Consider the demand for a good. At price Rs 4, the demand for the good is 25 units. Suppose price of the good increases to Rs 5, and as a result, the demand for the good falls to 20 units. Calculate the price elasticity.
Given: Initial price (P) = Rs 4, initial quantity (Q) = 25 units. New price = Rs 5, new quantity = 20 units.
Change in quantity (ΔQ): 20 – 25 = –5 units.
Change in price (ΔP): 5 – 4 = Rs 1.
Percentage change in quantity demanded: (ΔQ / Q) × 100 = (–5 / 25) × 100 = –20%.
Percentage change in price: (ΔP / P) × 100 = (1 / 4) × 100 = 25%.
Price elasticity of demand (e_D): = (Percentage change in quantity demanded) ÷ (Percentage change in price) = (–20%) / (25%) = –0.8. By convention, we consider the absolute value, so |e_D| = 0.8. Since |e_D| < 1, demand is inelastic.
Alternatively, using the formula e_D = (ΔQ/ΔP) × (P/Q) = (–5/1) × (4/25) = –0.8, giving the same result.
Thus, the price elasticity of demand is 0.8 (in absolute terms).
Explanation
The calculation follows the method illustrated in Example 2.2 of the textbook. Price elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price. The negative sign indicates the inverse relationship between price and quantity, but the absolute value is used for simplicity. When the absolute value is less than one, demand is inelastic, meaning the percentage change in quantity is less than the percentage change in price.
Solution Steps
Step 1: Identify initial price P = Rs 4, initial quantity Q = 25 units; new price = Rs 5, new quantity = 20 units.
Step 2: Compute change in quantity ΔQ = 20 – 25 = –5 units, and change in price ΔP = 5 – 4 = Rs 1.
Step 3: Calculate percentage change in quantity demanded = (ΔQ / Q) × 100 = (–5 / 25) × 100 = –20%.
Step 4: Calculate percentage change in price = (ΔP / P) × 100 = (1 / 4) × 100 = 25%.
Step 5: Compute price elasticity e_D = (–20%) / (25%) = –0.8. Absolute value |e_D| = 0.8.
Step 6: Interpret: Since |e_D| < 1, demand is inelastic.