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find the elasticity of demand at the price p=3 with the demand of p=sqrt(3600-x) the...

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rmunoz90 | Student, Undergraduate | Salutatorian

Posted May 10, 2013 at 3:30 PM via web

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find the elasticity of demand at the price p=3 with the demand of p=sqrt(3600-x)

the elasticity of demand is ED=

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 10, 2013 at 4:32 PM (Answer #1)

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You need to write the demand function such that:

`p = sqrt(3600 - x) => p^2 = 3600 - x => x = 3600 - p^2`

You need to evaluate price elasticity of demand such that:

`ED = (dx)/(dp)*(p/x)`

Differentiating the function `x = 3600 - p^2` with respect to p yields:

`(dx)/(dp) = -2p`

Replacing -`2p` for` (dx)/(dp)` and `3600 - p^2` for x yields:

`ED = -2p*p/(3600 - p^2)`

You need to find the price elasticity at p = 3, such that:

`ED = -2*3^2/(3600 - 3^2) => ED = -18/3591 => ED = -0.005`

Hence, evaluating the elasticity of demand at p = 3 yields ED = `-0.005 < 1` , thus the demand is price inelastic.

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