Assume a production function is given by . If
, the depreciation rate is
, and the saving rate is
The steady-state level of capital is about:
A) 0.3.
B) 1.3.
C) 2.8.
D) 0.8.
E) 1.6.

Question

Assume a production function is given by  . If 
, the depreciation rate is 
, and the saving rate is 
The steady-state level of capital is about:
A) 0.3. 
B) 1.3. 
C) 2.8. 
D) 0.8. 
E) 1.6.

Quizplus · Accepted Answer

In the steady state, capital per worker remains constant. Therefore, we can solve for steady-state capital per worker (k*) by setting investment per worker equal to depreciation per worker: 
sf(k*) = (n + δ)k*
Substituting in the given values: 
0.35k*^(1.5) = (0.05 + 0.07)k*
Simplifying, we get: 
0.35k*^(1.5) = 0.12k*
Multiplying both sides by (1/0.12), we get: 
k*^(0.5) = 0.343
Squaring both sides, we get: 
k* = 0.343^2 = 0.118
Since output per worker is given by: 
y* = Ak*^(0.5) = 2.8
The steady-state level of capital is approximately 0.118 times the level of output per worker, which is approximately 0.118 x 2.8 = 0.330, or about 0.3.

Assume a Production Function Is Given by