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8/10/2019 Finale Presentation Macroecons
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Comprehensive Quantitative Question
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Assumptions
! Assumption 1: There is no tax and assume the economyhas fixed exchange rate.Both consumption and importare increasing function of aggregate income. That is C= a+ MPC!Yand IM = f + MPM !Y, where aand f
are positive constants.
! Assumption 2:For every 1% increase (decrease) in theinterest rate, planned investment Idecreases (increases)by $0.2 billion.
! Assumption 3:For every $1 billion increase (decrease)in government spending G, the interest rate increases(decreases) by 1%.
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4.1
" What is thedefinition of equilibrium in the
goods market? Using this definition, derive
MPCand MPMmathematically according
to Figure 1 and Assumption 1. (8 marks)
At equilibrium,
AD (Y) = AE
AD = C + I + G + X - M
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Using this definition, derive MPC and MPM
mathematically according to Figure 1 and Assumption 1.
" AD = C + I + G + X - M
" MPC =
"
MPM =
!C
!Y
!M
!Y
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Using this definition, derive MPC and MPM
mathematically according to Figure 1 and Assumption 1.
" In a closed economy,
"AE = C + I + G
"From assumption 1, C = a + MPC x Y
"
Using b = MPC"AE = (a+bY) + I + G
"At eqm, Y = AE = (a+bY) + I + G
Y=1
1!ba +
1
1!bI+
1
1!bG
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Using this definition, derive MPC and MPM
mathematically according to Figure 1 and Assumption 1.
From the graph, when Y = 0, AE =20
AE = (a+bY) + I + G
20 = a + I + G
When Y =100, AE = 100
100 = a + b(100) + I + G
100 = 100b + a + I +G
100b = 80b = MPC = 0.8
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Using this definition, derive MPC and MPM
mathematically according to Figure 1 and Assumption 1.
In an open economy,
AE = C+I+G+EX-IM
From assumption 1, IM = f + MPM x Y
Using d=MPM,
AE = (a+bY) + I +G + EX (f + dY)When Y =0 and AE =20,
20 = a + I + G + EX f
When AE=25 and Y =25
25 = a + 25b + I + G + EX f 25d
25 = a + I + G + EX + 25(0.8) 25d
25d = 20 + 20 25 = 15
d = MPM = 0.6
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4.2
" Holding money supply constant, according toAssumptions 2 and 3, when government spendingincreases by $3 billion, what happens to the interestrate and planned investment?
(2 marks)
! Assumption 2:For every 1% increase (decrease) in theinterest rate, planned investment Idecreases (increases)by $0.2 billion.
! Assumption 3:For every $1 billion increase (decrease)in government spending G, the interest rate increases(decreases) by 1%.
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4.2
" Government spending
increases by $3 billion.
" 3% increase in interest
rate
" Investment decrease by
$0.6billion
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4.3
! Taking this crowding-out effect into consideration, if
government spending increases by $3 billion, how
much will be the new equilibrium aggregate output if
this is a closed economy? And how much will it be ifthis is an open economy? (8 marks)
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4.3
Closed Economy Open Economy
!YG =
1
1!MPC
!G
!YG =
1
1!(MPC
!MPM)
!G
!Ynet =!YG +!YI
!Ynet =!YG +!YI
!YI =
1
1! (MPC! MPM)!I
!YI =
1
1! (MPC)!I
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4.3
! In a closed economy,
! When G increases by 3 billion and I decreases by
0.6 billion
Y=1
1! ba +
1
1! bI+
1
1! bG
!Y=1
1! 0.8(!0.6)+
1
1! 0.8(3)= 12
!Y=1
1! 0.8(!0.6)+
1
1! 0.8(3)= 12
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4.3
! In an open economy,
! When G increases by 3 billion and I decreases by
0.6 billion
Y=1
1! (MPC!MPM)a +
1
1! (MPC!MPM)I+
1
1! (MPC!MPM)G +
1
1! (MPC!MPM)EX!
1
1! (MPC!MPM)f
!Y=1
1!(0.8
!0.6)
(!0.6)+1
1!(0.8
!0.6)
(3)=3
!Y= 11! (MPC!MPM)
!a + 11! (MPC!MPM)
!I+ 11! (MPC!MPM)
!G + 11! (MPC!MPM)
!EX!
11! (MPC!MPM)
!f
!Y=1
1! (MPC! MPM)!I+
1
1! (MPC! MPM)!G
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4.4
! Why does the same increase in government
spending have a larger effect on equilibrium output
in a closed economy than in an open economy?
Explain intuitively. (4 marks)
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4.4
Closed Economy Open Economy
Increase in government spending will
increase the circular flow of income in
that particular economy.
Y = C + I +G
Increase in government spending by the
same amount will increase the circular
flow of income by a smaller amount.
Some of extra government spending
that results is on foreign products and
not on home produced goods and
services
This results in a smaller Y in
Y = C + I +G + X - M
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4.4
Closed Economy Open Economy
Multiplier: Multiplier:
Magnitude of the multiplierClosed economy > Open economy
1
1! MPC
11! (MPC! MPM)
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Questions?