Quick Answer: What Elasticity Numericals Ask in CUET — Direct Lead
Elasticity of Demand Numericals: Smart CUET Shortcuts
Quick Answer: CUET elasticity of demand numericals revolve around three formulas. Price elasticity (PED) = percentage change in quantity demanded ÷ percentage change in price. Income elasticity (YED) = percentage change in quantity demanded ÷ percentage change in income. Cross elasticity (XED) = percentage change in quantity demanded of X ÷ percentage change in price of Y. The exam typically tests sign interpretation, base-value traps in percentage changes, and classifying goods from the numerical value you compute.
- Quick Answer: What Elasticity Numericals Ask in CUET — Direct Lead
- Price Elasticity of Demand (PED): Formula and Solved Example
- Common Percentage-Change Traps in PED Numericals
- Income Elasticity of Demand (YED): Formula and Solved Example
- Cross Elasticity of Demand (XED): Formula and Solved Example
- Shortcut Tricks to Solve Elasticity Numericals in Under a Minute
- Total Outlay (Expenditure) Method Numericals
- Midpoint (Arc) Elasticity: When CUET Uses It
- Mixed Practice Set: 10 Exam-Style Numericals with Answers
- Quick Revision Table: Formulas, Signs and Interpretations
- Frequently Asked Questions
- Q: What is the standard formula for price elasticity of demand?
- Q: Why is income elasticity negative for inferior goods?
- Q: When should I use the arc (midpoint) elasticity method?
- Q: How does the total outlay method determine elasticity?
- Q: Can cross elasticity be zero?
- Related reading
Price Elasticity of Demand (PED): Formula and Solved Example
Price elasticity of demand measures how responsive quantity demanded is to a change in price. Under the percentage method:
PED = (% Change in Quantity Demanded) ÷ (% Change in Price)
Because price and quantity move in opposite directions along a demand curve, PED computed this way is negative; CUET answer keys conventionally report the absolute value unless the question specifies “with sign”.
Solved Example 1: Price of a good falls from ₹20 to ₹16 and quantity demanded rises from 100 units to 130 units. Find PED.
- % change in quantity = (130 − 100)/100 × 100 = 30%
- % change in price = (16 − 20)/20 × 100 = −20%
- PED = 30 ÷ (−20) = −1.5, i.e., |PED| = 1.5 (elastic demand)
Since |PED| > 1, demand is elastic: buyers respond more than proportionately to the price cut. For the underlying theory, refer to NCERT Class 12 Economics Part I (Introductory Microeconomics), Chapter 2 and 4, available at ncert.nic.in.
Common Percentage-Change Traps in PED Numericals
Most lost marks in elasticity of demand numericals come from four recurring traps:
- Wrong base for percentage change. Always divide the change by the original value under the simple percentage method. Using the new value as base gives a wrong denominator (in Example 1, dividing 30 by 130 instead of 100).
- Sign errors. PED is negative by formula. If options include only positive values, the key expects the absolute value; if a question says “PED = +1.5”, treat the sign as dropped by convention, not as a property of the good.
- Swapping numerator and denominator. Quantity change goes on top; price change on the bottom. Reading “price elasticity” and putting price on top is the single most common MCQ error.
- Mixing up which variable changed. In XED especially, check whether the question changed the price of good Y (not X). Underline the changed variable before computing.
Income Elasticity of Demand (YED): Formula and Solved Example
YED = (% Change in Quantity Demanded) ÷ (% Change in Income)
Interpretation depends entirely on sign and magnitude:
- YED > 0: normal good (YED > 1 = luxury; 0 < YED < 1 = necessity)
- YED < 0: inferior good — quantity demanded falls as income rises
Solved Example 2: Income rises from ₹10,000 to ₹12,000 per month. Demand for coarse cloth falls from 60 metres to 54 metres. Find YED.
- % change in quantity = (54 − 60)/60 × 100 = −10%
- % change in income = (12,000 − 10,000)/10,000 × 100 = +20%
- YED = −10 ÷ 20 = −0.5 → inferior good
A negative income elasticity in a numerical signifies that the good is inferior: consumers abandon it as their purchasing power rises.
Cross Elasticity of Demand (XED): Formula and Solved Example
XED = (% Change in Quantity Demanded of Good X) ÷ (% Change in Price of Good Y)
Solved Example 3: Price of tea rises by 10%. Quantity demanded of coffee rises by 25%. Find XED and classify the goods.
- XED = 25 ÷ 10 = +2.5 → positive XED → tea and coffee are substitutes
Solved Example 4: Price of petrol rises 20%; demand for cars falls 10%.
- XED = −10 ÷ 20 = −0.5 → negative XED → complements
Solved Example 5: Price of cars rises 15%; demand for tea is unchanged (0%). XED = 0 → unrelated goods.
Shortcut Tricks to Solve Elasticity Numericals in Under a Minute
- Ratio shortcut: Skip percentage conversion. PED = (ΔQ/Q) ÷ (ΔP/P) = (ΔQ × P) ÷ (ΔP × Q). With Example 1: (30 × 20) ÷ (−4 × 100) = 600 ÷ −400 = −1.5. One line, no percentages.
- Quick magnitude estimation: If the quantity change looks bigger than the price change, |PED| > 1 (elastic); if smaller, inelastic. Eliminate two MCQ options instantly.
- Sign-first reading: Before computing anything, note the direction of both changes. Same direction → normal good (YED) or substitutes (XED); opposite direction → inferior good or complements. This often answers classification MCQs with zero arithmetic.
- Unit check: Elasticity is a pure ratio — it has no units. If your answer carries “₹” or “units”, you have inverted the formula.
Total Outlay (Expenditure) Method Numericals
The total outlay (TE) method, associated with Alfred Marshall, classifies elasticity by watching what happens to total spending (P × Q) when price changes — no percentage math needed:
| Price Change | Total Expenditure Change | Elasticity Grade |
|---|---|---|
| Falls | Rises | Elastic (|PED| > 1) |
| Falls | Falls | Inelastic (|PED| < 1) |
| Rises | Rises | Inelastic (|PED| < 1) |
| Rises | Falls | Elastic (|PED| > 1) |
| Rises/Falls | Unchanged | Unitary elastic (|PED| = 1) |
Solved Example 6: Price falls from ₹10 to ₹8; quantity rises from 50 to 70. TE before = ₹500; TE after = ₹560. Price fell, expenditure rose → elastic demand.
Midpoint (Arc) Elasticity: When CUET Uses It
When the change is large and the question gives two price–quantity points without naming a “original” value, the simple percentage method gives different answers depending on direction. The arc (midpoint) method removes the ambiguity by using averages:
PED (arc) = [(Q₂ − Q₁) ÷ (Q₁ + Q₂)] ÷ [(P₂ − P₁) ÷ (P₁ + P₂)]
(The ½ or 2 cancels from both numerator and denominator.)
Solved Example 7: Price falls from ₹10 to ₹8; quantity rises from 100 to 140.
- Quantity term: (140 − 100)/(100 + 140) = 40/240 = 1/6
- Price term: (8 − 10)/(10 + 8) = −2/18 = −1/9
- PED = (1/6) ÷ (−1/9) = 9/−6 = −1.5 → |PED| = 1.5
Use the arc method whenever the question words the change symmetrically (“when price moves from A to B”) or when options don’t match your simple-method answer.
Mixed Practice Set: 10 Exam-Style Numericals with Answers
- Price rises 10%, quantity demanded falls 5%. PED = ? — 0.5 (inelastic)
- Price falls from ₹50 to ₹45; demand rises 400 → 440. PED = ? — 1.25 (elastic)
- Income rises 20%; demand for dal rises 5%. YED = ? — +0.25 (necessity)
- Income rises 15%; demand for branded clothes rises 30%. YED = ? — +2 (luxury)
- Income rises 10%; demand for local bus travel falls 4%. YED = ? — −0.4 (inferior good)
- Price of Pepsi rises 8%; demand for Coke rises 12%. XED = ? — +1.5 (substitutes)
- Price of printers falls 10%; demand for cartridges rises 15%. XED = ? — −1.5 (complements)
- Price rises from ₹20 to ₹24; quantity falls 150 → 120. TE method: elasticity grade? — TE ₹3000 both times → unitary elastic
- Price falls ₹12 → ₹9; quantity 80 → 120. Arc PED? — Q: 40/200 = 0.2; P: −3/21 = −1/7; PED = 0.2 × 7 = −1.4 → |PED| = 1.4
- Price of cricket bats rises 25%; demand for footballs unchanged. XED = ? — 0 (unrelated goods)
Quick Revision Table: Formulas, Signs and Interpretations
| Measure | Formula | Sign / Value | Interpretation |
|---|---|---|---|
| PED (percentage method) | %ΔQd ÷ %ΔP | > 1 | Elastic |
| = 1 | Unitary elastic | ||
| < 1 | Inelastic | ||
| YED | %ΔQd ÷ %ΔIncome | + (and > 1) | Luxury (normal good) |
| + (0 to 1) | Necessity (normal good) | ||
| − | Inferior good | ||
| XED | %ΔQd of X ÷ %ΔP of Y | + | Substitutes |
| − | Complements | ||
| 0 | Unrelated goods | ||
| Arc (midpoint) PED | [(Q₂−Q₁)/(Q₁+Q₂)] ÷ [(P₂−P₁)/(P₁+P₂)] | — | Use for large changes / two-point data |
| Total outlay method | P × Q movement | P↓ TE↑ / P↑ TE↓ | Elastic |
| TE unchanged | Unitary elastic |
For the official CUET Commerce & Management syllabus scope, cross-check with the NTA information bulletin at nta.ac.in, and for concept depth, the NCERT Microeconomics chapters at ncert.nic.in.
Frequently Asked Questions
Q: What is the standard formula for price elasticity of demand?
PED = percentage change in quantity demanded ÷ percentage change in price. Always take the absolute value unless the question explicitly asks for the signed value, since PED is negative along a normal demand curve.
Q: Why is income elasticity negative for inferior goods?
Because quantity demanded falls as income rises, the numerator (%ΔQd) turns negative while the denominator (%ΔIncome) is positive, giving a negative ratio — the defining signature of an inferior good.
Q: When should I use the arc (midpoint) elasticity method?
Use it when price or quantity changes are large and the two situations have different base values, or when the question gives two points without identifying an “original”. It divides each change by the average of old and new values, so the answer is identical in both directions.
Q: How does the total outlay method determine elasticity?
Price up + expenditure up = inelastic; price up + expenditure down = elastic; expenditure unchanged = unitary elastic (the reverse pattern holds when price falls).
Q: Can cross elasticity be zero?
Yes. For unrelated goods — such as tea and cars — a change in the price of one leaves demand for the other untouched, so XED equals exactly zero.
Related reading
- Income Statement Decoded for Commerce Students: COGS, Gross Profit vs Net Profit with a Mini Case
- Accounting Part 1: Concepts to Journal – The Language of Business
Quick revision
- % change in quantity = (130 − 100)/100 × 100 = 30%
- % change in price = (16 − 20)/20 × 100 = −20%
- PED = 30 ÷ (−20) = −1.5, i.e., |PED| = 1.5 (elastic demand)
- Wrong base for percentage change.: Always divide the change by the original value under the simple percentage method.
- Sign errors.: PED is negative by formula.
- Swapping numerator and denominator.: Quantity change goes on top; price change on the bottom.
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