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प्रश्न
If the demand function is D = 50 – 3p – p2. Find the elasticity of demand at p = 2 comment on the result
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उत्तर
Given, demand function is D = 50 – 3p – p2
∴ `"dD"/"dp" = 0 - 3 - 2"p"`
= `- 3 - 2"p"`
Elasticity of demand is given by
`eta =- ("p")/"D" * "dD"/"dp"`
∴ `eta = (-"p")/(50 - 3"p" - "p"^2) * (- 3 - 2"p")`
∴ `eta = (p(3 + 2p))/(50 - 3p - p^2)`
(i) When p = 5
`eta = (5(3 + 2xx 5))/(50 - 3(5) - (5)^2) = (5xx13)/(50 - 15 - 25)`
= `65/10 = 6.5`
Since η > 1 the demand is elastic
(ii) When p = 2 then,
`eta = (2(3 + 2 xx 2))/(50 - 3(2) - (2)^2) = (2xx7)/(50 -6 - 4)`
= `14/40 = 7/20`
Since, < η < 1, the demand is inelastic.
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Profit π = R – C
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Differentiating w.r.t. x,
`("d"pi)/("d"x)` = `square`
Since Profit is increasing,
`("d"pi)/("d"x)` > 0
∴ Profit is increasing for `square`
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∴ `Q < square`
Hence, profit is increasing for `Q < square`
