In the Solow growth model of an economy with population growth but no technological progress,if in the steady state the marginal product of capital equals 0.10,the depreciation rate equals 0.05,and the rate of population growth equals 0.03,then the capital per worker ratio ______ the Golden Rule level.

Question

Quizplus · Accepted Answer

Capital per worker ratio in the steady state is given by: 
k* = (s/((n+δ)g))^(1/(1-α))
where s is the saving rate, δ is the depreciation rate, n is the population growth rate, g is the technological progress, and α is the share of capital in the production function. 
Since there is no technological progress, g=1. 
In the Golden Rule level, the consumption per worker is maximized. This occurs when the saving rate is such that the marginal product of capital equals the depreciation rate plus the rate of population growth: 
f'(k*) = δ + n 
Given that f'(k*) = 0.10, δ = 0.05, and n = 0.03, we have: 
0.10 = 0.05 + 0.03 
0.10 > 0.08 
Therefore, the capital per worker ratio in the steady state is below the Golden Rule level. Hence, the answer is B.

In the Solow Growth Model of an Economy with Population