Consider the demand function $X(p)=100-10\sqrt{p}$, $(0 \leq p \leq 100)$. Determine the elasiticty.
Antwoord 1 correct
Correct
Antwoord 2 optie
$\frac{-10}{2\sqrt{p}}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$\frac{1}{2}-\frac{\sqrt{p}}{20}$
Antwoord 3 correct
Fout
Antwoord 4 optie
$\frac{100\sqrt{p}-1000}{2p\sqrt{p}}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$\frac{\sqrt{p}}{2\sqrt{p}-20}$
Antwoord 1 feedback
Correct:
$$\begin{align*}
\epsilon & = X'(p)\cdot \frac{p}{X(p)}\\
& = \frac{-10}{2\sqrt{p}}\cdot \frac{p}{100-10\sqrt{p}}\\
& = \frac{-10p}{200\sqrt{p}-20p}\\
&= \frac{-10\sqrt{p}}{200-20\sqrt{p}}\\
& = \frac{\sqrt{p}}{2\sqrt{p}-20}.
\end{align*}$$
Go on.
Antwoord 2 feedback
Wrong: $\epsilon \neq X'(p)$.
See Elasticity.
Antwoord 3 feedback
Wrong: $\frac{-10\sqrt{p}}{200-20\sqrt{p}}\neq \frac{1}{2}-\frac{\sqrt{p}}{20}$.
Try again.
Antwoord 4 feedback
Wrong: $\epsilon \neq X'(p)\cdot \frac{X(p)}{p}$.
See Elasticity.