Engel curve

He derivation process of the Engel curve

The Engel curve is a fundamental concept in microeconomics that describes how household expenditure on a particular good or service varies with household income. Named after the German statistician Ernst Engel, the Engel curve is used to analyze consumer behavior and the relationship between income and spending patterns.

Definition

The Engel curve illustrates the relationship between the quantity of a good consumed and the level of income. It is typically represented graphically, with income on the horizontal axis and the quantity of the good consumed on the vertical axis. The shape of the Engel curve can provide insights into whether a good is a normal good, an inferior good, or a luxury good.

Types of Goods

• Normal Goods: For normal goods, the Engel curve slopes upwards, indicating that as income increases, the quantity demanded also increases. Examples include basic necessities such as food and clothing.
• Inferior Goods: For inferior goods, the Engel curve slopes downwards, indicating that as income increases, the quantity demanded decreases. Examples include lower-quality substitutes that are replaced as income rises.
• Luxury Goods: For luxury goods, the Engel curve is more elastic, showing a more than proportional increase in quantity demanded as income rises.

Applications

The Engel curve is used in various applications within economics:

• Consumer Demand Analysis: It helps in understanding how changes in income affect consumer demand for different goods and services.
• Welfare Economics: It is used to assess the impact of income changes on consumer welfare.
• Policy Making: Governments and policymakers use Engel curves to design tax policies and social welfare programs.

Mathematical Representation

The Engel curve can be represented mathematically using a function that relates income (Y) to the quantity demanded (Q) of a good. A common form is: \[ Q = f(Y) \] where \( f \) is a function that describes how quantity demanded changes with income.

Historical Context

The concept of the Engel curve was first introduced by Ernst Engel in the 19th century. Engel's pioneering work in the field of statistics and econometrics laid the foundation for modern consumer demand theory.

See Also

• Income elasticity of demand
• Consumer theory
• Budget constraint
• Utility function
• Demand curve