If the per-worker production function is given by y = k1/2, 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

The steady-state ratio of capital to labor (k*) can be found using the equation:

sf(k*) = (n+δ)k*

where s is the saving rate, f(k) is the production function (which is y=k1/2 in this case), n is the population growth rate (assumed to be zero), and δ is the depreciation rate.

Substituting the values given in the question, we get:

0.2(k*1/2) = 0.1k*

Simplifying, we get:

k*1/2 = 0.5k*

Dividing both sides by k*, we get:

k*-1/2 = 0.5

Taking the reciprocal of both sides, we get:

k* = 4

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

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