Local nonsatiation

In microeconomics, the property of local nonsatiation (LNS) of consumer preferences states that for any bundle of goods there is always another bundle of goods arbitrarily close that is strictly preferred to it. Formally, if X is the consumption set, then for any and every , there exists a such that and is strictly preferred to . Several things to note are: Local nonsatiation is implied by monotonicity of preferences. However, as the converse is not true, local nonsatiation is a weaker condition. 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. It rules out the extreme case where all goods are "bads", since the point x = 0 would then be a bliss point. Local nonsatiation can only occur either if the consumption set is unbounded or open (in other words, it is not 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. Local nonsatiation (LNS) is often applied in consumer theory, a branch of microeconomics, as an important property often assumed in theorems and propositions. Consumer theory is a study of how individuals make decisions and spend their money based on their preferences and budget. Local nonsatiation is also a key assumption for the First welfare theorem. An indifference curve is a set of all commodity bundles providing consumers with the same level of utility. The indifference curve is named so because the consumer would be indifferent between choosing any of these bundles. The indifference curve has a negative slope. This is caused because of nonsatiation. The indifference curve can not slope upward because the consumer can not be indifferent between two commodity bundles if contains more of both goods. Local nonsatiation is a key assumption in the Walras’ law theorem. Walras's law says that if consumers have locally nonsatiated preferences, they will consume their entire budget over their lifetime.