Principles of Macroeconomics / Unit 9 MAC 0831 worked example, 60 to 90 seconds
Sizing the Policy That Closes a Gap
The idea
Given a gap and a multiplier, find the change in spending that closes it. The required change is the gap divided by the multiplier, because the multiplier is what turns a change in spending into a larger change in output. Work it, then verify it against the algebra rather than trusting the formula alone.
In practice
The course's economy has a recessionary gap of 250 billion and a multiplier of 2.5. The required change in spending is 250 divided by 2.5, which is 100 billion. Verify: raising government purchases by 100 lifts the autonomous total from 2,700 to 2,800, and 2,800 divided by 0.4 is 7,000, which is potential GDP. The two routes agree. Doing it with a tax cut instead takes a larger cut, because only the propensity to consume of it is spent: the cut needed is 100 divided by 0.75, which is about 133 billion.
Where people slip
An inflationary gap runs the same arithmetic in reverse, with spending cut or taxes raised. The model gives the size of the move, and it assumes the move arrives on time and that nothing else changes. Unit fourteen takes both assumptions apart.
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