Question

Find the price elasticity of demand for chocolate pastries, when the price of a pastry increases from Rs. 10 per pastry to Rs. 15 per pastry and demand reduces from 20 pastries to 10 pastries.

• A. 1
• B. 0.5
• C. 0.33
• D. 0.25

Hint:

Percentage drop in quantity = \(\frac{10}{20} \times 100 = 50\%\).
Percentage rise in price = \(\frac{5}{10} \times 100 = 50\%\).
\(e_d = \frac{50\%}{50\%} = 1\). Quick mental checks save exam time!

Answer 1

The Correct Option is A

Concept:
Price elasticity of demand (\(e_d\)) measures the responsiveness of the quantity demanded of a commodity to a change in its unit price.
It is conventionally evaluated using the percentage method or the proportionate method.

Step 1: Key Formula:
The proportionate formula for price elasticity of demand is given by: \[ e_d = -\left( \frac{\Delta Q}{\Delta P} \times \frac{P_1}{Q_1} \right) \] where:
\(P_1\) is the initial price, and \(P_2\) is the new price.
\(Q_1\) is the initial quantity demanded, and \(Q_2\) is the new quantity demanded.

Step 2: Calculation:
From the given data: \[ P_1 = 10, \quad P_2 = 15 \implies \Delta P = P_2 - P_1 = 15 - 10 = 5 \] \[ Q_1 = 20, \quad Q_2 = 10 \implies \Delta Q = Q_2 - Q_1 = 10 - 20 = -10 \] Substitute these values into the elasticity equation: \[ e_d = -\left( \frac{-10}{5} \times \frac{10}{20} \right) \] \[ e_d = -\left( -2 \times 0.5 \right) = 1 \] Final Answer:
The absolute value of the price elasticity of demand is 1, indicating unitary elastic demand. Thus, option (A) is correct.