Lexicographic preferences

[RichaS]

Consider an exchange economy with 2 agents and 2 Goods

Both agents preferences are Lexicographic ( x over y)
endowment of A = (2,4)
endowment of B = (4,2)

Plot utility possibility frontier and set of all pareto efficient allocation.

Will the pareto efficient allocation be the endowment itself because B won't be willing to give up any x for more y?? And what will be the UPF?

[Amit Goyal]

All allocations are efficient including the endowment. You don't have UPFs in such cases, because preferences do not have utility representation.