Answer to Question #221504 in Macroeconomics for Dr sam

Question

the following information about an economy is givicen: C=100+0.7YD, I=80-150i, G=60, T=40, Md=Y-3000i and Ms=1000. a. Derive the IS curve b. Derive the LM curve c. find the equilibruim value of Y and i

Answer 1

Solution:

a.). Derive the IS curve:

IS equation: Y = C + I + G

C = 100 + 0.7YD = 100 + 0.7(Y – T) = 100 + 0.7(Y – 40)

Y = 100 + 0.7(Y – 40) + 80 – 150i + 60

Y = 100 + 0.7Y – 28 + 80 – 150i + 60

Y – 0.7Y = 100 + 80 + 60 – 28 – 150i

0.3Y = 212 – 150i

Y = 707 – 500i

IS Curve: Y = 707 – 500i

 

b.). Derive the LM curve:

Money market equilibrium: Md = Ms

Y – 3000i = 1000

Y = 1000 + 3000i

LM Curve: Y = 1000 + 3000i

 

c.). The equilibrium value of Y and i:

At equilibrium: IS = LM

707 – 500i = 1000 + 3000i

707 – 1000 = 3000i + 500i

-293 = 3500i

i = -0.084$\%$

The equilibrium rate of interest is = -0.084$\%$

Substitute the value of i in the IS equation to derive the equilibrium income:

Y = 707 – 500i

Y = 707 – 500(-0.084) = 707 + 42 = 749

The equilibrium level of income is = 749