Q.When the price of tea rose from Rs. 200 to Rs. 220 per kg, the quantity of coffee demanded rose from 50 kg to 55 kg per month. Calculate the cross elasticity of demand for coffee with respect to the price of tea, and state the relationship between the two commodities.

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