Exercise 2 | Wiskunde op Tilburg University

Consider the production function

$P(L,K)=10L^{\frac{1}{4}}K^{\frac{3}{4}}$ . Use marginality to determine the approximate number of units of capital that are necessary to increase the output of production with two units, whereas labor remains constant, given that

$(L,K)=(16,256)$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$1\frac{7}{8}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$\dfrac{1}{10}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$(64\frac{1}{10})^{\frac{4}{3}}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$\dfrac{8}{15}$

Antwoord 1 feedback

Correct:

$MPP_K(L,K)=P'_K(L,K)=7\frac{1}{2}L^{\frac{1}{4}}K^{-\frac{1}{4}}$ . Hence,

$MPP_K(16,256)=3\frac{3}{4}$ .

Then

$\Delta P \approx MPP_K\cdot \Delta K$ gives

$\Delta K \approx \frac{\Delta P}{MPP_K}=\dfrac{2}{3\frac{3}{4}}=\dfrac{8}{15}$ .

Go on.

Antwoord 2 feedback

Wrong:

$\Delta P \approx MPP_K\cdot \Delta K$ .

Try again.

Antwoord 3 feedback

Wrong: Use

$P'_K(L,K)$ .

Try again.

Antwoord 4 feedback

Wrong: Use marginality.

See Example.