Spending Multiplier Calculator
From the marginal propensity to consume (MPC), compute the spending multiplier: 1 ÷ (1 − MPC), how much total output one yen of spending ultimately drives.
Input Data
Results
At a glance:The spending multiplier shows how far an autonomous spend ripples out. Multiplier = 1 ÷ (1 − MPC), where MPC is the marginal propensity to consume. The closer MPC is to 1, the larger the multiplier and the bigger the boost to total output.
Formula
Spending multiplier = 1 ÷ (1 − MPC).
$$k = \dfrac{1}{1 - \text{MPC}} = \dfrac{1}{\text{MPS}}$$$$\Delta \text{GDP} = k \times \Delta \text{Spending}$$How to Use
- Enter the marginal propensity to consume (MPC, 0 to 1).
- Read the spending multiplier.
FAQ
How does the multiplier work — why can one dollar of spending become several?
The multiplier works because one round of spending becomes someone else's income, which is then partly spent again, rippling through the economy. With MPC = 0.8 (spend 0.8 of every extra dollar): a HK$100 injection becomes HK$80 of consumption → HK$64 → HK$51.2 → … Each round is 0.8 of the previous, a geometric series summing to 100 ÷ (1 − 0.8) = 500. So HK$100 of spending ultimately drives HK$500 of output — a 5× multiplier (= 1 ÷ (1 − MPC)). The money is not created from nothing; it is the same money re-spent across many hands. Each round shrinks (converges) because some is saved (leakage). A higher MPC (less leakage) means more rounds and a bigger multiplier.
Why is the multiplier larger when MPC is higher?
From the formula, multiplier = 1 ÷ (1 − MPC); as MPC approaches 1, the denominator (1 − MPC) approaches 0 and the multiplier grows. Intuitively, MPC is the share of extra income people re-spend, and that re-spending drives the chain. At MPC 0.9, only 10% leaks each round, so the chain runs many rounds (multiplier = 10); at MPC 0.5, half leaks each round and it converges fast (multiplier = 2). So in a high-consumption economy, fiscal stimulus has a larger effect; in a high-saving society, the same stimulus is weaker.
Is the real-world multiplier as large as the formula?
Usually smaller. The formula 1 ÷ (1 − MPC) considers only saving as leakage; reality adds more leakages. First, taxes: extra income is partly taxed, leaving less to spend. Second, imports: part of consumption leaks abroad and does not recirculate locally. With these, the open-economy multiplier 1 ÷ (1 − MPC×(1−t) + m) is clearly smaller. Also, near full employment, extra spending raises prices rather than output, and higher rates may crowd out private investment. So treat this calculator's result as a theoretical upper bound.
What are MPC and MPS, and why do they sum to 1?
MPC (marginal propensity to consume) is the share of each extra dollar of income spent; MPS (marginal propensity to save) is the share saved. They sum to 1 because in the simple model an extra dollar goes to either consumption or saving — no third use. That is why the two multiplier forms are equivalent: 1 ÷ (1 − MPC) = 1 ÷ MPS. MPS is the per-round leakage; a smaller MPS means the chain runs longer and the multiplier is larger.
Is the multiplier really that big in practice?
Empirically it is usually below the simple formula's value, because the base formula ignores tax and imports. Adding the open-economy, tax-inclusive multiplier 1 ÷ (1 − MPC×(1−t) + m) (t = tax rate, m = marginal propensity to import) gives a much smaller number. Empirical fiscal multipliers are mostly estimated between 0.5 and 2, depending on the state of the economy (larger in recessions). So use this tool as the theoretical ceiling, not the realistic estimate.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.