Q1. Suppose, as in the federal income tax code for the United States, that the representative consumer faces a wage income tax with a standard deduction. That is, the representative consumer pays no tax on wage income for the first x units of real wage income, and then pays a proportional tax t on each unit of real wage income greater than x. Therefore, the consumer's budget constraint is given by C=w(h-l)+? if w(h-l) ?x, or C=(1-t)w(h-l)+tx+? if w(h-1)?x. Now, suppose that the government reduces the tax deduction x. Using diagrams, determine the effects of this tax change on the consumer, and explain your results in terms of income and substitution effects. Make sure that you consider two cases. In the first case, the consumer does not pay any tax before x is reduced, and in the second case, the consumer pays a positive tax before x is reduced.
Q2-(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?
(Cf. C+T=Y -- C is consumption, T is tax, and Y is exogenous quantity of goods.
C=Y-G/q -- G is goods that government purchases, and q is public goods)
(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.