Question

A country is described by the Solow model, with a production function of y = k1/2. Suppose that k is equal to 400. The fraction of output invested is 50%. The depreciation rate is 5%. Is the country at its steady-state level of output per worker, above the steady state, or below the steady state? Show how you reached your conclusion.

Answer 1

Answer:

the country is above the steady state

Explanation:

An economy has the per-worker production function y =  $k^{1/2}$

Here,

y is the output per worker and k is the capital-labor ratio

depreciation rate d = 0.5.

Population growth rate is n = 0%

a. At steady state

Δk = 0

sy-k(d+n) = 0

sy = k(d+n)

0.5 ( $k^{1/2}$) = k (0.05 + 0)

0.5  $k^{0.5}$ = 0.05k

then resolve for k, and obtain k=100. The capital in steady state.

If the k=400, then the output

y = $k^{0.5}$

  =$400^{0.5}$

  =20

Thus, the country is above the steady state