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Q.For the given demand function p=40−xp=40-x, find the output when ηd=1\eta d=1.

Tamil Nadu DgeTamil Nadu HSC First Year (DGE) Commerce Board 2025Subjective· 2mImportance★★★★★
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Use ηd=−pxdxdp\eta_d=-\dfrac{p}{x}\dfrac{dx}{dp}; solving ηd=1\eta_d=1 for the demand p=40−xp=40-x gives x=20x=20.

Given: demand function p=40−xp=40-x.

Step 1 — express xx in terms of pp and differentiate.

x=40−p⇒dxdp=−1.x=40-p\quad\Rightarrow\quad \frac{dx}{dp}=-1.

Step 2 — write the elasticity of demand.

ηd=−px⋅dxdp=−px⋅(−1)=px=40−xx.\eta_d=-\frac{p}{x}\cdot\frac{dx}{dp}=-\frac{p}{x}\cdot(-1)=\frac{p}{x}=\frac{40-x}{x}.

Step 3 — apply the condition ηd=1\eta_d=1. …

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