Exercise 2 | Wiskunde op Tilburg University

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.

Antwoord 2 feedback

Wrong: Use that

$\Delta x =-2$ .

Try again.

Antwoord 3 feedback

Wrong: Use that

$\Delta x =-2$ .

Try again.

Antwoord 4 feedback

Wrong:

$\Delta y = - MRS(x,y) \cdot \Delta x$ .

See Applications 2: Marginal rate of subsitution.