Strong Montonicity my sources seem to agree on Strong monotonicity, i state equivalent definitions below. But weak montonicity i keep finding what appear to be conflicting definitions. In the following i refer to Wikipedia, Hal R. Varian, "Microeconomic Analysis," 3rd Edition, and my own Mathematical Economics coursepack.
Wikepedia: An agent's preferences are said to be strongly monotonic if, given a consumption bundle $x$ the agent prefers all consumption bundles $y$ that have more of at least one good, and not less in any other good.
- Wikipedia: $y \ge x$ and $y ≠ x$ $\implies y\succ x$
- Varian: $y \ge x$ and $y ≠ x$ $\implies y > x$
- Course pack: Calls this "Nonsatiation": Vectors $x > y$ implies $x_i \ge y_i , \forall \; i$ and $x_i > y_i$ for some $i$ then $x\succ y$
I understand these are all saying the same thing.
Wikipedia: "In economics, an agent's preferences are said to be weakly monotonic if, given a consumption bundle $x$ the agent prefers all consumption bundles $y$ that have more of all goods. That is, $y ≫ x$ implies $y\succ x$"
Course pack: My course pack does not mention monotnocity but also has this definition and refers to it as "Strict preferences" and that it satisfies nonsatiation: And I believe it means $x_i > y_i, \forall \;i$
Varian p.96: Weak Montonicity: $x \ge y$ then $x\succeq y$
This is confusing because Varian's definition seems be the complete opposite of Wikipedia's definition, and my course packs definition of Strict preferences.
- Could someone confirm the most standard definitions of weak and strong montonoicity, and weak and strict preferences. Thanks!