The Spending Multiplier

Money changes hands more than once. When the government spends 100 billion on highway repairs, that 100 billion becomes income for construction workers and suppliers. They don't save all of it. They spend a share of it, the marginal propensity to consume, or MPC, on groceries, rent, and everything else. That spending becomes someone else's income, who spends a share of it too. One round of spending keeps triggering another, smaller round, and the final change in GDP ends up bigger than the initial injection.

Run the numbers with MPC = 0.75. Round one: 100 billion spent. Round two: people receiving that income spend 75 billion of it (0.75 x 100). Round three: 56.25 billion (0.75 x 75). The rounds keep shrinking by the same fraction each time, forming a geometric series. Summed to infinity, that series equals the initial injection times 1/(1-MPC), which here is 1/0.25 = 4. So 100 billion in spending becomes 400 billion in total GDP. The multiplier formula just compresses that whole chain of shrinking rounds into one number.

The chain shrinks instead of exploding because of leakages: every round, some income leaks out of the spending stream into saving, taxes, and imports instead of getting respent. Those leakages are exactly what MPC leaves out. A bigger MPC means smaller leakage and a bigger multiplier; more saving, taxing, or importing means the geometric series shrinks faster and the multiplier shrinks too. This is why the multiplier connects directly to fiscal policy: a government choosing between a tax cut and a spending increase of equal size is really choosing between a smaller and a larger multiplier effect, since part of a tax cut leaks into saving before it ever enters the spending stream.