Q.The price of tea rises from ₹200 to ₹250 per kg. As a result, the quantity demanded of coffee (by the same group of consumers) rises from 100 kg to 110 kg per week. Calculate the cross elasticity of demand between coffee and tea, and state the relationship between the two goods.
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Cross Elasticity of Demand
Cross elasticity of demand measures the responsiveness of the quantity demanded of one good (X) to a change in the price of another good (Y). Its greatest value is that its sign reveals the relationship between the two goods.
The sign of cross elasticity classifies goods: positive ⇒ substitutes, negative ⇒ complements, zero ⇒ unrelated/independent.
Ec=% change in price of Y% change in quantity demanded of X
Interpreting the value
- Positive (Ec>0): substitutes (tea & coffee) — a rise in Y's price raises demand for X. Perfect substitutes give a very high value.
- Negative (Ec<0): complements (car & petrol) — a rise in Y's price cuts demand for X.
- Zero / near-zero: goods are independent / unrelated — a price change in one has no effect on the other (e.g. price of salt and demand for laptops).
The magnitude also matters: the larger the absolute value, the closer the relationship — a very high positive value means near-perfect substitutes, while a value close to zero means the goods barely affect each other.
A monopolist's product has no close substitutes, so its cross elasticity with any other good is zero or very small. This near-zero cross elasticity is itself a defining test of monopoly.
Quick example
Price of coffee rises 10% and, as buyers switch, quantity of tea demanded rises 15%:
- Ec=+10%+15%=+1.5. …
Cross elasticity compares the percentage change in quantity demanded of one good to the percentage change in the price of a related good. …
Step 1 — Percentage change in quantity demanded of coffee.
%ΔQcoffee=100110−100×100=10%
Step 2 — Percentage change in price of tea.
%ΔPtea=200250−200×100=25%
Step 3 — Cross elasticity.
Ec=%ΔPtea%ΔQcoffee=2510=0.4 …
Cross-check using the ratio-of-changes form directly (without converting to percentages first): $E_c = \dfrac{\Delta Q/Q_1}{\Delta P/P_1} = \dfrac{10/100}{50/200} = \dfr …
Mixing up which good's quantity and which good's price go in the numerator and denominator; a positive value must always be read as 'substitutes' and a negative va …
- CA Foundation 2026Set jan-20261 markMCQQ.If cross-price elasticity between two products is zero, the goods are best described as: (A) Close substitutes (B) Totally unrelated (C) Perfect substitutes (D) Complements to each other
›Reveal solutionSolution
Zero cross elasticity ⇒ a price change in one good leaves demand for the other unchanged ⇒ the goods are independent (totally unrelated).
Concept — cross-price elasticity
Cross-price elasticity of demand measures how the demand for one good responds to a change in the price of another:
Ec=%ΔPy%ΔQx
Reading the sign
- Positive Ec ⇒ substitutes (options A, C).
- Negative Ec ⇒ complements (option D).
- Zero Ec ⇒ the goods are unrelated / independent — a change in Py produces no change in Qx.
Since Ec=0 here, the correct description is 'totally unrelated'. …
- CA Foundation 2026Set jan-20261 markMCQQ.The cross elasticity of demand for monopolist's product and any other product is: (A) 1 (B) Greater than 1 (C) Less than 1 (D) Zero or very small
›Reveal solutionSolution
A monopoly product has no close substitutes, so its cross elasticity of demand with any other product is zero or very small.
Concept
Cross elasticity of demand measures how the demand for one good responds to a change in another good's price. A high positive cross elasticity signals close substitutes. Since a monopolist by definition produces a good with no close substitutes, changes in other products' prices leave its demand almost unchanged:
Ec=%ΔPother good%ΔQmonopoly good≈0
Thus the value is zero or very small — indeed, a very low cross elasticity is one test of monopoly.
Why the others are wrong
- (A), (B) and (C) all imply meaningful substitutability, which contradicts the definition of monopoly. …
- CA Foundation 2026Set may-20261 markMCQQ.When the price of sugar is ₹ 60 per kg, its demand is 10 Kgs. Subsequently, if the price of coffee declines from ₹ 500 per kg to ₹ 450 per Kg, the usage of sugar rises from 10 kgs to 15 kgs. Calculate the cross price elasticity. (A) −5 (B) 10 (C) −2.5 (D) 2.5
›Reveal solutionSolution
Ec=%ΔQsugar÷%ΔPcoffee=50%÷(−10%)=−5.
Step 1 — Formula
Ec=% change in price of good Y% change in quantity demanded of good X
Step 2 — Change in quantity of sugar
%ΔQsugar=1015−10×100=+50%
Step 3 — Change in price of coffee
%ΔPcoffee=500450−500×100=−10%
Step 4 — Cross elasticity
Ec=−1050=−5
The negative value shows sugar and coffee are complements (people sweeten coffee with sugar), so cheaper coffee raises sugar demand.
Why the other options are wrong …
- CA Foundation 2025Set jan-20251 markMCQQ.A shopkeeper sells two commodities A and B, which are close substitute of each other. It is observed that when the price of commodity A rises by 20% the demand for B increases by 30%. What is the cross price elasticity for commodity B against the price of commodity A ? (A) +1 (B) -1 (C) +1.5 (D) -1.5
›Reveal solutionSolution
Cross elasticity Ec=%ΔQB/%ΔPA=30/20=+1.5 (positive → substitutes).
Step 1 — Write the formula
Ec=% change in price of A% change in quantity demanded of B
Step 2 — Substitute the data
Price of A rises by 20%; demand for B rises by 30%.
Ec=+20%+30%=+1.5
Step 3 — Interpret the sign
A positive cross elasticity means the two goods move together — when A's price rises, buyers switch to B — confirming they are substitutes, which matches the question. Magnitude 1.5 (>1) shows a fairly strong substitution response. …
- CA Foundation 2025Set may-20251 markMCQQ.When two goods are complementary, the cross elasticity between them is : (A) Infinite (B) Positive and large (C) Zero (D) Negative
›Reveal solutionSolution
For complements, cross elasticity of demand is negative, so the answer is (D).
Step 1 — Definition
Cross elasticity of demand measures how the quantity demanded of good X responds to a change in the price of good Y:
EXY=%ΔPY%ΔQX
Step 2 — Sign for complements
Complementary goods (e.g. car and petrol) are consumed jointly. If PY rises, buyers use less of Y and therefore less of X too, so QX falls. A price rise causing a quantity fall means numerator and denominator have opposite signs → EXY<0 (negative).
Step 3 — Reject the others
- (A) Infinite / (B) Positive and large — describe substitutes (positive cross elasticity). …
- CA Foundation 2024Set sep-20241 markMCQQ.The price of 1 kg. of tea is ₹ 50. At this price, 10 kg. of tea is demanded. If the price of coffee rises from ₹ 30 to ₹ 40 per kg., the quantity demanded of tea rises from 10 kg. to 15 kg. What will be the cross price elasticity of tea ? (A) +1 (B) −1.5 (C) +1.5 (D) −1
›Reveal solutionSolution
Cross elasticity =%ΔPcoffee%ΔQtea=33.33%50%=+1.5 (substitutes).
Step 1 — Percentage change in the quantity of tea
%ΔQtea=1015−10×100=50%
Step 2 — Percentage change in the price of coffee
%ΔPcoffee=3040−30×100=33.33%
Step 3 — Apply the cross-elasticity formula
Ec=%ΔPcoffee%ΔQtea=33.3350=+1.5
The positive value means the two goods are substitutes — a costlier coffee pushes buyers toward tea.
Step 4 — Why the other options are wrong
- (B) −1.5 / (D) −1 — a negative sign would mean complements; here demand for tea rises with coffee's price, so the sign is positive. …
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