Again assume that the marginal propensity to consume out of permanent income equals 0.9 and the marginal propensity to consume out of transitory income equals 0.1. However, instead of a one-time increase in taxes, the infrastructure spending is financed by issuing a ten-year bond at the beginning of the first year. Taxes are then raised in each of the ten years to raise enough funds to retire the bond at the end of the ten years. Permanent income is reduced in each year by the amount of the tax increase in that year. The tax increases necessary to be able to retire the bond are: $15.33 billion in year 1; $15.79 billion in year 2; $16.26 billion in year 3; $16.75 billion in year 4; $17.25 billion in year 5; $17.77 billion in year 6; $18.30 billion in year 7; $18.85 billion in year 8; $19.42 billion in year 9; and $20.00 billion in year 10. (These are net tax increases in that it is assumed that the debt is purchased domestically. Therefore any interest expense paid by taxpayers is offset as income received by taxpayers.)
(a) Verify that the future valuea of each year’s tax increase in year 10 is $20 billion, given that the real interest rate the government can borrow at equals 3 percent. (Remember that the first year’s tax increase can earn interest in years 2 through 10; the second year’s tax increase can earn interest in years 3 through 10; and so on.)
(b) Compute the amounts of consumption expenditures and private saving in each of the ten years, given that the tax increase in each year results in a decrease in permanent income.
(c) Compute the amounts that the tax increases cause consumption expenditures and private saving to change in each of the ten years when compared to the amounts prior to the change in fiscal policy.
(d) Compute the initial change in aggregate demand in each of the ten years that results from this combination of changes in taxes and government spending.
(e) Compute the present discounted valueb of the changes in aggregate demand that result from this combination of changes in taxes and government spending, given that the real interest rate the government can borrow at equals 3 percent.
(f) Explain why the expansionary effect of the change in fiscal policy is less, both in the first
year and in terms of the present discounted value of the effect of the fiscal policy over ten years, when the increase in spending is financed by debt that is paid off by a permanent tax increase rather than a one-time tax increase.
(g) What value of the marginal propensity to consume out of transitory income would make the present discounted value of the one-time tax increase equal to the present discounted value of the combination of debt financing and permanent tax increases to pay off the debt?