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Cyrille gravatar image

How to elegantly transform a model in a recursive equation

I would like to know if there is an elegant way to develop a model as :

Ct=cYt1+C0, It=I0+γ(CtCt1), Yt=Ct+It

to obtain a resursive equation in Yt which can be put in a natural format to be solved by rsolve(). I can do it in a brute force way. The problem is to cope with the time index.

How to elegantly transform a model in a recursive equation

I would like to know if there is an elegant way to develop a model as :

Ct=cYt1+C0, It=I0+γ(CtCt1), Yt=Ct+It

to obtain a resursive equation in Yt which can be put in a natural format to be solved by rsolve(). I can do it in a brute force way. The problem is to cope with the time index.

My problem is the following

Y = Function('Y')
C = Function('C')
I = Function('I')
C(t)=c*Y(t-1)+C_0
I(t)= I_0 - γ* (C(t) - C(t-1))
Y(t)=C(t)-I(t)
A(t)=C(t)-C(t-1)
show(A(t))

Until there no problems. But I do not know you to substite the value of A(t) in I(t)