Question

Consider the demand for a good. At price 5, the demand for the goods is 15 units. Suppose the price of the goods increases to Rs. 7 and as a result, the demand for the goods falls 12 units. Calculate the price elasticity.

Hint:

When the price elasticity of demand (PED) is less than 1, demand is inelastic, meaning that consumers are less responsive to price changes.

Answer 1

Step 1: Formula for Price Elasticity of Demand (PED).
The formula for price elasticity of demand is: \[ PED = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}} \] Where: \[ \% \text{ change in quantity demanded} = \frac{Q_2 - Q_1}{Q_1} \times 100, % \text{ change in price} = \frac{P_2 - P_1}{P_1} \times 100 \]

Step 2: Applying the values from the question.
Given: \( P_1 = 5, P_2 = 7, Q_1 = 15, Q_2 = 12 \) First, calculate the percentage change in quantity demanded: \[ % \text{ change in quantity demanded} = \frac{12 - 15}{15} \times 100 = \frac{-3}{15} \times 100 = -20% \] Next, calculate the percentage change in price: \[ % \text{ change in price} = \frac{7 - 5}{5} \times 100 = \frac{2}{5} \times 100 = 40% \]

Step 3: Calculating PED.
Now substitute these values into the PED formula: \[ PED = \frac{-20}{40} = -0.5 \]

Step 4: Conclusion.
Since the absolute value of PED is less than 1 (\( |PED| = 0.5 \)), the demand is inelastic. This means that the percentage change in quantity demanded is less than the percentage change in price.