In economic surveys of households, many variables have the following characteristics: The variable has a lower, or upper, limit and takes on the limiting value for a substantial number of respondents. For the remaining respondents, the variable takes on a wide range of values above, or below, the limit. The phenomenon is quite familiar to students of Engel curve relationships showing how household expenditures on various categories of goods vary with household income. For many categories-"luxuries" -zero expenditures are the rule at low income levels. A single straight line cannot, therefore, represent the Engel curve for both low and high incomes. If individual households were identical, except for income level, the Engel curve would be a broken line like OAB in Figure 1. But if the critical income level OA were not the same for all households, the average Engel curve for groups of households would look like the curve OB. A similar kind of effect occurs under rationing of a consumers' good. The ration is an pper limit; many consumers choose to take their full ration, but some prefer to buy less.

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