In microeconomics, the price of an article decreases from Rs 240 to Rs 220 and, as a result, the quantity demanded increases from 200 units to 210 units. Using the point elasticity of demand formula based on averages, what is the price elasticity of demand?

Introduction / Context:
Price elasticity of demand measures how responsive quantity demanded is to changes in price. It is a key concept in microeconomics used to understand consumer behaviour, pricing strategies, and tax policies. This question asks you to calculate the point elasticity of demand between two nearby price–quantity combinations using the average or midpoint values. The sign of elasticity is important because it indicates the direction of the relationship between price and quantity demanded.

Given Data / Assumptions:

• Initial price P1 = Rs 240.
• New price P2 = Rs 220.
• Initial quantity Q1 = 200 units.
• New quantity Q2 = 210 units.
• We use the point elasticity formula based on averages for a small change.

Concept / Approach:
For small changes, a commonly used approximation of point elasticity of demand is: Elasticity (E) = (ΔQ / ΔP) * (P_avg / Q_avg) where ΔQ = Q2 - Q1, ΔP = P2 - P1, P_avg = (P1 + P2) / 2, and Q_avg = (Q1 + Q2) / 2. Since demand usually falls when price rises and rises when price falls, the elasticity for a normal good is typically negative. This negative sign reflects the inverse relationship between price and quantity demanded.

Step-by-Step Solution:
Step 1: Compute the change in quantity: ΔQ = Q2 - Q1 = 210 - 200 = 10 units. Step 2: Compute the change in price: ΔP = P2 - P1 = 220 - 240 = -20 rupees. Step 3: Compute the average price: P_avg = (P1 + P2) / 2 = (240 + 220) / 2 = 460 / 2 = 230 rupees. Step 4: Compute the average quantity: Q_avg = (Q1 + Q2) / 2 = (200 + 210) / 2 = 410 / 2 = 205 units. Step 5: Compute the ratio ΔQ / ΔP = 10 / (-20) = -0.5. Step 6: Now calculate elasticity: E = (-0.5) * (P_avg / Q_avg) = (-0.5) * (230 / 205). Step 7: Evaluate 230 / 205 which is approximately 1.12, giving E ≈ -0.5 * 1.12 ≈ -0.56, which rounds to about -0.6. Step 8: Therefore, the price elasticity of demand is approximately -0.6.

Verification / Alternative check:
We can check the magnitude of elasticity. Since the percentage change in quantity is small compared to the percentage change in price, we expect the elasticity to have magnitude less than 1, indicating inelastic demand. The negative sign is expected because price and quantity demanded move in opposite directions. The computed value of about -0.6 matches these expectations and is close to the option -0.6, confirming the result.

Why Other Options Are Wrong:

• 0.6: This ignores the negative sign and incorrectly suggests a direct relationship between price and quantity demanded, which contradicts the usual law of demand.
• -1.8: This magnitude is much larger than our calculation and would imply a much more responsive demand than observed. It does not match the correct computation.
• 1.8: This is not only the wrong magnitude but also positive, which again suggests an incorrect relationship between price and quantity.

Common Pitfalls:
Students often forget the negative sign in elasticity of demand or mix up the formula by using Q_avg / P_avg instead of P_avg / Q_avg. Another mistake is failing to use averages and instead using only initial values, which gives a less accurate approximation for discrete changes. Careful substitution and attention to signs are crucial to avoid these errors.

Final Answer:
The point price elasticity of demand is approximately -0.6.