Question

If the price of a commodity falls from ₹10 to ₹8, and the quantity demanded increases from 100 units to 120 units, the price elasticity of demand is:

• A. 1
• B. 1.5
• C. 0.5
• D. 0.75

Hint:

If elasticity is: \[ E_d=1 \] Demand is unitary elastic. \[ E_d>1 \] Demand is elastic. \[ E_d<1 \] Demand is inelastic.

Answer 1

The Correct Option is A

Concept: Price Elasticity of Demand measures the responsiveness of quantity demanded to a change in price. It indicates how much quantity demanded changes when the price of a commodity changes. The formula is: \[ E_d = \frac{%\text{ Change in Quantity Demanded}} {%\text{ Change in Price}} \] Using the percentage method: \[ E_d = \frac{\Delta Q}{Q} \times \frac{P}{\Delta P} \] where \[ \Delta Q = \text{Change in Quantity} \] and \[ \Delta P = \text{Change in Price} \]

Step 1: Identify the given information.
Original Price \[ P = ₹10 \] New Price \[ P_1 = ₹8 \] Original Quantity \[ Q = 100 \] New Quantity \[ Q_1 = 120 \]

Step 2: Calculate the change in quantity demanded.
\[ \Delta Q = 120-100 = 20 \] Therefore, \[ \frac{\Delta Q}{Q} = \frac{20}{100} = 0.2 \]

Step 3: Calculate the change in price.
\[ \Delta P = 10-8 = 2 \] Thus, \[ \frac{P}{\Delta P} = \frac{10}{2} = 5 \]

Step 4: Apply the elasticity formula.
\[ E_d = \frac{\Delta Q}{Q} \times \frac{P}{\Delta P} \] \[ = \frac{20}{100} \times \frac{10}{2} \] \[ = 0.2 \times 5 \] \[ = 1 \]

Step 5: Interpret the result.
Since \[ E_d = 1 \] the demand is said to be unitary elastic. A given percentage change in price causes an equal percentage change in quantity demanded. Therefore, \[ \boxed{E_d = 1} \] Hence, the correct answer is: \[ \boxed{(A)} \]