Pareto efficiency implies that resources are allocated in the most economically efficient manner, but does not imply equality or fairness. An economy is said to be in a Pareto optimum state when no economic changes can make one individual better off without making at least one other individual worse off.
Which allocations are Pareto efficient?
The only allocation that is Pareto efficient is that in which person 1 has all the applies and person 2 has all the bananas. For any other allocation, one of the persons has some units of the good she does not like, and would be better off if the other person had those units.
How do you know if something is Pareto efficient?
Definition. An allocation is Pareto efficient if there is no other allocation in which some other individual is better off and no individual is worse off.