What would be the I.C of this function? $u(x,y)=\min(x,√y)$
I understand since it is a perfect complements case it should be "L" shaped but I wanted a more detailed graph.
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For perfect complements like $u(x,y) = \min( g(x_1), h(x_2))$ the points at which kinks occur are such that $g(x_1)= h(x_2)$. In this case that would be $x= \sqrt(y)$ so in this case indifference curves would look like:
The picture above plots two indifference curves and the dashed line gives you all kinks of every indifference curve. Normally the kinks would lie on $45^°$ line because usually complements are given by functions where respective slopes of $x$ and $y$ are linear (e.g. $\min (\alpha x, \beta y ))$ but here you have case where you have $\sqrt(y)$, so the $x$ has to be consumed with exponentially increasing quantities $y$.