Analyze the dynamic path - difference equation, Mathematics

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One of the well-known class of models that involve a simple difference equation are models of mean reversion. These models typically take the form

yt+1 - yt = -a(yt - μ)where 0 < a< 1

In the equation above μ is the mean of yt.

a) Provide the intuitive explanation for the above equation.

b) Show homogenous, particular and then general solution for the difference equation.

c) Setting t=0 show the solution to the mean-reversion model.

d) Analyze the dynamic path of this model.

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