Lucia$$s utility function is $3$Xl $+$ G and Montiel$$s utility function is Xm$/$G$,$ where G is their expenditures on the nonexcludable and nonrival goods that they share in their RV and where Xl and Xm are their respective private consumption expenditures.

The total amount they have to spend on private goods and public goods is $$40,000$ and they agree on a Pareto optimal pattern of expenditures in which the amount that is spent on Lucia$$s private consumption is $$9,000.$

a$.[8]$ How much do they spend on public goods?

b$.[2]$ Can you think of a reason that two people in Lucia and Montiel$$s situation would fail to

consume in a Pareto optimal manner? If so$,$ why?