Question

For an economy the following functions are given:-
C=100+0.8Y
S=-100+0.2Y
I=120-5i
M^(S)=120
M^(D)=0.2Y-5i
Calculate
IS equation
LM equation
Equilibrium level of income and interest rate

Answer 1

Y = AD= C + I

Y = 100 + 0.8Y + 120 - 5i

0.2Y = 220 - 5i

2Y = 2200 - 50i

Y = 1100 - 25i

IS equation = Y = 1100 - 25i

LM equation; M(s) = M(d)

120 = 0.2Y - 5i

0.2Y = 120 + 5i

Y = 600 + 25i; this is the LM equation

Equilibrium level of interest; 1100 - 25i = 600 + 25i

500 = 50i

i = 10; this is the equilibrium interest rate

Equilibrium level of income, Y = 600 + 25(10) = 850