<p>Since we are working in $\mathbb{R}_+$ you can't go below (0,0). So consider the point (0,0). Are we guaranteed a point around it that is preferred? So using the notation you used, let $(x_1,x_2)=(0,0)$, then any other point $(y_1,y_2)$ where $y_1$ or $y_2$ is positive will be worse than $(0,0)$. So we have a satiation point at $(0,0)$. </p>

<p>Now consider anywhere else. We can also go lower by reducing either coordinate so there is always a better point until we reach both points =0. </p>

CC BY-SA 3.0
2016-08-30T19:28:28.987Z
2016-08-30T19:28:28.987Z
VCG
<p>I'm self studying my way through Varian's Microeconomic Analysis right now and am having trouble answering this question:</p>

<p>Consider preferences defined over the nonnegative orthant by $(x_1, x_2) \succ
(y_1, y_2)$ if $x_1+ x_2 &lt; y_1+ y_2$. Do these preferences exhibit local nonsatiation?
If these are the only two consumption goods and the consumer faces positive
prices, will the consumer spend all of his income? Explain. </p>

<p>The solution manual says the preferences are locally non satiable except at (0,0) but I don't know why that is. </p>

<p>any help would be greatly appreciated. </p>

<microeconomics><utility>
Preferences exhibiting local nonsatiation
nik
# Preferences exhibiting local nonsatiation

(Asked by: username_0 on 2016-08-30)

I'm self studying my way through Varian's Microeconomic Analysis right now and am having trouble answering this question:

Consider preferences defined over the nonnegative orthant by $(x\_1, x\_2) \succ
(y\_1, y\_2)$ if $x\_1+ x\_2 < y\_1+ y\_2$. Do these preferences exhibit local nonsatiation?
If these are the only two consumption goods and the consumer faces positive
prices, will the consumer spend all of his income? Explain.

The solution manual says the preferences are locally non satiable except at (0,0) but I don't know why that is.

any help would be greatly appreciated.

**Tags:** microeconomics, utility

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## 1 answers

### Answer by username_1 on 2016-08-30. Score: 4

Since we are working in $\mathbb{R}\_+$ you can't go below (0,0). So consider the point (0,0). Are we guaranteed a point around it that is preferred? So using the notation you used, let $(x\_1,x\_2)=(0,0)$, then any other point $(y\_1,y\_2)$ where $y\_1$ or $y\_2$ is positive will be worse than $(0,0)$. So we have a satiation point at $(0,0)$.

Now consider anywhere else. We can also go lower by reducing either coordinate so there is always a better point until we reach both points =0.


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