Exercise 1 | Wiskunde op Tilburg University

Consider the utility function

$U(x,y)=3x^3y^4$ . Determine the marginal rate of substitution at

$(x,y)=(4,1)$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$3$

Antwoord 2 correct

Fout

Antwoord 3 optie

$\frac{3}{4}\cdot 4^{\frac{2}{3}}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$\dfrac{3}{4}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$\dfrac{3}{16}$

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,

$MRS(4,1)=\dfrac{3\cdot 1}{4 \cdot 4}=\dfrac{3}{16}$ .

Go on.

Antwoord 2 feedback

Wrong:

$(x,y) \neq (1,4)$ .

Try again.

Antwoord 3 feedback

Wrong:

$\frac{9x^2y^4}{12x^3y^3}\neq \frac{3}{4}x^{\frac{2}{3}}y^{\frac{4}{3}}$ .

See Properties power functions.

Antwoord 4 feedback

Wrong: Use

$(x,y)=(4,1)$ .

Try again.