Formally if X is the consumption set, then for any and every , there exists a such that 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
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Last updated on Tuesday June 24, 2008 at 23:08:46 PDT (GMT -0700)
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