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Suppose that an economy has the per-worker production function given as:
yt = 5K^0.5_t where y is output per worker and k is capital per worker.
In addition, national savings is given as:
S_t = 0.20Y_t, where S is national savings and Y is total output.
Use the production and savings functions above and the depreciation and population growth rates below to answer the following questions. (Enter all responses a:s decimals rounded up to three places.)
The depreciation rate (d) = 0.15 and population growth rate (n) = 0.10
1. What is the steady-state value of the capital-labor ratio, k?

Respuesta :

Capricious23

Answer:

What is the steady-state value of the capital-labor ratio, k?

k = 16

Explanation:

Suppose that an economy has the per-worker production function given as follows:

yt = 5kt^0.5

where y = output per worker

k = capital per worker

k = sy - (n+d)×k

0 = s(5k^0.5) - (0.10+0.15)×k

0 = 0.20(5k^0.5) - 0.25k

0.25k = k^0.5

k^0.5 = 1/0.25

k^0.5 = 4

k^1/2 = 4

Taking square of both of the sides:

(k^1/2)² = (4)²

k = 16

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