Please Draw Graphs and Explain

Consider the static model of the household discussed in Lecture 3. Suppose that instead of be ing subject to a lumpsum tax, the consumer faces a labour income tax with a taxfree threshold. More precisely, the representative consumer pays no tax on wage income for the rst x units of real wage income, and then pays a proportional tax 1' 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(hl)+JI, ifw(hl)sx, and C: w(hl)r[w(hl)x]+7t, ifw(hl) >x, where C is consumption, 1 is leisure, to is the wage, 7: 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 taxfree threshold x. Using diagrams, deter mine the effects of this tax change on the optimal choices of the consumer under two cases: (a) The consumer pays a positive tax before x is reduced. (b) The consumer does not pay any tax before x is reduced, but pays tax after x is re duced. Explain your results in each case by alluding to income and substitution effects