1. Stating the problem: We need to graph a typical indifference curve for a utility function. An indifference curve shows combinations of goods that provide the same utility level. 2. Typical utility function: One common form is the Cobb-Douglas utility function $$U(x,y) = x^a y^b$$ where $x$ and $y$ are quantities of two goods, and $a,b>0$. 3. To graph an indifference curve for a fixed utility level $U_0$, set: $$x^a y^b = U_0$$ 4. Solve for $y$: $$y = \left(\frac{U_0}{x^a}\right)^{1/b} = U_0^{1/b} x^{-a/b}$$ 5. This function shows that as $x$ increases, $y$ decreases to keep utility constant, typical of indifference curves. 6. Example: For $a=b=1$ and $U_0=1$, the equation simplifies to: $$y = \frac{1}{x}$$ 7. This hyperbola represents a typical indifference curve. Final answer: The indifference curve for $U(x,y)=x^a y^b$ at fixed utility $U_0$ is $$y = U_0^{1/b} x^{-a/b}$$. For example, if $a=b=1$ and $U_0=1$, the curve is $y=1/x$.