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What's the difference between competitive (or Walrasian) equilibrium and Pareto optimal equilibrium. Is a price equilibrium with transfer a competetive equilibrium?

Dimitru
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  • "Pareto-optimal" is its own definiton. An equilibrium allocation can be Pareto-optimal. – Giskard Feb 16 '23 at 12:59
  • You might consider searching the already existing questions. – Giskard Feb 16 '23 at 13:01
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    Does this answer your question? Why is Pareto efficiency not always equitable or equilibrium? – Giskard Feb 16 '23 at 13:01
  • But I did not find an answer in your suggestions. A Walrasian (or competitive) equilibrium is a special case of a price equilibrium with transfers. It is a general equilibrium approach. An allocation is Pareto optimal if there is no other feasibile allocation that pareto dominates it. The allocation of a Walrasian equilibrium, under some conditions (first foundamental theorem), is Pareto optimal. But a Walrasian equilibrium and Pareto optimal allocation seems to be the same. What am I missing? – Dimitru Feb 16 '23 at 13:28
  • @Giskard is that because Pareto optimality is a concept coming from the social planner's problem, and so of a centralized equilibrium? And so, under the assumptions of the first welfare theorem (perfect competition, no externalities, no public goods, and local-non satiation of preferences), we get that a market based equilibrium (decentralized equilibrium) corresponds to a Pareto optimal equilibrium? – Dimitru Feb 16 '23 at 13:53
  • "Walrasian equilibrium and Pareto optimal allocation seems to be the same." How so...? Pareto optimality doesn't even suppose any individual endowments, while equilibrium does. The first welfare theorem indeed states that under certain conditions all Walrasian equilibria are Pareto-optimal. – Giskard Feb 16 '23 at 14:14
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    @Giskard. Thanks for your reply. Maybe, I got it. Pareto optimality is a property of a feasibile allocation, where we do not consider any individual endowment, or distributional issue. Whereas, a Walrasian equilibrium is a market based equilibrium with an initial endowment of commodities and shares of firms. Is that correct? Btw, you can also give a formal answer so that I can vote it – Dimitru Feb 16 '23 at 14:31
  • You can vote for my explanation here (: – Giskard Feb 16 '23 at 15:32
  • Done right now! Just a remark: do you agree with me about my last point? – Dimitru Feb 16 '23 at 15:36
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    Yes, that is why I 'upvoted' the comment. The phrasing is a little strange to me, but I think we mean the same thing. – Giskard Feb 16 '23 at 15:48

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