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I am new to Economics, but I have this doubt. The indifference curve and utility function both have the same equation, so their graph must also be similar, which is true I guess. Then why is it that the nature of graphs are different? I mean why is it that if the indifference curve is convex then utility function is quasi concave? How did we arrive at this conclusion?

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  • $\begingroup$ You can refer to qr.ae/TWvVSr for answer. $\endgroup$ – Amit Oct 30 '19 at 2:27
  • $\begingroup$ @Amit Link only answer $\endgroup$ – Giskard Oct 30 '19 at 5:18
  • $\begingroup$ It may be worth your time asking a separate question concerning the relationship between quasi-concave utility functions and their convex contour curves (indifference curves). Although I found this answer written by @Giskard as well. $\endgroup$ – Brennan Oct 30 '19 at 19:30
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    $\begingroup$ @Brennan That friggin' Giskard person is everywhere, dude... $\endgroup$ – Giskard Oct 30 '19 at 20:13
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You seem to be confusing some things.

The indifference curve and utility function both have the same equation

The utility function has a formula, not an equation.

$U(x_1,x_2)$ is a utility function.

The points $(x_1,x_2)$ for which $U(x_1,x_2) = 13$ form an indifference curve. (13 was picked as a random number)

The graph of a utility function has one more dimension than the graph of an indifference curve: in addition to the space of goods, this graph would also include the utility value, so its points would be something like $(x_1,x_2,u)$. Chances are you have not seen a graph of any such function, as 3D drawings are complicated. This is why maps of 2D indifference curves are used to get a feeling for the shapes of utility functions.

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Utility functions and indifference curves are the same object considered from different visual/conceptual angles. Below an illustration on $U(x_1, x_2) = x_1^{0.5} x_2^{0.5}$ (representing Cobb-Douglas preferences), done with excel:

enter image description here

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