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user 8560
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.
3
votes
1
answer
656
views
Diminishing Nature of Utility Function From Convexity of Preference $\succsim$?
Is diminishing nature of utility function in consumer theory stemming from the assumption of convexity on the preference relation $\succsim$?
My understanding is:
$\succsim$ is convex. Then, $u(. …
- 1,241
6
votes
2
answers
1k
views
Continuous rational and monotone preference relation implies $x\succsim0$?
I updated my proof to a general version as follows: please share your thoughts & 2cent. Thanks
Show a monotone continuous complete preorder on $\mathbb{R}^L_+$ has $y\geq x\rightarrow y\succsim x$.
P …
- 1,241
7
votes
1
answer
6k
views
(Preference Relation/Set) Continuous $\succsim$ imply closedness of upper and lower contour ...
[ADDED/MODIFIED] : I have put my proof where the commodity space is simply $\mathbb{R_+}$(e.g. nonnegative reals) for simplicity below. Please share your 2 cent. I have put words to aid my own underst …
- 1,241
1
vote
1
answer
856
views
Continuous Preference Relation Imply Continuous Utility Fn Existence
I am reading MWG's explanation in Chapter 3 when showing continuous preference relation implies the existence of continuous utility function.
First, the authors show $u(.)$ is continuous by using the …
- 1,241