Question

1. This question is about the effect of the Corona epidemic in the Solow model. As the result of the Corona virus the savings between time t and time t+1 is zero. Saving goes back to normal after time t+1. 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 N = 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

If S is amount of savings in the economy at time period t and per capita capital is k and K is total amount of capital in period t.The fundamental equation in solow model is dk/dt=sf(k)-(n+d)k, where d is depreciation rate. It is given that at time period t, economy is in steady state, for which dk/dt=0, which means sf(k)=(n+d)k.

a) The same equation in terms of actual capital can be written as dK/dt=sY-dK. For two period , dK/dt=K(t+1)-Kt. Kt is given as 100, and Savings are given as zero between t and t+1 period so that s=0. The amount of capital at t+1 period will be, K(t+1)-100=0- (0.1*100) ; K(t+1)=100-10=90.

b) The amount of capital per worker at time period t is given as 1. For capital per worker in t+1 period, we can use solow fundamental equation as given above, dk/dt=sf(k)-(n+d)k. For economy starts at time period t, dk/dt=kt+1-kt. Since s=0, due to corona epidemic, dk/dt=0-(n+d)k. kt+1=kt-(n+d)k ; substitution of given values will yield capital per worker in time period t+1 as kt+1=100-(0.15)*1 ; kt+1=100-0.15=0.85.

c) The figure below depict, solow steady state growth model in the longer run. Countries with high savings rate i.e countries which are poor have capital per worker k(0) , simliarly for rich countries with less savings rate at k(0) both of these countries converge in longer run to capital per worker k*, that is economy is in stable state is when sf(k)=(n+d)k, it is important note that f(k) is nothing but percapita output y for a given technology.  since sf(k)=sy which is zero at time period t+1 and (n+d)k=0.15 such that kt+1 is 0.85 as shown in above will converge to a point, where k(t+n)=k(t+n-1).

Growth rate > 0 -n +8 ---- Growth rate < 0 -s.f(k)/k - k k(0)poor k(0) rich k*