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 x \in X and every \varepsilon>0, there exists a y \in X such that \| y-x \| \leq \varepsilon and y is preferred to x.

Several things to note are:

1. Local nonsatiation is implied by 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 (in other words, it cannot be compact). If it were compact it would necessarily have a bliss point, which local nonsatiation rules out.

Notes[edit]

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