ECMA06 Tutorial #5 Answer Key
If r is held fixed at 0.06 & E is held fixed at 0.85 US$ per C$, then
I = 40 – 4.5(0.06 – 0.06) = 40
X = 180 – 2(0.85 – 0.85) = 180
IM = (1/4)Y + 2(0.85 – 0.85) = (1/4)Y
Part (a)
• Disposable income, DI:
DI = Y – T + TR
DI = Y – (5/11)Y + [120 – (1/11)Y] = 120 + (5/11)Y
• C = C(Y):
C = 10 + (11/12)[120 + (5/11)Y]
C = 120 + (5/12)Y
• The AE function:
AE = C + I + G + X – IM
AE = [120 + (5/12)Y] + 40 + 320 + 180 – (1/4)Y
AE = 660 + (1/6)Y
• Equilibrium output:
In equilibrium, Y = AE:
Y = 660 + (1/6)Y
Y* = 792
• Government (budget) deficit:
GBB = T – TR – G
GBB = (5/11)Y – [120 – (1/11)Y] – 320 = (6/11)Y – 440
GBB = (6/11)(792) – 440 = – 8
⇒ The government runs a budget deficit of 8.
Part (b)
Suppose government spending increases by 55, i.e., G = 375:
• The new AE function:
AE = [120 + (5/12)Y] + 40 + 375 + 180 – (1/4)Y
AE = 715 + (1/6)Y
• New equilibrium output:
In equilibrium, Y = AE:
Y = 715 + (1/6)Y
Y* = 858
• Government (budget) deficit:
GBB = (5/11)Y – [120 – (1/11)Y] – 375
GBB = – 27
⇒ The government budget deficit increases by 19 to 27.
• The (government expenditure) multiplier:
dY * ΔY * 858 - 792
dG = ΔG = 55 = 1.2
ECMA06 Tutorial #5 Answer Key 1 Part (c)
• In part (b), we showed that an increase in G by 55 will increase (autonomous) AE by 55.
• In order for a tax cut to have the same effect on Y*, we need a tax cut such that
(autonomous) AE will increase by 55 as well.
• Given a tax cut enters the AE function indirectly (through a change in DI and then the
consumption), and the marginal propensity to consume out of DI is 11/12, this implies the
amount of tax cut, α, is:
(11/12)α = 55
α = 60
• A tax cut of 60 would achieve the same result on Y* as shown in part (b).
• Note: You can check the result by finding the new AE function after a tax cut of 60 and then
find the new Y*.
Part (d)
Suppose exports fall by 55, i.e., X = 125:
• The new AE function:
AE = [120 + (5/12)Y] + 40 + 320 + 125 – (1/4)Y
AE = 605 + (1/6)Y
• New equilibrium output:
In equilibrium, Y = AE:
Y = 605 + (1/6)Y
Y* = 726
• Government (budget) deficit:
GBB = (5/11)Y – [120 – (1/11)Y] – 320
GBB = – 44
⇒ The government budget deficit

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