Principles of Macroeconomics / Unit 9 MAC 0829 worked example, 60 to 90 seconds
Shift or Rotation
The idea
Classify a policy by what it does to the expenditure line. Some changes shift the line without changing its tilt, leaving the multiplier alone. One kind of change tilts it, and changes the multiplier as well. Deciding which has happened comes before computing anything.
In practice
A change in government purchases shifts the line up or down by its own amount; the slope is untouched and the multiplier holds. A change in autonomous taxes shifts the line by the propensity to consume times the change; again the slope holds. A change in the income tax rate is different: it changes how much of each extra dollar reaches households, so the line rotates, the slope changes, and the multiplier changes with it. Raising the rate flattens the line and shrinks the multiplier; cutting it steepens the line and enlarges the multiplier.
Where people slip
When the line rotates, the new output has to be computed with the new multiplier, not the old one. Using the old multiplier after a rate change is an error the arithmetic will not reveal, because the answer still looks reasonable.
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