Consider the demand function $D(p)=5p^{-3}$, $(p>0)$. Use elasticity to determine the approximate percentage increase in $p$ if $D$ increases by $4 \%$.
Antwoord 1 correct
Correct
Antwoord 2 optie
Since no value for $p$ is given, this cannot be determined.
Antwoord 2 correct
Fout
Antwoord 3 optie
$-12$
Antwoord 3 correct
Fout
Antwoord 4 optie
$\frac{5}{64}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$-1\frac{1}{3}$
Antwoord 1 feedback
Correct:
$$\begin{align*}
\epsilon & = D'(p)\cdot \frac{p}{D(p)}\\
& = -15p^{-4}\cdot \frac{p}{5p^{-3}}\\
& = \frac{-15p^{-3}}{5p^{-3}}\\
& = -3.
\end{align*}$$
Hence, for every value of $p$ it holds that $\epsilon = -3$.
Then, pluggin in the values into $\% \Delta D \approx \epsilon \cdot \% \Delta p$ gives $4 \approx -3 \cdot \% \Delta p$. Hence, $\% \Delta p \approx \frac{4}{-3}=-1\frac{1}{3}$.
Go on.
$$\begin{align*}
\epsilon & = D'(p)\cdot \frac{p}{D(p)}\\
& = -15p^{-4}\cdot \frac{p}{5p^{-3}}\\
& = \frac{-15p^{-3}}{5p^{-3}}\\
& = -3.
\end{align*}$$
Hence, for every value of $p$ it holds that $\epsilon = -3$.
Then, pluggin in the values into $\% \Delta D \approx \epsilon \cdot \% \Delta p$ gives $4 \approx -3 \cdot \% \Delta p$. Hence, $\% \Delta p \approx \frac{4}{-3}=-1\frac{1}{3}$.
Go on.
Antwoord 2 feedback
Wrong: In this case the elasticity is not depending on $p$.
Try again.
Try again.
Antwoord 3 feedback
Antwoord 4 feedback