Question

c = 60 + 0.8yd, i=150−10r, g=250, t=200 ms=100, md=40 + 0.1y−10r, write the is and lm schedules for the new model, find the new equilibrium values for income (y1) and the interest rate (r1), show graphically the is and lm schedules and equilibrium point b(y1, r1)

Answer 1

C = 60 + 0.8yd

I=150−10r

G=250

T=200

MS=100

MD=40 + 0.1Y - 10r

Yd = Y - T

At Goods market equilibrium,

Y = C+I+G

Y = 60 + 0.8yd + 150−10r + 250

Y = 460 + 0.8 (Y-T) - 10r

Y = 460 + 0.8 (Y-200)- 10r

Y = 460 + 0.8Y - 160 - 10r

Y - 0.8Y = 300 - 10r

0.2Y = 300 - 10r

Y = (300-10r)/0.2

Y = 1500 - 50r                      (IS schedule) 

At Money market equilibrium 

MS = MD

100 = 40 + 0.1Y − 10r

100 - 40 = 0.1Y − 10r

Y = (60+10r)/0.1

Y = 600 + 100r                      (LM schedule)

At equilibrium IS = LM 

1500 - 50r = 600 + 100r

1500 - 600 = 100r + 50r

900 = 150r 

r = 900/150

r = 6

Therefore the new equilibrium interest rate (r1) is 6

Also, Y = 600 + 100 r

Y = 600 + 100(6)

Y = 1200

Therefore the new equilibrium income level (Y1) = 1200

Following below is the graphical representation of IS LM Schedules and equilibrium point b(Y1, r1):