1. The real GDP per capita in Eurasia in 1945 was $25, which reaches $800 in 201
ID: 1226162 • Letter: 1
Question
1. The real GDP per capita in Eurasia in 1945 was $25, which reaches $800 in 2016. On the other hand, the economy of Eastasia keeps shrinking. The real GDP per capita in Eastasia in 1945 was $4,096,000, which falls to $128,000 in 2016.
A) Calculate the average annual growth rate of real GDP per capita in Eurasia during the period of 1945-2016.
B) Calculate the average annual growth rate of real GDP per capita in Eastasia during the period of 1945-2013. (Hint:answer should be negative
C) Given your answer to parts A and B, approximately how long will it take for the real GDP per capita of Eurasia to catch up to that of Eastasia, assuming both countries keep their growth rates accordingly?
D) Now suppose instead that Eastasia stops shrinking and keeps a constant real GDP per capita thereafter. Approximately how long will it take for the real GDP per capita in Eurasia to catch to that of Eastasia?
Explanation / Answer
A.
GDP of 2016 = $800
GDP of 1945 = $25
Number of years = 2016 – 1945 = 71
Average annual growth = (GDP of 2016 - GDP of 1945) / Number of years
= (800 – 25) / 71
= $10.92
Average annual growth rate = (Average annual growth / GDP of 1945) × 100
= ($10.92 / $25) × 100
= 43.68%
B.
GDP of 2016 = $128,000
GDP of 1945 = $4,096,000
Number of years = 2016 – 1945 = 71
Average annual growth = (GDP of 2016 - GDP of 1945) / Number of years
= (128,000 – 4,096,000) / 71
= -$55,887.32
Average annual growth rate = (Average annual growth / GDP of 1945) × 100
= (-$55,887.32 / $4,096,000) × 100
= -1.36%%
C.
A = P (1 + r)^n = 800 (1.4368)^n
Again, A = P (1 – r)^n = 128,000 (0.9864)^n
As per the condition, 800 (1.4368)^n = 128,000 (0.9864)^n
n = 13.49 years
Answer: It will take 13.49 years.
D.
A = P (1 + r)^n = 800 (1.4368)^n
But, the other country’s growth is constant.
800 (1.4368)^n = 128,000
n = 14 years
Answer: It will take 14 years.
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