Question

Consider the Harrod-Domar model given by the following equations.

S _t = 0.3 Y _t

I _t = 0.25 (Y _t - Y _{t - 1})

I _t = S _t

a) Explain the significance of each variable and of all the constants. 

b) Use the same constants to write the continuous-time Harrod-Domar model. 

c) If Y ₀ = 500, derive the income trajectory for the given discrete model.

d) Compute the fixed point of the trajectory determined above and analyze the system’s stability

Answer 1

a) St- saving in t period; It- investment in t period; Yt/t-1- GDP/economy outcome in t period/previous period.

b) $0.3Y_{t-1}=0.25(Y_t-Y_{t-1})$

$Y_t=2.2Y_{t-1}$

c) $Y_1=2.2*500=1100$; $Y_2=2.2*1100=2420$ it is exponential growing function.

d) $Y_0=500$ is fixed point. The system is not stable because the function move away from the fixed point.