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Principles of Macroeconomics
Homework 3
Spring 2009 – Due
Consider the following Keynesian Macro model. The following four equations are consistent with our
class discussions. Feel free to reformat this page so you can include your answers following the
questions.
C= 500 + .8(1-.2)Y, where mpc=.8 and t=.2.
G= 450
I = 350 – 1500i, where i=interest rate is equal to 0.07
NX= -25
1) If the interest rate i=0.07, derive the aggregate expenditure equation. Recall the AE= C + I + G + NX.
The final form for the AE equation should be in the form AE = Autonomous Expenditures + mpc(1-t)Y.
AE = C + I + G + NX
AE = 500 + .8(1-.2)Y + 350 – 1500(.07) + 450 - 25
AE = 1170 + .64Y
2) Now derive the equilibrium level of real GDP (Y). Recall equilibrium is defined as AE = Y.
Y = AE = 1170 + .64Y
Y = 1170 + .64Y
Y - .64Y = 1170
Y(1 - .64) = 1170
.36Y = 1170
Y=1170/.36
Y = 3250
Conceptually we are solving for the level of income where the AE line intersects the 45degree line.
3) Suppose full employment GDP (Yf) is equal to 4000. Is this a recessionary or inflationary gap?
Recessionary gap = 4000 – 3250 = 750
4) By how much does government spending need to change to close this gap, assuming constant price
levels?
∆Y = Multiplier x ∆G
∆G = ∆Y / Multiplier
∆G = 750/ 2.78 = 270
Multiplier = 1/ 1-mpc(1-t)
Multiplier = 1/.36 = 2.78
5) Add the amount of the change to government spending to autonomous expenditures in the previous
AE equation from question 1. Now solve for the equilibrium level of real GDP.
AE = (1170 + 270)+ .64Y
AE = 1440 +.64Y
Y=1440 +.64Y
Y=1440/.36 = 4000
See Second Page
6) Plot the AE equations from questions 1 and 6 below. Explain how we went from the initial
equilibrium to the latter one. How much of the change in real GDP (Y) was due directly to the change in
government spending and how much was the result of induced or income dependent consumption.
Calculate these values and include them in your graph.
I’m having trouble with Microsoft drawing tools. The recessionary gap is 750, the direct effect (step 1
equals the change in government spending 270, so the amount of induced consumption is equal to the
difference 480.
Expenditures
rGDP (rY)