Final answer:
The process of economic convergence, where poorer countries grow faster than richer ones and thus close the income gap, is typically a slow process. Even if a follower country grows at 7% annually while a leader country's growth stalls, it may take decades to fully converge, and growth rates tend to slow as countries catch up.
Step-by-step explanation:
The concept of economic convergence suggests that poorer economies will tend to grow at a faster rate than richer ones, leading to a reduction in income disparities over time. However, this process can be quite slow, as illustrated by the hypothetical scenario of two countries. The example considers a leader country with a real GDP per capita of $80,000 and a follower country with a real GDP per capita of $40,000. If the leader country's growth falls to zero percent and the follower country's growth rises to 7 percent, over time, the income gap will narrow. Yet, the extent and duration of convergence can vary greatly.
Let's use the compounding growth formula to understand the potential impact of growth rates. In the given scenario, without growth, the leader country remains at $80,000, while the follower country with a 7% growth rate will double its GDP per capita approximately every 10 years (using the Rule of 70). After 10 years, it would have a real GDP per capita of around $80,000, effectively catching up to the leader country's stagnant economy. This example demonstrates the ability of rapid growth to dramatically reduce wealth disparities over time.
However, in reality, as countries progress and catch up, their growth rates tend to decrease. GDP per capita is a useful measure for classifying countries into different income levels and understanding global income distribution. For instance, low-income countries have per capita GDPs of $1,025 per year, while high-income countries have over $12,475 per year. Indeed, high-income countries earn a disproportionate share of world income despite representing a small fraction of the global population.