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Hi there math experts.

I would like to calculate the equilibrium of two linear equations. However, they're part of a time series, where $a_{-1}$ defines the lagged value of $a$. I don't know how to translate that into to linear equations from which I can calculate the equilibrium.

The system I have is:

$$ \log(C)=\log(C_{-1})+0.4\left(\log(Y)-\log(Y_{-1})\right)+0.407\left(\log(Y_{-1}^{0.9}\cdot W_{-1}^{0.1})-\log(C_{-1})\right)\\ W=W_{-1}+Y-C $$ where $C$ and $W$ are to be determined (endogene) and $Y$ is constantly maintained at 0.001.

How do I calculated the steady state of the system?

Thanks in advance.


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What do you mean by the "equilibrium of an equation"? – Eckhard Dec 19 '12 at 21:11
up vote 0 down vote accepted

At equilibrium, $X_{-1}=X$ for every $X$ in $\{C,Y,W\}$, then the equations become $Y^{0.9}W^{0.1}=C$ and $Y=C$. Hence the equilibrium is $$ W=C=Y. $$

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