Elasticity, with income and cross price elasticity of demand

Meaning of elasticity. In economics, elasticity measures how responsive buyers or sellers are to a change in the conditions of the market: the more strongly the quantity reacts, the more elastic it is. Applied to buyers it is called elasticity of demand, and applied to sellers, elasticity of supply. It is measured as a ratio of percentage changes, so its value is independent of the units in which quantities and prices are measured (NCERT notes this for the price elasticities of demand and supply):

elasticity = (% change in the quantity) ÷ (% change in the factor that caused it).

The best-known case is price elasticity of demand, the percentage change in the quantity demanded of a good divided by the percentage change in its own price, eD = (ΔQ/Q) ÷ (ΔP/P); it is negative because demand falls when price rises, and its absolute value is usually quoted. On the supply side, price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price. Demand also responds to income and to the prices of related goods, which gives the two measures below.

Income elasticity of demand. It measures how much the quantity demanded of a good changes when the consumer's income changes, with the good's own price, other prices and tastes held constant:

eY = (% change in quantity demanded of X) ÷ (% change in income) = (ΔX/ΔI) × (I/X).

• For a normal good, quantity demanded rises when income rises, so eY is positive.
• For an inferior good, quantity demanded falls when income rises, so eY is negative.

A change in income does not move the consumer along the demand curve; it shifts the whole curve. When income rises, the curve shifts to the right for a normal good and to the left for an inferior good.

Cross price elasticity of demand. It measures how much the quantity demanded of one good (X) changes when the price of a related good (Y) changes, with X's own price, income and tastes held constant:

eXY = (% change in quantity demanded of X) ÷ (% change in the price of Y) = (ΔQx/ΔPy) × (Py/Qx).

Its sign depends on how the two goods are related:

• Substitutes (goods that can replace each other): when Y becomes dearer, buyers switch to X, so the quantity of X rises. Both changes go the same way, so eXY is positive.
• Complements (goods used together): when Y becomes dearer, people buy less of Y and so less of X too. The two changes go in opposite directions, so eXY is negative.

Examples (our own figures).

• Income elasticity, normal good: a software engineer in Hyderabad gets a 10% pay rise and her spending on restaurant meals goes up from 8 to 10 meals a month, a 25% rise. eY = 25 ÷ 10 = +2.5: restaurant meals are a normal good for her, and strongly income-responsive.
• Income elasticity, inferior good: a household's income rises by 20% and it cuts its purchase of loose, unbranded biscuits by 10% as it moves to branded ones. eY = −10 ÷ 20 = −0.5: for this household the loose biscuits are an inferior good.
• Cross price elasticity, substitutes: app-cab fares in Mumbai rise by 20% and metro journeys on the same routes rise by 6%. eXY = 6 ÷ 20 = +0.3.
• Cross price elasticity, complements: the price of an LPG refill rises by 25% and sales of gas stoves fall by 5%. eXY = −5 ÷ 25 = −0.2.

Conclusion. Elasticity is a unit-free measure of responsiveness. Income elasticity relates demand to income, and its sign tells us whether a good is normal (positive) or inferior (negative); cross price elasticity relates the demand for one good to the price of another, and its sign tells us whether the goods are substitutes (positive) or complements (negative).