Question

given Y=C+I+G+X

C=100+0.9Yd I=200-500r M=0.8Y-2000r X=100-0.2Y-500r G=200 T=0.2 L=800

Compute the values of C,L,X and M

Calculate the monetary and fiscal policy multipliers and interpret them

Answer 1

Consumption Function $C=100+0.9Yd$

Investment Function$I=200-500r$

Real Money supply $M=0.8Y-2000r$

Net Export$X=100-0.2Y-500r$

Government Spending G=200

Tax Rate T=0.2

Real Money demanded L=800

$Y=C+I+G+X\\ = 100+0.9Yd+200-500r+200+100-0.2Y-500r\\ = 600 + 0.9(0.8y) - 1000r -0.12y\\ = 600 + 0.6Y -1000r$

$0.4Y = 600 - 1000r$

  $Y = 1500 - 2500r$ ..................Equation for IS

At equilibrium Money supply is equal to the money demanded

$Ms = Md\\ Y - 100 r = 800$

$Y = 800 + 100r$ .............................Equation for LM

 

We Now AT equilibrium IS curve Intersect LM curve so,

$1500 + 2500r = 800+ 100r\\ r = \frac{7}{26}$

Thus,

$Y = 800 + 100(\frac{7}{26})\\ = \frac{21500}{26}$

$C = 100 + 0.72Y\\ = 100 + 0.72(\frac{21500}{26})\\ =100 + 577\\ = 677$

$I = 200 - 500(\frac{7}{26})\\ = \frac{1700}{26}$

$X = 100 -0.12(\frac{21500}{26}) - 500(\frac{7}{26})\\ =\frac{-3480}{26}$