My lecturer went on and on for about two hours and I still didn't understand (and neither did my classmates). After listenng to your lectures for about half an hour, I can understand all of it! That's called the ART OF TEACHING! Thank you, dear professor!
Thank you so much for this detailed explanation. My professor didn't give a lot of detail to why the lexicographic preference is important in the grand scheme of utility in preferences and I think you cleared that up for me very nicely. I also understand now why the generating intervals that we pull from for our rational numbers are disjoint. As someone with a relatively non-rigorous undergrad coming to graduate econ, I sometimes find it a little bit disingenuous when these proof strategies are used without credit given to where the proof comes from. During the first micro lecture I actually (perhaps naively) believed the professor was coming up with this proof strategy on the fly (and expected me to be able to do the same). After some research I realized how widespread the proof is, seeing that virtually every other source I could find used the same approach. I have a feeling I will have many similar experiences as I continue in grad school...
Thanks for your comment, I'm glad the video helped. I think you can assume that just about anything you see, at least in your first year, is already well known, although it wouldn't be uncommon for someone to present a proof that's slightly different than ones that are known, or even a lot different. But there will be known proofs for probably everything, unless it's presented as an "open question." Good luck!
Dear Professor, Just this year I became an eco student and I barely understand what is written in the book. But my god your lectures are a life saver. Please continue enlightening us with your great lectures/videos!
I don't see how this is unique to lexicographic preferences. Consider any strongly monotonic, strictly convex, and locally non-satiated preferences in R^2. You can draw a similar image as you have done such that u(a) < u(b) < u(a') < u(b'). And the rest follows as before. But this would imply that the familiar diminishing MRS preferences don't have a utility representation.
The proof requires that we can do this for *every* x' that's larger than x -- i.e., if x'>x then it has to be the case that (x',0) is preferred to (x,1). That can't happen for every x'>x if the preference is continuous: continuity says the weak upper-contour set of (x,1) is closed, so if a sequence of points (x(n),0) converges to (x,0) and every point in the sequence is even weakly preferred to (x,1), then (x,0) must be as well -- but we know that in fact (x,1) is strictly preferred to (x,0). And of course the representation theorem tells us that if the preference is continuous then there *will* be a utility function for it, and in that case we can't do the construction of the function f(.) in the proof.
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My lecturer went on and on for about two hours and I still didn't understand (and neither did my classmates). After listenng to your lectures for about half an hour, I can understand all of it! That's called the ART OF TEACHING! Thank you, dear professor!
I'm glad they were helpful. Thanks for the positive comment.
Thank you so much for this detailed explanation. My professor didn't give a lot of detail to why the lexicographic preference is important in the grand scheme of utility in preferences and I think you cleared that up for me very nicely. I also understand now why the generating intervals that we pull from for our rational numbers are disjoint.
As someone with a relatively non-rigorous undergrad coming to graduate econ, I sometimes find it a little bit disingenuous when these proof strategies are used without credit given to where the proof comes from. During the first micro lecture I actually (perhaps naively) believed the professor was coming up with this proof strategy on the fly (and expected me to be able to do the same). After some research I realized how widespread the proof is, seeing that virtually every other source I could find used the same approach. I have a feeling I will have many similar experiences as I continue in grad school...
Thanks for your comment, I'm glad the video helped. I think you can assume that just about anything you see, at least in your first year, is already well known, although it wouldn't be uncommon for someone to present a proof that's slightly different than ones that are known, or even a lot different. But there will be known proofs for probably everything, unless it's presented as an "open question." Good luck!
Dear Professor, Just this year I became an eco student and I barely understand what is written in the book. But my god your lectures are a life saver. Please continue enlightening us with your great lectures/videos!
Thanks! I'm glad they've been helpful.
This video is so helpful and much more straightforward than the lecture in my uni!!!
Great, I'm glad it was helpful! Check out some of my other videos.
It saves me a lot before micro midterm. Thank u very much.
Good, I'm glad they've been helpful.
Excellent explanation not in MWG!! Thanks! 🤠🤠
Glad it was helpful!
The video sound is pretty good, beyond my imagination
macam mana nak buat?
Specify the goal and need money
I don't see how this is unique to lexicographic preferences. Consider any strongly monotonic, strictly convex, and locally non-satiated preferences in R^2. You can draw a similar image as you have done such that u(a) < u(b) < u(a') < u(b'). And the rest follows as before. But this would imply that the familiar diminishing MRS preferences don't have a utility representation.
The proof requires that we can do this for *every* x' that's larger than x -- i.e., if x'>x then it has to be the case that (x',0) is preferred to (x,1). That can't happen for every x'>x if the preference is continuous: continuity says the weak upper-contour set of (x,1) is closed, so if a sequence of points (x(n),0) converges to (x,0) and every point in the sequence is even weakly preferred to (x,1), then (x,0) must be as well -- but we know that in fact (x,1) is strictly preferred to (x,0). And of course the representation theorem tells us that if the preference is continuous then there *will* be a utility function for it, and in that case we can't do the construction of the function f(.) in the proof.
The video sound is pretty good, beyond my imagination