Draw the indifference curves for a preference relation which is neither monotonous or strictly convex, yet convex.
My solution was to draw a circle but I'm pretty sure that is wrong.
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2$\begingroup$ That might work on "not monotonous" depending on what that means (related to satiation?), but a circle might be seen a strictly convex, so some adjustment might be needed, such as a rectangle $\endgroup$– HenryCommented Jan 13, 2021 at 12:21
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2 Answers
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Consider the utility function $u(x, y)= -|x-5|-|y-5|$.
Indifference map for $u$ is as follows :
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How do you define monotonicity? The definition of monotonicity in economics is usually:
$x\geq y$ implies that $U(x)\geq U(y)$.
Then a solution could be:
$U(x_1,x_2)=x_1-x_2$
However, if you use the mathematical definition of monotonic function, then here is one of the solutions:
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You need to add the coordinates by yourself.
