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The property of '''local nonsatiation''' of consumer preferences states that for any [[bundle]] of goods there is always another bundle of goods arbitrarily close that is preferred to it.<ref>''Microeconomic Theory'', by [[Andreu Mas-Colell|A. Mas-Colell]], et al. ISBN 0-19-507340-1</ref>
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Formally if X is the [[consumption set]], then for any <math>x \in X</math> and every <math>\varepsilon>0</math>, there exists a <math>y \in X</math> such that <math>\| y-x \| \leq \varepsilon</math> and <math>y</math> is preferred to <math>x</math>.
 
Several things to note are:
 
1. Local nonsatiation is implied by [[monotone preferences|monotonicity of preferences]], but not vice versa. Hence it is a weaker condition.
 
2. There is no requirement that the preferred bundle y contain more of any good - hence, some goods can be "bads" and preferences can be non-monotone.
 
3. It rules out the extreme case where all goods are "bads", since then the point x = 0 would be a [[bliss point]].
 
4. The consumption set must be either [[unbounded]] or [[open set|open]] (in other words, it cannot be [[compact space|compact]]). If it were compact it would necessarily have a bliss point, which local nonsatiation rules out.
 
== Notes ==
 
<references/>
 
{{DEFAULTSORT:Local Nonsatiation}}
[[Category:Microeconomics]]
[[Category:General equilibrium and disequilibrium]]
 
 
{{Economics-stub}}
{{microeconomics-stub}}

Revision as of 16:00, 12 February 2014

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