If you have seen the second one of these that you mention (the one with a positive MPC on top of the fraction), I do not believe it could possibly be correct. The reason for this is that the tax multiplier **must always** be negative.

Think about it -- if...

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If you have seen the second one of these that you mention (the one with a positive MPC on top of the fraction), I do not believe it could possibly be correct. The reason for this is that the tax multiplier **must always** be negative.

Think about it -- if taxes go up, do we get more aggregate demand? No -- we get less. So if taxes go up, the change in AD must be negative.

When we use the tax multiplier, what we are saying is this:

Change in taxes times multiplier = change in AD.

So a positive change in taxes (they go up) has to equal a negative change in AD. Mathematically, that means the multiplier must be negative.

If you have a positive MPC on the top of your fraction, the multiplier will be positive and that can't be.