Re: Linear algebra applications in economics

In article <dclqlr$184v$1@xxxxxxxxxxxxxxxxxx>, Santiago Canez
<canez@xxxxxxxxxxx> wrote:

> Hello,
>
> I'm teaching a linear algebra/differential equations course this summer
> and would appreciate suggestions on applications of these topics I could
> mention. I've given applications of both linear algebra and differential
> equations to physics, engineering, chemistry, biology, and computer
> science, but applications to economics have alluded me. Can anyone give
> some concrete applications I could give my students? Specifically, I
> would appreciate an application of eigenvalues/eigenvectors to economics
> and an application of systems of linear differential equations (I
> already have matrix applications to input/output models and applications
> of partial differential equations planned).
>
> Thanks
> SC

The numeraire in this essay

<http://www.dreamscape.com/rvien/Economics/Essays/sraffa.html>

is an eigenvector corresponding to the Perron-Frobenius root of the
given input/output matrix. So this is an extension of what
you say you have planned to an application of eigenvectors. For
more, see, for example,

Luigi L. Pasinetti, _Lectures on the Theory of Production_,
Columbia University Press, 1977.

As for linear differential equations, consider
multiplier-accelerator models of business cycles. You might
be able to find something by throwing out terms in the models
in

Richard M. Goodwin, _Chaotic Economic Dynamics_, Claredon Press,
1990.

--
Mostly economics: <http://www.dreamscape.com/rvien/#PublicationsForFun>
r c
v s a Whether strength of body or of mind, or wisdom, or
i m p virtue, are found in proportion to the power or wealth
e a e of a man is a question fit perhaps to be discussed by
n e . slaves in the hearing of their masters, but highly
@ r c m unbecoming to reasonable and free men in search of
d o the truth. -- Rousseau
.

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