<p>Hint: First find the total derivative of <span class="math-container">$u(x_1,x_2)$</span>, set it to zero as utility does not change along an indifference curve, then solve for <span class="math-container">$dx_2/dx_1$</span></p>

CC BY-SA 4.0
2019-02-06T10:33:51.960Z
What do you mean by total derivative?
Fozoro
CC BY-SA 4.0
2019-02-06T10:41:37.570Z
See: https://en.m.wikipedia.org/wiki/Total_derivative and look for the differential form.
Maarten Punt
CC BY-SA 4.0
2019-02-06T10:22:00.803Z
2019-02-06T10:42:37.610Z
2019-02-06T10:42:37.610Z
Maarten Punt
<p>The easy way is to set utility constant <span class="math-container">$u_0$</span>, </p>

<p>Now, <span class="math-container">$u_0 = 2x_1+x_2$</span></p>

<p><span class="math-container">$x_2$</span> as a function of <span class="math-container">$x_1$</span> is <span class="math-container">$u_0-2x_1 = x_2$</span>, this is the indifference curve for a given level of utility. </p>

<p>As you can see the indifference curve is linear with slope -2.</p>

<p>Regards</p>

CC BY-SA 4.0
2019-02-06T13:30:13.597Z
2019-02-06T17:38:18.593Z
2019-02-06T17:38:18.593Z
Mikkel Karsten
<p>in the economics book that I'm reading right now it is written that this utility function:
<span class="math-container">$$u(x_1,x_2) = 2x_1 + x_2$$</span>
yields indifference curves with a slope of <span class="math-container">$−2$</span>.
Could someone please explain me how they found the <span class="math-container">$-2$</span>? </p>

<p><em>Initially, I was thinking that they derivated the utility function in respect of <span class="math-container">$x_1$</span> and <span class="math-container">$x_2$</span> but this would give <span class="math-container">$2$</span> instead of <span class="math-container">$-2$</span>. Thank you very much for your help</em></p>

<microeconomics><utility><preferences>
indifference curve slope from utility function
Fozoro
# indifference curve slope from utility function

(Asked by: username_0 on 2019-02-06)

in the economics book that I'm reading right now it is written that this utility function:
$$u(x\_1,x\_2) = 2x\_1 + x\_2$$
yields indifference curves with a slope of $−2$.
Could someone please explain me how they found the $-2$?

*Initially, I was thinking that they derivated the utility function in respect of $x\_1$ and $x\_2$ but this would give $2$ instead of $-2$. Thank you very much for your help*

**Tags:** microeconomics, utility, preferences

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## 2 answers

### Answer by username_1 on 2019-02-06. Score: 3

Hint: First find the total derivative of $u(x\_1,x\_2)$, set it to zero as utility does not change along an indifference curve, then solve for $dx\_2/dx\_1$

> **Comments:**
> **username_0**: What do you mean by total derivative?  
> **username_1**: See: https://en.m.wikipedia.org/wiki/Total_derivative and look for the differential form.  

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### Answer by username_2 on 2019-02-06. Score: 2

The easy way is to set utility constant $u\_0$,

Now, $u\_0 = 2x\_1+x\_2$

$x\_2$ as a function of $x\_1$ is $u\_0-2x\_1 = x\_2$, this is the indifference curve for a given level of utility.

As you can see the indifference curve is linear with slope -2.

Regards


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