A small country's aggregate production function per hour of labor is given by Y = K1/2. Its depreciation rate is 5 percent and its investment rate is 25 percent. What is its steady-state level of real GDP?
A) 25
B) 5
C) 1.25
D) You need to know the steady-state level of capital stock to answer this question.

Question

Quizplus · Accepted Answer

In the steady-state, the economy's capital stock will be such that investment equals depreciation. Therefore, the steady-state level of capital stock is:
I = δK
0.25Y = 0.05K
Y/K = 0.2
Substituting the production function gives:
K1/2/K = 0.2
K = 0.2^2 = 0.04
Substituting into the production function gives:
Y = K1/2 = (0.04)1/2 = 0.2
Therefore, the steady-state level of real GDP is 0.2 (or 20% of the initial level of capital stock). The closest answer choice is B (5).

A Small Country's Aggregate Production Function Per Hour of Labor