There are relatively few known demand systems that are theoretically satisfactory and practically implementable. This paper investigates building more complex demand systems from simpler known ones by considering sums and products of basic utility functions, an approach that does not seem to have been exploited previously in the literature. Some of the systems that result are interesting and usefully extend the range of available functions. Even the simpler systems that are not sufficiently flexible for the analysis of real world consumption data may still be useful for applied general equilibrium studies and for theoretical explication. Although some systems, instead of being new, turn out to be rediscoveries of already known ones, the way in which they arise as combinations of simple components is of interest in itself in showing them as sub sets of wider classes.
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