Exercise 1 | Wiskunde op Tilburg University

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.