Calculate the change in government purchases of goods and services necessary to close the recessionary or inflationary gaps in the following cases. Assume that the short-run aggregate supply curve is horizontal, so that the change in real GDP arising from a shift of the aggregate demand curve equals the size of the shift of the curve.

a. Real GDP equals $100 billion, potential output equals $160 billion, the government collects 20% of any change in real GDP in the form of taxes, and the marginal propensity to consume is 0.75.

b. Real GDP equals $250 billion, potential output equals $200 billion, the government collects 10% of any change in real GDP in the form of taxes, and the marginal propensity to consume is 0.5.

c. Real GDP equals $180 billion, potential output equals $100 billion, the government collects 25% of any change in real GDP in the form of taxes, and the marginal propensity to consume is 0.8.