Income Elasticity of Demand vs Engel Curve
Income Elasticity of Demand and Engel Curve are related concepts in AP Economics that students often mix up. Income elasticity of demand measures how responsive the quantity demanded is to a change in consumers' income. An Engel curve shows how the quantity of a good a consumer buys changes as income changes, holding prices constant: upward-sloping for normal goods, downward for inferior goods. Here is how they compare side by side.
It is calculated as the percentage change in quantity demanded divided by the percentage change in income. Demand is considered a normal good if the ratio is positive, meaning demand increases as income increases. Demand is considered an inferior good if the ratio is negative.
Named after statistician Ernst Engel, the curve plots income against quantity demanded of a single good. A normal good has an upward-sloping Engel curve (more income, more bought), while an inferior good has a downward-sloping one over some income range. The steepness reflects income elasticity: necessities flatten as income rises (income elasticity between 0 and 1), whereas luxuries rise more than proportionally (income elasticity above 1). It is the income analogue of the ordinary (price) demand curve.
Income Elasticity vs the Engel Curve: One Number and the Picture It Was Taken From
| Income Elasticity of Demand | Engel Curve | |
|---|---|---|
| What it is | A ratio computed between two income levels | A curve plotting quantity bought against income |
| How much it covers | One stretch of income at a time | Every income level in the range drawn |
| What marks a normal good | A positive coefficient | An upward sloping stretch |
| What marks an inferior good | A negative coefficient | A downward sloping stretch |
| What marks a luxury | A coefficient above 1 | A stretch where quantity grows faster in percentage terms than income |
| Can it show a good switching category | No, one calculation returns one value | Yes, the curve simply bends |
| Where it shows up in questions | Calculate and classify tasks | Sketch and explain tasks |
The same good can hand you two opposite elasticities on one curve
Follow one household's bus travel as income climbs. Over the first stretch, weekly income rises from an illustrative $300 to $600 and monthly bus rides go from 10 to 24. On the midpoint method income changes by 300 over the average of 450, which is 66.67 percent, and rides change by 14 over the average of 17, which is 82.35 percent. Dividing gives about 1.24, so bus travel is normal here and behaves like a luxury, because the household is finally able to afford to go places. Over the next stretch income rises from $600 to $900 and rides fall from 24 to 18. Income changes by 300 over the average of 750, which is 40 percent, and rides change by 6 over the average of 21, which is 28.57 percent downward. Dividing gives about negative 0.71, so bus travel has turned inferior as a car came within reach. Both figures are right, and neither describes the good in general. The Engel curve holds both facts at once: it rises, bends over and then slopes down. An elasticity is a single reading taken from one part of it. Try other stretches at /calculate/income-elasticity-of-demand.
The slope of the curve is not the elasticity, and the units give it away
Students often treat a steep Engel curve as a large elasticity. It is not the same measurement. Take the stretch where income moves from $600 to $900 and rides drop from 24 to 18. The slope is 6 fewer rides over 300 extra dollars, which is 0.02 rides lost per dollar of weekly income, a number carrying units. The elasticity for the same stretch was about negative 0.71, a pure ratio of percentages with no units attached. Two goods measured in different physical units can be compared with elasticities and cannot be compared with slopes, which is the whole reason economists convert. There is a second consequence. Because elasticity divides by the level of income and quantity as well as the changes, the same straight stretch of an Engel curve gives a different elasticity depending on where along it you stand. A curve can keep a constant slope while its elasticity falls steadily as the household gets richer. So read the sign off the picture, and read the size off the calculation. The wider elasticity toolkit is at /micro/elasticity.
Frequently asked questions
What is the difference between income elasticity of demand and an Engel curve?
Income elasticity is a single number measuring the percentage change in quantity demanded divided by the percentage change in income, while an Engel curve is a graph of quantity against income across a whole range. The number is one reading; the curve is every reading at once. That is why a curve can show a good turning from normal to inferior and a single elasticity cannot.
Can one good be both normal and inferior?
Yes, for the same household at different income levels, which is exactly what a bending Engel curve shows. Second hand clothing, long distance coach travel and instant noodles often rise with income among poorer buyers and fall away among richer ones. Normal and inferior describe a stretch of the curve rather than a permanent property of the product.
Is the slope of an Engel curve the same as income elasticity?
No, the slope measures units of the good per dollar of income while elasticity measures percentage against percentage, so the two answer different questions. A curve with a constant slope still has a changing elasticity as income and quantity rise. Only the elasticity can be compared across goods measured in different units.
Live Elasticity graph. Drag the curves, or open the full version.
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