Question

Assume that two countries both have the per-worker production function y = k1/2, 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–labor ratio of 4 and B starts out with a capital–labor ratio of 2, in the long run:

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

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

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

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

Answer 1

Answer

The correct answer is (C) A's capital–labor ratio will be 4 whereas B's will be 16

In the long run all countries are in steady state and Steady state occurs when Change in capital per worker(k) = 0 i.e.$\Delta k = 0$.

As $\Delta$k = sy - dk

where y = output per worker = k^1/2, s = saving rate , d = depreciation rate

Thus Steady state occurs when Change in capital per worker(k) = 0 i.e.$\Delta k = 0$ and $\Delta$k = sy - dk = sk^1/2 - dk

=> In Long run(when steady state occurs) we have $\Delta$k = sk^1/2 - dk = 0

=> k^1/2 = (s/d)

=> k = (s/d)² -------------------Long run value for capital per worker

For Country A,

s = saving rate = 10% = 0.10 and depreciation rate = 5% = 0.05

=> k = (s/d)² = (0.10/0.05)² = 4 -----------Long run value of capital labor ratio in Country A.

For Country B,

s = saving rate = 20% = 0.20 and depreciation rate = 5% = 0.05

=> k = (s/d)² = (0.20/0.05)² = 16 -----------Long run value of capital labor ratio in Country B

Note In long run or steady state(Initial capital labor ratio does not play any role in determining steady state value of capital - labor ratio).

Hence, the correct answer is (C) A's capital–labor ratio will be 4 whereas B's will be 16