Answer to Question #286682 in Macroeconomics for Msb

Question

The following equations describe an economy 

C = 200 + 0.25YD

I = 150 + 0.25Y – 1000r

G = 250

T = 200

(M/P)d = 2Y – 8000r

(M/P) = 1600

a) Derive the IS curve

b) Derive the LM curve

c) Solve for equilibrium output

d) Solve for the equilibrium interest rate

e) Solve for the equilibrium values of C and I, and verify the value you obtained for Y by 

adding C, I, and G.

f) Now suppose that the money supply increases to M/P = 1,840. Solve for Y, r, C, and I, and 

summarize the effects of an expansionary monetary policy.

Answer 1

IS= C+I+G

Y= 200+0.25(Y-200)+150+0.25Y-1000r+250

Y=550+0.5Y-1000r

Y= 1100-2000r

b) LM curve

2Y-8000r =1600

2Y= 8000r-1600

Y=4000r-800

c) Equilibrium output

From LM, r= 0.00025Y-0.2

From IS, Y= 1100-2000( 0.00025Y-0.2)

Y= 1100- 0.5Y+400

1.5Y= 1500

Y= 1000

d) Equilibrium Interest rate

From LM curve, Y= 4000r+800

But Y= 1000

Therefore, 1000= 4000r+ 800

4000r= 200

r= 0.05

e) Equilibrium of C and I

C=200+0.25( 1000-200)

= 400

I= 150+0.25(1000)-1000(0.05)

=350

G=250

Y= 400+350+250= 1000

f) If money supply increases to 1840

2Y-8000r =1840

Y= 920+400r

r= 0.0025Y-2.3

From IS, Y= 1100-2000(0.0025Y-2.3)

Y= 1100-5Y+4600

6Y= 5700

Y= 950

From LM, Y= 920+400r

950= 920+ 400r

400r= 30

r= 0.075

C= 200+0.25( 950-200)

387.5

I=150-0.25(950)+1000(0.075)

= -12.5

Expansionary monetary policy has an effect of increased interest rate which in turn reduces output. Reduced output leads to reduced consumption and investment.