Pareto optimality

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• #21819
patterico
Participant

OK, I give up. How do you move from Pareto suboptimality to Pareto optimality, and still make some people worse off? I keep trying to figure this out and it just makes my head spin.

#21820
bob.murphy.ancap
Participant

Heh it’s a fun one, isn’t it? It’s easier to do on a blackboard, but here goes:

Picture a 2-person, 2-good economy. It’s Xavier and Yolinda, and they have apples and bananas. There is no production, just a total of 10 apples and 10 bananas, that can be split between them.

Assume their preferences are such that each person always wants more of either good, but also prefers variety.

Now suppose Xavier has 10 apples and 10 bananas, while Yolinda has 0 apples and 0 bananas. This is Pareto optimal. You can’t make Xavier happier because he has all the goods already. And if you make Yolinda happier, you necessarily hurt Xavier. So since it’s impossible to make one person better off without hurting the other, the original allocation is Pareto optimal.

Now consider a different allocation, where Xavier start with 9 apples and 1 banana, while Yolinda has 1 apple and 9 bananas. It’s plausible that this is *not* Pareto optimal, because I said they like variety. E.g. we can imagine their preferences are such that if Xavier trades away 4 of his starting apples in exchange for 4 bananas from Yolinda, that they are both getting more utility (or end up with a preferable combination of goods).

So, I hope you find it plausible that this 2nd allocation I’ve described–where Xavier starts with 9 apples and 1 banana, while Yolinda starts with 1 apple and 9 bananas–is Pareto suboptimal.

Now, imagine we move from this 2nd allocation to the 1st allocation (the one where Xavier has everything). We’ve moved from a Pareto suboptimal to a Pareto optimal allocation, and yet in doing so we made Yolinda worse off, because now she has nothing.

#21821
bigqueue_qlewis
Participant

The secret is that the definition only applies to movement OUT of a state…..it optimal is defined by “leaving” the optimal state…..defined by the negative. So moving INTO a state is irrelevant when the state you left was sub-optimal. Also….once in a place (state) called Pareto Optimal….that does not mean that this state is the BEST place for any one of the people…there may in fact be individuals where this OPTIMAL state is the worst, so coming from any other would represent a “downgrade”…….so while the other states the society may move to might make their life better, if could also make ANYONE other individual worst, therefore this state would be by definition Pareto Optimal….

I don’t think that was clear…..but to me, the key is that the Paredo optimal designation only relies on current to next state transitions…in fact, as Bob said, it is really defined by the negative…..that is, the transition OUT of Optimal.

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