Economics
Macroeconomics: Growth & the Multiplier
Real growth rates, the Rule of 70, and the spending multiplier — how economies expand.
Real growth strips out inflation: , where is the inflation rate. At a steady growth rate (in percent), output doubles in roughly years — the Rule of 70. The simple spending multiplier is , where is the marginal propensity to consume.
1. Real vs nominal growth
easyAn economy's nominal GDP grows by in a year while inflation is . Approximately what is the real growth rate?
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.
Only the real increase reflects more goods and services; the remaining is just higher prices.
2. Doubling time
mediumCountry A grows at per year and Country B at . Using the Rule of 70, how long does each take to double its real output, and what does the gap show?
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Country A: years. Country B: years.
A modest difference in the annual rate produces a huge difference in outcomes: B doubles more than three times faster. Small, sustained growth-rate differences compound into vast gaps in living standards over a generation.
3. The spending multiplier
hardThe marginal propensity to consume is . The government increases spending by \50$ billion. Assuming the simple Keynesian model, by how much does equilibrium output rise?
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Multiplier .
\Delta Y = \text{multiplier} \times \Delta G = 5 \times \50\text{bn} = $250\text{bn}$.
The initial spending is re-spent in successive rounds ( of each round consumed), so total output rises by five times the injection. A higher would give a larger multiplier; leakages to saving, taxes, and imports shrink it in richer models.