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?

Question

Business

Sarai Haley

12 April, 18:06

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?

+5

Answers (1)

Know the Answer?

Janiya · Answer 1

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