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

Question

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

✓

Answer

The demand function is
$
\begin{aligned}
D & =\frac{p+6}{p-3} \\
\therefore \frac{d D}{d p} & =\frac{d}{d p}\left(\frac{p+6}{p-3}\right) \\
& =\frac{(p-3) \frac{d}{d p}(p+6)-(p+6) \frac{d}{d p}(p-3)}{(p-3)^2} \\
& =\frac{(p-3)(1+0)-(p+6)(1-0)}{(p-3)^2} \\
& =\frac{p-3-p-6}{(p-3)^2}=\frac{-9}{(p-3)^2}
\end{aligned}
$
Elasticity of demand is given by
$
\begin{aligned}
\eta & =\frac{-p}{D} \cdot \frac{d D}{d p} \\
& =\frac{-p}{\left(\frac{p+6}{p-3}\right)} \times \frac{-9}{(p-3)^2}
\end{aligned}
$
$
=\frac{9 p}{(p+6)(p-3)}
$
When $p=4$, then
$
\eta=\frac{9(4)}{(4+6)(4-3)}=\frac{36}{10 \times 1}=3.6 .
$
Hence, the elasticity of demand at $p=4$ is 3.6

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