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  3. Chapter 4: Differentiation of functions of two variables
  4. Applications 1
  5. Partial elasticity
  6. Exercise 3

Exercise 3

Consider the production function $P(L,K)=38L^{\frac{3}{13}}K^{\frac{10}{13}}$. Determine the elasticity with respect to labor.
$\dfrac{3}{13}$
$\dfrac{10}{13}$
$\frac{4332}{13}L^{-\frac{20}{13}}K^{\frac{20}{13}}$
$\frac{114}{13}L^{\frac{3}{13}}K^{\frac{10}{13}}$
Consider the production function $P(L,K)=38L^{\frac{3}{13}}K^{\frac{10}{13}}$. Determine the elasticity with respect to labor.
Antwoord 1 correct
Correct
Antwoord 2 optie
$\dfrac{10}{13}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$\frac{4332}{13}L^{-\frac{20}{13}}K^{\frac{20}{13}}$
Antwoord 3 correct
Fout
Antwoord 4 optie
$\frac{114}{13}L^{\frac{3}{13}}K^{\frac{10}{13}}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$\dfrac{3}{13}$
Antwoord 1 feedback
Correct: $P(L,K)$ is a Cobb-Douglas function. (See Extra explanation: Cobb-Douglas functions.)

Go on.
Antwoord 2 feedback
Wrong: That is the partial elasticity with respect to capital, not to labor.

Try again.
Antwoord 3 feedback
Wrong: $\epsilon_L \neq P'_L(L,K)\cdot \dfrac{P(L,K)}{L}$.

See Partial elasticity.
Antwoord 4 feedback
Wrong: $\epsilon_L \neq P'_L(L,K)\cdot L$.

See Partial elasticity.