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When someone spends money in an economy, that money does not just disappear — it gets passed on. Imagine a government spends 100 dollars building a road. The construction workers receive that 100 dollars as income. They then spend some of it at local shops. The shopkeepers earn income and spend some of it too. This chain reaction means that the final increase in national income is larger than the original injection of spending.
The multiplier is the number that tells us how many times bigger the final change in national income is compared to the original change in spending (the injection).
Definition: The multiplier is the ratio of the change in national income to the initial change in aggregate demand (spending) that caused it.
In formula form:
Multiplier (k) = Change in National Income (ΔY) ÷ Change in Aggregate Demand (ΔAD)
Or rearranged: ΔY = k × ΔAD
Every time income is received, people spend some of it and save (or pay tax on, or spend on imports with) the rest. The part they spend becomes someone else's income, which gets partly spent again, and so on. The multiplier keeps going until there is no more spending left in the cycle.
Three things can take money out of the circular flow and reduce the size of the multiplier:
These are called withdrawals or leakages.
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