Tax Multiplier
What is Tax Multiplier?
The tax multiplier measures the change in real GDP from a change in taxes; it is negative and smaller in size than the spending multiplier.
A tax cut raises disposable income, but households save part of it, so only the consumed share is spent in the first round. That makes its initial effect smaller than direct government spending. It is negative because higher taxes reduce GDP.
Tax Multiplier: a worked example
Take an MPC of 0.75, so MPS is 0.25. The tax multiplier is negative 0.75 divided by 0.25, which equals negative 3, while the spending multiplier is 1 divided by 0.25, or 4. A legislature cuts taxes by $50 billion, a change of negative $50 billion. Real GDP changes by negative 3 times negative $50 billion, a rise of $150 billion. Trace the first round to see why that trails the spending case: households receive $50 billion of extra disposable income, save 25 percent of it, or $12.5 billion, and spend $37.5 billion. That $37.5 billion then multiplies by 4, giving $150 billion. Spending $50 billion directly instead would raise GDP by 4 times $50 billion, or $200 billion. Doing both at once, a $50 billion tax rise paired with $50 billion of purchases, nets $200 billion minus $150 billion, or $50 billion.
The mistake students make with tax multiplier
Handed a $60 billion tax cut and an MPC of 0.5, students reach for the multiplier they memorized first and report $120 billion of extra GDP. The mix up is easy because the same MPC feeds both formulas. Taxes work through disposable income, though, so only the consumed share of the cut enters the spending stream in round one. Scale by MPC before multiplying through and the answer is $60 billion. Sign errors follow close behind, since a tax cut is a negative change in taxes and a negative multiplier times a negative change gives a positive change in GDP.
Tax Multiplier questions
Why is the tax multiplier negative?
Taxes and GDP move in opposite directions. Raising taxes takes disposable income away from households, cutting consumption and shifting aggregate demand left, while cutting taxes hands income back and shifts it right. The negative sign encodes that inverse relationship, so you plug in the actual change in taxes and let the arithmetic handle the direction. A tax increase of $20 billion with a tax multiplier of negative 3 lowers real GDP by $60 billion.
How do you calculate the tax multiplier?
The tax multiplier equals negative MPC divided by MPS, which is the same as negative MPC divided by 1 minus MPC. With an MPC of 0.8, the tax multiplier is negative 0.8 divided by 0.2, or negative 4. Multiply it by the change in taxes to get the change in real GDP. Some courses add a transfer payment multiplier with the same size but a positive sign, since transfers raise disposable income the way tax cuts do.
Is the tax multiplier always weaker than the spending multiplier?
In absolute value, yes, whenever the marginal propensity to consume is below 1, because the tax multiplier is exactly MPC times the spending multiplier. An MPC of 0.6 gives a spending multiplier of 2.5 and a tax multiplier of negative 1.5. Subtracting sizes, the two always differ by exactly 1, since 1 divided by MPS minus MPC divided by MPS leaves MPS divided by MPS. In proportional terms the gap narrows as MPC rises, so the two tools come closest where households spend nearly every extra dollar.
Formula / Example
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Common comparisons
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