Engel curve

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By tabulating data from a survey of Belgian working-class families, Engel (1857) was the first to show that a household’s expenditure on food and other items depended on its income or total expenditure. The graphical representation of this dependence, particularly as it appears in cross-section data, soon became known as the Engel curve. Efforts to demonstrate its relevance to other countries met with considerable success; for a centennial review see Houthakker (1957). Although discovered at a time when economists thought in terms of price rather than income, the Engel curve gradually came to be recognized as a cornerstone of demand analysis. The Keynesian consumption function may be considered an extension of the Engel curve; it is outside the scope of this article. In what follows the basic relation will be written$$ {x}_i={f}_i\left(y,z\right), $$where x i is a household’s expenditure (in money terms) on the i th commodity, y is some indicator of the household’s overall resources, and z stands for a vector of other variables influencing x i . Engel curves may be conveniently characterized by the income elasticity, which is the partial derivative of log x i with respect to log y. Expenditure items are called luxuries, necessities and inferior goods depending on whether the income elasticity is greater than 1, between zero and one, or less than zero. In general these elasticities are not independent of income, however, and an item may be a luxury in a certain income range and a necessity or an inferior good in another. The extensive research on the Engel curve, which became active after the emergence of econometrics in the 1930s, will be reviewed under four headings: the dependent variable x i , the independent variable y, the mathematical form of f i , and the nature of the catchall variable z.