Exercise 2 | Wiskunde op Tilburg University

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.