Engel curve

As Engel curve is referred to in the economics and there especially in microeconomics a mathematical function which - relative to a particular good - indicating for each income level, how many units a consumer should optimally demand of this commodity.

Named the Engel curve to the statistician Ernst Engel (1821-1896), of the relationship between the expenses borne by a household for food, and household income examined ( the related trades found in the literature as an angel 's Law).

Construction

The angel curve underlies the so-called income-consumption curve (also: income expansion path). The income-consumption curve is - assuming two-goods case - in a x1 -x2 - graph all combinations of goods that (ie, utility-maximizing ) are for a given income level optimal. The income-consumption curve is correspondingly given the fact that for given prices of goods and preferences given the disposable income of the household varies, the resulting optimum each inscribing and constructed of all the obtained optimal points a corresponding curve.

The Engel curve is contrast, no relationship between good 1 and good 2 on, but between the quantity of a good and the disposable income. To get them, you have to only match the corresponding coordinate of each point of the income-consumption curve with the income level, from which he emerged. The resulting each resulting pairs (y, x1 ) and ( y, x2 ) are then transferred to a separate graph; their compound gives the Engel curve.

Generally, the revenue is plotted on the horizontal axis. You turn the axes but regularly for the sake of graphic design.

Course

In the course of the Engel- curve is directly visible, if it is a good to a normal good - ie a good whose demand increases with an income increase - or an inferior good - one that drops its demand for an increase in income - is. In the former case the angels curve is an increasing function in an inferior good it falls. Figure 2 distinguishes between the following cases:

• Inferior Good: The Angels curve drops in income ( in the graph to the right of the inferior area yA ); the income elasticity is negative.
• Normal Good: The Engel curve increases in income; the income elasticity is positive.

• Property Number: Angels curve is strictly convex (an increase of income by 1% increases the demand for goods by more than 1 %); the income elasticity is greater than 1
• The Engel curve is a line through the origin, meaning demand is proportional to income (an increase of income by 1% increases the demand for goods by exactly 1 %); the income elasticity is 1
• Necessary Good: The Angels curve is strictly concave (an increase of income by 1% increases the demand for goods by less than 1 %); the income elasticity is between 0 and 1