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]

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 either if the consumption set is unbounded (open) (in other words, it cannot be compact) or if x is on a section 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 does not hold.


  1. ^ Microeconomic Theory, by A. Mas-Colell, et al. ISBN 0-19-507340-1