Worked Problem: Mind the Gap
The Congressional Budget Office is an independent federal agency founded in 1974 to provide Congress with nonpartisan and timely economic data on budgetary matters. One of its tasks is to produce estimates of GDP and potential GDP and then make projections about recessionary or inflationary gaps. Congress then uses this information to make decisions about the need for expansionary or contractionary fiscal policies. In June of 2009, the Congressional Budget Office estimated that actual U.S. GDP was $14.22 trillion and potential GDP was $14.44 trillion for 2008. Knowing this, what was the size of the recessionary gap in 2008? Assuming that the marginal propensity to consume is 0.5, what is the change in government purchases of goods and services necessary to increase GDP by this amount if there are no price changes?
As you have learned, in February 2009 Congress passed the American Recovery and Reinvestment Act that provided for a nominal stimulus of $787 billion. By March 2010, only $62 billion of the nominal stimulus had actually been spent. Based on our assumptions above, by how much would this amount of government spending be expected to increase nominal GDP?
Find the size of the recessionary gap in 2008.
Read the section “The Business Cycle and the Cyclically Adjusted Budget Balance” beginning on page 462. A recessionary gap is when real GDP is below potential output.
As potential GDP is valued in 2008 dollars, the size of the recessionary gap in 2008 dollars was $14.44 trillion − $14.22 trillion = $0.22 trillion, or 220 billion dollars. 
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Find the multiplier.
Read the section “Multiplier Effects of an Increase in Government Purchases of Goods and Services” beginning on page 457.
The multiplier is equal to 1/(1 − MPC), so in this case, the multiplier is 1/(1 − 0.5) = 2.
Find the change in government purchases of goods and services necessary to close the gap with a multiplier of 2.
Again, read the section “Multiplier Effects of an Increase in Government Purchases of Goods and Services,” beginning on page 457.
With no price changes and a multiplier of 2, government purchases of goods and services need to increase by $110 billion in order to close a recessionary gap of $220 billion. Without a change in the aggregate price level, a shift of the aggregate demand curve results in an equivalent change in equilibrium GDP. This assumption has the same effect as assuming that the short-run aggregate supply curve is horizontal.
By how much would $62 billion of government spending be expected to increase nominal GDP?
Use the multiplier from Step 2.
With a multiplier of 2, $62 billion of government spending would be expected to increase nominal GDP by $124 billion. Through the first half of 2009, the recessionary gap continued to widen, reaching an estimated $1.07 trillion during the second quarter of 2009—much larger than the estimated recessionary gap of $220 billion in 2008. During the last half of 2009 and the first quarter of 2010, the recessionary gap began to narrow, but slowly. The gap was still $996 billion at the end of 2011. Stimulus spending in 2009 and the first quarter of 2010 was not enough to quickly and significantly narrow a very wide recessionary gap.