Consider the following Macro-Model (Multiplier –Accelerator Interaction):
Yt= Ct + It+ Gt
Ct= C0+ Yt-1
It = I0 + ( Ct–Ct-1)
Where 0 < < 1 ;
> 0 ; and Gt= G0
i) Find the time path Y(t) of national income, and
ii) Comment on the stability conditions.
To find the time path of national income (Yt) in the given Macro-Model (Multiplier-Accelerator Interaction), we need to solve the equations iteratively. Let's go step by step:
i) Time path of national income (Yt):
The equation for national income is given as:
Yt = Ct + It + Gt
First, we need to find the consumption function (Ct):
Ct = C0 + αYt-1
Next, we need to find the investment function (It):
It = I0 + β(Ct – Ct-1)
Let's substitute these equations back into the national income equation:
Yt = (C0 + αYt-1) + (I0 + β(Ct – Ct-1)) + G0
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