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  3. Chapter 2: Differentiation of functions of one variable
  4. Applications 1
  5. Marginality
  6. Exercise 2

Exercise 2

A production function is given by $P(L)=L^4\cdot (\frac{8}{9})^{L}$, $(L\geq 0))$. Determine the marginal production function.
$MP(L)=L^3\cdot (\frac{8}{9})^{L}(4+L\ln(L))$
$MP(L)=4L^3\cdot (\frac{8}{9})^{L}\ln(\frac{8}{9})$
$MP(L)=L^3\cdot (\frac{8}{9})^{L}(4+L)$
$MP(L)=L^3\cdot (\frac{8}{9})^{L}(4+L\ln(\frac{8}{9}))$
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.