Question

1. Using the solow growth model, given y(K) = k^0.4, S=0.20, depreciation rate=0.04 and n=1%,

a. What is the steady-state level of capital per worker?

b. What is the steady-state of output per worker?

c. What is the steady-state level of consumption per worker?

2. Now assume population growth is instead-0.5% (approximately the growth rate when every couple has 1.7 children), but that all other parameters stay the same.

a. What is the new steady-state output per worker? Is it higher or lower than with faster population growth? [A numerical answer and a 1 sentence response is fine.]

b. What is the new steady- state of consumption per worker? Is it higher or lower than with faster population growth? [A numerical answer and 1 sentence response is fine].

Answer 1

(1) y = k^0.4

s = 0.2

Depreciation rate (d) = 0.04

n = 1% = 0.01

(a)

In steady state, [s / (d+ n) = k / y

s / (d + n) = k / (k)^0.4

s / (d + n) = (k)^0.6

0.2 / (0.04 + 0.01) = (k)^0.6

(k)^0.6 = 0.2 / 0.05

(k)^0.6 = 4

Raising both sides to the power (1/0.6),

k = 10.08 [Steady state capital per worker]

(b) When k = 10.08,

y = (10.08)^0.4 = 2.52 [Steady state income (output) per capita]

(c)

Steady state consumption per capita = y - (s x y) = y x (1 - s) = 2.52 x (1 - 0.2) = 2.52 x 0.8 = 2.02

(2) n = - 0.5% = - 0.005

0.2 / (0.04 - 0.005) = (k)^0.6

(k)^0.6 = 0.2 / 0.035

(k)^0.6 = 5.71

Raising both sides to the power (1/0.6),

k = 18.26 [Steady state capital per worker]

y = (18.26)^0.4 = 3.20 [Steady state income (output) per capita]

Steady-state output per capita is higher than with faster population growth.

(b)

Steady state consumption per capita = y - (s x y) = y x (1 - s) = 3.2 x (1 - 0.2) = 3.2 x 0.8 = 2.56

Steady-state consumption per capita is higher than with faster population growth.