Principles of Macroeconomics / Unit 16 MAC 1507 worked example, 60 to 90 seconds
Doubling Time and the Convergence Gap
The idea
Use unit four's rule of 72 to turn growth rates into doubling times, then compound them over a working life. Divide 72 by the annual growth rate to get the years to double. The point is not the arithmetic but what small differences in rate do when they run for decades.
In practice
An economy growing at 2 percent a year doubles its income in about 36 years. One growing at 6 percent doubles in about 12. Now run both for 72 years. The slow economy doubles twice, so income is about four times its starting level. The fast economy doubles six times, so income is about sixty-four times its starting level. Two economies starting level, differing by four percentage points of growth, end a lifetime apart.
Where people slip
That is the whole convergence story, and it cuts both ways. A country growing fast from a low base can close an enormous gap within a lifetime, which several have done. A country growing a point or two slower than its neighbours for a generation falls behind without anything dramatic ever happening. Remember also that per capita growth is output growth minus population growth, so a fast-growing economy with fast-growing population may deliver little per person.
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