What is convergence hypothesis? Why should we expect convergence in the long run?

The convergence hypothesis holds that nations with low levels of productivity tend to have high productivity growth rates, so that international productivity differences shrink over time. In some poor countries, the supply of capital may be growing very rapidly. In others, educational attainment may be rising quickly, albeit from a low base. But the main reason to expect convergence in the long run is that low-productivity countries should be able to learn from high-productivity countries as scientific and managerial know-how spreads around the world.