If people are Pareto optimal in a trade, then yes, that trade is Pareto optimal.
However if there are three trades between three people (12, 23 and 31) and each trade is Pareto-optimal, that does not mean that the set of three trades as a whole is Pareto-optimal. It’s generally possible to change these trades and get a better outcome for everyone (which is kinda what a market with price signals tries to do).
The only cases where you cannot do this is precisely where there is an agreed upon weighting of everyone’s utility function etc...
The individuals need not be interchangeable, the weighting need not be fair. But Pareto-optimality is only possible in this situation (when the outcome set is smooth).
If people are Pareto optimal in a trade, then yes, that trade is Pareto optimal.
However if there are three trades between three people (12, 23 and 31) and each trade is Pareto-optimal, that does not mean that the set of three trades as a whole is Pareto-optimal. It’s generally possible to change these trades and get a better outcome for everyone (which is kinda what a market with price signals tries to do).
The only cases where you cannot do this is precisely where there is an agreed upon weighting of everyone’s utility function etc...
The individuals need not be interchangeable, the weighting need not be fair. But Pareto-optimality is only possible in this situation (when the outcome set is smooth).