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:

Question

Quizplus · Accepted Answer

Using the per-worker production function, we can find the steady state capital-labour ratio using the formula k* = ((s * u * p^(1/2))/(1-d)), where s is savings rate, u is the elasticity of output with respect to capital, p is the elasticity of output with respect to labour, and d is depreciation rate.

For country A, k* = ((0.1 * 1 * 1^(1/2))/(1-0.05)) = 4
For country B, k* = ((0.2 * 1 * 1^(1/2))/(1-0.05)) = 16

Therefore, in the long run, A's capital-labour ratio will be 4 whereas B's capital-labour ratio will be 16. Thus, the correct answer is C.

Assume That Two Countries Both Have the Per-Worker Production Function