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# A Simple Lesson About Money and Models

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Summary:
Imagine you are in your high school algebra class and you are presented with the following two equations: Two linear equations with 2 unknowns. This is a simple problem to solve. Now suppose that your teacher gives you the following three equations: Note that this is still a simple problem to solve. The first two equations are identical to the previous example. You can use those first two equations to solve for x and y. Then, knowing x, you can solve for z. The central point is that the third equation is not important for determining the value of x. The first two equations are sufficient to solve for x and y. So why am I bringing this up? This is precisely how the New Keynesian model deals with money. The baseline New Keynesian model does not include money. The model is complete

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Imagine you are in your high school algebra class and you are presented with the following two equations:

$x + y = 20$
$2x + 10y = 100$

Two linear equations with 2 unknowns. This is a simple problem to solve.

Now suppose that your teacher gives you the following three equations:

$x + y = 20$
$2x + 10y = 100$
$x + z = 5$

Note that this is still a simple problem to solve. The first two equations are identical to the previous example. You can use those first two equations to solve for x and y. Then, knowing x, you can solve for z. The central point is that the third equation is not important for determining the value of x. The first two equations are sufficient to solve for x and y.

So why am I bringing this up?

This is precisely how the New Keynesian model deals with money. The baseline New Keynesian model does not include money. The model is complete and a solution exists. Subsequently, to examine whether money would be important in the model, a money demand function is added to this system of equations. There is a solution to the model that exists. Money is then shown to be irrelevant in the determination of the other variables. But, then again, so was z.