Use an example to explain why, after periods of rapid growth, a low-income country that has not caught up to a high-income country may feel poor.

Rapid growth refers to an increase in a country's output or income at a rate that is significantly higher than its historical average. A low-income country is a nation with a relatively low average or per capita income when compared to other countries. A high-income country, on the other hand, is a nation with a relatively high average or per capita income.

Consider two countries, A and B. Country A is a low-income country with a per capita income of \(1,000, while Country B is a high-income country with a per capita income of \)10,000. Suppose both countries experience rapid growth for a certain period, with Country A growing at a rate of 10% per year, while Country B grows at 5% per year.

Let's assume the rapid growth period lasts for five years. At the end of this period, we can calculate the new per capita incomes for both countries using the formula: New per capita income = Initial per capita income * (1 + growth rate) ^ number of years For Country A: New per capita income = $1,000 * (1 + 0.1) ^ 5 New per capita income = $1,000 * (1.6105) New per capita income = $1,610.5 For Country B: New per capita income = $10,000 * (1 + 0.05) ^ 5 New per capita income = $10,000 * (1.2763) New per capita income = $12,763

Even after the rapid growth period, Country A's per capita income has only increased to \(1,610.5, whereas Country B's has reached \)12,763. Despite Country A's higher growth rate, it is still far behind Country B. This is because even a 10% increase on a lower base (\(1,000) amounts to smaller absolute growth than a 5% increase on a higher base (\)10,000). Therefore, after the rapid growth period, the citizens of Country A may feel poor compared to their counterparts in Country B due to the still existing income disparity. To catch up, Country A must maintain higher growth rates for extended periods of time and invest in human capital, infrastructure, and technological advancements to boost its productivity. Otherwise, the feeling of being poor may persist, even if the country is growing at a noticeable pace.