Question

please be careful z.

Suppose the Xavier values each apple at $1 and each banana at $2; Yolanda values each apple at $2 and each banana at $4; and Zoe value each apple at $2 and each banana at $1. Consider the following three allocations: Allocation 1: Xavier has 4 apples and 3 bananas, Yolanda has 2 apples and 2 bananas, and Zoe has 3 bananas and 4 apples. Allocation 2: Xavier has 3 apples and 4 bananas, Yolanda has 2 apples and 2 bananas, and Zoe has 4 bananas and 3 apples. Allocation 3: Xavier and Zoe have nothing, Yolanda has 9 apples and 9 bananas. Rank the three allocations according to the Pareto criterion. Allocation 1 Pareto dominates Allocation 2, but no other pair of allocations can be ranked No allocation Pareto dominates another. Allocation 3 Pareto dominates Allocation 1, but no other pair of allocations can be ranked. Allocation 1 Pareto dominates Allocation 2 and Allocation 3, and Allocation 3 Pareto dominates Allocation 2. Allocation 2 Pareto dominates Allocation 3, but no other pair of allocations can be ranked.

Answer 1

In allocation 1,

Value for Xavier = 4*1 + 3*2 = 10

Value for Yolanda = 2*2 + 4*2 = 12

Value for Zoe = 3*1+4*2= 11

In allocation 2,

Value for Xavier = 3*1 + 4*2 = 11

Value for Yolanda = 2*2 + 4*2 = 12

Value for Zoe = 4*1+3*2= 10

In allocation 3,

Value for Xavier = 0

Value for Yolanda = 2*9 + 4*9 = 54

Value for Zoe = 0

Allocation 1 has more value Zoe than allocation 2 but at the same time it also has lesser value for Xavier than his value in allocation 2. So allocation 2 will hurt Zoe whereas allocation 1 will hurt Xavier.

Allocation 3 only has value for Yolanda and least values for Xavier and Zoe.So allocation 3 will hurt both Xavier and Zoe.

So we can say that no allocation Pareto dominates another.