Question

Consider a hypothetical economy characterized by the following behavioral equation 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 simultaneously.

Answer 1

(a)

C$=400-200r+0.2Y$

I$=240-400r$

G$=200$

Y$=C+I+G$

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

Y$-0.2Y=$ 840$-$ 600r

0.8Y$=$ 840$-$ 600r

LS:

Y$=$ 1050$-$750r

LM;

Md$=$ Y$-$ 1000r

Ms$=$ 800

P$=$ 2

Ms$=$ Mt$+$ Mz

800$=$ Y$-$1000r$+$ 2

800$+$ 1000r$-$ 2$=$ Y

Y$=$ 798$+$ 1000r

(b)

1050$-$ 750r$=$ 798$+$ 1000r

1050$-$ 798$=$ 1000r$+$ 750r

r$=$ 0.144

$=$ 14.4%

Substitute r$=$0.144

Y$=$ 1050$-$750$(0.144)$

Y$=$ 1050$-$ 108

Y$=$ 942