Q.The price of petrol rises from ₹100 to ₹110 per litre. As a result, the demand for cars (a complementary good) falls from 1,000 to 950 units per month. Calculate the cross elasticity of demand and interpret the result.

Cross elasticity of demand measures the responsiveness of the quantity demanded of one good ($X$) to a change in the price of another good ($Y$). Its greatest value is that its sign reveals the relationship between the two goods.

Interpreting the value

• Positive ($E_c > 0$): substitutes (tea & coffee) — a rise in $Y$'s price raises demand for $X$. Perfect substitutes give a very high value.
• Negative ($E_c < 0$): complements (car & petrol) — a rise in $Y$'s price cuts demand for $X$.
• Zero / near-zero: goods are independent / unrelated — a price change in one has no effect on the other (e.g. price of salt and demand for laptops).

The magnitude also matters: the larger the absolute value, the closer the relationship — a very high positive value means near-perfect substitutes, while a value close to zero means the goods barely affect each other.

Quick example

Price of coffee rises 10% and, as buyers switch, quantity of tea demanded rises 15%:

1. $E_c = \dfrac{+15\%}{+10\%} = +1.5$. …