š What Is the Multiplier?
Multiplier effect.
How it works ā a simple example
The government spends $100 million building a new hospital. Construction workers earn $100 m. If they spend 80% and save 20%, they inject $80 m back into the economy. The recipients of that $80 m then spend 80% ($64 m), and so on. Total increase in GDP = much more than the initial $100 m.
The multiplier works for ANY injection into the circular flow ā government spending, investment, or exports. It also works in reverse: a fall in spending causes a multiplied contraction.
š§® The Multiplier Formula
At SL, the simple multiplier formula uses the marginal propensity to consume (MPC):
Multiplier = 1 / (1 ā MPC) which is the same as 1 / MPS (marginal propensity to save).
If MPC = 0.8: Multiplier = 1 / (1 ā 0.8) = 1 / 0.2 = 5. A $100 m injection ā $500 m total increase in GDP.
What reduces the multiplier? (Leakages)
- Savings (S) ā income saved = not spent in next round.
- Taxes (T) ā income taxed = withdrawn from the spending stream.
- Imports (M) ā spending on imports = leaks out to foreign economies.
- The higher the leakages, the smaller the multiplier.
A more open economy (high imports) or a heavily taxed economy will have a smaller multiplier, because more income leaks out at each round.
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š The Negative Multiplier & Diagrams
The negative (reverse) multiplier
The multiplier works both ways. A withdrawal (fall in G, I, or X) causes a multiplied contraction in GDP. If the government cuts spending by $50 m with a multiplier of 4, GDP falls by $200 m.
Showing the multiplier on AD/AS
- Initial Gā = initial rightward shift of AD (say, $100 m).
- With the multiplier, the FINAL shift of AD is larger ($500 m if k = 5).
- On the diagram: AD shifts right by more than the initial injection.
- The new equilibrium shows a larger increase in real GDP and price level than the initial stimulus alone.
In practice, the multiplier is much smaller than the simple formula suggests ā typically between 1 and 2 for most economies ā because of high leakages and supply-side constraints.