Thread: Forming first-order difference equation

Hi,

I was wondering if anyone can help with this mathematical economics problem:


The multiplier-accelerator model of growth has the following three equations


St = aYt
It+1 = b(Yt+1 - Yt)
St = It


a) Briefly interpret the above three equations and combine them as a first-order difference equation.


b) Assume that output at time zero is Y₀ and solve the difference equation. Which are the determinants of output growth in the model? Explain intuitively.



It's clear from b) that the difference equation must refer to Y(t). But I can't work out how to get a single first-order difference equation that includes the three equations, that is set up to refer to Y(t).

I assume "Yt+1" is , not " " and that " " is . So the middle equation is the difference equation:

Since you are given that and , it follows that so that . Putting that into your equation, which is the same as . I would write that as is relatively easy to solve.

Excellent, thanks