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
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.
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