Assume a Cobb-Douglas production function, where the share of labor (N) and capital (K) is each 1/2 and A = 1.If the growth rate of labor is n = 0.06, the rate of depreciation is d = 0.04, and the savings rate is s = 0.2, what is the value of the steady-state capital-labor ratio?
A)0)5
B)1
C)2
D)4
E)5

Question

Quizplus · Accepted Answer

The steady-state capital-labor ratio (k*) in a Cobb-Douglas production function can be found using the formula: k* = (s / (n + d))^1/(1-α), where s is the savings rate, n is the growth rate of labor, d is the depreciation rate, and α is the share of capital. Given α = 1/2 (since the share of labor and capital is each 1/2), s = 0.2, n = 0.06, and d = 0.04, we substitute these values into the formula: k* = (0.2 / (0.06 + 0.04))^1/(1-0.5) = (0.2 / 0.1)^2 = 2^2 = 4.

Assume a Cobb-Douglas Production Function, Where the Share of Labor