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Let the utility function be: $U(x,y) = \log x +y^2$. In this case, the MRS is coming out to be $\frac{1}{2xy}$. Thus, how will the shape look like?

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    $\begingroup$ $y^{2}$ is a strange utility function over $y$ because it has increasing marginal utility. $\endgroup$ – BKay Oct 29 '19 at 17:30
  • $\begingroup$ Thanks for the feedback . But why does that affect the the utility function. We can have utility functions like x^2 + y^2. $\endgroup$ – DARE2ZLATAN Oct 29 '19 at 17:45
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Wolfram Alpha might come with some help. Try entering $\log x+y^2=n$ for different n's (levels of utility). You will get the idea of how the indifference curve looks like.

e.g. https://www.wolframalpha.com/input/?i=logx%2By%5E2+%3D+1.4

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