Consider the demand function $X(p)=100-10\sqrt{p}$, $(0 \leq p \leq 100)$. Determine by the use of elasticity the approximate percentage change in $X$ if $p$ decreases by $2 \%$, given that $p=49$. (Consider Exercise 1.)
Antwoord 1 correct
Correct
Antwoord 2 optie
$-2\frac{1}{3}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$1\frac{5}{7}$
Antwoord 3 correct
Fout
Antwoord 4 optie
$-1\frac{5}{7}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$2\frac{1}{3}$
Antwoord 1 feedback
Correct:
$\epsilon = \frac{\sqrt{p}}{2\sqrt{p}-20}$ (See Exercise 1).
Hence, at $p=49$: $\epsilon = \frac{\sqrt{49}}{2\sqrt{49}-20}=-\frac{7}{6}$.
Therefore, $\% \Delta X \approx \epsilon \cdot \% \Delta p=-\frac{7}{6}\cdot -2=\frac{14}{6}=2\frac{1}{3}$.
Go on.
$\epsilon = \frac{\sqrt{p}}{2\sqrt{p}-20}$ (See Exercise 1).
Hence, at $p=49$: $\epsilon = \frac{\sqrt{49}}{2\sqrt{49}-20}=-\frac{7}{6}$.
Therefore, $\% \Delta X \approx \epsilon \cdot \% \Delta p=-\frac{7}{6}\cdot -2=\frac{14}{6}=2\frac{1}{3}$.
Go on.
Antwoord 2 feedback
Wrong: Note that $p$ decreases.
Try again.
Try again.
Antwoord 3 feedback
Antwoord 4 feedback