<p>You seem to be confusing some things.</p>

<blockquote>
  <p>The indifference curve and utility function both have the same
  equation</p>
</blockquote>

<p>The utility function has a formula, not an equation.</p>

<p><span class="math-container">$U(x_1,x_2)$</span> is a utility function.</p>

<p>The points <span class="math-container">$(x_1,x_2)$</span> for which <span class="math-container">$U(x_1,x_2) = 13$</span> form an indifference curve. (13 was picked as a random number)</p>

<p>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 <span class="math-container">$(x_1,x_2,u)$</span>. 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.  </p>

CC BY-SA 4.0
2019-10-29T17:28:16.593Z
2019-10-29T17:28:16.593Z
Giskard
<p>Utility functions and indifference curves are the same object considered from different visual/conceptual angles. Below an illustration on <span class="math-container">$U(x_1, x_2) = x_1^{0.5} x_2^{0.5}$</span> (representing <em>Cobb-Douglas preferences</em>), done with excel:</p>

<p><a href="https://i.sstatic.net/dImU3.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/dImU3.png" alt="enter image description here"></a></p>

CC BY-SA 4.0
2019-10-30T02:01:59.567Z
2019-10-30T07:43:20.310Z
2019-10-30T07:43:20.310Z
keepAlive
<p>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?</p>

CC BY-SA 4.0
2019-10-30T02:27:52.017Z
You can refer to https://qr.ae/TWvVSr for answer.
Amit
CC BY-SA 4.0
2019-10-30T05:18:41.967Z
@Amit [Link only answer](https://meta.stackexchange.com/questions/225370/your-answer-is-in-another-castle-when-is-an-answer-not-an-answer)
Giskard
CC BY-SA 4.0
2019-10-30T19:30:40.590Z
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](https://economics.stackexchange.com/questions/26498/if-a-utility-function-is-quasi-concave-can-we-say-that-the-ic-curve-associated) written by @Giskard as well.
Brennan
CC BY-SA 4.0
2019-10-30T20:13:33.117Z
@Brennan That friggin' Giskard person is everywhere, dude...
Giskard
<utility><preferences>
Why is the nature of graph of utility function different from indifference curve?
Shakeel Holmes
# Why is the nature of graph of utility function different from indifference curve?

(Asked by: username_0 on 2019-10-29)

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?

**Tags:** utility, preferences
> **Comments:**
> **username_1**: You can refer to https://qr.ae/TWvVSr for answer.  
> **username_2**: @Amit [Link only answer](https://meta.stackexchange.com/questions/225370/your-answer-is-in-another-castle-when-is-an-answer-not-an-answer)  
> **username_3**: 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](https://economics.stackexchange.com/questions/26498/if-a-utility-function-is-quasi-concave-can-we-say-that-the-ic-curve-associated) written by @Giskard as well.  
> **username_2**: @Brennan That friggin' Giskard person is everywhere, dude...  

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## 2 answers

### Answer by username_2 on 2019-10-29. Score: 3

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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### Answer by username_4 on 2019-10-30. Score: 1

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](https://i.sstatic.net/dImU3.png)](https://i.sstatic.net/dImU3.png)


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