Originally posted by aethsilgneHi aethsilgne. Where I was planning to get with my initial post is that for you to even begin using an utility function as a modeling device, you need to prove its existence and that its properties reflect the preference relation.
Let me rephrase, minimal costs maximum utility. Me being on this website now gives me more utility than for eg. sleeping.
Taking bets may give you more utility than the opportunity cost for the given sum of money. Say you gain two utils of betting 1$ and only 1 util of saving that 1$ on the bank than you've acted rationally given your set of consumer preferences imo.
Can you prove its existence for any given set of choices X?
Originally posted by PalynkaAre you asking him to prove a Utility Function?
Hi aethsilgne. Where I was planning to get with my initial post is that for you to even begin using an utility function as a modeling device, you need to prove its existence and that its properties reflect the preference relation.
Can you prove its existence for any given set of choices X?
Originally posted by RoostyGame theory and utility functions are merely two sides of the same coin. Optimising your strategy (dominant strategy) in game theory also gives you the maximum attainable utility given the possibility matrix.
Have a look at Game Theory bud, it's very interesting and while it doesn't answer your questions it shows a train of thought.
I don't understand where your contribution talks of betting and saving, and the payoffs for that behaviour. They are the same thing just dressed up nicely in 1 respect as opposed to the other
Originally posted by PalynkaLet me reread your first post! I tend to skip numbers opossed to general theory 🙂
I'm asking if he can do it, although I doubt he can. I will do it if anybody cares to think about this things and shows me by answering the (relatively) simple homework of my initial post.
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Originally posted by ivan2908That one!
I read the 700 page psychology book recently... The big part of the book was dedicate to that theme.. "Is human behavior predetermined ?" Apparently NOT.
Me too.
Dunno the answer but I would prefer...No, too, personally I think it says more about us
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Originally posted by ivan2908I can see how it can be very opaque if you're not used to "reading" theorems in mathematics... But rigorous proof requires a certain degree of formalization. Let me start differently.
I have to agree here ! Palynka, that was just too advanced for start. 😲
Instead of thinking of all possible choices that you have in all possible moments, let's start more simply. You're presented with a finite group of different items in a display. Call the set (the group) of all items: X. Small caps denote individual items.
You have preferences over each item but they are defined only between pairs of items. You can then say that you prefer the car (x) over the screwdriver (y) and do this for any pair (x,y) as long as x and y are in the display. We DON'T assume that you can do this for any groups of items, but we assume you can do it for each pair. Sounds reasonable?
How am I doing so far? Is it more clear? 😵
Originally posted by PalynkaFrom what I understand you want proof that completeness is reached given transivity occurs? I don't really understand the question..
I'm asking if he can do it, although I doubt he can. I will do it if anybody cares to think about this things and shows me by answering the (relatively) simple homework of my initial post.
- completeness implies you can rank your goods x over y etc
- transivity implies as you explained if the cons. weakly prefers bundle z over y and y over x than he also prefers z over x
- rationally more is always preferred than less (except pollution etc)
as i said before, im allergic to algebraic notation but I assume you are talking about the formula for indifference curve for goods x and y?
Originally posted by aethsilgneI'll go a bit more slowly to get more people on board. Hopefully, when (if!) I reach that stage it will become more clear what I was asking...
From what I understand you want proof that completeness is reached given transivity occurs? I don't really understand the question..
- completeness implies you can rank your goods x over y etc
- transivity implies as you explained if the cons. weakly prefers bundle z over y and y over x than he also prefers z over x
- rationally more is always prefer ...[text shortened]... tation but I assume you are talking about the formula for indifference curve for goods x and y?
Originally posted by PalynkaI've studied maths Palynka and sort of know how it fits but I couldn't take your post earlier to mean anything ( as regards , Is man free to make his own choices?) I don't think Maths is the way forward here,...frankly
I'll go a bit more slowly to get more people on board. Hopefully, when (if!) I reach that stage it will become more clear what I was asking...
What were trying to show is that man is free to make his choices but that the choices man makes are always quite logic given his/ her preferences. If we would know what your preferences are, how many utils you would give to all your goods in your 'basket' than we would be fairly able to predict your behaviour.
NB. try to see goods not only materialistically, but also as 'going for a walk' , 'going on a date'