Question

2. The production function of an economy is y = 2-kas, where y is output per labor and k is capital per labor. The growth rate of the labor force is 2% and the rate of capital depreciation is 5%. There is no Calculate the steady state capital-labor ratio (k*) if the saving rate is 10%! (3 points) What is the saving rate corresponding to the 'golden rule' growth path? (3 points) technological change a) b) c) Calculate the growth rate of total output! (3 points)

Answer 1

Production function y = 2 K^0.5 (x) growth rate of the labor force = 2% (d) rate of capital depreciation = 5% No technological change. (a) (s) saving rate = 10% To calculate steady-state capital-labour ratio In steady state Delta k = 0 + 0.02 k, Also Delta k = i - dk - nk Therefore i - dk - nk = 0 i - 0.05k - 0.02k = 0 i = 0.07k And i = sY sY = 0.07 K 0.1 Y = 0.07 K 0.1 times (2 K^0.5) = 0.07 K 0.2 K^0.5 = 0.07 k 0.2/0.07 = k/k^1/2 \r\n 20/7 = k^1 - 1/2 20/7 = k^1/2 or k = (20/7)^2 k = 400/49 (b) Steady state output = > y = 2 middot k^0.5 = 2 times (400/49)^0.5 = 2 times (20/7)^2 times 1/2 Therefore Y = 40 Golden rule level of capital is the steady state at which
we can say that if

$Y=Ak^\alpha$

Then the golden level savings rate is " $\alpha$ "

In the given equation

Y=2k^0.5

^so,

s^* _=0.5