Q.The price of tea rises from ₹200 to ₹250 per kg. As a result, the quantity demanded of coffee (by the same group of consumers) rises from 100 kg to 110 kg per week. Calculate the cross elasticity of demand between coffee and tea, and state the relationship between the two goods.

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