Find the elasticity of supply for the supply function x = 2p² + 5 when p = 3.

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x = 2p^2 + 5

Tamil Nadu DgeTamil Nadu HSC First Year (DGE) Commerce Board 2020Subjective· 2mImportance★★★★★

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Use $E_s=\dfrac{p}{x}\dfrac{dx}{dp}$ . Here $\dfrac{dx}{dp}=4p$ , and at $p=3$ , $x=23$ , giving $E_s=\dfrac{36}{23}\approx1.565$ .

This tests elasticity from the Applications of Differentiation unit of the Tamil Nadu HSC Class-11 Business Mathematics syllabus.

Step 1 — Formula. The elasticity of supply is

$E_s=\frac{p}{x}\cdot\frac{dx}{dp}.$

Step 2 — Differentiate the supply function. $x=2p^2+5\Rightarrow \dfrac{dx}{dp}=4p.$

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

CBSE 2025Set ANNUAL1 mark
$R_A$
›Reveal solutionSolution

Use the relation $R_M = R_A\left(1 - \frac{1}{\eta}\right)$ with $R_A = 50$ and $\eta = 5$ .

The relationship between marginal revenue $R_M$ , average revenue $R_A$ and the elasticity of demand $\eta$ is

$R_M = R_A\left(1 - \frac{1}{\eta}\right).$

…

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CBSE 2023Set ANNUAL1 mark
$0 < \eta < 1$
›Reveal solutionSolution
When $0 < \eta < 1$ , the percentage change in demand is smaller than the percentage change in price, so demand is inelastic.

The (numerical value of the) price elasticity of demand $\eta$ compares the proportional change in quantity demanded with the proportional change in price. The standard classification is:

$\eta > 1$ : demand is elastic (demand is highly responsive to price);

$\eta = 1$ : demand is unitary elastic; …
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CBSE 2022Set MARCH1 markMCQ
$Q. If the demand function is said to be elastic, then :$
(a) $|\eta_d| < 1$
(b) $|\eta_d| > 1$
(c) $|\eta_d| = 0$
(d) $|\eta_d| = 1$
›Reveal solutionSolution
Elastic demand corresponds to $|\eta_d|>1$ (quantity responds more than proportionally to price).

The price elasticity of demand $\eta_d$ compares the proportional change in quantity demanded to the proportional change in price. Its magnitude classifies demand:

$|\eta_d| > 1$ : elastic — quantity changes more than proportionally.

$|\eta_d| = 1$ : unit elastic. …
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Q.Find the elasticity of supply for the supply function $x = 2p^2 + 5$ when $p = 3$ .

Concept understanding — Elasticity of Demand

Q.Find the elasticity of supply for the supply function x=2p2+5x = 2p^2 + 5x=2p2+5 when p=3p = 3p=3.

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Q.Find the elasticity of supply for the supply function $x = 2p^2 + 5$ when $p = 3$ .

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