Question

2. Suppose that the US is initially at the golden-rule level of steady-state capital accumulation given the current rates of depreciation, technological progress, and population growth

a. What does “the golden-rule level of steady-state capital accumulation” mean?

b. When there are positive rates of depreciation, technological progress, and population growth, explain how each of the following variables is changing over time when the economy is at the golden-rule level of capital:

i. Labor

ii. Labor efficiency units

iii. Total capital stock

iv. Capital stock per labor efficiency unit

v. Capital stock per worker

vi. Total output

vii. Output per labor efficiency unit

viii. Output per worker

Answer 1

The golden rule level of capital is that level of steady state of capital at which Consumption in the economy is maximum. The savings rate is chosen such that the distance between output and investment is maximum. Since the output - investment gives Consumption, therefore Consumption is maximum at the golden rule level of steady state capital accumulation.

B) steady state takes place in solow model when capital stock grows at the rate of n+π+d i.e. it grows to cover for depreciation, growth of labour force and growth of technology.

n= rate of growth of population

π = rate of depreciation

g= rate of growth of technology

AL = efficient Labour

I) labour

Labour will grow at the growth rate of population.

ii) labor efficiency unit = AL

The rate of growth of labour efficiency unit will be n+ π as L grows at n and A grows at π.

iii) total capital stock = K

At steady state capital stock per efficient unit of labor i.e. K/AL = k is constant. To keep k constant , this means that K has to grow at the rate at AL is growing i.e. n+π .

iv) capital stock per labor efficiency unit i.e. k

At steady state k is constant . Therefore its rate of growth is zero.

v) capital stock per worker i.e. K/L

K/L = (k) (A)

k is constant and A grows at the rate π, therefore, to make sure k remains constant at steady state, (K/L) should also grow at π.

vi) total output i.e. Y

At steady state y = Y/AL remains constant. To make sure this happens, Y has to grow at the same rate as AL ,i.e. n+π.

vii) output per labor efficiency unit i.e. y

At steady state this is constant therefore its rate of growth is zero.

viii) output oer worker i.e. Y/L

To keep y constant at steady state, we need to make sure that (Y/L) grows at the same rate as A ( so (Y/L)/A remains constant. Hence output per worker grows at π.