Example
Alice's utility given `X` chocolates and `Y` strawberries is
$$ u \left( X, Y \right) = X \times Y $$Her indifference curve at a level of utility equal to 1 satisfies
$$ u \left( X, Y \right) = X \times Y = 1 $$Solving for Y
$$ Y = 1 / X $$Similarly, she gets utility 2 if `Y = 2 / X`.
Question
Alice's utility function is `u(X, Y) = X^3Y^2`.
What is the equation of her indifference curve for a level of utility equal to 9?
Draw that indifference curve.
The indifference curve satisfies `u(X, Y) = X^3Y^2 = 9`.
Solving for `Y`.
$$ \begin{align*} Y^2&= \frac{9}{X^3}\\Y &= \frac{9^{\frac{1}{2}}}{X^{\frac{3}{2}}}\\Y &= \frac{3}{X^{\frac{3}{2}}}\end{align*} $$