In microeconomics, what is the arc elasticity of demand when quantity demanded falls from 1000 to 950 units as price rises from Rs 240 to Rs 280?

Introduction / Context:
Arc elasticity of demand is a widely used concept in microeconomics and business studies to measure how responsive quantity demanded is to a change in price over a finite range. Instead of using point elasticity at a single price quantity combination, arc elasticity uses average price and average quantity across two points on a demand curve. This makes it very useful for analysing real data from markets where prices and quantities change between two levels rather than by tiny amounts.

Given Data / Assumptions:
• Initial quantity demanded Q1 = 1000 units.
• Final quantity demanded Q2 = 950 units.
• Initial price P1 = Rs 240.
• Final price P2 = Rs 280.
• Arc elasticity of demand is defined using average price and average quantity over the two points.

Concept / Approach:
The formula for arc price elasticity of demand E on a straight segment of the demand curve is
E = (ΔQ / ΔP) * (P_avg / Q_avg).
Here ΔQ is Q2 minus Q1, ΔP is P2 minus P1, P_avg is the average of P1 and P2, and Q_avg is the average of Q1 and Q2. For a normal downward sloping demand curve, when price increases, quantity demanded falls, so ΔQ and ΔP have opposite signs and the elasticity is negative. In exam answers, it is common to retain the negative sign to reflect the inverse relationship.

Step-by-Step Solution:
Step 1: Compute the change in quantity demanded, ΔQ = Q2 − Q1 = 950 − 1000 = −50 units. Step 2: Compute the change in price, ΔP = P2 − P1 = 280 − 240 = 40 rupees. Step 3: Compute the average quantity, Q_avg = (Q1 + Q2) / 2 = (1000 + 950) / 2 = 1950 / 2 = 975 units. Step 4: Compute the average price, P_avg = (P1 + P2) / 2 = (240 + 280) / 2 = 520 / 2 = 260 rupees. Step 5: Substitute into the arc elasticity formula, E = (ΔQ / ΔP) * (P_avg / Q_avg) = (−50 / 40) * (260 / 975). Step 6: Simplify −50 / 40 to −5 / 4 and simplify 260 / 975 by dividing numerator and denominator by 65, giving 4 / 15. Step 7: Multiply the simplified fractions, E = (−5 / 4) * (4 / 15) = −5 / 15 = −1 / 3. Step 8: Convert −1 / 3 to decimal form, which is approximately −0.33.

Verification / Alternative check:
As a quick reasonableness check, notice that price increased by about 16 to 17 percent from 240 to 280, while quantity fell by 50 units out of 975 on average, which is a fall of a little over 5 percent. A 5 percent fall in quantity for about a 16 percent rise in price suggests an elasticity magnitude a little less than 0.4, which is close to one third. The sign must be negative because the quantity moved in the opposite direction to price. This sanity check supports the detailed calculation of about −0.33 as the correct arc elasticity.

Why Other Options Are Wrong:
0.33: This ignores the negative sign and therefore hides the inverse relationship between price and demand, which is not standard in theory questions.
0.3: This is a rough number but not the correct value from the exact formula and also ignores the sign.
−0.3: The sign is correct but the magnitude is slightly off compared with the more precise calculation of one third.
0: This would mean quantity demanded did not react at all to the price change, which is clearly not true because quantity did fall from 1000 to 950.

Common Pitfalls:
A common mistake is to use only initial price and initial quantity rather than average values, which gives point elasticity rather than arc elasticity. Another frequent error is to forget the negative sign when price increases and quantity falls. Some students also mix up percentage changes and absolute changes, or they round intermediate steps too early, leading to inaccurate final values. To avoid these issues, always write the formula clearly, compute ΔQ and ΔP with attention to sign, use average price and average quantity, and simplify the fractions step by step before converting to decimal form.

Final Answer:
The arc elasticity of demand is approximately −0.33.