Suppose that instead of being subject to a lump-sum tax, the consumer faces a labor income tax with a tax-free threshold. More precisely, the representative consumer pays no tax on wage income for the rs x units of real wage income, and then pays a proportional tax on each unit of real wage income greater than x (in Australia, for example, this threshold is $18,200 per annum).
The consumer's budget constraint is then given by C= w(h-l) + pi if w(h-l) is less than or equal to x, and C= w(h-1)-t[w(h-l)-x]+pi if w(h-l) is greater than x.
where C is consumption, l is leisure, w is the wage, denotes dividends, and h is the total amount of time available.
1. Draw the consumer's budget constraint on the (l;C) plane.
2. Suppose that the government reduces the tax deduction x. Using diagrams, determine the e ects of this tax change on the optimal choices of the consumer. Explain your results in terms of income and substitution e ects and consider two cases:
CASE 1: The consumer pays a positive tax before x is reduced.