Talk:Pareto efficiency

'Corollary'

I removed the text:

A corollary of a Pareto efficient economy that is desirable is that all workers make the same wage and all firms operate with the same profit margins.

I tend to think that this is value judgement. If the writer meant this in general, then they are saying that a coal miner (a dangerous, dirty job) should recieve the same wage as a librarian in a small town. Since the jobs are different, having the same wage would be unfair. Even Twin Oaks provides slightly different benefits to workers who do different jobs. Profit margins in industries are also likely to be different for reasons such as different risk and different capital startup costs. I have no objection to the idea in general that equality is good, but I would hesitate to call it a corollary, and inso much as it is mentioned in an article on Pareto efficientcy, it should probably be mentioned that it is trying for a different idea. Jrincayc 16:13, 3 Jan 2005 (UTC)

Reply by 69.107.96.61 5 Jan 2005. Hi Mr. Jrincayc. I am not a professional economist (like you?) but I believe that the corollary is not a value judgement but in fact a consequence of a pareto efficient economy (one that is at the boundary of the production possibility curve). This I recall from memory, years ago, from my Econ 101 class. I could be mistaken, but I think that once you reach the boundary, by definition all wage differentials, at the margin, will equal zero. That is, suppose that a wage differential exists for rocket scientists. A bunch of people will 'retool' and become rocket scientists, which will drive down the wage differential to zero. (In fact, in the aerospace industry, that's exactly what happened! Too many smart people in aeronautics, that's why I switched majors and became a lawyer). So, in a 'steady-state', long-term, quisscent 'Pareto optimal' economy, everybody makes the same amount of money (kinda like Communism and Sweden, but different). Anyhoo, I could be mistaken so I will let your revision stand. PS--I see we share some similar interests: IP and programming. Try C#.NET for a cool, easy to learn OOP language.--Cheers, User:69.107.96.61

Well, assuming that everyone was alike, there would still be differences in the amount that different jobs payed since the jobs themselves are different. A dangerous, dirty job that required lots of education would pay better than an safe easy job that required no education because if the jobs payed the same, then a person in the hard job would switch to the easy job. What would happen if everyone was the same is that the wages would hit a point so that people would be indifferent between the jobs, because the wage difference would exactly compensate for the differences in danger, effort and education... So the benefit of each job would be the same, but the monetary wage would be different. Since people are different, not even this happens completely, but there are effects to even out the overall benefits of different jobs. Jrincayc 13:58, 6 Jan 2005 (UTC)

Not to beat a dead horse, but I think confusion is with transient versus steady-state effects. "You" are thinking more transient, while "I" am thinking equilibrium (end-point) steady state. At the "steady state" time is infinity, so while people are different, and some jobs take more time to learn, and are more dangerous than others, and should and do initially yield more than safe, easy to learn jobs, at the limit (t = infinity) the wage differential goes to zero regardless of the job (so crab fisherman in Alaska, the world's most dangerous job next to conflict diamond mining in Angola, make the same as a desk receptionist in Peoria). Of course in the 'real world' this would never happen, but keep in mind Pareto optimal is a mathematical construct, not necessarily a real-world event (kinda like Adam Smith's 'perfect competition' where nobody has market power). Another corollary of Pareto optimal efficiency, as I recall, was that all investments and all corporations returned and earned an equal amount of money. The same principle applied: risky investment prices were 'bid up' by eager investors, until the return was the same as what the bank gives you. In fact, in a book called "Triumph of the Optimists: 101 Years of Global Investment Returns" by Elroy Dimson, Paul Marsh, Mike Staunton (good book if you can find a copy), it has been shown, on rather sketchy data, that in fact over the last 100 years, world wide, risky investments yielded about the same as riskless investments (I can relate to that--since the mid 90s my investments are running at about 3% a year compounded! Dang dot-com crash!). But let's agree to disagree on this one. For one thing, I support Wikipedia (have given money to them) but I think long-term it is best to keep the explanation of topics simple, for high-school kids and for quick rough outlines of topics rather than get into grad level discourse, which tends to confuse in an abbreviated format such as here. Cheers, 69.107.96.61 6 Jan 2005

I think that we may be in violent agreement. Let me try and define what I am talking about for the wages. First of all for a given job you have benefits you recieve such as money, health care, retirement and so forth. For a given job you also have costs such as your time, risk of death and dismemberment, physical effort, mental effort and so forth. You also have effort to get the job which includes things such as education, security clearences, licences and so forth. Lets call these benefit, cost, and obtain respectively. First, assuming that obtain is the same for two jobs, I would expect that under the long run people are the same assumetions (LRPS) for any two jobs a and b with the same obtain, benfit_a - cost_a = benfit_b - cost_b. I am pretty sure that this is the invariant, since if say benefit_a - cost_a > benefit_b - cost_b, then more people would want to work at job a than at job b. Since there are extra people trying for job a, and too few people trying for job b, supply and demand would tend to raise the benefits for job b and lower the benefits for job a. So, in the long run, I expect that benefit_a - cost_a = benefit_b - cost_b for all jobs a and b where obtain is the same. Note that this says that benefit_a = benefit_b only if cost_a = cost_b, and I am pretty sure that cost_a and cost_b will be different for many jobs (risk of death, physical effort and so forth vary for jobs). Now, how to deal with obtain. I hope we can agree that being a grocery clerk and being a professor of physics have different obtaining costs. One requires around a month or so of training, and the other requires around a 6-10 years of training (beyond high school). So, there is a different obtaining cost for each. Now, in the LRPS equilibrium, you will only choose a job with a higher obtain if you get greater net benefits later on. So, I think the equilibrium equation is: lifetime(benefits_a - costs_a) - obtain_a = lifetime(benefits_b - costs_b) - obtain_b. Lifetime is a rather complicated intergral that incorperates things like discounting and so forth (that I lack the interest to really calculate), but taking it as the sum of yearly benifits - cost for every working year is a reasonable aproximation. Now, if this is higher for job a than job b, then again, you would expect that there would be supply and demand mismatch issues, so benefits would be raised and lowered to fix that problem. So, as long as the obtain cost and the regular cost are different for different jobs, the benefits of each job will be different in the long run people same assumptions. However, each person will be indifferent to which job that they get (I think this is what you are remembering from your economics class).

As for businesses, I agree that in the long run, each business sector should be earning the same economics profits (but very different accounting profits). I hope this makes sense. If it doesn't tell me where so I can try and figure out if I made a mistake or I am being unclear. Jrincayc 16:20, 7 Jan 2005 (UTC)

Warning - Problems

The formal basis of the article is problematic, since it works with sets (which are identical under permutations of elements) instead of with n-tuples. The German version of the article is much better and the reader might want to check that. Here, in the english version, the formalism is simply and plainly: Wrong. — Preceding unsigned comment added by 217.95.167.213 (talk) 10:20, 16 October 2019 (UTC)

Pareto optimality and the Prisoner's dilemma

In the Prisoner's dilemma, are three out of the four possible outcomes Pareto optimal?

It looks that way to me, but I'm no expert on Pareto efficiency:

• From (cooperate, defect), a change to (cooperate, cooperate) makes the second player worse off while making the first better.
• The same is true from (defect, cooperate), as a change to (cooperate, cooperate makes the first player worse off but the second better.
• Only (defect, defect) is NOT Pareto efficient, because changing to (cooperate, cooperate) makes both better off.

Is this correct? If yes, this example would be made more useful by saying that (cooperate, defect) and (defect, cooperate) are also Pareto efficient, but (defect, defect) is not.

If this is NOT correct, then it seems to me that something is wrong with the definition. ??? Thanks for your work in maintaining this Wikipedia article. DavidMCEddy (talk) 03:20, 31 May 2024 (UTC)

Yes, this makes sense given the definitions. Another agreement: https://economics.stackexchange.com/a/27181 Honestrosewater (talk) 08:49, 1 September 2024 (UTC)

Perfect knowledge and Pareto efficiency

Using the Prisoner's dilemma as an example seems to entirely miss the point of the game: neither player has 'perfect information'. There's no external observer helping the players decide, and thus no way of performing a gradient-flow to the 'best possible outcome'.

Furthermore, as pointed out in the comment above, the Pareto optimal solution is DD not CC. Why? Because moving from CD to CC makes one of the players worse off. Moving from DD to CD makes one of the players worse off. Only DD is stable against single-point change, i.e. Pareto-optimal. This is whole point of the game and why it is discussed!

I'm going to uhh, be bold and blank that entire section shortly. 67.198.37.16 (talk) 16:12, 19 March 2025 (UTC)

Phase transitions and paths to optimality

I'm not sure why, but the article does not seem to mention the concepts of local traps or phase transitions. In machine learning, the phenomenon of "local minima" (gradient descent) or "local maxima" (hill-climbing) are well-known: if one takes steps to improve the 'welfare' of all variables in the system (improving one, hurting none of the others), one gets trapped in local traps. In hill-climbing, this is getting trapped at the top of a hill, even though there is a taller mountain nearby: there is no way to get from hill-top to mountain without also hurting some, maybe many or maybe even most of the population along the way. This is also noted in evolutionary biology: no way to improve overall fitness of a species without first going through a less fit stage. Methinks this article should at least mention that this is a generic issue in optimization problems, of which Pareto optimization is one.

I'm also surprised that phase transitions and liquidity is not mentioned. It's well known from economics that markets can "freeze up" if no one is willing to take the first step (i.e. make things a little worse-off for themselves). Thus we have "liquidity providers" to "unfreeze" the system. Again, the idea is to go from a local trap by explicitly making things worse for some of the population.

Finally, there's the idea of a first-order phase transition, where to get to the optimal location, everyone (and not just some subset of the population) must suffer. A terrible example of this is the so-called "belt-tightening" imposed on national economies that have high inflation and high joblessness. Its a bad example, only because there are better solutions; sadly, "belt-tightening" is the go-to strategy for World Bank and the IMF. At any rate, it seems odd that the article fails to even mention the non-smooth nature of the "Pareto landscape". 67.198.37.16 (talk) 16:38, 19 March 2025 (UTC)