The indifference curve of $U(x,y)=\min(x,y)^2+\max(x,y)$

Question

I am trying to draw the indifference curves for $U(x,y)=\min(x,y)^2+\max(x,y)$. It should not come as a straight line, right? I tried to calculate it by setting one variable $= 0$ and the other variable greater than zero. But, it is coming as $(0,1)$ and $(1,0)$. Any help is appreciated. thank you.

Answer 1

You want to obtain level curves for $U(x,y)$. Those are only called indifference curves by economists when $U(·)$ is what they call a utility function. Fix $U(x,y)=k$ for some $k>0$ and the level curve is formed by all the $(x,y)$ that satisfy the resulting equation. For instance, if you choose $k=6$, any of the following will result in $U(x,y)=6$: $(0,6),(\frac{1}{2},\frac{23}{4}),(1,5),(\frac{3}{2},\frac{15}{4})$ and $(2,2).$