DSE 2014 Question 40: Welfare economics and social choice

An economy has $n\ge2$ individuals with preferences over $X$. Let $S=\{a,b,c,d,e\}$ and $T=\{a,b,c,d\}\subset S$. Consider:

A. If $a$ is Pareto optimal (PO) in $S$, then $a$ is PO in $T$.

B. If $a$ is PO in $T$, then $a$ is PO in $S$.

C. If $a$ is PO in $S$ and $b$ is not PO in $T$, then $a$ is Pareto superior to $b$.

D. If $a$ is the only PO alternative in $S$ and $b$ is not PO in $S$, then $a$ is Pareto superior to $b$. How many are correct?