Engels law

Engel's law is an economic observation stating that as household income rises, the percentage of income spent on food decreases. German statistician Ernst Engel first published this finding in 1857 after analyzing budget data from Belgian and Saxon families. The relationship has proven remarkably durable across cultures and time periods.

Historical background

Ernst Engel (1821-1896) worked as director of the Statistical Bureau of Saxony when he formulated his famous observation. He analyzed household budget data originally collected by Edouard Ducpetiaux and Frederic Le Play^[1]. Engel remarked that these earlier researchers "had delivered the pearls but not the string" - meaning they gathered data without recognizing the underlying pattern.

The year 1857 marked the publication of Engel's analysis in the bulletin of the International Statistical Institute. His approach demonstrated the inductive method in economics, deriving general principles from observed data rather than theoretical assumptions.

Hendrik Houthakker of Harvard University tested Engel's law across dozens of countries in a 1957 paper commemorating its centennial. His research confirmed the law's validity across diverse economic conditions. The Federal Reserve Bank of St. Louis continues to track this relationship in contemporary data.

The law explained

Engel's law does not claim that food spending remains constant as income grows. Households do spend more on food in absolute terms when incomes rise. They simply spend a smaller share of their total income on food.

A family earning $30,000 annually might spend $6,000 on food (20% of income). The same family with $100,000 income might spend $12,000 on food (12% of income). Total food expenditure doubled, but the percentage fell significantly.

This pattern occurs because food represents a basic necessity with limited expandability. A person can only eat so much. Rising income allows greater spending on housing, transportation, entertainment, healthcare, and education. These categories absorb increasing proportions of household budgets as prosperity grows.

The Engel curve

Economists developed the Engel curve as a graphical representation of spending patterns^[2]. The horizontal axis shows income levels while the vertical axis displays expenditure amounts.

For normal goods with positive income elasticity, Engel curves slope upward. Food shows a concave downward curve - spending increases but at a declining rate. Inferior goods display negative slopes as consumers substitute preferred alternatives when income permits.

Demographic variables affect curve shapes. Age, gender, household size, and education level all influence spending patterns. Urban and rural households show different curves for the same goods.

Engel coefficient

The Engel coefficient measures the proportion of income spent on food. It serves as an indicator of economic development and living standards:

Coefficients above 60% indicate poverty
Coefficients between 50-60% suggest developing economy status
Coefficients between 40-50% reflect moderate prosperity
Coefficients between 30-40% characterize wealthy households
Coefficients below 30% indicate affluence

The United States shows an Engel coefficient around 10-13% at the national level. Developing nations often exceed 40%. These figures make international welfare comparisons possible.

Applications

Engel's law has several practical applications in economic analysis:

Development assessment - Countries with falling Engel coefficients demonstrate improving living standards. Rapid decreases signal successful economic development policies.

Agricultural policy - As nations develop, agriculture constitutes a smaller share of economic activity. This shift has implications for farm subsidies, land use, and rural employment.

Consumer behavior analysis - Market researchers use Engel curves to project demand across income segments. Companies adjust product strategies accordingly.

Poverty measurement - High food expenditure shares indicate economic vulnerability. Social programs target households exceeding threshold percentages.

Limitations

The law applies to aggregates and averages rather than individual cases. Some wealthy individuals spend large portions of income on premium food products. Cultural factors influence food expenditure patterns.

The law also assumes food quality remains constant. In practice, higher-income households often substitute expensive foods for cheaper alternatives, complicating expenditure analysis.

References

Engel, E. (1857). "Die Productions- und Consumptionsverhaltnisse des Konigreichs Sachsen." Zeitschrift des Statistischen Bureaus des Koniglich Sachsischen Ministeriums des Innern, 8-9.
Houthakker, H.S. (1957). "An International Comparison of Household Expenditure Patterns, Commemorating the Centenary of Engel's Law." Econometrica, 25(4), 532-551.
USDA Economic Research Service (2024). Food Expenditure Series.

Footnotes

[1] Ducpetiaux and Le Play were pioneering social researchers who collected detailed household budget data in Belgium and France during the mid-19th century.

[2] The Engel curve concept was developed by later economists building on Engel's original observations.

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