$[10]$ Lucia$$s utility function is $3"!+$ $ and Montiel$$s utility function is $"!$

# $,$ where G is their expenditures

on the nonexcludable and nonrival goods that they share in their RV and where $"!$ and $"$$ 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?