Show that whether an outcome x is Pareto efficient:

a) cannot change when a strictly increasing function fi is applied to each agent i's utility

over outcomes.

b) can change when an increasing function fi is applied to each agent i's utility over

outcomes.

Hint: For part a, you need an argument, since your answer needs to be valid for all possible functions. You might want to proceed by contradiction: suppose x is Pareto efficient when each agent i's utility is ui, but not Pareto efficient when it's fi(ui) instead. Then show that this assumption leads to something that is impossible. For part b, you just need an example, since you're only asked to show that something can occur.