Question

If the price elasticity of demand for a commodity is -2.5 and the percentage decrease in the quantity demanded is 10%, find out the percentage change in its price.

• A. 25%
• B. -25%
• C. 4%
• D. -4%

Hint:

Pay close attention to the signs (positive or negative) when calculating price elasticity. A negative Ed indicates an inverse relationship between price and quantity demanded.

Answer 1

The Correct Option is C

Price elasticity of demand (Ed) is calculated as: Ed = (% Change in Quantity Demanded) / (% Change in Price).
Given Ed = -2.5 and % Change in Quantity Demanded = -10%
(because it's a decrease), we have:
-2.5 = (-10) / (% Change in Price)
% Change in Price = (-10) / (-2.5) = 4%

Answer 2

Use the law of demand to fix the sign before doing any arithmetic: price and quantity move in opposite directions along a demand curve, so if quantity demanded has fallen, price must have risen - this immediately rules out both negative-percentage options, (2) and (4), leaving only 25% and 4% as candidates. To find the magnitude, use the elasticity ratio directly: \[ |E_d| = \frac{|\%\Delta Q|}{|\%\Delta P|} \implies |\%\Delta P| = \frac{|\%\Delta Q|}{|E_d|} = \frac{10}{2.5} = 4 \] A magnitude of 4% (not 25%, which would result from dividing 2.5 by 10 instead) confirms that price rose by 4%, matching option (3).