Question

Given the equation IS 0.3Y +100i-252=0 and LM 0.2Y -200i-176=0.Find the equilibrium level of income Y and rate of interest i

Answer 1

$0.3Y+100r-252=0$

$100r=252-0.3Y$

$r=2.52-0.003Y$ - The IS Curve

$0.2Y-200r-176=0$

$-200r=176-0.2Y$

$r=-0.88+0.002Y$ - The LM Curve

$At$ Equilibrium, IS Curve should intercept the LM Curve

$2.52-0.003Y=-0.88+0.002Y$

$2.52+0.88=0.002Y+0.003Y$

$3.4=0.005Y$

$Y=680$

Replacing the value of Y to get the value of interest rate r

$r=2.52-0.003(680)$

$r=2.52-2.04$

$r=0.48$

Therefore the Output and interest rate at equilibrium are Y=680 and r=0.48%