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A Country Has the Per-Worker Production Function

Question 74

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A country has the per-worker production function
yt = 5, A country has the per-worker production function y<sub>t</sub> = 5, where y<sub>t</sub> is output per worker and k<sub>t</sub> is the capital-labor ratio.The depreciation rate is 0.2 and the population growth rate is 0.05.The saving function is S<sub>t</sub> = 0.2Y<sub>t</sub>, where S<sub>t</sub> is total national saving and Y<sub>t</sub> is total output. (a)What is the steady-state value of the capital-labor ratio? (b)What is the steady-state value of output per worker? (c)What is the steady-state value of consumption per worker?
where yt is output per worker and kt is the capital-labor ratio.The depreciation rate is 0.2 and the population growth rate is 0.05.The saving function is
St = 0.2Yt,
where St is total national saving and Yt is total output.
(a)What is the steady-state value of the capital-labor ratio?
(b)What is the steady-state value of output per worker?
(c)What is the steady-state value of consumption per worker?

Correct Answer:

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(a)sf(k)= (n + d)k,so 0.2 × 5k0.5 ...

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