Local nonsatiation Illustration of preferences that are locally nonsatiated but not strongly monotonic. x1 and x2 are two goods and the blue line indicates an indifference curve. 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 x ∈ X {\displaystyle x\in X} and every 0}" xmlns="http://www.w3.org/1998/Math/MathML"> ε > 0 {\displaystyle \varepsilon >0}, there exists a y ∈ X {\displaystyle y\in X} such that ‖ y − x ‖ ≤ ε {\displaystyle \|y-x\|\leq \varepsilon } and y {\displaystyle y} is strictly preferred to x {\displaystyle x}. Several things to note are: 1. Local nonsatiation is implied by monotonicity of preferences. However, as the converse is not 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 no