# Engel curve

In microeconomics, an Engel curve describes how household expenditure on a particular good or service varies with household income.[1][2] There are two varieties of Engel curves. Budget share Engel curves describe how the proportion of household income spent on a good varies with income. Alternatively, Engel curves can also describe how real expenditure varies with household income. They are named after the German statistician Ernst Engel (1821–1896), who was the first to investigate this relationship between goods expenditure and income systematically in 1857. The best-known single result from the article is Engel's law which states that the poorer a family is, the larger the budget share it spends on nourishment.

## Shape

Graphically, the Engel curve is represented in the first quadrant of the Cartesian coordinate system. Income is shown on the horizontal axis and the quantity demanded for the selected good or service is shown on the vertical.

The shapes of Engel curves depend on many demographic variables and other consumer characteristics. A good's Engel curve reflects its income elasticity and indicates 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.

For normal goods, the Engel curve has a positive gradient. That is, as income increases, the quantity demanded increases. Amongst normal goods, there are two possibilities. Although the Engel curve remains upward sloping in both cases, it bends toward the X-axis for necessities and towards the Y-axis for luxury goods.

For inferior goods, the Engel curve has a negative gradient. That means that as the consumer has more income, they will buy less of the inferior good because they are able to purchase better goods.

For goods with a Marshallian demand function generated from a utility function of Gorman polar form, the Engel curve is a straight line.

Many Engel curves feature saturation properties in that their slope tends toward infinity at high income levels, which suggests that there exists an absolute limit on how much expenditure on a good will rise as household income increases.[3] This saturation property has been linked to slowdowns in the growth of demand for some sectors in the economy, causing major changes in an economy's sectoral composition to take place.[4]

## Other properties

When considering a system of Engel curves, the adding-up theorem dictates that the sum of all total expenditure elasticities, when weighted by the corresponding budget share, must add up to unity. This rules out the possibility of saturation being a general property of Engel curves across all goods as this would imply that the income elasticity of all goods approaches zero starting from a certain level of income. The adding-up restriction stems from the assumption that consumption always takes place at the upper boundary of the household's opportunity set, which is only fulfilled if the household cannot completely satisfy all its wants within the boundaries of the opportunity set.[5]

Other scholars argue that an upper saturation level exists for all types of goods and services.[4][6]

## Applications

In microeconomics Engel curves are used for equivalence scale calculations and related welfare comparisons, and determine properties of demand systems such as aggregability and rank.

Engel curves have also been used to study how the changing industrial composition of growing economies are linked to the changes in the composition of household demand.[7]

In trade theory, one explanation of inter-industry trade has been the hypothesis that countries with similar income levels possess similar preferences for goods and services (the Lindner hypothesis), which suggests that understanding how the composition of household demand changes with income may play an important role in determining global trade patterns.[8]

Engel curves are also of great relevance in the measurement of inflation,[9] and tax policy.[10]

## Problems

### Low explanatory power

Heteroscedasticity is a well known problem in the estimation of Engel curves: as income rises the difference between actual observation and the estimated expenditure level tends to increase dramatically. Engel curve and other demand function models still fail to explain most of the observed variation in individual consumption behavior.[2]

As a result, many scholars acknowledge that influences other than current prices and current total expenditure must be systematically modeled if even the broad pattern of demand is to be explained in a theoretically coherent and empirically robust way.[5]

For example, some success has been achieved in understanding how social status concerns have influenced household expenditure on highly visible goods.[11][12]

### Accounting for their shape

No established theory exists that can explain the observed shape of Engel curves and their associated income elasticity values. Ernst Engel himself argued that households possessed a hierarchy of wants that determined the shape of Engel curves. As household income rises some motivations become more prominent in household expenditure as the more basic wants that dominate consumption patterns at low-income levels, such as hunger, eventually become satiated at higher income levels.[13]

## References

1. ^ Chai, A.; Moneta, A. (2010). "Retrospectives: Engel Curves" (PDF). Journal of Economic Perspectives. 24 (1): 225–240. doi:10.1257/jep.24.1.225.
2. ^ a b Lewbel, A (2007). "Engel Curves" (PDF). The New Palgrave Dictionary of Economics.
3. ^ Chai, A.; Moneta, A. (2010). "The evolution of Engel curves and its implications for structural change" (PDF). Griffith Business School Discussion Papers Economics. No. 2010-09. Archived from the original (PDF) on 2011-06-29.
4. ^ a b Pasinetti, L. (1981). Structural Change and Economic Growth. Cambridge: Cambridge University Press. ISBN 978-0-521-23607-2.
5. ^ a b Deaton, A.; Muellbauer, J. (1980). Economics and Consumer Behavior. Cambridge: Cambridge University Press. ISBN 978-0-521-22850-3.
6. ^ Metcalfe, S.; Foster, J.; Ramlogan, R. (2006). "Adaptive Economic Growth". Cambridge Journal of Economics. 30 (1): 7–32. doi:10.1093/cje/bei055.
7. ^ Krüger, J. J. (2008). "Productivity and Structural Change: A Review of the Literature". Journal of Economic Surveys. 22 (2): 330–363. doi:10.1111/j.1467-6419.2007.00539.x.
8. ^ Hallak, Juan Carlos (2010). "A Product-Quality View of the Linder Hypothesis". Review of Economics and Statistics. 92 (3): 453–466. CiteSeerX 10.1.1.664.8434. doi:10.1162/REST_a_00001.
9. ^ Bils, M.; Klenow, P. J. (2001). "Quantifying Quality Growth". American Economic Review. 91 (4): 1006–1030. CiteSeerX 10.1.1.163.2111. doi:10.1257/aer.91.4.1006.
10. ^ Banks, J.; Blundell, R.; Lewbel, A. (1997). "Quadratic Engel Curves and Consumer Demand". Review of Economics and Statistics. 79 (4): 527–539. CiteSeerX 10.1.1.557.9739. doi:10.1162/003465397557015.
11. ^ Charles, K. K.; Hurst, E.; Roussanov, N. (2009). "Conspicuous Consumption and Race". Quarterly Journal of Economics. 124 (2): 425–468. doi:10.1162/qjec.2009.124.2.425.
12. ^ Heffetz, Ori (2011). "A Test of Conspicuous Consumption: Visibility and Income Elasticities". Review of Economics and Statistics. 93 (4): 1101–1117. doi:10.1162/REST_a_00116.
13. ^ Witt, U. (2001). "Learning to consume – A theory of wants and the growth of demand". Journal of Evolutionary Economics. 11 (1): 23–36. CiteSeerX 10.1.1.469.1839. doi:10.1007/PL00003851.