Question

Consider a hypothetical economy characterized by the following behavioral equations.

IS:                                   LM:

C=400-200r+0.2Y             Md=Y-1000r

I= 240-400r                        Ms=800

G=200                                 P=2

a)derive the equations of the IS and LM curves of the economy

b) Find the equilibrium income level and the interest rate

Answer 1

(a) Derivation of IS curve equation

Given;

$C=400-200r+0.2Y$

$I=240-400r$

$G=200$

$Y=400-200r+0.2Y+240-400r+200$

$Y-0.2Y=840-600r$

$0.8Y=840-600r$

Thus the IS curve equation is ; $Y=1050-750r$

Derivation of LM curve

Given;

$Md=Y-1000r$

$Ms=800$

$P=2$

$Ms=Mt+Mz$

$800=Y-1000r+2$

$800+1000r-2=Y$

$798+1000r=Y$

The LM curve equation is ; $Y=798+1000r$

(b)

To find interest rate , equate IS curve equation with LM curve equation

$1050-750r=798+1000r$

$1050-798=1000r+750r$

$r=0.144= 14.4$ %

To find equilibrium income, substitute the value of r in the IS curve equation:

$Y=1050-750r$

$Y=1050-750(0.144)$

$Y=942$