As the title suggests why is the indifference equations in mean variance portfolio theory convex shaped?
Indifference Equation: https://en.wikipedia.org/wiki/Indifference_curve
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I agree with @MattWolf The graph you show is confusing and evil, it makes me feel dumb every time I look at it. So I inverted the axis.
Now we see the familiar shape of an utility curve, discussed in your previous question. It is upward sloping at a declining rate. In this case $u$ takes the place of $R_p$ and the general form of mean variance utility is $$u(R_p, \sigma_p) = R_p - \lambda \sigma^2_p$$
This derivation might be of interest.