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# Questions tagged [preferences]

Binary relations that reflect which states of the world an agent considers to be most desirable. Preferences are a fundamental ingredient in the axiomatic study of consumer choice decision theory.

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### Is it possible and logical to have an upwards sloping budget line?

The question I have is, for example, say Garry has two goods, cookies he pays 1 to consume a cookie and a maximum of 10 can be consumed, whilst he gets PAID 2 to consume vegetables. Garry is also ...
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### $x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R^n$, then the preference is linear?

$x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (or disprove by counterexample) that: Suppose $x\sim y$ ...
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### Prove that a preference is linear

Given the following two conditions: $x\succ y$ implies $x+a\succsim y+a$, And, $x\prec y$ implies $x+a\precsim y+a$ We want to prove that $\succsim$ is a linear preference. One of the ...
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### Relationship between strictly convex preference and convex preference

Let X be a convex subset of linear topological space and let binary relation >= be a complete preordering. prove: If preference relation is strictly convex and continuous, then it is convex. Since ...
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### Axiom: More is Better; But when is more better?

I'm taking an introductory microeconomics course and have been introduced to the 3 axioms of economic preferences. These include Completeness Transitivity Non-satiation My understanding of non-...