Consider the model of public goods in the last section of this chapter.

(a) Suppose that preferences over private consumption C and public goods G are such that these two goods are perfect substitutes, that is, the marginal rate of substitution of public goods for private goods is a constant b > 0. Determine the optimal quantity of public goods that the government should provide, and interpret your results. Make sure you show all of the relevant cases. What happens when b changes, or when q changes?

(b) Repeat part (a), except with perfect complements preferences, that is, for the case where the representative consumer always wishes to consume private consumption goods and public goods in fixed proportions, or C = aG, with a > 0.