Keynesian Multiplier Calculator

Last updated: 2026-05-19

The Keynesian multiplier: definition

The Keynesian multiplier calculator computes how a single injection of new spending reverberates through an economy to produce a larger final change in GDP. Economists, students, and policy analysts use it to estimate the output effect of government spending programs, tax cuts, or changes in investment.

The core insight is straightforward: when a government builds a $1 billion highway, construction workers receive that money as income. They spend roughly 80 cents of each dollar earned (if MPC = 0.8) at local restaurants, hardware stores, and services. Those businesses then pay their workers, who spend 80% of that income, and so on — an infinite chain of smaller and smaller spending rounds. The total effect is far larger than the initial $1 billion.

The formula: a geometric series

Each round of spending is MPC times the previous round. Summing the geometric series gives the spending multiplier formula:

$k_G = 1 + \text{MPC} + \text{MPC}^2 + \text{MPC}^3 + \cdots = \frac{1}{1 - \text{MPC}}$

For MPC = 0.8:

$k_G = \frac{1}{1 - 0.8} = \frac{1}{0.2} = 5$

Every dollar of new autonomous spending raises equilibrium GDP by $5 in the long run. The Marginal Propensity to Save (MPS = 1 − MPC) controls the leak from each round — a higher MPS means money exits the spending chain sooner, reducing the multiplier.

Spending multiplier vs. tax multiplier

A $1 government spending increase directly injects $1 into the economy in the first round. A $1 tax cut is different: households only spend MPC of the tax savings, saving the rest. The first-round injection is therefore MPC × $1 = $0.80, not $1.00. This explains why the tax multiplier is always smaller in magnitude:

$k_T = -\frac{\text{MPC}}{1 - \text{MPC}} = \text{MPC} \times k_G$

For MPC = 0.8, the tax multiplier is −4. A $1 tax cut raises GDP by $4; a $1 tax increase reduces GDP by $4. The negative sign means a tax increase shrinks output, and a tax cut expands it.

The balanced budget multiplier: always 1

One of the most counterintuitive results in macroeconomics is the Haavelmo theorem: if a government simultaneously increases spending and taxes by the same amount, GDP rises by exactly that amount — regardless of the MPC.

The proof follows directly from the two multipliers:

$k_G + k_T = \frac{1}{1 - \text{MPC}} - \frac{\text{MPC}}{1 - \text{MPC}} = \frac{1 - \text{MPC}}{1 - \text{MPC}} = 1$

Intuitively: the spending side produces the full multiplier chain, but the tax side only partially offsets it (because some of the tax is paid from savings, not from spending). The net effect is always $1 of GDP per $1 of balanced-budget expansion.

Worked example: US infrastructure bill

Suppose the US government passes a $200 billion infrastructure program, financed by borrowing (no tax increase), during a period when surveys suggest MPC ≈ 0.72.

1. MPS = 1 − 0.72 = 0.28
2. Spending multiplier = 1 / 0.28 ≈ 3.57
3. Total GDP impact = $200 billion × 3.57 ≈ $714 billion
4. Tax multiplier = −0.72 / 0.28 ≈ −2.57

If the program were deficit-neutral (spending +$200B, taxes +$200B), the net GDP impact would be only $200B × 1 = $200B — the Haavelmo result.

At the same MPC, a tax cut of $200B would raise GDP by approximately $200B × 2.57 ≈ $514B, notably less than the spending route.

Limitations and real-world caveats

The simple Keynesian multiplier is a teaching model, not a forecasting tool. Real fiscal multipliers depend on many factors not captured here:

• Open-economy leakage: consumers spend some income on imports, which leave the domestic economy and reduce the re-spending multiplier.
• Crowding out: government borrowing can raise interest rates, reducing private investment and partially offsetting the fiscal stimulus.
• Ricardian equivalence: rational households may save today's tax cut, anticipating higher future taxes — driving effective MPC toward zero.
• State of the economy: multipliers tend to be larger in recessions (when there is slack capacity and the central bank is at the zero lower bound) and smaller in full-employment expansions.
• Monetary policy response: if the central bank tightens policy in response to fiscal expansion, interest rates rise and output returns toward potential.

Empirical estimates of the fiscal multiplier range from approximately 0.5 (small open economies with flexible exchange rates) to above 2 (deep recessions with accommodative monetary policy). The simple-model value of 5 for MPC = 0.8 is an upper bound, not an empirical prediction.