One of the most important developments in recent applied economics has been the increased availability of data on large samples of individual households, particularly in the United States. Although the analysis of such data poses formidable problems of its own, it is possible, at least in principle, to apply the microeconomic theory of the preceding chapters. If, however, as is frequently the case, the data are available only for aggregates of households, there are no obvious grounds why the theory, formulated for individual households, should be directly applicable. The transition from the microeconomics of consumer behavior to the analysis of market demand is frequently referred to as the “aggregation problem.” Aggregation is seen as a nuisance, a temporary obstacle lying in the way of a straightforward application of the theory to the data. In this view, the role of aggregation theory is to provide the necessary conditions under which it is possible to treat aggregate consumer behavior as if it were the outcome of the decisions of a single maximizing consumer; this case we shall refer to as that of exact aggregation. These aggregation conditions often turn out to be stringent, which has tempted many economists to sweep the whole problem under the carpet or to dismiss it as of no importance. Some economists, indeed, see for example Hicks (1956), have held the view that microeconomic theory has greater relevance for aggregate data, arguing on largely intuitive grounds that the variations in circumstances of individual households average out to negligible proportions in aggregate, leaving only the systematic effects of variations in prices and budgets.