ENGEL CURVES Entry for The New Palgrave Dictionary of Economics, 2nd edition

An Engel curve describes how a consumer’s purchases of a good like food varies as the consumer’s total resources such as income or total expenditures vary. Engel curves may also depend on demographic variables and other consumer characteristics. A good’s Engel curve determines its income elasticity, and hence whether the good is an inferior, normal, or luxury good. Empirical Engel curves are close to linear for some goods, and highly nonlinear for others. Engel curves are used for equivalence scale calculations and related welfare comparisons, and determine properties of demand systems such as aggregability and rank. An Engel curve is the function describing how a consumer’s expenditures on some good or service relates to the consumer’s total resources holding prices fixed, so qi = gi (y, z), where qi is the quantity consumed of good i , y is income, wealth, or total expenditures on goods and services, and z is a vector of other characteristics of the consumer, such as age and household composition. Usually y is taken to be total expenditures, to separate the problem of allocating total consumption to various goods from the decision of how much to save or dissave out of current income. Engel curves are frequently expressed in the budget share form wi = hi [log(y), z] where wi is the fraction of y that is spent buying good i . The goods are typically aggregate commodities such as total food, clothing, or transportation, consumed over some weeks or months, rather than discrete purchases. Engel curves can be defined as Marshallian demand functions holding the prices of all goods fixed.