Question

An economy is initially described by the following equations: a. Derive and graph the IS and LM curves. Use the accompanying diagram to graph the IS and LM curves by placing the endpoints at the correct location, then place point A at the equilibrium interest rate and level of income. C = 60+ 0.8(Y-T) I = 120-5r M/P=Y-25r G = 200 T= 200 M = 3000 P=3 IS: Y= LM: Y= IS-LM Graph 800 850 900 950 1,000 1,050 1,100 1,150 1,200

Answer 1

A) IS Equation;Y=C+I+G=60+0.8(Y-200)+120-5r+200=380-160+0.8y-5r=220+0.8y-5r

Y=1100-25r{ Is Equation}

LM Equation;y-25r=M/p=3000/3=1000

Y-1000=25r

r=0.04Y-40{ LM equation}

Equilibrium,

Y=1100-25(0.04y-40)=1100-y+1000

2y=2100

Y*=1050

r*=0.04*1050-40=2

egation cunet Pregnationlume 1000 loso 1150

B)NEw taxes=200*0.75=150

New IS Equation;Y=60+0.8(y-150)+120-5r+200=380-120+0.8y-5r=260+0.8y+5r

Y=1300-25r { New IS Equation after tax cut}

Initial LM Equation;r=0.04y-40

Equilibrium,

r=0.04(1300-25r)-40=52-r-40

2r=12

New equilibrium r=6

New EQUILIBRIUM Y=1300-25*6=1300-150=1150

Tax multiplier=∆Y/∆T=100/50=2

C) Initial Equilibrium r=2

So fed will keep interest rate at 2.

New EQUILIBRIUM r=2

New IS equation;Y=1300-25r

New EQUILIBRIUM Y=1300-25*2=1250

To maintain interest rate at 2,

Money supply/3=y-25r=1250-25*2=1200

New Money supply=1200*3=3600

Tax multiplier=∆Y/∆T=150/50=3

D) initial equilibrium Y=1050

new EQUILIBRIUM Y=1050

New IS equation;Y=1300-25r

1050-1300=-25r

New r*=-250/-25=10

Money supply/3=1050-25*10=800

New Money supply=800*3=2400

Tax multiplier=∆Y/∆T=0/50=0