Spending Multiplier
Plain definition
The number by which an initial change in government spending (or any autonomous spending) is multiplied to give the total change in GDP; equal to 1/(1-MPC), or equivalently 1/MPS.
In economics
The spending multiplier exceeds 1 because government purchases directly become someone's income, which is partly respent in further rounds. It is larger than the tax multiplier because spending hits demand dollar-for-dollar, while tax cuts leak into saving first. Crowding out and imports reduce it in practice.
Example
With an MPC of 0.75, the spending multiplier is 1/(1-0.75) = 4. A 400 billion, as contractors, suppliers, and workers spend and respend the new income.
The spending multiplier is confused with the tax multiplier. The spending multiplier (1/(1-MPC)) is larger because all of the initial spending enters demand; the tax multiplier (-MPC/(1-MPC)) is smaller in absolute value because households save part of a tax cut before spending any of it.