Question

1. This question is about the effect of the Corona epidemic in the Solow model. As a result of the

Coronavirus the savings between time t and time t+1 is zero.Assume that the epidemic starts at

time t and lasts for one year. The amount of capital at time t is Kt =100. The depreciation rate is

d = 0.1 . The population at time t is Nt =100. The rate of population growth is n = 0.05 and Nt+1 =105.

At time t the economy is in the steady-state and the amount of capital

per worker is 1.

(a) What will happen to the amount of capital in the economy after one year (at time t+1)?

(b) What will happen to the amount of capital per worker after one year?

(c) What will be the amount of capital per worker in the long run (after many years)?

Answer 1

a).

Consider the given problem here in “period t” the economy is in steady state and level of capital stock and population size are “Kt=100” and “Nt=100”, => at the steady state the capital stock per worker is “kt = Kt/Nt = 100/100 = 1”.

The capital stock in period t+1 is given by.

=> Kt+1 = Kt + It – d*Kt, where “d=depreciation rate”, “d*Kt = depreciated capital stock” and “It=level of investment in period t”. The savings rate between “period t” to “period t+1” is zero implied the level of investment is also zero. So, the capital stock in period t+1 is given by.

=> Kt+1 = Kt – d*Kt < Kt, where “d*Kt > 0”.

=> Kt+1 < Kt, because “d*Kt > 0”. So, the level of capital stock after one year decreases.

b).

Here the population growth is “n = 5% = 0.05”, => in “period t+1” the population size is “Nt+1 = 105”, => the capital per worker after one year is “Kt+1/Nt+1 < Kt/Nt”, because “Kt+1 < Kt” and “Nt+1 > Nt”. So, the capital stock per worker also decreases.

c).

But in the LR the savings rate will further increases to the initial level and the “investment” further increases to the initial amount. So, the economy will further get back to the initial level. So, in the LR the capital stock per worker also increases to “Kt/Nt = 100/100 = 1”. Once the economy get back to the steady state will not change further.