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)+π if w(h-l) ≤x, or C=(1-t)w(h-l)+tx+π 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.