Question

# Assume the following model of the economy, with the price level fixed at 1.0: C =...

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 Ms/P = Md/P = 0.4Y – 40r Ms = 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 short-run equilibrium values of Y, r, YT, 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 short-run equilibrium? What is the government-purchases multiplier (the change in Y divided by the change in G)?

Solution

(a)

AE=Y

Y= C+I+G

Y=0.8(Y-1000)+800-20r+1000

Y-0.8Y=1000-20r

0.2Y= 1000-20r

Y=5000-100r

(b)

Ms/P=Md/P= 0.4Y-40r

12000/1=0.4Y-40r

Y=12000/0.4+40/0.4

Y=3000+100r

(c)

IS=LM

5000-100r=3000+100r

2000=200r

r=10

Y=3000+100*10=4000

Y-T=4000-1000=3000

C=0.8(4000-1000)=2400

I=800-20*10=600

Sp=(Y-T)-C= 3000-2400=600

Sg= T-G= 1000-1000=0

S= Sp+Sg= 600+0= 600

We know

Y=C+I+G

Y-C-G=I and Y-C-G= S

So, S=I

(d)

G1=G0+200= 1000+200=1200

IS2:

Y=C+I+G

Y= 0.8(Y-1000)+800-20r+1200

Y= 0.8Y+1200-20r

(Y-0.8Y)=1200-20r

0.2Y=1200-20r

Y=6000-100r

LM1=LM0: Y=3000+100r

IS=LM

6000-100r= 3000+100r

3000=200r

r1=15

Y1= 4500

Y1-Y0=

change in G,

So,

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