Exercise 1 | Wiskunde op Tilburg University

Consider the utility function $U(x,y)=2x^{\frac{3}{2}}y^3$ . Determine the indifference curve with $U$ -value 54.

Antwoord 1 correct

Correct

Antwoord 2 optie

$y=\dfrac{9}{\sqrt{x}}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$y=\dfrac{9}{x^{\frac{3}{2}}}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$y=\dfrac{3}{x^{\frac{3}{2}}}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$y=\dfrac{3}{\sqrt{x}}$

Antwoord 1 feedback

Correct:

$\begin{align} U(x,y) = 54 & \Leftrightarrow 2x^{\frac{3}{2}}y^3=54\\ & \Leftrightarrow y^3=\frac{54}{2x^{\frac{3}{2}}}\\ & \Leftrightarrow y^3=\frac{27}{x^{\frac{3}{2}}}\\ & \Leftrightarrow y=\Big(\dfrac{27}{x^{\frac{3}{2}}}\Big)^{\frac{1}{3}}\\ & \Leftrightarrow y=\dfrac{3}{x^{\frac{1}{2}}}\\ & \Leftrightarrow y=\frac{3}{\sqrt{x}}.\\ \end{align}$

Go on.

Antwoord 2 feedback

Wrong: $27^{\frac{1}{3}}\neq 9$ .

See Properties power functions.

Antwoord 3 feedback

Wrong: $27^{\frac{1}{3}}\neq 9$ .

See Properties power functions.

Antwoord 4 feedback

Wrong: $(x^{\frac{3}{2}})^{\frac{1}{3}}\neq x^{\frac{3}{2}}$ .

Try again.