Question

Question #11 from Chpt. 3 of Macroeconomics (9th edition) Suppose that the government increases taxes and government purchases by equal amounts. What happens to the interest rate and investment in response to this balanced-budget change? Explain how the answer depends on the marginal propensity to consume.

Answer 1

The national savings are the sum of private and public savings. National Savings=(Y − C(Y − T) − T)+(T − G)=Y − C(Y − T) − G = Y − C(Y^d ) − G. The total change in national savings, therefore, will be equal to the sum of the change in total output (income) (∆Y ); the change in consumption due to the change in disposable income times the change in disposable income ( ); and the change in government spending (∆G). We know that the total output (income) is fixed by the availability of the factors of production. Thus, ∆Y = 0. We also know that the change in consumption due to the change in disposable income is the marginal propensity to consume (MPC); and that the change in disposable income will be equal to the change in total income less the change in total taxes. Therefore, ∆ National Savigns=MPC×(–∆T)+∆G=(MPC–1)×∆T=∆I, where the next to last equality comes from the fact that the change in government spending is equal to the change in aggregate taxes; and the last equality comes from the national accounts identity—that national savings are equal to aggregate investment. We know that MPC is bounded between 0 and 1, and so, in general, the change in investment will be negative if an increase in government spending is followed by the equal change in taxes. Thus, in general, investment will fall in response to a balanced budget increase in government spending. To accommodate the fall in investment, real interest rate should increase. (We may draw a national savings/investment diagram to clearly see this. On the diagram, the national savings curve will shift to the left.) If MPC is one, investment will not change since the fall in C will be equal to the rise in G, leaving national savings unchanged. The closer the MPC is to 0 (and therefore the larger is the amount saved out of a one dollar change in disposable income), the greater is the impact on savings, investment, and the real rate of interest.