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I am wondering if an equitable distribution is also pareto optimal in nature. I know the reverse is untrue, that a pareto optimal distribution is not necessarily a fair/equitable distribution.

If you can give me an example that will be much appreciated.

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    $\begingroup$ Hi! Have you tried producing an example yourself? Can you please share it? In that case was the equitable allocation PO or not? $\endgroup$
    – Giskard
    Jul 20, 2022 at 8:00
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    $\begingroup$ By equitable distribution, you mean equal distribution? $\endgroup$
    – Amit
    Jul 20, 2022 at 8:03
  • $\begingroup$ Draw a utility-frontier and the indifference curves of a social-welfare function superimposed on it, and consider that the economy is in some pareto-efficient point, i.e., it is on any point in the utility frontier. Is it possible to shift to a less efficient state but one with more social welfare? Is it possible to shift to another efficient state but with more social welfare? Remember: points on higher indifference curves correspond to more social welfare i.e., more equity; points farther away from the social-welfare curve are less efficient. $\endgroup$ Jul 21, 2022 at 10:53

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Sometimes Pareto optimal distribution can be equitable but this is not often seen naturally.

In any case when government has to redistribute resources around using distortionary taxes in order to improve equity the resulting distribution won’t be Pareto optimal. This is because Pareto improvements requires that nobody is made worse off (Pareto optimality is reached when all Pareto improvements are exhausted). Since most countries engage in some sort of redistribution, presumably to make results more equitable, it stands to reason that equitable outcomes in most places won’t be Pareto optimal.

However, locally in some situations it is possible to get equitable Pareto optimal results. There might be some local beneficial trades where people end up with the same outcomes while both parties get better off.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – 1muflon1
    Jul 20, 2022 at 13:53
  • $\begingroup$ Hi @1muflon1 and thank you for answering my question. So, is my understanding correct? - A Pareto Optimal distribution may or may not be equitable, and an equitable distribution may or may not be Pareto optimal. $\endgroup$
    – user41791
    Aug 23, 2022 at 3:16

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