**income elasticity of demand**is the responsiveness of the quantity demanded to changes in a consumer's income, as measured by the percentage change in the quantity demanded divided by the percentage change in consumers' income. It tells how much consumers respond to a change in income and in what direction. If a consumer receives a large pay raise, they are likely to spend more money. The income elasticity of demand ($E_y$) is calculated by dividing the percentage change in quantity demanded ($\%\Delta \text{Q}_{\text{D}}$) by the percentage change in income ($\% \Delta Y$).

To use another example, suppose a person's salary is $100,000 and this person goes to (consumes) 10 movies per year. Now suppose this person gets a pay raise and their income increases to $110,000 (a change of $+10\%$), so they begin to go to 15 movies a year (an increase of 50%). This would mean an income elasticity of demand of $50\%/10\%=5$, which would make movies a luxury good. When this person's income went up, they consumed disproportionately more of this particular good relative to their income increase.

The relative size of the income elasticity for normal goods can help determine if the good is a necessity or a luxury (both necessities and luxuries are normal goods). Goods that are necessities have an income elasticity between zero and 1. This occurs because a change in income doesn't have a large impact on the amount demanded for necessities. However, the income elasticity for luxuries is greater than 1. A fall in income will lead to a greater decline in the demand for luxuries, making the income elasticity value greater. For example, if the moviegoer discussed above suffered a pay cut of 10% but their movie consumption dropped by 20%, that would mean the movies were a luxury good for that person, because the income elasticity of their demand for movies would be $20\%/10\%=2$.

An inferior good is a good for which demand falls when income rises. Therefore, the numerator (the percentage change in demand) and the denominator (the percentage change in income) will have different signs, and the income elasticity of demand will be negative. Suppose that the income elasticity of demand for ramen noodles is –0.7. A 10% increase in income leads to a 7% decline in the quantity of ramen noodles demanded. Because the denominator is positive and the numerator is negative, the ratio will be negative. Therefore, the income elasticity for ramen noodles, an inferior good, is negative.