Assume that a leader country has real gdp per capita of $80,000, whereas a follower country has real gdp per capita of $40,000. next suppose that the growth of real gdp per capita falls to zero percent in the leader country and rises to 7 percent in the follower country.

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We are asked in this problem to determine the number of years it takes for a country to catch up with the living  standard of the leader country. In this case, we apply the Rule of 70 which states that the the time for a country to double its ouput is equal to 70 divided by the rate growth. With 7% real GDP of the fellower country, the doubling time is 70/7 or 10 years. Thus, in 10 years,the GDP of this country doubles from $20,000 to $40,000. Since the leader country has no GDP growth, it stays as is in $40,00. Therefore, it takes 10 years for the fellower country to catch up with the leader country then.

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