Spending Multiplier
What is Spending Multiplier?
The spending multiplier measures how much real GDP changes for each dollar change in autonomous spending.
A higher marginal propensity to consume produces a larger multiplier because more of each dollar is re-spent. It is used to estimate the GDP impact of fiscal policy. It assumes spare capacity and ignores crowding out.
Spending Multiplier: a worked example
Suppose the marginal propensity to consume is 0.8. The spending multiplier is 1 divided by 1 minus 0.8, which equals 1 divided by 0.2, or 5. Government now buys $40 billion of bridge repair. Round one adds the full $40 billion to GDP. The construction workers and suppliers who receive it spend 80 percent, adding $32 billion in round two. Round three adds 0.8 times $32 billion, or $25.6 billion, and round four adds $20.48 billion. The rounds shrink toward zero and sum to 5 times $40 billion, which is $200 billion of extra real GDP. Run it backwards for policy: to close a recessionary gap of $200 billion with this multiplier, divide $200 billion by 5 and spend $40 billion. If the MPC were 0.75 instead, the multiplier would be 4 and closing the same gap would take $50 billion.
The mistake students make with spending multiplier
Given a recessionary gap of $150 billion and a multiplier of 4, students multiply and answer that the government must spend $600 billion. Pairing the two numbers by multiplication feels natural because the formula shows the change in GDP equal to the multiplier times spending. The gap, though, is the change in GDP you want, so it belongs on the output side of that equation. Divide the gap by the multiplier and the injection is $37.5 billion. A second slip writes the multiplier as 1 divided by MPC instead of 1 divided by MPS, which turns an MPC of 0.8 into a multiplier of 1.25 rather than 5.
Spending Multiplier questions
How do you calculate the spending multiplier?
The spending multiplier equals 1 divided by 1 minus the marginal propensity to consume, which is the same as 1 divided by the marginal propensity to save. With an MPC of 0.9 the multiplier is 10, and with an MPC of 0.5 it is 2. Multiply the multiplier by the change in autonomous spending to get the change in real GDP, so $30 billion of new investment with a multiplier of 4 raises GDP by $120 billion.
Why is the spending multiplier bigger than the tax multiplier?
Government purchases hit the spending stream at full strength, since every dollar of a road contract is a dollar of GDP in the first round. A tax cut instead hands households a dollar of disposable income, and they save a slice of it, so only MPC times that dollar reaches the spending stream in round one. Both amounts then multiply through the same later rounds, which is why the tax multiplier equals the spending multiplier scaled down by MPC.
What makes the real multiplier smaller than the formula suggests?
Leakages shrink it. Suppose each round of new income loses 20 percent to saving, another 20 percent to income tax, and 10 percent to imported goods. Only half of each round gets re-spent on domestic output, so the multiplier lands near 2 rather than the 5 that an MPC of 0.8 suggests on its own. Crowding out shrinks it further when government borrowing lifts interest rates and displaces private investment, and none of the spending raises real output once an economy already sits at full employment.
Formula / Example
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Related terms
The same idea in another course
Where 1/(1-MPC) comes fromSuccessive rounds of spending form a geometric series, and 1/(1-MPC) is just the standard sum a/(1-r) of that series. On CalcLearn, a sister site.
Common comparisons
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