Monotone preferences
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In economics, a consumer's preferences are said to be weakly monotone if adding more of a good to the consumer's consumption bundle does not make her worse off. They are said to be strongly monotone if adding more of a good to the consumer's consumption bundle makes her strictly better off.
Note that in cases where the good in question is a "bad" (i.e.undersirable) it is a simple matter to redefine the notion of the good as its negative. For example the "bad" "annoying noise" can be redefined as the good "absence of annoying noise".
An example of preferences which are weakly monotone but not strongly monotone are those represented by a Leontief utility function of the form U=Min(x,y) where x and y are amounts of two different goods.
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