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.)
$2\frac{1}{3}$
$-2\frac{1}{3}$
$1\frac{5}{7}$
$-1\frac{5}{7}$
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.
Antwoord 2 feedback
Wrong: Note that $p$ decreases.

Try again.
Antwoord 3 feedback
Wrong: $\% \Delta X \approx \epsilon \cdot \%\Delta p$.

See Elasticity or Example.
Antwoord 4 feedback
Wrong: $\% \Delta X \approx \epsilon \cdot \%\Delta p$.

See Elasticity or Example.