Assume the following model of the economy, with the price level fixed at 1.0:
C = 0.8(Y – T) 
T = 1,000 

I = 800 – 20r 
G = 1,000 

Y = C + I + G 
M^{s}/P = M^{d}/P = 0.4Y – 40r 

M^{s} = 1,200 
A. Write a numerical formula for the IS curve, showing Y as a function of r alone. (Hint: Substitute out C, I, G, and T.)
B. Write a numerical formula for the LM curve, showing Y as a function of r alone. (Hint: Substitute out M/P.)
C. What are the shortrun equilibrium values of Y, r, Y – T, C, I, private saving, public saving, and national saving? Check by ensuring that C + I + G = Y and national saving equals I.
D. Assume that G increases by 200. By how much will Y increase in shortrun equilibrium? What is the governmentpurchases multiplier (the change in Y divided by the change in G)?
Solution
(a)
AE=Y
Y= C+I+G
Y=0.8(Y1000)+80020r+1000
Y0.8Y=100020r
0.2Y= 100020r
Y=5000100r
(b)
Ms/P=Md/P= 0.4Y40r
12000/1=0.4Y40r
Y=12000/0.4+40/0.4
Y=3000+100r
(c)
IS=LM
5000100r=3000+100r
2000=200r
r=10
Y=3000+100*10=4000
YT=40001000=3000
C=0.8(40001000)=2400
I=80020*10=600
Sp=(YT)C= 30002400=600
Sg= TG= 10001000=0
S= Sp+Sg= 600+0= 600
We know
Y=C+I+G
YCG=I and YCG= S
So, S=I
(d)
G1=G0+200= 1000+200=1200
IS2:
Y=C+I+G
Y= 0.8(Y1000)+80020r+1200
Y= 0.8Y+120020r
(Y0.8Y)=120020r
0.2Y=120020r
Y=6000100r
LM1=LM0: Y=3000+100r
IS=LM
6000100r= 3000+100r
3000=200r
r1=15
Y1= 4500
Y1Y0=
change in G,
So,
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