Local nonsatiation

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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.[1] What this means is that a consumer always either prefers more of an item or less of an item, never a particular amount of a good. An additional requirement is that there is some good that consumer does prefer more of. [2]

Formally if X is the consumption set, then for any and every , there exists a such that and is preferred to .

Several things to note are:

1. Local nonsatiation is implied by monotonicity of preferences. Because the converse isn't true, local nonsatiation 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 the point x = 0 would then be a bliss point.

4. Local nonsatiation can only occur if the consumption set is either unbounded (open) (in other words, it cannot be compact) or on sections of a bounded consumption set sufficiently far away from the ends. Near the ends of a bounded set, there would necessarily be a bliss point where local nonsatiation doesn't hold.

Notes[edit]

  1. ^ Microeconomic Theory, by A. Mas-Colell, et al. ISBN 0-19-507340-1
  2. ^ http://www.economist.com/blogs/freeexchange/2007/11/satiation