How this calculator works
Income elasticity of demand compares the percentage change in the quantity demanded with the percentage change in income. A value above 1 marks a luxury good: demand grows faster than income. A value between 0 and 1 marks a normal necessity: demand grows, but more slowly than income. A negative value marks an inferior good, such as instant noodles or bus travel, whose demand falls as households become richer. The standard method divides by the initial values, while the midpoint method uses averages so that a rise and an equal fall give the same answer.
Formula
Standard: income elasticity = ((Q2 - Q1) / Q1) / ((Y2 - Y1) / Y1). Midpoint: ((Q2 - Q1) / ((Q1 + Q2) / 2)) / ((Y2 - Y1) / ((Y1 + Y2) / 2)). Q is quantity demanded and Y is income.
Worked example
Income rises from $50,000 to $55,000 while quantity demanded rises from 100 to 110. Standard: 10 / 100 = 0.1 and 5,000 / 50,000 = 0.1, so elasticity is 1.0. Midpoint: 10 / 105 = 0.0952 and 5,000 / 52,500 = 0.0952, also 1.0. A value of exactly 1 is the boundary between a necessity and a luxury.
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Frequently asked questions
Why do some sources use a negative sign for inferior goods?
The formula produces a negative number when quantity falls as income rises. Some textbooks report the absolute value and state the sign separately. Keep the sign: it carries the meaning of an inferior good.
Is income elasticity stable over time?
No. A good can be a luxury at low incomes and a necessity at high incomes. Estimates also depend on prices, tastes and the time period studied, so treat a single figure as a snapshot.
What does a zero income elasticity mean?
Demand does not respond to income at all, which is rare for consumer goods. It may appear for necessities bought in fixed quantities regardless of income, or reflect a data problem.