Taxes

Starting from

Y=C+I+G

and

C=a+b(Y-T)

and solving, we get a slightly different "Multiplier Formula:"

This difference:

tells us two things:

Taxes reduce equilibrium income and expenditure.
Each dollar of additional taxes cuts equilibrium income by dollars.

We call the quotient

the "tax multiplier." More generally, remembering that in our model b is the marginal propensity to consume, the tax multiplier can be written as

. Notice that it is different from the "autonomous spending multiplier." In more complex economic models, we may have many "impact multipliers."
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A Numerical Example