<p>a.) Consider utility with a bliss point. It may represent continuous preferences, but clearly the budget will not bind if you can afford more than the bliss point.</p>

<p>b.) This statement is true, and there is a <a href="https://economics.stackexchange.com/questions/8449/local-non-satiation-proof">proof here</a>.</p>

<p>c.) Strict monotonicity implies local non-satiation, so same as in b.)</p>

<p>d.) An example of convex preferences is indifference everywhere. So the budget would not bind in this case.</p>

<p>e.) Strict convexity rules out thick indifference curves like in d.), but does not rule out bliss points. Consider concentric indifference curves moving in towards a bliss point. Each of those upper countour sets are convex shapes.</p>

CC BY-SA 3.0
2016-12-03T03:58:25.187Z
Why does strict convexity rule out bliss points?
Theoretical Economist
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2016-12-03T04:16:58.817Z
@TheoreticalEconomist I've made a careless mistake. I'll correct my answer.
Kitsune Cavalry
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2016-12-04T22:19:40.913Z
why would the budget not bind for d.)? thanks
bs2293
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2016-12-03T03:38:29.660Z
2016-12-03T04:17:41.573Z
2017-04-13T12:51:38.253Z
Kitsune Cavalry
<p>Suppose that a consumer has a complete and transitive preference relation  over R<code>+. Further suppose that the consumer faces prices p = (p1,p2,...,p</code>)  0 and has income w >> 0. Which of the following statements are false? </p>

<p>(a) If ≿  is continuous, then the consumer exhausts her budget.
(b) If ≿  is locally nonsatiated, then the consumer exhausts her budget. 
(c) If ≿  is strictly monotonic, then the consumer exhausts her budget. 
(d) If ≿  is convex, then the consumer exhausts her budget. 
(e) If ≿  is strictly convex, then the consumer exhausts her budget.</p>

CC BY-SA 3.0
2016-12-02T16:43:00.450Z
Have you looked at this question? http://economics.stackexchange.com/q/14474/8595
Theoretical Economist
<microeconomics><consumer-theory><preferences><theory>
What consumer preferences exhaust the budget?
dimi
# What consumer preferences exhaust the budget?

(Asked by: username_0 on 2016-12-02)

Suppose that a consumer has a complete and transitive preference relation over R`+. Further suppose that the consumer faces prices p = (p1,p2,...,p`) 0 and has income w >> 0. Which of the following statements are false?

(a) If ≿ is continuous, then the consumer exhausts her budget.
(b) If ≿ is locally nonsatiated, then the consumer exhausts her budget.
(c) If ≿ is strictly monotonic, then the consumer exhausts her budget.
(d) If ≿ is convex, then the consumer exhausts her budget.
(e) If ≿ is strictly convex, then the consumer exhausts her budget.

**Tags:** microeconomics, consumer-theory, preferences, theory
> **Comments:**
> **username_1**: Have you looked at this question? http://economics.stackexchange.com/q/14474/8595  

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## 1 answers

### Answer by username_2 on 2016-12-03. Score: 1

a.) Consider utility with a bliss point. It may represent continuous preferences, but clearly the budget will not bind if you can afford more than the bliss point.

b.) This statement is true, and there is a [proof here](https://economics.stackexchange.com/questions/8449/local-non-satiation-proof).

c.) Strict monotonicity implies local non-satiation, so same as in b.)

d.) An example of convex preferences is indifference everywhere. So the budget would not bind in this case.

e.) Strict convexity rules out thick indifference curves like in d.), but does not rule out bliss points. Consider concentric indifference curves moving in towards a bliss point. Each of those upper countour sets are convex shapes.

> **Comments:**
> **username_1**: Why does strict convexity rule out bliss points?  
> **username_2**: @TheoreticalEconomist I've made a careless mistake. I'll correct my answer.  
> **username_3**: why would the budget not bind for d.)? thanks  

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