🔄 The Multiplier Effect
Definition: The multiplier.
How it works: the government spends $100 million building a bridge → construction workers earn income → they spend, say, 80% of that ($80m) → those recipients spend 80% ($64m) → and so on. Each round is smaller because part of the income 'leaks' out through saving, taxation, and imports.
The multiplier formula
Key formulas: $$k = \frac{1}{1 - MPC} = \frac{1}{MPS}$$ where MPC = marginal propensity to consume and MPS = marginal propensity to save. \n With taxation and imports (open economy): $$k = \frac{1}{1 - MPC(1-t) + MPM}$$ where t = tax rate and MPM = marginal propensity to import.
Worked example: If MPC = 0.8: k = 1/(1 − 0.8) = 1/0.2 = 5. \n An injection of $100m → final increase in GDP = $100m × 5 = $500m.
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💧 Marginal Propensities and Leakages
- MPC (marginal propensity to consume) = fraction of additional income spent on domestically produced goods.
- MPS (marginal propensity to save) = fraction of additional income saved.
- MPT (marginal propensity to tax) = fraction taken in taxation.
- MPM (marginal propensity to import) = fraction spent on imports.
- MPC + MPS + MPT + MPM = 1 (all income is either consumed domestically, saved, taxed, or spent on imports).
What affects the multiplier size?
- Higher MPC → larger multiplier (more re-spending per round).
- Higher MPS, MPT, or MPM → smaller multiplier (more leakages per round).
- Developing countries often have smaller multipliers (high import dependence, limited tax base).
- Open economies have smaller multipliers than closed economies (imports are a major leakage).
Open economy example: MPC = 0.7, t = 0.2, MPM = 0.1. \n k = 1/(1 − 0.7(1 − 0.2) + 0.1) = 1/(1 − 0.56 + 0.1) = 1/0.54 ≈ 1.85. \n Much smaller than the closed-economy multiplier of 1/0.3 = 3.33!
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➖ Negative Multiplier and Evaluation
The negative (reverse) multiplier
The multiplier works in reverse too. A withdrawal of spending (cut in government expenditure, fall in investment, fall in exports) leads to a multiplied decrease in GDP. If G falls by $50m and k = 4, GDP falls by $200m.
Evaluation / Limitations
- Time lags: The multiplier effect takes time — each round of spending doesn't happen instantly.
- Spare capacity: If the economy is at or near full employment, the multiplier may cause inflation rather than real GDP growth (AD hits the vertical part of AS).
- Confidence: If consumers/firms are pessimistic, they may save the extra income (lower MPC) → smaller multiplier.
- Crowding out: Government borrowing may raise interest rates → reduce private investment → offset part of the multiplier.
- Supply-side constraints: Bottlenecks in production may limit the real output response.
- Assumes constant MPC: In reality, MPC may change as income changes.
In IB essays, the multiplier is a powerful analysis tool. Combine it with AD/AS analysis: 'The initial injection of $X will be multiplied by k, shifting AD to the right. However, the actual increase in real GDP depends on the shape of the AS curve and the size of the multiplier.'