<p>The key in this video is the utility function he is taking the derivative of. We can notice that (if we use some graphing software) that in 3 dimensions it makes a bowl (see: <a href="https://www.geogebra.org/3d?lang=en" rel="nofollow noreferrer">here</a> ). In the function bar, write {U = x^2 + y^2} and you will see the &quot;bowl&quot;. The vertical axis is our utility (U), the axis pointing away from us is Y and the left-right is X. If we rotate the graph to &quot;look down&quot; into the bowl, this is the 2D representation we often see for indifference curves in classes or textbooks. You will notice now (since we have a 2D graph with axes Y and X) that the indifference curve is concave to the origin. That is, in the upper right quadrant, we get semi circle. &quot;Well behaved&quot; indifference curves are <em>convex</em> to the origin. Here, the second derivative is positive because as we increase X, the  <em>change</em> in the slope is increasing (the curve is actually getting steeper)! This is why we get the result that Uxx is positive.</p>
<p>Hope this helps :)</p>

CC BY-SA 4.0
2021-10-27T15:02:32.600Z
You're most welcome :)
KeithRoberts
CC BY-SA 4.0
2021-10-27T12:36:47.267Z
2021-10-27T12:36:47.267Z
KeithRoberts
<p>I have just watched the first part of this video and noticed that the second derivative of the utility function is positive. But I thought the second derivative had to be negative to be a concave function. Please could someone clarify this for me?</p>
<p><a href="https://www.youtube.com/watch?v=G7JSe9xofFQ" rel="nofollow noreferrer">https://www.youtube.com/watch?v=G7JSe9xofFQ</a></p>

CC BY-SA 4.0
2021-10-27T14:12:08.637Z
I’m voting to close this question because crucial parts of information are not included inside the body of the question. (Which is bad because links break over time.)
Giskard
<microeconomics><preferences>
Does the second derivative of a concave function need to be negative?
Sofia
# Does the second derivative of a concave function need to be negative?

(Asked by: username_0 on 2021-10-27)

I have just watched the first part of this video and noticed that the second derivative of the utility function is positive. But I thought the second derivative had to be negative to be a concave function. Please could someone clarify this for me?

<https://www.youtube.com/watch?v=G7JSe9xofFQ>

**Tags:** microeconomics, preferences
> **Comments:**
> **username_1**: I’m voting to close this question because crucial parts of information are not included inside the body of the question. (Which is bad because links break over time.)  

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## 1 answers

### Answer by username_2 on 2021-10-27. Score: 1

The key in this video is the utility function he is taking the derivative of. We can notice that (if we use some graphing software) that in 3 dimensions it makes a bowl (see: [here](https://www.geogebra.org/3d?lang=en) ). In the function bar, write {U = x^2 + y^2} and you will see the "bowl". The vertical axis is our utility (U), the axis pointing away from us is Y and the left-right is X. If we rotate the graph to "look down" into the bowl, this is the 2D representation we often see for indifference curves in classes or textbooks. You will notice now (since we have a 2D graph with axes Y and X) that the indifference curve is concave to the origin. That is, in the upper right quadrant, we get semi circle. "Well behaved" indifference curves are *convex* to the origin. Here, the second derivative is positive because as we increase X, the *change* in the slope is increasing (the curve is actually getting steeper)! This is why we get the result that Uxx is positive.

Hope this helps :)

> **Comments:**
> **username_2**: You're most welcome :)  

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