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.
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.
Try again.
Antwoord 3 feedback
Wrong: Use $P'_K(L,K)$.
Try again.
Try again.
Antwoord 4 feedback