Question

Suppose the following represents the economy

Y = F (K, L) = √ KL
s = 0.3
δ = 0.1
k₀ = 4

Suppose that the steady-state occurs in the year “SS” above. Calculate the steady-state level of capital per worker, and fill in the remaining rows, (SS) to (SS+2).

What do you notice happens to economic growth, gy, once steady state is reached (and beyond the steady state)? Why does this happen?

Note: Economic growth is

gY = Y_t – Y_t-1/ Y_t-1

Since, in this model there is no population change, this is the same as

gY = (Y_t/L – Y_t-1/L) / (Y_t-1/L)

= y_t – y_t-1 / y_t-1 = gy

Year

k

y

gy

i

δk

∆k

SS			N/A
SS + 1
SS + 2

Answer 1

We have the following function and parameters

Y = F (K, L) = √ KL

Per worker production function y = √k
s = 0.3
δ = 0.1
k0 = 4

At the steady-state level of capital per worker, we have kss/yss = s/δ

kss/√kss = 0.3/0.1

√kss = 3

kss = 9.

This is the steady state of capital per worker

Below is the table showing k at time 0 equal to kss = 9 and kss + 1 and kss + 2. We see that output per worker falls with time because as the steady state is surpassed, economic growth retards

Time	k	y	gy	i	δk	∆k
0	9	3.000		0.900	0.090	0.810
1	9.810	3.132	4.403	0.940	0.094	0.846
2	10.656	3.264	4.221	0.979	0.098	0.881