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Q.If the demand function is D=50−3p−p2D = 50 - 3p - p^2. Find the elasticity of demand at p=5p = 5 comment on the result.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2026Subjective· 3mImportance★★★★★
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For D=50−3p−p2D = 50 - 3p - p^2, the price elasticity of demand is η=−pD⋅dDdp\eta = -\frac{p}{D}\cdot\frac{dD}{dp}. At p=5p = 5: dDdp=−13\frac{dD}{dp} = -13 and D=10D = 10, giving η=6.5>1\eta = 6.5 > 1, so demand is elastic.

The demand function is D=50−3p−p2D = 50 - 3p - p^2.

Step 1 — Rate of change of demand.

dDdp=−3−2p\frac{dD}{dp} = -3 - 2p

At p=5p = 5:

dDdp=−3−2(5)=−3−10=−13\frac{dD}{dp} = -3 - 2(5) = -3 - 10 = -13

Step 2 — Demand at p=5p = 5.

D=50−3(5)−(5)2=50−15−25=10D = 50 - 3(5) - (5)^2 = 50 - 15 - 25 = 10

Step 3 — Elasticity of demand.

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