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?
4
-
$\begingroup$ You can refer to qr.ae/TWvVSr for answer. $\endgroup$– AmitOct 30, 2019 at 2:27
-
$\begingroup$ @Amit Link only answer $\endgroup$– GiskardOct 30, 2019 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. $\endgroup$– BrennanOct 30, 2019 at 19:30
-
1$\begingroup$ @Brennan That friggin' Giskard person is everywhere, dude... $\endgroup$– GiskardOct 30, 2019 at 20:13
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
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.
$\begingroup$
$\endgroup$
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:
