In the text, we have called an allocation x¯ Pareto efficient if there exists no other feasible allocation x such that for at least one j. Sometimes, an allocation x¯ is called Pareto efficient if...

In the text, we have called an allocation x¯ Pareto efficient if there exists no other feasible allocation x such that
for at least one j. Sometimes, an allocation x¯ is called Pareto efficient if there exists no other feasible allocation x such that

(a) Show that when preferences are continuous and strictly monotonic, the two definitions are equivalent.

(b) Construct an example where the two definitions are not equivalent, and illustrate in an Edgeworth box.