Aggregate Expenditure Model. Chapter 11
This written homework will count as the week 7
MyEconLab No. 6 assignment. Do your work on this page and turn it in.
Answers.
NAME _________________
UID______________
You are a consultant to Sir Alan of Greenspan the leader of the country of Bernankistan. Sir Alan
gives you the following information about the economy:
C = 75 + 0.6Yd (consumption function)
I = 125 (Investment)
G = 81 (Government Spending)
X = 25 (Exports)
T = - 40+.35Y (Tax function)
Yd = Y – T
M = 0.05Y (Import function)
Note the T has two components: a lump-sum component (- 40) that is not related to the level of
Y; and a component that is related to the level of Y.
1. What is the tax rate in Bernankistan?
t = 0.35
2. Solve for the equilibrium level of income in Bernankistan. Plug the information given into
the equilibrium condition: Y = C + I + G + X - M
Y=
C
+I
+G+ X -M
Y = 75 + 0.6[Y – (-40 + .35Y)] + 125 + 81 +25 - .05Y
Y = 306 + 0.6[ Y – (-40 + .35Y)] -.05Y
Y = 330 + .6Y - .21Y -.05Y
Y( 1 – 0.6 + .21 +.05) = 330
Y = 330 / ( 1 – 0.6 + .21 +.05) = 330 / 0.66
Y = 500
3. What is the value of the Government spending multiplier for Bernankistan (to 3 decimal
places)?
The gov’t spending multiplier is ΔY/ΔG = 1 / 1-[b(1-t) -m],
Where b = MPC
t = tax rate
m = MPI
Gov’t spending multiplier = ΔY/ΔG = 1/ .66 = 1.51515
4. What is the value of the Tax multiplier for Bernankistan (to 3 decimal places)?
The tax multiplier is ΔY/ΔT = -b / 1-[b(1-t) -m],
Where b = MPC
t = tax rate
m = MPI
The Tax multiplier = ΔY/ΔT = -.6/ .66 = -.909
5. At equilibrium, how much does the government collect in taxes?
T = -40 + .35 (500) = 135
6. Is the Government of Bernankistan running a budget deficit or budget surplus?
Surplus: T = 135 > G = 81
7. What is the size of the surplus or deficit?
T = 135 and G = 81 => (T - G) = 54 which is a surplus
8. Sir Alan’s economic advisors tell him the full employment level of GDP is Y = $803. Holding
taxes constant, what change in government spending is needed to get to full employment?
ΔY = 303
Spending multiplier = ΔY/ΔG = 1.51515
=> ΔG = ΔY/ 1.5151 = 303 / 1.5151 = 199.98 (call it 200)
9. Holding government spending constant, what change in taxes is needed to get to full
employment?
ΔY = 303
Tax multiplier = ΔY/ΔT = -.909 => ΔT = ΔY/ -.909 = 333.33
10. Sir Allen tells you he wants to increase G by 100 and cut T by 100. What will be the change
in the equilibrium level of GDP?
ΔY = 1.5151 x ΔG = 1.5151 x 100 = 151.51
ΔY = -.909 x ΔT = -.909 x -100
= 90.9
ΔY = 242.41