Engel curve
Encyclopedia
An Engel curve describes how household expenditure on a particular good or
service varies with household income. 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.
Graphically, the Engel curve is represented in the first-quadrant of the cartesian coordinate system
. Income is shown on the Y-axis and the quantity demanded for the selected good or service is shown on the X-axis.
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 y-axis for necessities
and towards the x-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 Marshallian demand function
generated from a utility function of Gorman polar form
, the Engel curve has a constant slope.
Many Engel Curves feature saturation properties in that their slope tends to diminish 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 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.
When considering a system of Engel curves, the adding-up theorem also 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
Other scholars argue that an upper saturation level exists for all types of goods and services.
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
In trade theory, one explanation 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.
Engel curves are also of great relevance in the measurement of inflation and tax policy.
function models still fail to explain most of the observed variation in individual consumption behavior.
As 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.
For example, some success has been achieved in understanding how social status concerns have influenced household expenditure on highly visible goods.
service varies with household income. 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
Ernst Engel
Ernst Engel was a German statistician and economist, famous for the Engel curve and the Engel's law.Ernst was born in Dresden in 1821...
(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
Engel's law
Engel's law is an observation in economics stating that as income rises, the proportion of income spent on food falls, even if actual expenditure on food rises...
which states that the poorer a family is, the larger the budget share it spends on nourishment.
The Shape of Engel Curves
The shape 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.Graphically, the Engel curve is represented in the first-quadrant of the cartesian coordinate system
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...
. Income is shown on the Y-axis and the quantity demanded for the selected good or service is shown on the X-axis.
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 y-axis for necessities
Necessity
In U.S. criminal law, necessity may be either a possible justification or an exculpation for breaking the law. Defendants seeking to rely on this defense argue that they should not be held liable for their actions as a crime because their conduct was necessary to prevent some greater harm and when...
and towards the x-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 Marshallian demand function
Marshallian demand function
In microeconomics, a consumer's Marshallian demand function specifies what the consumer would buy in each price and wealth situation, assuming it perfectly solves the utility maximization problem...
generated from a utility function of Gorman polar form
Gorman polar form
Gorman polar form is a functional form for indirect utility functions in economics. Imposing this form on utility allows the researcher to treat a society of utility-maximizers as if it consisted of a single 'representative' individual. W. M...
, the Engel curve has a constant slope.
Many Engel Curves feature saturation properties in that their slope tends to diminish 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 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.
Engel Curves in microeconomics
In microeconomics, an Engel curve shows how the quantity demanded of a good or service changes as the consumer's income level changes. In order to be consistent with the standard model of utility-maximization, Engel Curves must possess certain properties. For example, Gorman (1981) proved that a system of Engel curves must have a matrix of coefficients with rank three (or less) in order to be consistent with utility maximization.When considering a system of Engel curves, the adding-up theorem also 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
Other scholars argue that an upper saturation level exists for all types of goods and services.
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
In trade theory, one explanation 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.
Engel curves are also of great relevance in the measurement of inflation and tax policy.
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 demandfunction models still fail to explain most of the observed variation in individual consumption behavior.
As 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.
For example, some success has been achieved in understanding how social status concerns have influenced household expenditure on highly visible goods.