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Find the elasticity of demand at the price p=8.5 with the demand of p.x^2=498.75 the...
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You need to find the demand function, such that:
`p*x^2 = 498.75 => x^2 = 498.75/p => x = +-sqrt(498.75/p)`
You need to find the price elasticity of demand using the following formula, such that:
`ED = (dx)/(dp)*(p/x)`
`(dx)/(dp) = (d(sqrt(498.75/p)))/(dp) => (dx)/(dp) = (-498.75/p^2)/2sqrt(498.75/p) => (dx)/(dp) = (-sqrt(498.75p)/(2p^2))`
Replacing `(-sqrt(498.75p)/(2p^2))` for `(dx)/(dp)` and `sqrt(498.75/p)` for x yields:
`ED = (-sqrt(498.75p)/(2p^2))*(p/(sqrt(498.75/p)))`
`ED = -1/2 < 1`
Hence, evaluating the price elasticity of demand yields `ED = -1/2 < 1,` thus the demad is price inelastic.
Posted by sciencesolve on May 10, 2013 at 4:48 PM (Answer #1)
`px^2= 498.75` `x=sqrt(498.75/p)` `sqrt(498.75) xx p^-(1/2)`
`dx/dp= sqrt(498.75) xx (-1/2) xx p^(-1/2-1)= (-1/2)sqrt(498.75)p^(-3/2)`
`ED=((dx)/(dp)) xx (p/x)= (-1/2)sqrt(498.75) p^(-3/2) xx p sqrt(p)/sqrt(498.75)=`
`= (-1/2) p^(-3/2+1+1/2)=(-1/2)<1`````
Posted by oldnick on May 10, 2013 at 11:48 PM (Answer #2)
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