In microeconomics, if the price of a single article decreases from Rs 12 to Rs 10 and, as a result, the quantity demanded increases from 1000 units to 1400 units, what is the point price elasticity of demand for this good?

Introduction / Context:
In microeconomics, the concept of price elasticity of demand measures how sensitive the quantity demanded of a good is to a change in its price. It is a core tool for understanding consumer behaviour, revenue implications, and policy decisions such as taxation or price controls. In this question, we are given a change in price and the associated change in quantity demanded for a single article, and we are asked to calculate the point price elasticity of demand using the standard formula based on percentage changes. This helps to classify the demand as elastic, inelastic, or unit elastic and to interpret how strongly consumers respond to price changes in this numerical example.

Given Data / Assumptions:

• Initial price of the article, P1 = Rs 12 per unit.
• New price of the article, P2 = Rs 10 per unit.
• Initial quantity demanded, Q1 = 1000 units.
• New quantity demanded, Q2 = 1400 units.
• We assume all other factors (income, tastes, prices of related goods) remain constant, so only price is changing.
• The standard formula for point price elasticity of demand based on percentage changes is used.

Concept / Approach:
Price elasticity of demand (Ed) is defined as the percentage change in quantity demanded divided by the percentage change in price. In simple numerical questions, we often use the formula Ed = (ΔQ / Q1) * (P1 / ΔP), where ΔQ is the change in quantity, Q1 is the original quantity demanded, P1 is the original price, and ΔP is the change in price. Because the law of demand indicates an inverse relationship between price and quantity demanded, elasticity of demand is normally negative, and we retain the sign here. If the absolute value of elasticity is greater than 1, demand is considered elastic; if it is less than 1, demand is inelastic; and if it equals 1, demand is unit elastic.

Step-by-Step Solution:
Step 1: Compute the change in quantity demanded, ΔQ = Q2 - Q1 = 1400 - 1000 = 400 units.Step 2: Compute the change in price, ΔP = P2 - P1 = 10 - 12 = -2 rupees.Step 3: Substitute into the formula Ed = (ΔQ / Q1) * (P1 / ΔP).Step 4: First compute ΔQ / Q1 = 400 / 1000 = 0.4.Step 5: Next compute P1 / ΔP = 12 / (-2) = -6.Step 6: Multiply the two parts: Ed = 0.4 * (-6) = -2.4.Step 7: Therefore, the point price elasticity of demand for this good at the original price and quantity is -2.4, indicating highly elastic demand in absolute terms.

Verification / Alternative check:
To verify the calculation, one can recompute step by step. The price falls by 2 rupees from 12, so the percentage change in price is ΔP / P1 = -2 / 12 = -1/6. The quantity rises by 400 from 1000, so the percentage change in quantity demanded is 400 / 1000 = 0.4. Dividing 0.4 by -1/6 is equivalent to 0.4 * (-6), which again gives -2.4. Since both methods lead to the same elasticity, the numerical answer is consistent. The negative sign reflects the inverse relationship between price and quantity demanded, which is exactly what the law of demand predicts.

Why Other Options Are Wrong:
Option A (2.4) ignores the negative sign that arises because price and quantity move in opposite directions; it does not fully represent the law of demand. Option B (-2) underestimates the magnitude of responsiveness and does not match the calculated elasticity of -2.4. Option D (2) again ignores the correct sign and does not match the computed value. Therefore, none of these options correctly reflect the numerical result and the demand relationship at the same time.

Common Pitfalls:
A common mistake is to reverse the initial and final values when calculating changes, leading to incorrect ΔQ or ΔP. Another frequent error is to forget that ΔP is negative when price decreases, which removes the negative sign from the final elasticity. Some learners also mistakenly use the new quantity and new price instead of the original ones in the simple point elasticity formula. It is also easy to drop units and forget that the interpretation of elasticity is based on percentage changes, not absolute rupee or unit changes, so careful substitution into the formula is essential.

Final Answer:
The calculated point price elasticity of demand is -2.4, which shows that the quantity demanded is highly responsive to price changes in this situation.