Question

Pareto Efficiency: In the island of Zeta live only two people, Jim and Jessica and the island only produces two fruits, apples and pears. Both Jim and Jessica like both fruits, but value them differently. For Jim, 1 apple is exactly equivalent to 2 pears. For Jessica, 2 apples are exactly equivalent to 1 pear.

When do we have Pareto Efficiency and Why? (list the three pareto efficient allocations)

Answer 1

An allocation is said to be pareto efficient if no further gains from trade are possible. All the individuals cannot be made simultaneously well off by any exchange, and hence, improvement in one's well being comes at a cost of the well being of other's.

If A denotes Apples and P denotes pears, the the utility functions of the two individuals can be written as

Jim : 2A + P
Jessica : A + 2P

In such a case, possible Pareto efficient allocations are :

(1) Jim getting all the product, or,
(2) Jessica getting all the product.
Here, both cannot be made simultaneously better off if we transfer any product further. Hence, the allocation is pareto efficient.

(3) Jim getting all apples and Jessica getting all Pears, as they value those products the most. Any transfer of apples or pears will make atleast one of them worse off than this allocation and both cannot be made well off simultaneously.