Compare the expenditure function of this new model, to the expenditure function with no income taxes. The new aggregate expenditure function

Suppose that instead of just fixed level of taxes T = Texogenous, we also include an income tax (t) in our Keynesian model (t = tax rate = .1) . Now the tax function is T = Texogenous + t (Y). The tax revenues T include the exogenous component Texogenous and an endogenous component tY. Revenues increase as income increase.
Derive an expression for equilibrium income using this new tax function and determine the value of the government spending multiplier. The model is given by Y = C + I + G, C = a + bYD, I = Iexogenous, and G = Gexogenous. Recall that YD = disposable income and YD = Y – T

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a. The government spending multiplier is 1/1-b-bt
 
 . . .

b. The government spending multiplier is 1/1-b+bt

 . . .

c. The government spending multiplier is -b/1-b+bt+T
 
 . . .

d. The government spending multiplier is -b/1-b+bt

Consider the new Keynesian Model of question 13 that includes income taxes. Compare the expenditure function of this new model, to the expenditure function with no income taxes. The new aggregate expenditure function

…

a. is steeper
…

b. is flatter 
…

c. has shifted parallel upward 
…

d. has shifted parallel downward