Talk:Fundamental theorems of welfare economics

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Can we not have something short and to the point in the opening paragraph introducing these? I was thinking of something along the lines of:

The Two Fundamental Theorems of Welfare Economics are two well-known axiomatic propositions in welfare economics. The first proves the efficiency of free markets and the second that in a free market it is possible to redistribute wealth.

I don't really understand the technical bits well enough to precis them (the above are mostly guesses), but I'm sure that somebody else does. — KayEss | talk 16:37, 12 July 2005 (UTC)

Contents 1 Really Bad 2 Major Problems with assumptions! 3 cleanup 4 of, not, in 5 Requested move

[edit] Really Bad

The theorems were really hopelessly mangled. I just fixed the first theorem, though I don't have time right now to do the second (the proof is quite long). Regarding the comments below about monotonicity of preferences, that isn't actually necessary for the FFT. The weaker assumption of local nonsatiation is sufficient.

Also, why are the two theorems together in one article? I recommend splitting them into two and then just cross-referencing. Also, there seem to be a few other articles mascarading as treatments of the FFT. These should probably be deleted.

--Ossanha

[edit] Major Problems with assumptions!

Firstly, I disagree with the use of the term "axiomatic", these propositions are based on a number of lower-level assumptions (e.g. the rationality/selfishness of all players, assuming that all traders have monotonic utility functions, and so on). The fact that this statement is proven given other assumptions shows, in my opinion, that it is not axiomatic but built on more basic axioms.

More importantly, I believe that the statement of the theorem (or perhaps of Walrasian equilibrium) is incorrect. Unless I am misinterpreting the definition, there is no assumption here that utility functions are monotonic. This assumption is necessary for a proof of the theorem.

The proof sketch shown is also flawed, due to this missing assumption. Consider the case where we have two traders. Player 1's utility functions is a constant (i.e. he/she couldn't care less about the allocation he/she receives) and Player 2's utility function is monotonic. A Walrasian Equilibrium will lie at some point on player 2's budget constraint curve. This point will not be Pareto efficient, because if Player 1 gives their goods to Player 2, Player 1 will be no worse off (their utility remains constant) and Player 2 will be better off (due to their monotonic utility function).

To summarize, this statement of the theorem is lacking the monotonic assumption, without it the theorem is false. (With it, it is provable, though with all respect I still do not like the proof sketch provided, I would like something more mathematical - personal preference)

See Feldman, "Welfare Economics and Social Choice Theory", Chapter 3 for further discussion.

You don't need monotonicity for the first theorem. All you need is local non-satiation. See Mas-Colell, Whinston and Green chapter 16. radek 19:02, 17 January 2006 (UTC)

[edit] cleanup

I may have messed up some mathematical notation in my recent edits. The page was such a mess that whoever created it should check that. Next I'm going to change the title of the article to conform to the style manual. Michael Hardy 23:05, 6 November 2005 (UTC)

[edit] of, not, in

It should be Fundemental Theorems OF Welfare economics, not IN Welfare Economics. Just like Fundemental Theorem of Algebra or Calculus or whatever. Please don't change it to IN.radek 03:11, 15 March 2006 (UTC)

Agreed, I tried moving too "of", but I got an error message, hopefully someone can help fix this.--Bkwillwm 19:37, 16 March 2006 (UTC)

[edit] Requested move

Support It's 'of' not 'in'. Also per comment above, good idea would be to have two seperate pages for the theorems and then this page just a short statement and redirect.radek 22:21, 19 March 2006 (UTC)

Done. —Nightstallion (?) ^{Seen this already?} 09:03, 21 March 2006 (UTC)