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

Question

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, 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 short-run equilibrium? What is the government-purchases multiplier (the change in Y divided by the change in G)?

e.

Assume that G is back at its original level of 1,000, but Ms (the money supply) increases by 200. By how much will Y increase in short-run equilibrium? What is the multiplier for money supply (the change in Y divided by the change in Ms)?

I have all answers just need to see the problems worked out to understand please.

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

Explanation / Answer

Ans a) AE=Y
   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=1200/0.4 +40/0.4r
Y=3000+100r

c)
IS=LM
5'000-100r = 3'000+100r
2'000 = 200r
r = 10
Y = 3'000+100*10 = 4'000
Y-T = 4'000-1'000 = 3'000
C = 0.8(4'000-1'000) = 2'400
I = 800 - 20*10 = 600
Sp = (Y-T)-C = 3'000-2'400 = 600
Sg = T-G = 1'000-1'000 = 0
S = Sp+Sg = 600+0 = 600

Y=C+I+G
4'000 = 2'400+600+1'000 = 4'000 [OK]

Y=C+I+G
Y-C-G = I
Y-C-G = S
S=I
600=600 [OK]

d)
G¹ = G°+200 = 1'000+200 = 1'200
[IS¹] Y = 6'000-100r
[LM¹]=[LM°] Y = 3'000+100r
IS=LM
6'000-100r = 3'000+100r
3'000 = 200r
r¹=15
Y¹=4'500
Y = Y¹-Y° = 4'500-4'000 = +500
G = +200
Y/G = 500/200 = 2.5

e)
M¹ = M°+200 = 1'200+200 = 1'400
[IS¹]=[IS°] Y = 5'000-100r
[LM¹] Y = 3'500+100r
IS=LM
5'000-100r = 3'500+100r
1'500 = 200r
r¹=7.5
Y¹=4'250
Y = Y¹-Y° = 4'250-4'000 = +250
M = +200
Y/M = 250/200 = 1.25

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.