Q.The price of a commodity falls from ₹20 to ₹18 per unit, and as a result the quantity demanded rises from 40 units to 50 units per week. Calculate the price elasticity of demand by the percentage method and state its degree.
Concept understanding — Price Elasticity of Demand and Its Measurement
Price elasticity of demand measures how responsive quantity demanded is to a change in the commodity's own price: Ed=%ΔP%ΔQd. Based on its numerical value, demand ranges from perfectly elastic (Ed=∞) to perfectly inelastic (Ed=0), with unitary (Ed=1), relatively elastic (Ed>1) and relatively inelastic (Ed<1) in between. It is measured in practice by the percentage method (ratio of percentage changes), the total outlay method (comparing price × quantity before and after a price change), and the point/geometric method (the ratio of the lower to the upper segment of a straight-line demand curve at the point in question). This is one of the most exam-important topics in the AP Board Intermediate Economics (Commerce stream) curriculum, since numerical problems on all three measurement methods appear regularly.
Price elasticity of demand compares the percentage change in quantity demanded to the percentage change in price.
Applying the percentage method, Ed=−10%25%, so the numerical value of elasticity is 2.5 — demand is relatively elastic.
Ed=2.5 (relatively elastic, since Ed>1)
Step 1 — Percentage change in quantity demanded.
%ΔQd=4050−40×100=25%
Step 2 — Percentage change in price.
%ΔP=2018−20×100=−10%
Step 3 — Price elasticity of demand.
Ed=%ΔP%ΔQd=−1025=−2.5
Ignoring the sign (as is conventional), Ed=2.5.
Since Ed=2.5>1, demand for this commodity is relatively elastic.
Ed=2.5 — demand is relatively elastic.
Cross-check by the total outlay method. Outlay before the price fall =20×40=₹800; outlay after =18×50=₹900. Since price fell and total outlay rose, demand must be relatively elastic (Ed>1) — this agrees with the value 2.5 obtained by the percentage method.
Forgetting to drop the negative sign before comparing Ed to 1 leads students to mis-classify elastic demand as inelastic; also, using the wrong base (new price/quantity instead of the original) in the percentage formula changes the answer — always divide the change by the ORIGINAL value unless the arc/average method is specifically asked for.
- CBSE 2023Set ANNUAL1 markMCQQ.The demand for necessaries is :(a) Elastic(b) Inelastic(c) Unitary elastic(d) Perfectly elastic
›Reveal solutionSolution
Necessaries must be consumed regardless of price, so their quantity demanded changes very little with price — their demand is inelastic. Answer: (b) Inelastic.
Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. Demand is elastic when a small price change causes a large change in quantity, and inelastic when even a large price change causes only a small change in quantity.
Necessaries — such as salt, basic foodgrains, or essential medicines — are goods a household cannot easily do without. People go on buying almost the same amount even if the price rises, and they do not buy much more if the price falls, because the need is fixed. As a result the quantity demanded is relatively unresponsive to price, i.e. demand is inelastic (elasticity less than one). This is why options (a) elastic, (c) unitary elastic and (d) perfectly elastic are incorrect.
This is a standard elasticity application from the Demand Analysis unit of the CHSE Odisha +2 Commerce Business Economics syllabus, which draws on the NCERT/CBSE commerce curriculum.
✓Final answerOption (b) Inelastic. Necessaries are bought in nearly fixed quantities whatever the price, so their demand is inelastic.
- CBSE 2023Set ANNUAL1 markQ.Examine the correctness of the following statement and correct it if incorrect, without changing the underlined portion : The shape of Unitary elastic demand curve is Vertical.
›Reveal solutionSolution
The statement is incorrect; a unitary elastic demand curve is a rectangular hyperbola, not vertical. Correct statement: 'The shape of unitary elastic demand curve is a rectangular hyperbola.'
The shape of a demand curve reflects its price elasticity:
- Unitary elastic demand (elasticity exactly equal to one) means a given percentage change in price causes an equal percentage change in quantity demanded, so total expenditure stays constant at every price. A curve that keeps price times quantity constant everywhere is a rectangular hyperbola.
- A vertical demand curve represents perfectly inelastic demand (elasticity = 0) — quantity demanded does not change at all when price changes.
- A horizontal demand curve represents perfectly elastic demand (elasticity = infinity).
The statement wrongly assigns the vertical shape to unitary elasticity. Keeping the underlined phrase 'unitary elastic demand curve', the description 'vertical' must be corrected to 'rectangular hyperbola'.
✓Final answerINCORRECT. Corrected statement: 'The shape of unitary elastic demand curve is a rectangular hyperbola' (a vertical curve is perfectly inelastic).
- CBSE 2019Set ANNUAL1 markMCQQ.The shape of a perfectly elastic demand curve is(a) Downward sloping(b) Vertical(c) Horizontal(d) Rectangular hyperbola
›Reveal solutionSolution
The correct answer is (c) Horizontal.
The shape of a demand curve reflects its price elasticity — a key topic in CHSE Odisha +2 Business Economics (aligned with the NCERT/CBSE curriculum).
- Downward sloping (a) is the shape of a normal demand curve with finite elasticity, not the perfectly elastic case.
- Vertical (b) represents perfectly inelastic demand (elasticity = 0), where quantity does not change with price.
- Horizontal (c) represents perfectly elastic demand (elasticity = infinity): at the ruling price consumers buy any amount, but a tiny rise in price reduces demand to zero.
- Rectangular hyperbola (d) represents unitary elastic demand (elasticity = 1), where total expenditure stays constant.
Hence a perfectly elastic demand curve is horizontal.
✓Final answerOption (c) Horizontal — a perfectly elastic demand curve is parallel to the X-axis.
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