Assume that two countries both have the per-worker production function y = k 1/2, neither has population growth or technological progress, depreciation is 5 percent of capital in both countries, and country A saves 10 percent of output whereas country B saves 20 percent. If A starts out with a capital–labour ratio of 4 and B starts out with a capital–labour ratio of 2, in the long run:

A) both A and B will have capital–labour ratios of 4.

B) both A and B will have capital–labour ratios of 16.

C) A's capital–labour ratio will be 4 whereas B's will be 16.

D) A's capital–labour ratio will be 16 whereas B's will be 4.

The answer is C, but please show all work and explain steps so it is clear. Thank you

Answer is Option C:  A's capital–labour ratio will be 4 whereas B's will be 16

Explanation:

The calculation of the problem is as follows:

In the long run, economy reaches a steady state and steady state occurs when delta k is 0 .

Delta k = sy - (d + n + g)k = 0, steady state would occur when sy = (d + n + g)k

here k = capital to labor ratio i.e. K/L, s = saving rate , d = depreciation rate , n = population growth rate and g = technical growth rate.

Calculating for Country A:

s = 10% = 0.10 , d = 5% = 0.05 , g = 0 and n = 0  

In long run, sy = (d + n + g)k => 0.1k1/2 = 0.05k

=> k1/2 = 2 => k = 4

Long run capital labor ratio of country A = 4

Now, calculating for country B:

s = 20% = 0.20 , d = 5% = 0.05 , g = 0 and n = 0

In long run, sy = (d + n + g)k => 0.2k1/2 = 0.05k

=> k1/2 = 4 => k = 16

Long run capital labor ratio of country B = 16

Hence, the correct answer is Option C: A's capital–labour ratio will be 4 whereas B's will be 16.

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hope i explained myself