The convergence hypothesis implies that countries with lower levels of per capita income will grow faster and they will catch up with the wealthier countries.

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The convergence hypothesis suggests that poorer economies' per capita incomes will tend to grow at faster rates than richer economies. Therefore, over time, they will converge in terms of per capita income levels, allowing the poorer countries to catch up with the wealthier ones.

The Convergence Hypothesis Implies That Countries with Lower Levels of Per