Exercise 2 | Wiskunde op Tilburg University

A production function is given by

$P(L)=L^4\cdot (\frac{8}{9})^{L}$ ,

$(L\geq 0))$ . Determine the marginal production function.

Antwoord 1 correct

Fout

Antwoord 2 optie

$MP(L)=4L^3\cdot (\frac{8}{9})^{L}\ln(\frac{8}{9})$

Antwoord 2 correct

Fout

Antwoord 3 optie

$MP(L)=L^3\cdot (\frac{8}{9})^{L}(4+L)$

Antwoord 3 correct

Fout

Antwoord 4 optie

$MP(L)=L^3\cdot (\frac{8}{9})^{L}(4+L\ln(\frac{8}{9}))$

Antwoord 4 correct

Correct

Antwoord 1 optie

$MP(L)=L^3\cdot (\frac{8}{9})^{L}(4+L\ln(L))$

Antwoord 1 feedback

Wrong: What is the derivative of a fuction

$y(x)=a^x$ ?

See Derivatives elementary functions.

Antwoord 2 feedback

Wrong: You have to use the product rule.

See Rules of differentiation.

Antwoord 3 feedback

Wrong: What is the derivative of a fuction

$y(x)=a^x$ ?

See Derivatives elementary functions.

Antwoord 4 feedback

Correct:

$\begin{align*} MP(L) & = P'(L)\\ & = 4L^3\cdot (\tfrac{8}{9})^{L}+L^4\cdot(\tfrac{8}{9})^{L}\cdot \ln(\tfrac{8}{9})\\ & =L^3\cdot (\tfrac{8}{9})^{L}(4+L\ln(\tfrac{8}{9})). \end{align*}$

Go on.