Pareto Optimality (Stokey-Lucas)

Definition (Allocation)
An (I+J)-tuple [(xi),(yj)] describing the consumption xi of each consumer and the production yj of each firm is an allocation for the economy.

Definition (Feasible Allocation)
An allocation is feasible if xi ∈ Xi, all i; yj ∈ Yj, all j; and Σxi - Σyj =0.

Definition (Pareto Optimality)
An allocation [(xi), (yj)] is Pareto optimal if it is feasible and if there is no other feasible allocation [(xi'), (yj')] such that ui(xi') ≥ ui(xi), all i; ui(xi') > ui(xi), some i.


Stokey, Lucas "Recursive Methods in Economic Dynamics," p.453