[bob.murphy.ancap]

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.