Engel's Law

Engel's law is the name that has been given to a robust relationship between income levels and expenditure on food first discovered by the German statistician Ernst Engel. In its most basic form, Engel's law states that, other things being equal, the share of the household budget spent on food will rise as household income falls. Conversely, as household income rises, a smaller relative share of the household budget will be spent on food, even as expenditure on food increases in absolute terms.

Figure 1 Engel curve

Engel's law can be expressed graphically as a curve where the level of household income is measured on the y axis and the quantity demanded of food is measured on the x axis such that it takes the form of a positively sloped curve with an increasing gradient as household income rises to higher levels (see Figure 1).

The shape of the curve implies that the income elasticity of demand for food (a coefficient measuring the responsiveness of demand to changes in income) is between one and zero, which is the range for all so-called “normal” goods such as food and other necessities. “Inferior” goods, by contrast, are ones that have an inverse (negative) relationship between changes in levels of income and quantity demanded of those goods; consumption of them falls as income levels rise and households switch expenditure from these goods to higher quality substitutes. Inferior goods thus have an income elasticity of demand that is less than zero. Luxury goods, on the other hand, reveal a positive relationship with changing levels of income (i.e., income elasticity of demand is greater than one) so that as incomes rise, proportionally greater quantities of these goods are desired. Engel's law (and the associated curve) implies that [Page 528]the relationship between the level of income and expenditure on food is dynamic: initially, increases in the level of income yield increases in the quantity demanded of food, but this relationship weakens as income levels rise to the point where large increases in household income yield little or no additional demand for food. In other words, at lower levels of income, demand for food is like demand for a luxury good until a point is reached at higher levels of income when it becomes an inferior good. At that point, any additional expenditure on food is substituted by expenditure on luxury goods. It should be noted that the foregoing discussion has been simplified for the sake of clarity and that other characteristics of households also determine consumption patterns, notably the composition of the household (number, age, and gender), seasonal effects, and price discrepancies, among other things. Moreover, there is considerable variation within the income elasticity of demand of food: some are inferior goods (cabbage) while others are luxuries (caviar).

What became known as Engel's law was first observed by Engel while analyzing the household budgets of Belgian workers in the 1850s. Engel was influenced in this by his teacher Frédéric LePlay with whom he had studied in Paris in the late 1840s and who had pioneered an inductive method of social inquiry stressing the importance of direct field investigation and studying the family unit. Another important influence on Engel was the Belgian astronomer and statistician Adolfe Quetelet with whom Engel developed contacts after leaving Paris. Quetelet had applied the mean values used in astronomy to suicide, which he showed occurring with uncanny regularity in large population groups and which he believed suggested an underlying causal factor. Applying these empirical and statistical techniques, Engel set out to investigate the standard of living of workers aided by the work of Belgian journalist and statistician Édouard Ducpétiaux, who had collected detailed information from some two hundred Belgian worker budgets. Engel discovered that lower worker incomes had corresponding budgets that devoted a larger proportion of that income to food than those of workers with higher incomes. Engel subsequently tested the validity of his observations by extending his study of consumption to his native Saxony, where he had been appointed head of the Royal Statistical Bureau in 1854. In 1857, he published an article titled “The Consumption-Production Relationships in the Kingdom of Saxony” in which he confirmed his Belgian observations and formally stated his budget law, as Engel's law was first known. Engel came to believe that the proportion of household budget spent on food was the most accurate measure of the material standard of living.

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