This evidence suggests that our theory can explain the behavior over time of some but not all countries. If we look at relatively rich countries, then we do see evidence of convergence. Across broader groups of countries, we do not see convergence, and we see some evidence of divergence. Explaining Divergence Why is it that, contrary to what Figure 6.8 “Convergence through the Accumulation of Capital” seems to suggest, not all countries converge? The logic of that picture rests on the diminishing marginal product of capital. If rich countries have lower marginal product of capital than poor countries, then we expect poor countries to catch up. If, for some reason, richer countries sometimes also have a higher marginal product of capital than poorer countries, then the argument for convergence disappears. “Divergence Arising from Increasing Marginal Product of Capital” shows an example where the aggregate production function looks a bit different. This production function has a range where increases in capital stock lead to a higher rather than a lower marginal product of capital. That is, for some amounts of capital, we see increasing marginal product of capital rather than diminishing marginal product of capital. In the figure, country A and country B converge, just as in our previous diagram. But country C is rich enough to lie on the other side of the range where there is an increasing marginal product of capital. Country C therefore has a higher marginal product of capital than country B, even though country C is richer. Countries B and C will diverge, rather than converge.
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