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Consider the following simple model with investment and government spending exogenous:
Y = C + I + G
C = a + bYd
Disposable income Yd is given by Y - T where T is total taxes. Suppose that taxes are not directly related to income, so that T can be increased or decreased independent of income.
a. Derive the change in Y associated with an increase in taxes T. Show the results graphically and algebraically. What is the tax multiplier?
b. Now increase government spending G and taxes T by the same amount. For this change, the balanced government budget deficit G - T does not change. If the budget was balanced before, it will still be balanced. What happens to income Y in this case? Perhaps surprisingly, it increases. Calculate by how much. The result is called the balanced budget multiplier.