Kelly earned gross income of 40,000 last year. According to the income tax structure, taxes are 25% of the first 20,000 of gross income plus 50% of the excess over 20,000. Thus Kelly paid 15,000 in taxes and had after-tax income (ATI) of 25,000. Inflation is forecast at 5% this year, and Kelly's gross income will rise by 5% this year, and Kelly's gross income will rise by 5% to 42,000. The government is considering a new tax structure of 25% of the first 21,000 plus 50% of the excess over 21,000 (full indexing).

(a) Show that if the government adopts the new tax structure then the real annual rate of growth in both Kelly's ATI and in her paid taxes is 0%.

(b) Find the real annual rate of growth in Kelly's ATI and his taxes paid if the government continues with the old scheme (no indexing).