e. The average worker in China our produces with about 90% of the capital of the average worker in...

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e. The average worker in China our produces with about 90% of the capital of the average worker in Argentina.
For the following questions, consider the information given below: Suppose an economy has the following production model
And the dmamic equation of capital is
Yt = AK,1/342/3
AKt+i = sYt OKt
Furthermore, it begins with a capital stock equal to $200 billion, and suppose its steady :state level c (.apital is $600 billion. The economy now receives a generous _gift of foreign aid in the form of $20 billion worth of capital.

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Robert · Accepted Answer

Suppose an Economy has the following production model.
Yt=AK(sub)t^1/3L(sub)t^2/3
Dynamic Equation of Capital
DeltaK(sub)t+1 = sY(sub)t-GK(sub)t
(lowercase letters are denoted as sub*)
Furthermore it begins with a capital stock equal to $200 billion, and suppose its steady state level of capital is $600 billion. The economy now receives a generous gift of foreign aid in the form of $200 billion worth of capital.
By what proportion does income per capita y=y/l initially increase?
A-0%
B-about 16%
C- about 26%
D- about 36 %
e- about 46%
i know the answer is C but im not sure how to get it.
Answer:
We can prove it with an example. Suppose labor force  (L) = 50 and A = 10
Now with given initial capital stock (K) = 200,  Economy’s output (Y) = 10*200^(1/3)*50^(2/3) 
= 793.7005. So per capital income (y = Y/L) = 793.7005/50 = 15.

e. The average worker in China our produces with about 90% of the capital of the average worker in Argentina. For the following questions, consider the information given below: Suppose an economy has...

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