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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 strictly preferred to it.
Formally, if X is the consumption set, then for any x ∈ X {\displaystyle x\in X} and every 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:
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