Question:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: For a demand function \(P=60-Q^2\) and at price \(P=44\), point elasticity of demand is \(-1.375\). Reason R: Demand is inelastic.
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: For a demand function \(P=60-Q^2\) and at price \(P=44\), point elasticity of demand is \(-1.375\). Reason R: Demand is inelastic.
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If \(|E_d|>1\), demand is elastic. If \(|E_d|<1\), demand is inelastic.
Updated On: May 22, 2026
- Both A and R are correct and R is the correct explanation of A
- Both A and R are correct but R is NOT the correct explanation of A
- A is correct but R is not correct
- A is not correct but R is correct
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept: Point elasticity of demand measures responsiveness of quantity demanded to a change in price at a particular point on the demand curve.
\[
E_d=\frac{dQ}{dP}\cdot \frac{P}{Q}
\]
Step 1: Find \(Q\) when \(P=44\).
Given, \[ P=60-Q^2 \] Put \(P=44\): \[ 44=60-Q^2 \] \[ Q^2=16 \] \[ Q=4 \]
Step 2: Find \(\frac{dQ}{dP}\).
\[ P=60-Q^2 \] Differentiate with respect to \(Q\): \[ \frac{dP}{dQ}=-2Q \] So, \[ \frac{dQ}{dP}=\frac{1}{-2Q} \] At \(Q=4\): \[ \frac{dQ}{dP}=-\frac{1}{8} \]
Step 3: Calculate elasticity.
\[ E_d=\frac{dQ}{dP}\cdot \frac{P}{Q} \] \[ E_d=-\frac{1}{8}\cdot \frac{44}{4} \] \[ E_d=-\frac{44}{32} \] \[ E_d=-1.375 \] So Assertion A is correct.
Step 4: Check Reason R.
Since \(|E_d|=1.375>1\), demand is elastic, not inelastic. \[ |E_d|>1 \Rightarrow \text{Elastic demand} \] Therefore, Reason R is incorrect. Hence, the correct answer is option (C).
Step 1: Find \(Q\) when \(P=44\).
Given, \[ P=60-Q^2 \] Put \(P=44\): \[ 44=60-Q^2 \] \[ Q^2=16 \] \[ Q=4 \]
Step 2: Find \(\frac{dQ}{dP}\).
\[ P=60-Q^2 \] Differentiate with respect to \(Q\): \[ \frac{dP}{dQ}=-2Q \] So, \[ \frac{dQ}{dP}=\frac{1}{-2Q} \] At \(Q=4\): \[ \frac{dQ}{dP}=-\frac{1}{8} \]
Step 3: Calculate elasticity.
\[ E_d=\frac{dQ}{dP}\cdot \frac{P}{Q} \] \[ E_d=-\frac{1}{8}\cdot \frac{44}{4} \] \[ E_d=-\frac{44}{32} \] \[ E_d=-1.375 \] So Assertion A is correct.
Step 4: Check Reason R.
Since \(|E_d|=1.375>1\), demand is elastic, not inelastic. \[ |E_d|>1 \Rightarrow \text{Elastic demand} \] Therefore, Reason R is incorrect. Hence, the correct answer is option (C).
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