility maximizing behavior. Among the results are: (i) in a region of the relative price domain an arbitrary polynomial function can be generated as an excess demand function for a particular commodity, and (ii) for any p in the relative price domain, a given configuration of excess demands and rates of change in excess demand can be generated at p if and only if it is consistent with Walras' Law.