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)
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):
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