Question

Consider the following Macro-Model (Multiplier –Accelerator Interaction):

Yt= Ct + It+ Gt

Ct= C0+ \alphaYt-1

It = I0 + \beta( Ct–Ct-1)

Where 0 < \alpha< 1 ; \beta> 0 ; and Gt= G0

i) Find the time path Y(t) of national income, and

ii) Comment on the stability conditions.

09 Dec 2020
Answer :
Word Count : 436

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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