<p><strong>A counterexample</strong></p>
<p>Suppose the preference relation <span class="math-container">$\preceq$</span> is such that for all bundles <span class="math-container">$x,y$</span> we have <span class="math-container">$x \sim y$</span>. This relation satisfies transitivity and continuity (it satisfies all four &quot;axioms&quot;) but does not satisfy non-satiation.</p>

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2021-06-23T09:14:51.370Z
Could you please re-explain this? I don't understand. Are we considering a set of indifferent bundles?
not tdm's twin
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2021-06-23T11:01:31.380Z
We are considering the preference relation which is indifferent between all bundles.
Giskard
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2021-06-23T11:33:40.210Z
Yes, I meant that- the consumer is indifferent between the bundles. Thanks for clarifying!
not tdm's twin
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2021-06-23T07:00:25.800Z
2021-06-23T07:00:25.800Z
Giskard
<p>Let's assume on the contrary that the indifference curve is &quot;thick&quot; or crosses. We can only assume the four axioms: completeness, transitivity, reflexivity and continuity. We do not assume strict monotonicity of preferences.</p>
<p>Define the IC as <span class="math-container">$\{y \in X: y \sim x\}$</span> where <span class="math-container">$X$</span> is a (possibly non-finite) set of consumption bundle and <span class="math-container">$x$</span> is arbitrarily chosen from <span class="math-container">$X$</span>.</p>
<p>I do not see a way to prove this without assuming monotonicity at all.</p>

<microeconomics><preferences>
Do the continuity axiom and transitivity axiom justify non-satiation?
not tdm's twin
# Do the continuity axiom and transitivity axiom justify non-satiation?

(Asked by: username_0 on 2021-06-23)

Let's assume on the contrary that the indifference curve is "thick" or crosses. We can only assume the four axioms: completeness, transitivity, reflexivity and continuity. We do not assume strict monotonicity of preferences.

Define the IC as $\{y \in X: y \sim x\}$ where $X$ is a (possibly non-finite) set of consumption bundle and $x$ is arbitrarily chosen from $X$.

I do not see a way to prove this without assuming monotonicity at all.

**Tags:** microeconomics, preferences

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## 1 answers

### Answer by username_1 on 2021-06-23. Score: 3 | Accepted answer

**A counterexample**

Suppose the preference relation $\preceq$ is such that for all bundles $x,y$ we have $x \sim y$. This relation satisfies transitivity and continuity (it satisfies all four "axioms") but does not satisfy non-satiation.

> **Comments:**
> **username_0**: Could you please re-explain this? I don't understand. Are we considering a set of indifferent bundles?  
> **username_1**: We are considering the preference relation which is indifferent between all bundles.  
> **username_0**: Yes, I meant that- the consumer is indifferent between the bundles. Thanks for clarifying!  

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