Consider the utility function $U(x,y)=3x^3y^4$. Let $(x,y)=(4,1)$. Determine by the use of the marginal rate of substitution (See Exercise 1) by how much $y$ should approximately increase, if $x$ decrease by $2$, to keep utility at the same level.
Antwoord 1 correct
Correct
Antwoord 2 optie
$\dfrac{3}{16}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$-\dfrac{3}{16}$
Antwoord 3 correct
Fout
Antwoord 4 optie
$-\dfrac{3}{8}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$\dfrac{3}{8}$
Antwoord 1 feedback
Correct: $MRS(x,y)=\dfrac{U'_x(x,y)}{U'_y(x,y)}=\dfrac{9x^2y^4}{12x^3y^3}=\dfrac{3y}{4x}$.
Hence, $MRS(4,1)=\dfrac{3\cdot 1}{4 \cdot 4}=\dfrac{3}{16}$.
Then $\Delta y \approx -\frac{3}{16} \cdot -2 =\frac{3}{8}$.
Go on.
Hence, $MRS(4,1)=\dfrac{3\cdot 1}{4 \cdot 4}=\dfrac{3}{16}$.
Then $\Delta y \approx -\frac{3}{16} \cdot -2 =\frac{3}{8}$.
Go on.
Antwoord 2 feedback
Wrong: Use that $\Delta x =-2$.
Try again.
Try again.
Antwoord 3 feedback
Wrong: Use that $\Delta x =-2$.
Try again.
Try again.
Antwoord 4 feedback