If the demand function is D = (p+6 p-3 ), find the elasticity of … - Vidyadip

Question

If the demand function is $D =\left(\frac{p+6}{p-3}\right)$, find the elasticity of demand at $p =4$.

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Answer

$\text { Given, demand function is } D =\left(\frac{p+6}{p-3}\right)$
$\therefore \frac{ dD }{ dp }=\frac{(p-3) \frac{ d }{ dp }(p+6)-(p+6) \frac{ d }{ dp }(p-3)}{(p-3)^2}$
$\therefore \frac{ dD }{ dp }=\frac{(p-3)(1+0)-(p+6)(1-0)}{(p-3)^2}$
$\therefore \frac{ dD }{ dp }=\frac{\not p-3-\not p-6}{(p-3)^2}$
$\therefore \frac{ dD }{ dp }=\frac{-9}{(p-3)^2}$
$\eta=\frac{-p}{ D } \cdot \frac{ dD }{ dp }$
$\therefore \eta=\frac{-p}{\left(\frac{p+6}{{p-3}}\right)} \cdot \frac{-9}{(p-3)^{\not 2}}$
$\therefore \eta=\frac{9 p}{(p+6)(p-3)}$
Substituting $p=4$, we get,
$ \therefore \eta=\frac{9 \times 4}{(4+6)(4-3)}$
$\therefore \eta=\frac{36}{10 \times 1}$
$\therefore \eta=\frac{36}{10}$
$\therefore \eta=3.6 $
$\therefore \eta$ (elasticity of demand at $p=4)=3.6$.

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