The Harrod–Domar model of the growth of an economy is

The Harrod–Domar model of the growth of an economy is based on three assumptions. (1) Savings, S_t, in any time period are proportional to income, Y_t, in that period, so that

S_t = aY_t (a > 0)
(2) Investment, It, in any time period is proportional to the change in income from the previous period to the current period so that
It = b(Y_t − Y_t-1) (b > 0)
(3) Investment and savings are equal in any period so that
I_t = S_t
Use these assumptions to show thatand hence write down a formula for Y_t in terms of Y₀. Comment on the stability of the system in the case when a = 0.1 and B = 1.4.