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  3. Chapter 3: Functions of two variables
  4. Applications
  5. Utility functions and indifference curves
  6. Exercise 2

Exercise 2

Consider the utility function $U(x,y)=\frac{xy}{5x+y}$. Determine the indifference curve with $U$-value 4.
$y=\dfrac{20x}{x-4}$
$y=\dfrac{-20x}{1-x}$
$y=\dfrac{xy-20x}{4}$
$y=\dfrac{5x}{1-x}$
Consider the utility function $U(x,y)=\frac{xy}{5x+y}$. Determine the indifference curve with $U$-value 4.
Antwoord 1 correct
Correct
Antwoord 2 optie
$y=\dfrac{-20x}{1-x}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$y=\dfrac{xy-20x}{4}$
Antwoord 3 correct
Fout
Antwoord 4 optie
$y=\dfrac{5x}{1-x}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$y=\dfrac{20x}{x-4}$
Antwoord 1 feedback
Correct:

$$\begin{align*}
U(x,y) = 4 & \Leftrightarrow \frac{xy}{5x+y}=4\\
& \Leftrightarrow xy=20x+4y\\
& \Leftrightarrow 4y-xy=-20x\\
& \Leftrightarrow (4-x)y=-20x\\
& \Leftrightarrow y=\frac{-20x}{4-x}\\
& \Leftrightarrow y=\frac{20x}{x-4}\\
\end{align*}$$

Go on.
Antwoord 2 feedback
Wrong: $(5x+y)\cdot 4\neq 20x+y$.

Try again.
Antwoord 3 feedback
Wrong: The function $y$ cannot be part of its own description.

See Function of one variable.
Antwoord 4 feedback
Wrong: $U\neq 1$

See Utility functions and indifference curves.