Question

Chinese economic growth is the outstanding feature of the world economic scene over the past two decades. a. In 2022, US output was $25.5 trillion, and Chinese output in 2022 was $16.5 trillion. Suppose that from 2022 the output of China grows at an annual rate of 7.9%, whereas the output of the United States grows from 2022 at an annual rate of 2.2%. These are the values in each country for the most recent periods, respectively. Using these assumptions and a spreadsheet, calculate and plot US and Chinese output from 2022 over the next 20 years.

a)How many years will it take for China to have a total level of output equal to that of the United States?

Answer 1

To calculate the output for each country from 2022 over the next 20 years, we can use a spreadsheet and the following formula:

Output(t) = Output(t-1) * (1 + Growth Rate)

where Output(t) is the output in year t, Output(t-1) is the output in the previous year, and Growth Rate is the annual growth rate.

Using these assumptions and starting with the given output levels for 2022, we can calculate the output for each country from 2022 to 2042 as follows:

Year US Output China Output ($trillion)
2022 25.5 16.5
2023 26.1 17.8
2024 26.7 19.2
2025 27.4 20.7
2026 28.1 22.4
2027 28.8 24.1
2028 29.5 25.9
2029 30.3 27.9
2030 31.1 29.9
2031 32.0 32.1
2032 33.0 34.4
2033 34.0 36.9
2034 35.1 39.5
2035 36.2 42.2
2036 37.4 45.2
2037 38.6 48.3
2038 39.9 51.6
2039 41.3 55.1
2040 42.7 58.8
2041 44.2 62.7
2042 45.7 66.8
To determine how many years it will take for China to have a total level of output equal to that of the United States, we can use the formula:

t = ln(China Output / US Output) / ln(Growth Rate China / Growth Rate US)

where ln is the natural logarithm.

Using the values from our spreadsheet, we get:

t = ln(25.5 / 16.5) / ln(0.079 / 0.022) = 13.5

Therefore, it will take approximately 13.5 years for China to have a total level of output equal to that of the United States, assuming the given annual growth rates.