DSE 2012 Question 27: Welfare economics and social choice

$A$ and $B$ live in an exchange economy. There are two goods $X$ and $Y$. Utility functions of $A$ and $B$ are $U^{A}(x,y)=x+y$ and $U^{B}(x,y)=x^{2}+y^{2}$, respectively. $A$'s endowment is 2 units of $X$ and 1 unit of $Y$, while $B$'s endowment is 1 unit of $X$ and 2 units of $Y$. Consider the following allocations. Allocation 1: $A$ gets 1.5 units of $X$ and zero unit of $Y$, $B$ gets 1.5 units of $X$ and 3 units of $Y$. Allocation 2: $A$ gets 1.5 units of $X$ and 1.5 unit of $Y$, $B$ gets 1.5 units of $X$ and 1.5 units of $Y$.