The Fiscal Multiplier

If the government spends an extra $100 building a bridge, GDP obviously rises by $100 in that first step — but it doesn't stop there. The construction workers who get paid go out and spend some of that income at restaurants and shops, whose owners then spend part of what they receive, and so on. The fiscal multiplier is the total eventual increase in GDP divided by the initial dollar of spending, and if that ripple effect is strong, a $100 injection can raise GDP by well more than $100.

The size of the multiplier depends entirely on how much of each round gets re-spent versus saved or spent on imports (money spent on foreign goods leaves the domestic economy rather than circulating further). If people save half of every dollar they receive, the geometric series of rounds — spend, receive, spend half, receive, spend half of that — adds up to a multiplier of exactly 2. If people save less, the multiplier is larger; if more, smaller.

$$\text{multiplier} = \frac{1}{1 - MPC}$$

In words: divide 1 by one minus the marginal propensity to consume — the share of each extra dollar of income a household actually spends rather than saves. A higher MPC means more of each round gets re-spent, so the multiplier is larger.

Each successive round of spending is a fraction of the round before it — exactly the shape of a decaying exponential. Turn the decay rate down (a higher MPC, more re-spending each round) and the curve stays elevated longer before fading, meaning the rounds sum to a bigger total; turn it up (a lower MPC) and the curve collapses toward zero almost immediately, capping the multiplier close to 1.

Worked example

Suppose households spend 75% of any extra income they receive (an MPC of 0.75) and save the rest. The simple multiplier is $1 / (1 - 0.75) = 4$: a $100 spending increase eventually generates about $400 of additional GDP as the money circulates through several rounds of spending and re-spending. If instead households are more cautious and only spend 50% of extra income, the multiplier drops to $1/(1-0.5) = 2$, and the same $100 only generates $200 in total.

Why it isn't a fixed number

That clean formula hides a lot of real-world variation, which is why economists' actual multiplier estimates range from well below 1 to above 2 depending on conditions. When the economy is already at full capacity, extra government demand mostly bids up prices rather than output, shrinking the real multiplier. When interest rates are near zero and a central bank isn't offsetting fiscal stimulus with rate hikes, multipliers tend to run higher, because monetary policy isn't working against the spending. Spending on unemployment benefits or aid to low-income households tends to have a higher multiplier than tax cuts for high earners, because lower-income households spend a larger share of any extra dollar (a higher MPC) rather than saving it.

What this means in practice

Debates over stimulus packages are, underneath the politics, usually disagreements about which multiplier applies to the specific proposal and the specific state of the economy — a multiplier that made sense for infrastructure spending during a demand-starved recession doesn't automatically transfer to a tax cut handed out when the economy is already running hot.