The price of a commodity was Rs. 15 per unit when 40 units were demanded. The price then rose to Rs. 25 per un

Worked Examples · Example 4

Q. The price of a commodity was Rs. 15 per unit when 40 units were demanded. The price then rose to Rs. 25 per unit, and quantity demanded fell to 20 units. Calculate the price elasticity of demand using the Arc Method.

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The Arc Method formula is:

E_d = \dfrac{\Delta Q}{\Delta P}\times\dfrac{P_1+P_2}{Q_1+Q_2}

where $P_1=15, Q_1=40$ (first point) and $P_2=25, Q_2=20$ (second point).

First find the changes:

\Delta Q = 20-40=-20, \qquad \Delta P = 25-15=10

Substituting:

E_d = \dfrac{-20}{10}\times\dfrac{15+25}{40+20} = (-2)\times\dfrac{40}{60} = -2\times0.667 = -1.33

Ignoring the negative sign (which only reflects price rising as quantity fell), $E_d \approx 1.33$ . …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2023Set ANNUAL1 markMCQ
$Q. In the following diagram, AE is the linear demand curve of a commodity. On the basis of the given diagram, state whether the following statement is True or False. Give a reason for your answer. Demand at point ‘C’ is relatively elastic demand.$
(a) True
(b) False
›Reveal solutionSolution

False. By the geometric (point) method, the midpoint C of a linear demand curve AE has Ed = 1, i.e. unitary elastic demand — not relatively elastic. So the statement about point C is false.

On a straight-line (linear) demand curve, elasticity is different at every point and can be found by the point (geometric) method: Ed at a point = lower segment of the curve / upper segment of the curve. With five points A, B, C, D, E from the price axis down to the quantity axis, the midpoint C divides the curve into two equal halves, so its lower and upper segments are equal and Ed = 1 (unitary elastic). Above C (points like B) demand is relatively elastic (Ed greater than 1), and below C (points like D) i …

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CBSE 2023Set ANNUAL1 markMCQ
$Q. In the following diagram, AE is the linear demand curve of a commodity. On the basis of the given diagram state whether the following statement is True or False. Give a reason for your answer. Demand at point ‘B’ is unitary elastic demand.$
(a) True
(b) False
›Reveal solutionSolution

False. Point B lies above the midpoint of the linear demand curve, so by the point method Ed is greater than 1 — demand there is relatively elastic, not unitary elastic. Unitary elasticity occurs only at the midpoint C.

By the geometric (point) method on a linear demand curve, Ed at a point equals the lower segment divided by the upper segment of the curve from that point. For point B, which lies in the upper half (between A and the midpoint C), the lower segment is longer than the upper segment, so Ed is greater than 1 — relatively elastic demand. Unitary elastic demand (Ed = 1) occurs only where the two segments are equal, …

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CBSE 2023Set ANNUAL1 markMCQ
$Q. In the following diagram, AE is the linear demand curve of a commodity. On the basis of the given diagram state whether the following statement is True or False. Give a reason for your answer. Demand at point ‘D’ is perfectly inelastic demand.$
(a) True
(b) False
›Reveal solutionSolution

False. Point D lies below the midpoint of the linear demand curve, so Ed is less than 1 — demand there is relatively inelastic, not perfectly inelastic. Perfectly inelastic demand (Ed = 0) occurs only where the curve touches the quantity (X) axis, i.e. at point E.

Using the point method, at any point below the midpoint C the lower segment of the demand curve is shorter than the upper segment, so Ed is less than 1 — relatively inelastic demand. Perfectly inelastic demand means Ed = 0, which occurs only at the point where the demand curve meets the quantity axis (the lowest point, E), where the lower segment is zero.

…

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CBSE 2023Set ANNUAL1 markMCQ
$Q. In the following diagram, AE is the linear demand curve of a commodity. On the basis of the given diagram state whether the following statement is True or False. Give a reason for your answer. Demand at point ‘A’ is perfectly elastic demand.$
(a) True
(b) False
›Reveal solutionSolution

True. Point A lies on the price (Y) axis at the top of the linear demand curve. By the point method Ed = lower segment / upper segment, and at A the upper segment is zero, making Ed infinity — perfectly elastic demand.

On a straight-line demand curve AE, elasticity increases as we move up towards the price axis. At the very top point A (where the curve meets the Y-axis), the upper segment of the curve is zero, so Ed = lower segment / upper segment = infinity. An infinite coefficient means perfectly elastic demand — an infinitely small change in price causes an in …

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←Previous questionExample 3 — On a straight-line demand curve DD', point M lies such that the lower …→Next questionExample 5 — When a consumer's monthly income rose from Rs. 20,000 to Rs. 25,000, t…

Q.The price of a commodity was Rs. 15 per unit when 40 units were demanded. The price then rose to Rs. 25 per unit, and quantity demanded fell to 20 units. Calculate the price elasticity of demand using the Arc Method.

Concept understanding — Point Method and Arc Method of Measuring Elasticity

Q.The price of a commodity was Rs. 15 per unit when 40 units were demanded. The price then rose to Rs. 25 per unit, and quantity demanded fell to 20 units. Calculate the price elasticity of demand using the Arc Method.

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