If the per-worker production function is given by y = k^1/2, the saving rate (s) is 0.2, and the depreciation rate is 0.1, then the steady-state ratio of capital to labor is: A)1. B)2. C)4. D)9.

Question

Quizplus · Accepted Answer

In the steady state, output per worker is constant (y*) and capital per effective worker (k*) is constant. Therefore, we can write the steady-state equation as:
y* = k*S^1/2*U1*(P1/2)/(S+δ) 
where δ is the depreciation rate which is given as 0.1.

We know that s = 0.2, and accordingly, we can express k* in terms of S as follows. 
s*Y* = δK*
0.2*Y*/K* = δ
K*/Y* = 0.2/δ = 2

Substituting this value for K*/Y* in the steady-state equation and solving for K*/S^1/2 will give us the steady-state ratio of capital to labor:

y *= k *S^1/2*U1*(P1/2)/(S+δ) 
y* = k*S^1/2*U1*(P1/2)/(S+0.1) 
1 = k*/(S^1/2*U1*(P1/2)/(S+0.1))
K*/S^1/2 = (U1*(P1/2))/(1-0.1/0.2)

K*/S^1/2 = 4

Therefore, the steady-state ratio of capital to labor is 4 (Option C).

If the Per-Worker Production Function Is Given by Y =