Motivating linear algebra for economics students?

I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors.

This is a typical linear algebra course that focuses on things like linear dependence, subspaces, eigenvalues, etc. and does not spend time on "practical applications". As a result, a lot of the economics students have no idea why they should be taking the course. Since I don't know the first thing about economics, I also have no idea why they should be taking the course.

Is it possible to convince economics students that linear algebra is important for their field? More precisely:

Are there any motivating examples where linear algebra is used in economics?

Solution 1:

In linear regression linear algebra is used to determine the coeffecients of the predictor equation from the data. Linear regression is the backbone of econometrics.

In modern Portfolio Theory the optimal portfolio is defined in terms of the covariance matrix of asset returns, and the expected volatility of the portfolio is a quadratic form.

Given a matrix showing how each of $n$ sectors depends on resources from the others, the intermediate consumption and demand of each sector is expressed by solving a system of linear equations (i.e. inverting a matrix).

Apart from these examples, I use linear algebra every day at work - I work in high frequency trading for an investment bank. So it's clearly relevant, at least for some people, some of the time.

Solution 2:

A standard example is the Leontief input-output model, see http://en.wikipedia.org/wiki/Input-output_model